Nuclear Energy Levels of ³¹S and ³³Cl Citation Moss, Calvin Elroy (1968) Nuclear Energy Levels of ³¹S and ³³Cl. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6WP8-MY34. https://resolver.caltech.edu/CaltechTHESIS:04012015-155922591 Abstract The reaction 32 S( 3 He, α) 31 S has been used to locate 42 levels in 31 S. For 11 of the first 17 levels ℓ n -values have been determined. The first 6 excited states of 31 S have been studied by applying the particle-gamma correlation method of Litherland and Ferguson (their Method II) to the reaction 32 S( 3 He, αγ) 31 S. The resulting spins and parities are: E X , J π = 1.25 MeV, 3/2 + ; 2.23 MeV, 5/2 + ; 3.08 MeV, 1/2 + ; 3.29 MeV, 5/2 + , 3/2 + ; 3.35 MeV, 7/2, 3/2; 3.44 MeV, 3/2 + . Mixing and branching ratios have also been determined. The ground state Q-value for the reaction 32 S( 3 He, α) 31 S has been measured to be 5.538 ± 0.006 MeV. Analysis of the spectra of the reaction 32 S( 3 He, α) 33 Cl which were obtained as a by-product of the spectra of the reaction 32 S( 3 He, α) 31 S located levels in 33 Cl at the following excitation energies: 0, 810 ± 9, (1978 ± 14), 2351 ± 9, 2686 ± 8, 2848 ± 9 (a known doublet), 2980 ± 9, and 4119 ± 10 keV. The 2.0 MeV level was only weakly populated, and to confirm its existence the reaction 36 Ar(p, α) 33 Cl has been studied. In this reaction the 2.0 MeV level was strongly populated and the measured excitation energy was 1999 ± 20 keV. The experimental results for 31 S and 33 Cl are compared with their analogs and with nuclear model predictions. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Whaling, Ward Thesis Committee: Unknown, Unknown Defense Date: 6 December 1967 Record Number: CaltechTHESIS:04012015-155922591 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:04012015-155922591 DOI: 10.7907/6WP8-MY34 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 8810 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 02 Apr 2015 15:58 Last Modified: 03 Apr 2024 23:46 Thesis Files Preview PDF - Final Version See Usage Policy. 63MB Repository Staff Only: item control page

NUCLEAR ENERGY LEVELS OF 31 s AND 33c1 Thesis by Calvin Elroy Moss In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1968 (Submitted December 6, 1967) ii Acknowledgments The author expresses sincere gratitude to all of the Kellogg Radiation staff, and in particular to Dr. W. Whaling. Special thanks are due to Dr. L. G. Earyvaker, who was a research fellow in this laboratory at the beginning of this work, for numerous illuminating discussions about the correlation me~surements. Special thanks are also due to Mrs. Barbara Zimmerman for assistance with the computer programing. Financial support for this research from the Office of Naval Research and a fellowship from the National Aeronautics and Space Administration are greatly appreciated. iii Abstract . 32 3 31 The reaction S( He, a.) S has been used to locate 42 31 levels in s. For 11 of the first 17 levels -e. -values have been n 31 determined. The first 6 excited states of s have been studied by applying the particle-gamma correlation method of Litherland 32 3 31 and Ferguson (their Method II) to the reaction s( He, a.y) s. The resulting spins and parities are: E , JTT = 1. 25 MeV, 3/2+; X 2. 2 3 MeV, 5/ 2+ ; 3. 0 8 MeV, 1;+ 2 ; 3. 2 9 MeV, 5;+ 2 , 3I 2+ ; 3. 3 5 MeV, 7/2, 3/2; 3. 44 MeV, 3/2+. Mixing and branching ratios have also been determined. The ground state Q-value for the . 32 3 31 reactwn S( He, a.) S has been measured to be 5. 538 ± 0. 006 32 3 33 MeV. Analysis of the spectra of the reaction s( He, d) cl which were obtained as a by-product of the spectra of the reaction 32 3 s( He, a.) 31 s located levels in 33 c1 at the following excitation energies: 0, 810 ± 9, (1978 ± 14), 2351 ± 9, 2686 ± 8, 2848 ± 9 (a known doublet), 2980 ± 9, and 4119 ± 10 keV. The 2. 0 MeV level was only weakly populated, and to confirm its existence the 36 33 reaction Ar(p, a.) Cl has been studied. In this reaction the 2. 0 MeV level was strongly populated and the measured excitation 31 energy was 1999 ± 20 keV. The experimental results for s and 33 c1 are compared with their analogs and with nuclear model I predictions. iv TABLE OF CONTENTS PART I. II. PAGE Introduction 1 A. Justification for this Experiment 1 B. Outline of Present Experiment 2 32S(3He, 4He)3ls 31 A. Mass of s B. C. 4 4 1. Introduction 4 2. Targets 4 3. Spectra Collection Details 5 4. Analysis of the Thick Target Spectrum 6 5. Calibrations 10 6. Calculation of the Result Excitation Energies of Levels in 12 31 s 13 1. Introduction 13 2. Targets 14 3. Supplementary Data 17 4. Spectra Collection Details 18 5. Reduction of Data to Spectra 19 6. Discussion of Spectra 20 7. Calculations of Excitation Energies 21 8. Results 21 Angular Distributions of 31 s States 23 1. Introduction 23 2. Experimental Procedure 23 3. Analysis of Experimental Data 25 4. DWBA Predictions 25 v III. IV v. 32 5. Discussion 27 6. Results 30 3 4 S( He, Hey) 31 . S Angular Correlatwns 32 A. Introduction 32 B. Theory 33 C. Correlations in the Reaction 32 3 4 31 s( He, He y) s 36 1. Excitation Functions 36 2 •. Experimental Setup for the Correlations 37 3. Spectra 40 4. Analysis of the Data 44 5. Branching Ratios 54 31 Discussion of s Levels . w1•t'n 31p A . C ompanson 61 B. 63 32 A. 61 Comparison with Models 33 3 s( He, d) Cl Excitation Energies of Levels in 69 33 c1 1. Introduction 2. Sixteen Counter Array Spectra 3. 69 69 70 (i) Experimental details 70 (ii) Discussion of spectra (iii) Calculations of excitation energies 71 72 (iv) Results 72 Single Counter Spectra 74 (i) Experimental details 74 (ii) Discussion of spectra 75 (iii) Calculations of excitation energies 75 (iv) Results 76 vi 4. B. VII. 76 (i) Experimental details 76 (ii) Discussion of spectra 77 (iii) Calculation of excitation energies 77 (iv) Results 78 Angular Distributions of 1. VI. Four Counter Array Spectra 33 c1 States Introduction 78 78 2. , Experimental Details 79 3. DWBA Predictions 79 4. Discussion 80 5. Results 81 4 33 Ar(p, He) Cl 82 1. Introduction 82 2. Target 82 3. 83 4. Supplementary Data 36 33 Ar(p, a) cl Spectra Collection Details 84 5. Discussion of Spectra 85 6. Calculation of Excitation Energy 86 36 Discussion of 33 33 s A. Comparison with B. Comparison with Theory Appendix A. 86 c1 Levels 86 87 Program for Calculating the Q- Values and Excitation Energies of Levels in 31 s 90 Appendix B. Program for 8 e ff ec t·1ve 102 Appendix C. Array Data Reduction Program 104 Appendix D. Program for the Analysis of Particle-Gamma Correlations 108 vii Appendix E. Program for the Angular Distributions of Gamma Rays from Aligned States Appendix F. Appendix G. 124 Array Electronics Non-existence of a Level at 1. 35 MeV in 143 33 s 146 References 151 Tables 157 Figures 178 1 I. A. INTRODUCTION Justification for This Experiment Relative to the nuclei with A :s 28 there has been little work reported on the nuclei with 28 < A :s 40. The nuclear models, some of which are discussed in Section IV. B., have in general not been very successful in describing the observed properties of these nuclei. Probably the main. reason for this is that the models are too simple. With the computers now available it appears feasible to study more realistic models. In particular, a generalization of the shell model calculation of Glaudemans et al. (1964) seems promising. More experimental information is needed so that the parameters in the theories can be determined and the 31 predictions can be checked. The nucleus s was chosen for study in the present experiment because it was the lightest nucleus in this mass region which could be studied with the CIT-ONR tandem accelerator and for which there was little experimental information 31 (see below). The primary objective was to study s, but 33 fragmentary information about c1 was also obtained. 31 31 P and The information on s available at the start of present investigation was essentially that contained in the compilation by Endt and van der Leun (1962) and is summarized in Figure 1. The shell model calculation by Glaudemans et al. (1964) predicted a low-lying 1/2+ level and a 7/2+ level, neither of which had been identified (see Figure 2). An earlier Nilsson model calculation by Braude et al.(1958) also predicted these two levels. 2 The information on 33 s and 33 c1 available at the start of the present investigation was also essentially the same as that contained in the compilation by Endt and van der Leun (1962) and is. summarized in Figure 3. On the basis of the level scheme shown 33 here for s, two unreported levels were expected at an excitation 33 energy of 3 MeV in c1. The shell model calculation by Glaudemans et al.(l964) predicted the levels shown in Figure 4. B. Outline of Present Experiment The present experiment may be divided into seven parts as follows: 1) The ground state Q-value of the reaction was measured. 32 3 s( He, a.) 31 s This work is described in Section II. A. , pages 4 through 13 . 32 3 31 2) Alpha parti~le spectra from the reaction s( He, a.) s 31 were measured to locate levels in s below 7. 8 MeV excitation energy. This work is described in Section II. B. , pages 13 through 23 . 3) Angular distributions of the alpha particles from the . 32 3 31 reactwn S( He, a.) S were measured for 14 of t he 31 first 21 levels in s and compared with DWBA distributions to determine ,e, -values. ' This work is described n in Section II. C., pages 23 through 31 . 4) Angular correlations for the first six excited states 31 32 3 populated in the reaction s( He, a.y ) s were measured to determine the spins of these states. This work is 3 described in Section ill, pages 32 through 60 . 5) Deuteron spectra from the reaction 32 3 33 s( He, d) cl which were obtained as a by- product of the alpha particle . 32 3 31 spectra from the reaction S( He, a.) S were analyzed 33 to locate levels in c1 below 4. 2 MeV excitation energy. This work is described in Section V. A., pages 69 through 78 • 6) Angular distributions of the deuterons from the reaction 32 3 33 s( He, d) cl were analyzed for three of the levels in 33 c1 and compared with DWBA distributions to determine -values. This work is described in Section V. B., p pages 78 through 81 . t 7) Alpha particle spectra from the reaction 36 Ar(p, a.) 33 cl were measured to confirm the existence of a level in 33 c1 near 2. 0 MeV which was only weakly populated in the 32 3 33 reaction s( He, d) Cl. This work is described in Section VI, pages 82 through 85 . 4 A. Mass of 1. 31 S Introduction The 1964 Mass Table of Mattauch et al.(1965) gives -18992 ± 11 keV for the mass excess of 31 s. -When we discovered that the mass excess calculated from the ground state Q-value for 32 3 31 the reaction s( He, a.) s derived from our spectra described in II. B. lay well outside of the 11 keV error quoted here, a careful · measurement of this Q-value was made with the 61-cm magnetic spectrometer. This instrument has been described by Groce (1963) and McNally (1966), and this thesis assumes familarity with either of these theses or the operation of the spectrometer. 2. Targets A thin target was used to check for possible contributions 3 . 32 3 31 from other ( He, a.) reactwns near the peak from S( He, a.) S (G. S. ), and a spectrum is shown in Figure 5(a). This target was made by evaporating ZnS containing natural sulfur from a tantalum boat onto tungsten of 0. 178 mm thickness which had been carefully cleaned with a solution recommended by Misch and Ruther (1953) consisting of one part by volume of concentrated HF and three parts of concentrated HN0 , ·and then thoroughly rinsed with distilled 3 water. A thick target was made in a similar manner, and a spectrum is shown in Figure 5(b). 0. 254 mm thick. The backing in this case was 5 No deterioration of this kind of target was observed provided the beam was kept below 0. 3 ~-t-A on a .5 mm 2 area. No 3 evidence was observed for ( He, a) reactions with the zinc isotopes at E ;; 8. 5 MeV. 3 He For both the thin target spectrum and the thick target spectrum the 61-cm spectrometer was placed at 150° to the incident beam. The normal to the target bisected the angle between the incoming beam and the spectrometer. The thin target spectrum shows no interference from other groups. The thick target spectrum has been used to compute Q, since the analysis of a thick target spectrum (after the method of Bardin, 1961) is not subject to errors introduced by an rmcertain target thickness. 3. Spectra Collection Details The thin target spectrum was obtained with the 16detector array with a 3. 18 mm (FW perpendicular to the mean orbit) slit in front of each detector which accepted a momentum interval 6p;; p/720. No foil was placed in front of the detectors. Details of the operation of the array are discussed in Appendix F. Two slightly different settings of the magnetic field of the spectrometer were made in such a way that alternate points shown in Figure 5(a) correspond to the same field setting. An electron suppressor upstream from the target was placed at -300 volts, and the target and beam catcher were placed at +300 volts relative to the chamber walls. These voltages were used for all of the spectra described below. The spectrometer angular acceptance was 1. 50 ° (FW) in the e direction and 11.6° (FW) in the ¢ direction. The slits in front of the target chamber were 2. 03 mm (FW) in both the vertical 6 direction and the horizontal direction. The widths of the image slit and the object slit of the beam analyzing magnet were both 3. 81 mm (FW). The thick target spectrum was obtained with a single surface barrier detector in the focal plane of the spectrometer. A slit 0. 794 mm (FW) was placed in front of the detector (6p/p == 1/2800), and again no detector foil was used. of the electronics is shown in Figure 6. A block diagram The window of the single channel analyzer was set so that only t he alpha particles were counted (deuterons and protons were also present), and the RIDL 400-channel analyzer was used as a monitor. The spectrometer current was cycled from 0 to 700 amperes to 0 to the current for the lowest point on the spectrum, and then always increased between data points so that the shift due to hysteresis would be reproduced. The beam analyzing magnet was also cycled. The spectrometer angular acceptance was 2. 0° (FW) in the 8 direction and 9. 0 ° (FW) in the ¢ direction. The slits in front of the target chamber were 0. 508 mm (FW) in the vertical direction and 1. 016 mm (FW) in the horizontal direction. The widths of the image slit and the object slit of the beam analyzing magnet were both 1. 916 mm (FW). The slit settings and detector foil thickness for the thin and thick target spectra are tabulated in Table I, columns a and b, respectively. In the discussions below of other spectra, only a tabulation will be given. 4. Analysis of the Thick Target Spectrum To determine the Q-value, the true momentum position of the thick target step shown in Figure 5(b) must be determined 7 by unfolding the various experimental resolution functions from the spectrum. The step profile depends on the following: 1) The vertical dimension of the beam spot, or . The · s,sp maximum energy (frequency) spread of the alpha particles geometrically allowed by or = 0. 508 mm s,sp FW was 3. 7 keV FW (5. 4 kc/sec, t.p/p == 1/5500) and is shown in Figure 5 (b). 2) The variation of the beam intensity across the beam analyzer slits. The maximum energy spread in the == or = 1. 016 mm FW was s, a c, a 19. 7 keV FW (.M sp == 28.6 kc/sec, t.p sp/p sp = 1/1 0 00) ~ · However, because Pearson (1963) and Groce (1963) beam allowed by or reported that the beam energy resolution was much smaller (~ 10%) than this maximum beam energy spread, it is estimated that the variation of the beam intensity across the beam analyzer slits caused an energy spread in the beam of ::.;; 2. 0 keV (t.fsp ~ 2. 9 kc/sec , , t.p sp/p sp == 1/10000). 3) The variation of the beam analyzing magnet current. On the basis of the stability of the signal observed on the scope monitoring the N:MR magnetometer in the beam analyzing magnet, it is estimated that this current variation caused an energy spread in the beam of 1 ke V FW (~£sp =L 5 .kc/ sec, L\psp/p sp :;;; 1/206.00). 4) The energy dependence of the reaction cross section. Since the compound state lies at 20 MeV excitation in 8 35 Ar, it is assumed that the cross section does not change significantly over the energy range of the step. 5) Surface contaminants. A fresh target was used to take tlie thick target spectrum shown in Figure 5(b) so as to minimize surface contaminants which sometimes build up during long runs, and it is assumed that effects from surface contaminants are negligible. 6) The energy dependence of the stopping cross section in the target. Because the stopping powers for the incident and emergent particles change < 0.. 5% in the energy range of the step (Demirlioglu and Whaling, 1962), the spread in the alpha particle energy caused by this energy dependence is ignored. 7) Aberrations in the spectrometer. An accurate measure of this contribution is not available, but Groce (1963) found that the aberrations round the upper step edge and decrease the absolute value of the slope of the step. On the basis of his data this latter effect shifts the location of the midpoint by ~ 1. 3 keV (~ 1. 9 kc/sec, t.p/p = 1/15000) in the present measurement. This uncertainty is inc:luded in the error assigned to the true momentum position of the thick target step (see below). 8) The angular acceptance 6 8 of the spectrometer and the variation of do/dO over this angular acceptance range. The spread in the alpha particle energy (frequency) from the kinematic shift within 68 = 2. 0° FW was 29 9 keV (42 kc/sec, Llp/p = 1/1000) and is shown in Figure 5(b). On the basis of the .k nown variation of angular distributions from direct reactions (see Section II. C.), it is assumed that cross section dcr /dO is constant over o e. 9) The variation of the magnetic spectrometer current. On the basis of the stability of the signal observed on the scope monitoring the NMR magnetometer in the magnetic spectrometer it is estimated that this current variation caused an energy (frequency) spread. in the alpha particle energy of .:5 2 keV FW (.:52. 9 kc/sec, 6p/p = 1/10000). 10) The detector slit width or . The slit width c,sp or c,sp = 0. 794 mm FW contributes 7 keV FW (10. 2 kc/sec, 6p/p = 1/2900) to the step width and is shCM711 in Figure 5(b). In summary, it is assumed that the step width is deter- mined predominantly by or , oe, and or with small contris,sp c,sp butions from t11e variation of the beam intensity across the beam analyzer slits, the variations of the magnet currents, and the aberrations. The contributions from all of these except the aberrations are symmetric in momentum and when folded into the ideal step, the midpoint of the resulting curve should quite accurately represent the momentum of the alpha particles emitted from the surface. The midpoint frequency shown in Figure 5(b) is 29694 ± 4 kc/sec (= ±2. 8 keV; 6p/p = ± 1/7400) where the error includes the statistical uncertainty and the uncertainty due to the aberrations. 10 5. Calibrations The calibration procedure was similar to the one used by 212 McNally (1966). A standard Po source with a 0. 795 mm horizontal slit in front of it was placed at the target position 7. 925 em from the bottom of the lucite lid on the target chamber (see Groce, 1963) with the aid of a height gauge and a magnifying glass. That the target position was 7. 925 em from the lucite was checked by sighting down the beam tube with a telescope from the switching magnet. The spectrometer current was cycled as described in Section II. A. 3. above. The calibration spectrum shown in Figure 7(a) was taken with the same electronics shown in Figure 6 and the same detector slit (. 794 mm FW) and the same spectrometer slit settings (e = 2. 0°, ¢ = 9. 0° FW) used to observe the thick target spectrum described above. The peak frequency of 27689 ± 1 is taken as the calibration point as recommended by Groce (1963). This same number was also obtained when this calibration was repeated three weeks later. To calibrate the beam analyzing magnet a carefully drilled 0. 203 mm diameter hole in a 0. 127 mm thick sheet of tantalum was placed at the target position and the spectrometer was placed at 0°. Mter cycling the beam analyzing magnet current, it was set to a current corresponding to an NMR magnetometer frequency of 20935 kc/sec. The slit settings are given in Column c of Table I. Figure 4 7(b) shows the spectrum of He ++ particles passing through the hole. This spectrum was obtained by varying the spectrometer current after cycling the spectrometer current as described above. The peak frequency was 27672 ± 1 kc/sec and was reproducible provided the steering and focusing controls of the ·tandem were set at approximately the same values. 11 The calibration "constant" .k for the magnetic spectros meter is defined by the formula E M E ks = f2Z2 Mp (1 +2M) substituting E = 8785. 0 ± 0. 8 keV (Wapstra, 1964) and f = 27689 so: = 0. 0113934 ± 0. 0000013 ± 1 kc/sec into this formula yields k 2 so: MeV /(Me/sec) . The ratio of k at other frequencies to k has s so: been accurately measured by McNally (1966). This curve is a function of the geometry and the permeabilities of the materials in the spectrometer and is assumed to be constant with time. The calibration constant .k for the beam analyzing magnet a is defined by an analogous formula. Since the analyzing magnet has a uniform field, ka may be assumed to be constant for the purposes of this experiment. This assumption was checked by Fisher and Whaling (1964) to 1 part in 3000. The ratio curve indicates that k (f = 27672) equals k to better than 0. 001%. s s so: f2 k a = k so: Hence s beam f 2 a 2 gives .k = 0. 0199062 ± 0. 0000033 MeV/(Mc/sec) (measured July a 2 14, 1966). Miller (1966) quotes 0. 019905 ± 0. 000012 MeV /(Me/sec) 9 6 (measured October 30, 1965) from a Li(o:, n) B threshold measure- ment , and McNally (1966) quotes 0. 019881 ± 0. 000005 from a measurement similar to the present one (measured May 12, 1964). 12 6. Calculation of the Q-value A relativistic Q-value and excitation energy program which calculates the errors has been written and is described in detail in Appendix A. The program was intended for transmission targets, but by setting all of the input target thicknesses equal to zero, it may be used for thick targets in a reflection geometry. Table III lists the inputs, the assumed errors, and the results. The spectrometer track reading of 150° was not used but rather a value obtained by averaging over the angular acceptance of the spectrometer with a program listed in Appendix B. Except at 90° this observation angle will differ from the track reading because of 6¢. The error of . 05° in the spectrometer angle is based on the uncertainty in the track protractor readings described by Groce (1963). The result for the Q-value is: Other measurements of this Q-value were obtained in the transmission target spectra discussed in Section II. B., and the results are given ill Table DC As a further check, transmission target 34 3 spectra from the reaction s( He, a.) 33 s (see Section II. B. 8.) and 32 3 34 3 35 33 the reactions s( He, d) cl and s( He, d) cl (see Section V. A. 2. (iv)) which were observed simultaneously with the spectra from . 32 3 31 the reactwn S( He, a.) S were used to compute the Q-values for those levels which corresponded to emitted particles of approximately the same momentum as that of the alphas corresponding to 31 the ground state of s, and the results were compared with previously reported measurements. 13 Using Q = 5. 538 ± 0. 006 and the 1964 Mass Table (Mattauchet al. ,1965) for the mass excesses 328 3 4 -26012.7 ± 0. 9 He 14931. 34 ± . 21 He 2424.75 ± • 39 yields 318 -19045 ± 6 This disagrees with the mass excess quoted for 31 8 in the 1964 Mass Table: -18992 ± 11 The mass links shown in the schematic diagram of the input data which is given with the 1964 Mass Table indicate that this number is based on a measurement of the threshold of the reaction 28 31 8i(a., n) 8 and on either a measurement of the threshold of the 31 31 reaction P(p, n) 8 or a measurement of the end-point energy 31 of the ~-decay of 8 or both. B. Excitation Energies of Levels in 31 8 1. Introduction The purpose of the work described in this section was to 31 locate energy levels in 8. The reactions which can provide 31 information about s are listed (Endt and van der Leun, 1962):. 14 1) 28Si(a, n) 318 Q - - 8. 149 MeV 2) 31P(p, n)31 8 - 6.232 3) 32S(y, n)31 8 -15. 095 29 31 3 Si( He, n) s 3. 951 5) 31P(3He, t)31s - 5. 468 6) 32s(p, d)31 8 -12.870 7) 32s(d, t)31s - 8. 837 4) 8) 32S(3He, a)31s 9) 33s(p, t)31 8 Only (8) was suitable. 5.483 -15. 254 Reactions (1) - (4) emit neutrons and were therefore unsuitable because closely spaced levels were expected. Reactions (5), (6), (7), and (9) have large negative Q-values. 2. Targets Several kinds of sulfur targets were tested. Elemental sulfur was not tried because it melts at 113°C. A target of Sb s 2 3 on thin gold foil was made by evaporating BaC1 , gold, and Sb s 2 2 3 onto a glass slide and then floating off the gold and Sb S combination 2 3 on distilled water and mounting it on tantalum sheet over a hole 9 mm in diameter. This combination was abandoned when it was discovered 3 that the Sb s slowly evaporated with 0. 3 f,.lA of 12. 0 MeV He ++ on a 2 3 0. 8 mm 2 area. The compound Mos was tried but it appeared to 2 15 decompose during the evaporation from the boat. The combination 0 of Zn8 on a nickel foil was made by mounting 5000 A nickel foils (obtained from the Chromium Corporation of America) on a tantalum frc;tme and then evaporating Zn8 onto it. Even though this combination was durable under bombardment, it was abandoned because it was feared that at E 3 = 12. 0 MeV weak reactions from the zinc and He nickel would be seen. Carbon foils with 8b 8 or Zn8 were tried but 2 3 repeatedly broke when the beam hit them. However, Ajzenberg- 8elove and Wiza (1966) have recently reported success with 8b S 2 3 on a carbon foil. The combination used for this experiment was Cd8 on a gold foil. The procedure used to prepare the 8b 8 targets was 2 3 used to prepare the Cd8 targets. No evaporation was observed for 3 ++ 2 beams of less than 0. 3 11A of 12. 0 MeV He on a 0. 8 mm area. The Coulomb barrier for cadmium (Z = 48) is so high t hat no significant reactions were expected and none were observed. Targets 32 were made from Cd8 containing natural sulfur (95. O% 8, 0. 76 % 33 34 36 8, 4. 22% 8, 0. 014% 8) and from CdS containing sulfur enriched 32 in 8 which was obtained from the Oak Ridge National Laboratory. 32 The isotopic analysis supplied with the material gave 98. 1% 8, 33 34 36 0.1% 8, 1. 5% 8, and 0. 1% 8. In all of the target making operations great care was taken to avoid contaminants. The tantalum frames and glass slides were boiled in cleaning solution, rinsed several times in distilled water, blotted dry with tissue, and wiped with lens paper to remove lint and dust. The bell jar was thoroughly cleaned before each evapo- ration even though the user before had already cleaned it once. boats were heated to a temperature well above that required to evaporate Cd8 before anything was placed in them and before the The 16 glass slides were placed in the bell jar. This precaution degassed the evaporation area and evaporated any contaminants that might have been present. After the foils were floated off, they were allowed to float on the water for several minutes to dissolve and disperse the trace of BaCl present. The targets, including the 2 frames, were never handled with the fingers because close observation has shown that perspiration will condense on a cold target several millimeters from the· point of contact with the skin. The targets were never left in the target chamber when the cold trap in the target chamber was not cold because it has been observed that under these conditions the target 'w ill pick up traces of diffusion pump oil. The thicknesses of the gold and CdS deposited on the glass slide were monitored by a Sloan Deposit Thickness Monitor (Model 2a) during the evaporation. This device measures the change in frequency of a resonating quartz crystal as a deposit condenses on its surface. The change in frequency is proportional to the mass of the deposit. Because the spatial distribution of material coming from the boat was not isotropic, the thickness monitor did not receive the same amount of material as the glass slide. Typically the thic.k nesses calculated from the thickness monitor differed by 15% from those measured by elastic scattering as described below. The largest observed difference was 40% which occurred when the glass slide and the resonating crystal were close to the boat (. . . . 6 em) for the evaporation of the CdS containing enriched sulfur. In order to determine the target thickness more accurately, 3 the loss in energy of 10- MeV He++ scattered from the target was measured with the spectrometer and the 16-detector array. It was assumed that sulfur was still in the form of CdS on the target, which 17 was convenient because cadmium has a much larger Rutherford scattering cross section than does sulfur. Vlith the target turned to present the gold foil to the incident beam the peak due to scattering from cadmium was shifted down by the energy lost in passing twice through the gold. Similarly, with the target turned to present the CdS to the incident beam, the peak due to scattering from gold was shifted down by the energy lost in passing twice through the CdS (see Figure 8). The target thicknesses were calculated with the aid of the stopping power curves of Demirlioglu and Whaling (1962) and the results are given in Table IV. 3. Supplementary Data The calibration constant of the spectrometer for detector 8 in the array with the 1. 84 mm (measured perpendicular to the mean orbit) detector slits was determined in the same way as described in Section II. A. 5 for the single detector. The array preamplifier and amplifier were not used but rather the detector was connected to a Tennelec preamplifier and a double delay line amplifier as shown in Figure 6. The spectrum is shown in Figure 9 and the peak frequency was 27703 ± 1 kc/ sec. The result was 2 k = 0. 0113819 ± 0. 0000012 MeV/(Mc/sec) . sex. At a given magnetic field setting, McNally (1966) showed that the ratio of the momentum corresponding to any one detector to the momentum corresponding to detector 8 is a constant, independent of the magnetic field. Equivalently, a frequency can be associated with each detector, and the ratios of these frequencies have the same values as the ratios of momenta. Table II lists the frequency ratios as measured by McNally (1966) and used in this analysis. To calculate the frequency associated with detector x, 18 it is only necessary to multiply the frequency for detector 8 by the ratio for detector x. The procedure described by McNally (1966) was used to measure the yield factors. A beam of 12. 0 MeV 3 He ++ particles was scattered from a clean sheet of tantalum of thic.k ness 0. 127 mm. The spectrometer was set at 150°, and the same slit settings used for the reaction spectra described in Section II. B. 4. (see Table I, , or , o e, 6¢, and or . s,sp s,sp c , sp A region of the spectrum well below the maximum energy of t he 3 elastically scattered He++ particles was scanned with detector 8 column d) were used here for oz and the spectrum is shown in Figure 10 (open circles). line is an approximation to this spectrum. observed with the array (solid circles). The straight Then the region was Dividing the yields observed by the array into the yields given by the line at the frequencies corresponding to the detectors in the array gives the yield factors listed in Table II, column a. To calculate the corrected yield for detector x, it is only necessary to multiply the yield recorded in detector x by yield factor x. In effect, the frequency factors and yield factors transform the data to a single detector spectrum. 4. 32 s( 3He, a) 31 s Spectra Collection Details A beam of from 0. 1 to 0. 3 ~A of 12 MeV 3 He++ particles bombarded the target. The beam analyzing magnet was cycled (as described in Section II. A. 3) at the beginning of the data collection. The slit settings and detector foil used are given in Table I, column d. With 20 volts bias on the detectors the alpha particles and deuterons were completely stopped in the depleted region whereas the protons were not and produced smaller pulses than the deuterons. Because 19 the detectors were separated by 5. 79 mm as measured perpendicular to the central orbit, four (or five) steps of the magnetic field corresponding to a displacement of approximately 1. 4 (or 1. 2) mm of the spectrum relative to the detectors were made for each of the regions of the spectrum. were overlapped. As a check the ends of adjacent regions The data were read out on the Nuclear Data Optikon (Model ND307). 5. Reduction of Data to Spectra The 16 alpha particle groups were summed with a desk calculator, and then these sums were punched on cards along with the frequency of detector 8. Near the end of this work, 100 runs with little background could be processed in 8 hours. From these data along with the frequency factors and yield factors the program given in Appendix C calculated the frequency and corrected yield for each detector and plotted the resulting spectra, which are shown in Figure 11. An attempt to read the data directly into the CIT !BM 7094 computer through a data link for immediate analysis was abandoned because graphical output could not be obtained immediately. Typically there was a 30 minute wait for a plot. The system was inconvenient to use because the ·ranges of channels to sum had to be fed into the computer remote console and because approximately ten switches had to be set each time data were read into the computer. More serious difficulties were the fact that the computer sometimes lost the data and the fact that the computer did not operate 24 hours a day. A CRT with a light pen, a data storage facility such as a magnetic tape unit, and full-time computer service would expedite the analysis of spectrometer data. 20 6. Discussion of Spectra The contributions to the resolution of peak (9) in Figure 11(b), which is typical of all of the peaks shown in Figure 11, are listed in Table V. This list includes all of the factors that determine the thick target profile as well as variations in the energy loss in the target and the straggle. If the resolution function for each of these contributions were known, then they could .be convoluted to obtain the total resolution function. The observed resolution is 31 keV (FWHM) for peak (9) in Figure 11(b). The peaks in Figure 11 were first identified by a nonrelativistic kinematics program. The input consisted of the incident beam energy, the thicknesses of the CdS and gold, the spectrometer frequencies of a group at two· or more angles, the corresponding spectrometer angles, and the corresponding angles between the beam and the normal to the target. The program calculated the energies of the emerging alphas from the spectrometer frequencies, and then corrected these energies and the energy of the incident beam for the target thickness in a manner similar to that used in the program described in Appendix A. The resulting alpha particle energies at two or more angles and the beam energy were used to calculate the mass of the target nucleus and the Q-value. The mass was typically determined to ±1 AMU and never worsethan ±3 AMU. The identifications given by the non-relativistic program were checked by calculating the spectrometer frequencies with a 31 relativistically correct program. For s the mass of the ground state was taken from Section II. A. 6 and the excitation energies were taken from II. B. 7. For other nuclei the compilations of Lauritsen and Ajzenberg-Selove (1962) and Endt and van der Leun (1962) were used. Since some levels were seen at only two angles, 21 the spectra were carefully checked for groups from the target nuclei 12 13 16 28 . 33 34 12 . C, C, 0, 81, 8, and 8. Peaks from C are labeled m 16 Figure 11. The identification of the peaks from 0 was facilitated 16 by some spectra taken by David Hensley with a 0 target under similar conditions. Note in particular the strong peak from the 15 6. 18 MeV level in 0 at f = 30100 in Figure 11(b) for example. The 34 8 was facilitated by some spectra identification of the peaks from 34 taken by Dr. J. Dubois with a 8 target under similar conditions. 13 28 . 33 C, 81, or 8. As a further No groups were observed from check on these identifications the yields in the natural spectra and in the enriched spectra were compared. 7. Calculations of Excitation Energies and Q-values For each spectrum shown in Figure 11 the program described in Appendix A was used to calculate the excitation 31 8. A final excitation energy energies and Q-values for levels in was calculated by averaging the excitation energies calculated from selected peaks. The criteria for selection were that the peaks be symmetric and not confused by a large background. The results are shown in Tables VI and IX. The excitation energies and Q-values for the reaction 34 3 33 8( He, a.) 8 were also calculated with this program after setting 34 33 . M and M4 equal to the masses of 8 and 8, respectively. The 2 results are listed in Table VII. 8. Results The last two columns of Table VI compare the present 31 results for 8 with those reported by Ajzenberg-8elove and Wiza 22 (1966). The correspondence between the levels is based more on the relative excitation energies and strengths than on the absolute excitation energies. The third excited state was located at an excitation energy of 3. 075 ± • 010 MeV in the present experiment but was not reported by Ajzenberg-Selove and Wiza (1966). A group which is tentatively attributed to a weakly populated level at an 31 excitation energy of (5. 026 ± . 016) MeV in s was found in the present experiment but was not reported by Ajzenberg-Selove and Wiza (1966). Levels forming closely spaced doublet which were not resolved by Ajzenberg-Selove and Wiza (1966) were found at excitation energies of 5. 407 ± • 010 and 5. 440 ± • 010, 6. 540 ± • 012 and (6. 593 ± • 015), (6. 711 ± • 013) and 6. 743 ± • 013, and 7. 161 ± . 011 and 7. 199 ± . 013 MeV in the present experiment. The strong group seen at elab == 15° by Ajzenberg-Selove 31 and Wiza (1966) and attributed to a level in s at an excitation energy of 6. 896 ± • 025 was also seen in the present experiment (at f == 30100 in Figures 11(b) and (c)) but attributed to a strong 15 group from the 6. 180 MeV level in 0. The "group" seen at elab == 15° and 45° by Ajzenb..erg-Selove and Wiza (1966) and attri3 buted by them to a level in ..Ls at an excitation energy of 7. 522 ± 15 . 020 MeV, was also attributed to 0 in the present experiment. At elab == 15° this "group" was attributed to the 6. 792 MeV level in 15o and at elab == 45° to the 6. 180 MeV level. The group seen at elab = 15° py Ajzenberg-Selove and Wiza (1966) and attributed by 31 them to a level in s at an excitation energy of 7. 60 ± • 030 MeV 15 was attributed to the 6. 860 MeV level in 0 in the present experiment. No evidence was seen in the present experiment for levels at 6. 99 ± • 030 and 7. 66 ± • 030 MeV. 23 The last two columns of Table VII compare the present 33 results for s with those reported by Endt and Paris (1958). The good agreement of the excitation energies for the 3. 83 MeV level 32 3 31 is a check on the ground state Q-value for the reaction s( He, a) s (see Section IT. A. 6) because the group from the 3. 83 MeV level in 33 s is close to the group from the ground state of 31 s (see Figure 11). C. Angular Distributions of 31 s States 1. Introduction The purpose of the work described in this section was to 32 3 measure the angular distributions from the reaction s( He, 4 He) 31 s. The experimental distributions were fitted with the angular distributions computed from direct reaction theory to determine the angular momentum ,e, of the neutron extracted from the target nucleus. n J- dependence was used to make tentative spin assignments for some 31 levels in s. 2. Experimental Procedure A target of 97 ± 29 ~g/cm of CdS containing enriched 32 34 36 33 sulfur (98. 1% s, 0. 1% s, 1. 5% s, and 0. 1% s) on 289 ± 87 ~g/ em 2 gold foil was used for all of the distributions except those 2 2 for levels 3, 4, and 6 for which a target of 289 ± 87 ~g/cm of Sb S containing natural sulfur on 289 ± 87 ~g/cm .of gold was used, 2 3 because CdS had not been tried when these distributions were 2 measured. Evaporation was not a problem with a beam of no more than 0. 3 ~A of 12. 0 MeV 3 He++ on the CdS target and no more than 0. 1 ~A on the Sb S target. 2 3 Because of the severe elastic scattering 24 from the gold, an attempt to monitor the elastic scattering from the sulfur with a solid state counter in the target chamber was unsuccessful. Instead, equal amounts of charge as measured by the Eldorado Electronics (Model Cl-110) current integrator were allowed to strike the target at each angle, and the measurement at 20° was repeated several -times during the measurement of a distribution to check for target deterioration. In the one case where a change was noted, the measurements were repeated. The alpha particles were detected with the 16 detector array. The slit settings and detector foil thickness listed in Table I, column f, were used for all of the distributions except those from levels 3, 4, and 6. For these three, which were measured nine months earlier, the slit settings and detector foil thickness listed in Table I, column g,. were used. The energy resolution (typically 35 keV) was comparable to that shown in Figure 11 except for levels 3, 4, and 6 which was not as good (typically 50 keV). The same yield factors used for the spectra from the 32 3 31 reaction s( He, a) s described in Section II. B., and listed in Table IT, column a, were used for all of the distributions except those from levels 3, 4, and 6. For these three, another set measured by the procedure described in Section II. B. 3 and given in Table IT, column b, was used. Angular distributions for levels in one span of the array were measured simultaneously. Other spectra collection details are similar to those described in Section IT. B. 4. 25 3. Analysis of Experimental Data The data were reduced to spectra by the procedure described in Section II. B. 5. Suppose N is the number of particles striking the focal plane, f is the frequency, andY is the number of counts in a peak. Then it was assumed that Y = J peak dN df ~ _!_ (area of peak) df Llf where Llf is the collector slit width. The area was estimated by drawing a triangle through the experimental points as shown in Figure 11. . The resulting yields were corrected for target angle, converted to center-of-mass yields,. and normalized so that the maximum value was unity. The center-of-mass distributions were then plotted (Figures 13- 26) along with the DWBA distributions (see Section II. C. 4 below). 4. DWBA Distributions For these calculations it was assumed that the reaction mechanism was simple pick-up. The zero-range approximation was used and spin-orbit coupling was neglected. The optical model parameters used here for the reaction 32 s( 3He, a.) 31 s were those used by Blau et al.(1965) for the reaction 39 K( 3 He, a.) 38 :K and are given as Set I in Table X. Woods-Saxon shapes were used for the real and imaginary parts of the optical potential 26 U(r) = v e x= X w i X' + 1 e r-R a x' = R :;:: r (M)1/3 0 + 1 r- R' a' R' :;:: r'0 (M)1/3 . 3 He parameters were found by Blau et al. (1965) by fitting the 3 39 elastic scattering of He by K at E :::: 9. 00 MeV with the 3 He search code HUNTER. The alpha parameters were derived by The Blau et al.(1965) from an optical model analysis by Basse! et al. (1962) of measurements of elastic scattering of 18 MeV alpha 40 particles from Ar by Seidlitz et al. (1958). Variations of the 32 3 31 parameters for the reaction s( He, a) s by up to 50% caused only small variations in the predicted distributions, and the distributions were never shifted by more than 3° in the range 8CM = 0° to 40°. No case was found where the distribution for one t -value and one set of parameters could be confused with n the distribution for another tn-value and a different set of parameters. Because of these findings, and because it is well known that these parameters are insensitive to the mass and energy, (Hodgson, 1963a) it was assumed that the parameters 39 3 38 K( He, a) K reaction were appropriate for the used for the 32 3 31 . S( He, a) S reactwn. Another set of parameters, labeled Set II in Table X, was obtained by interpolating the values of Hodgson (1963b) for nuclei in this mass region. The predicted distributions are very 27 similar to those with Set I parameters. The parameters labeled Set ill in Table X were used by 32 3 31 Fou and Zurmuhle (1966) for the reaction s( He, a.) s at E = 15. 0 3 . He MeV. These parameters were obtained from the analysis of elastic 40 3 scattering of He from ca at 15 MeV and elastic scattering of 40 alphas from Ca at 24 MeV. The predicted distributions are very similar to those for Set I and again the distributions are very insensitive to variations in these parameters. The distributions for these three sets of parameters were calculated with the code TSALL Y which uses the zero- range approximation and was written by Bassel, Drisko, and Satchler (1962). This is not a search code and only calculates the distributions for given sets of input parameters. The distributions calculated by TSALL Y were manually punched on cards and then normalized and plotted along with the experimental distributions by the computer. Figure 12 shows a typical comparison of the angular distributions predicted by Sets I, II, and m. Attempts to improve the fits by varying the parameters met with little success, and it was decided to use Set I parameters for all of the levels. Figures 13 - 26 show the results. 5. Discussion Figure 13 shows the angular distribution for which must have t 31 s(G. S.) 11 n = 0 because for this state J = 1/2+ (Endt and van der Leun, 1962). The second peak is larger relative to the first peak than the theory predicts but the edge of the forward peak is correctly positioned. The theoretical distributions fort n = 0, 1, 2, 3, and 4 are shown. These distributions are similar for different excitation energies. 28 The angular distributions for 31 s(l. 25) and 31 s(2. 23) were not measured because they had already been measured by Fou and Zurmuhle (1966). Figure 14 shows the angular distribution for The theoretical distribution for t n 31 = 0 fits the data best. s(3. 08). The second peak is larger relative to the first peak than the theory 31 predicts, just as it was for the ground state. Level s(3. 08) is assigned t n = 0 and therefore J 11 = 1/2+. Figure 15 shows the angular distribution for 31 s(3. 29). The theoretical distribution for -t.n = 2 fits the data quite well. Fou and Zurmuhle (1966) found a J-dependence in t = 2 angular distrin 32 3 31 butions from the reaction s( He, a) s. They found that the main peak in the t n = 2 angular distribution to the 3/2+ level at an excitation energy of 1. 25 MeV was shifted to a more forward angle by a few degrees relative to the forward peak for the 5/2+ level at 2. 23 MeV (see Section Ill. C. for the spin assignments). Glashausser and Rickey (1967) observed a similar J-dependent shift for these 32 31 same levels in the reaction s(p, d) s, and they discuss other reactions which show that J -dependence in neutron pickup reactions is a widely occurring phenomenon. In the present experiment the 31 angular distribution for s(3. 44) (discussed below) which has J = 3/2 (see Section m. C. for the spin assignment) falls between the theoretical distributions for t = 1 and 2 (see Figure 16). 31 n Because of J-dependence level s(6) is assigned .e.,n = (2) and J 11 = (3/2+) (parentheses mean the assignmEnt is tentative) and level 31 . s(3. 29) which fa lls close r t o the t heoret ical dist ribution fo:t~ .tn • 2 is assigned t = 2 and .f" = (5/2t. n No attempt was made to obtain the angular distribution for 31 s(3. 35) because this weak group was not well resolved from 31 the strong s(3. 29). 29 Figure 16 shows the angular distribution for 31 8(3. 44). As mentioned above, the distribution falls between the theoretical distributions fort 3 n = 1 and 2, and because of J-dependence ~8(3. 44) is assigned -tn = (2) and J 11 = (3/2+). 31 Fig-ure 17 shows the angular distribution for 8(4. 08). 0 31 11 For e ab,::: 20 , 8(4. 08) was obscured by C (G. 8. ). The 1 theoretical distribution for -t = 2 is consistent with the measured n distribution, and because the measured distribution is not shifted 11 forward relative to the theoretical distribution, J = (5/2+) is 31 suggested. Level 8(4. 08) is assigned t = (2) and J 11 = (5/2+). n No attempt was made to obtain the angular distribution 31 11 for 8(4. 21) because this group was obscured by c(G. 8. ). 31 8(4. 45). Figure 18 shows the angular distribution for 11 The gap in the distribution was caused by c (G. 8. ). Level 31 8(4. 45) is assigned t = 3. n 31 Figure 19 shows the angular distribution for 8(4. 52). 11 The gap in the distribution was caused by c(G. 8. ). Level 31 8(4. 52) is assigned t = 2. n 31 Figure 20 shows the angular distribution for 8(4. 58). 11 The gap in the distribution was caused by c (G. 8. ). No assign31 ment is made for level 8(4. 58) because the fit is poor. 31 Figure 21 shows the angular distribution for 8(4. 72). 11 The gap in the distribution was caused by c (G. 8. ). Level 31 s(4. 72) is assigned ,e, = 2, (3). The fact that the experimental n distribution is shifted to a greater angle than the theoretical distri- bution is attributed to J-dependence, and J = (5/2) is assig11ed t o this level. Figure 22 shows the angular distribution for 31 s(4. 87). For this level and all higher levels discussed below, the point at 30 eCM = 6°was obscured by elastic scattering of 3 He++ particles. The minimum at 8 CM = 28° is best fitted by the theoretical distribution fort n = 1, but since a point was not obtained near enough to SCM= 0° to confirm the predicted decrease in do/dD there, this level is assigned t n = (1). Figure 23 shows the angular distribution for 31 8(4. 97). The minimum at 8 CM = 28° is best fitted by the theoret~cal distribution fort of 31 n = 1, and therefore this level is assigned t n = 1. No attempt was made to obtain the angular distribution 31 8(5. 03) because this group was not resolved from 8(4. 97) . 31 . Figure 24 shows the angular distribution for 8(5. 15). This level is assigned t n = 0 and therefore i 1 = 1/2+. Figure 25 shows the angular distribution for 31 8(5. 30). The lack of structure suggests that this level is not populated by . a pick-up reaction, and no assignment is made. for 31 No attempt was made to obtain the angular distribution 31 8(5. 41) and 8(5. 44) because these groups were not resolved. 31 Figure 26 shows the angular distribution for 8(5. 52). No assignment is made. 6. Results work. Table XI summarizes the results of this and previous 31 The present assignment of-t = 3 to 8(4. 45) disagrees with the assignment of t n = 2 to this level by Fou and Zurmuhle (1966). However, there is an 7/2- level in the mirror nucleus 1ieV excitation energy (Harris et al., 1964). 31 P at 4. 43 Furthermore, Fou 31 . and Zurmuhle (1966) did not resolve the 4. 45 MeV level from the 4. 52 MeV level which has -C. = 2. n The assignment of .t n = 2 to 31 s(3. 29) disagrees with the assignment of .t = 1 to this level by Kavaloski (1963) but n agrees with Fou and Zurmuhle (1966) and Glashausser and Rickey (1967). 32 A. Introduction This section describes the application of a correlation technique called Method ll by Litherland and Ferguson (196 1) to 32 s( 3 H 4 H ) 31 s '""h" . ' . ' gives . infore, ey . 1 IS met'no d , wmcn th e reac t 1011 mation about the spin, parity, and mixing ratio for levels in the residual nucleus, was first mentioned by Newton (1952), but its power was not widely recognized until Litherland and Ferguson (1961) again pointed it out. One of the first applications that 16 3 18 illustrated its power was a study of the reaction o ( He, p y) F by Poletti and Warburton (1965). Following this study, numerous other studies employing this technique were published. What is new in the present application is a refinement in the experimental technique. Most previous applications have used an annular solid-state detector at 180° and studied only the well separated low-lying states of the residual nucleus. For high- lying levels information about the spin, parities, and mixing ratios has usually been obtained by resonance experiments. technique serves well in the intermediate region. The present Because the levels are closely spaced, high resolution is needed for either the particles or the gammas. The former was chosen. A magnetic spectrometer was placed at 0° to detect the particles, and the gammas in coincidence were detected with a Na!(T1) crystal. The main disadvantage is the small solid angle of the spectrometer. This disadvantage can be overcome with an array of detectors in the focal plane of spectrometer and with an array of Na!(Tl) crystals, but this was not done in the present experiment. Similar 33 experiments employing magnetic spectrometers are in progress at Chalk River and MIT. B. - Theory The formulas which will be discussed here are similar to those given by Poletti and Warburton (1965). Derivations of them will_not be given (see Ferguson, 1965). The essential feature of Method IT is that it limits the gamma rays which are observed to those from aligned states with a small number of magnetic substates populated. Consider the reaction: a Spins J + b .... c Jb a Orbital Angular Momentum Lab Magnetic Quantum Number M Mab Mb a J + d Jd c Led M c Mcd Md Since the beam direction is the z axis, Mab = 0. Suppose c is detected at 0° (or 180°). Then for these particles Mcd = 0. conservation of angular momentum and therefore l J a l + I :Jb I + I :J c I By 34 If the gamma rays from the decay of d are detected in coin- cidence with the particles c observed at 0° (or 180°) and if the beam and target are unpolarized, then the angular distribution of the gamma rays can be expressed by k k where 8 is the angle between the direction of the gamma-ray detector and the axis of alignment• . The Pk(cos 8) are Legendre polynomials and k takes on even values from 0 to 2Jd" The Qk are the standard attenuation coefficients for the gamma- ray detector, the pk (Jd) are statistical tensors which describe the alignment of the state d, and the F {(JdJ e ) depend specifically on the gamma-ray transition. 1 In more detail, the statistical: tensors are given by (2) where P(Md) is the normalized population parameter for the magnetic substate Md and (3) j · ,' 35 The F {(JdJe ) are given by the following if no more than two 1 multipolarities Land L' ::;; L + 1 are involved in the gamma-ray transition. 2 Fk(LLJdJ ) - (-)cr2xF(LL'JdJ )+x Fk(L'L'JdJ ) F (J J ) = . e e . e k. d e +X (4 ) 1 where J -J -1 1 2 Fk(LL'JeJd) = (-) e d [(2L+1)(2L'+1)(2Jd+1)J / (L1L-1jk 0) (5) In formula (5),W(JdJdLL', kJe) is the Racah coefficient, and the mixing parameter xis given by x = <ell L+1Jjd) I (eJJ Lj jd). The exponent cr is 0 for an ML, EL + 1 mixture, and 1 for an EL, ML + 1 mixture. In the following analysis, it was assumed initially that cr = 0 regardless of the suspected nature of the transition. For comparison with experiment it is more convenient to rewrite formula (1) in the form L W(e) = M ~ oI(Md)[ pk(Jd' Md)Fk(JdJe)QkPk(cos 8)] dk . even where pk(JdMd) is given by formula (3), and I(Md) is the unnormalized population parameter, that is, (6) 36 (7) M '> 0 d - Formula (6) clearly shows that W(e) is linear in I(Md) and nonlinear 2 in x. The best fit to the data corresponds to the lowest value of Q , 2 where Q is given by 1 - ii Ii Y(e.) - w(e.) [ 1 1 E(e.) ]2 (8) 1 where E(e.) is the uncertainty in the gamma-ray yield Y(e .) at e. 1 1 1 and n is the number of degrees of freedom. . 32 3 4 31 In the reactwn S( He, Hey) S, Md = ±1/2, and formula (6) becomes W(e) = 1(1/2) L pk(Jd' 1/2)Fk(JdJ e)QkPk(cos e) • (9) k Only the two parameters 1(1/2) and x must be ~itted. C. Correlations in the Reaction 32 3 s( He, 4 Hey) 31 s 1. Excitation Functions To maximize the yield of alphas at 0° in the correlation and branching ratio measurements it was necessary to measure 37 rough excitation functions for the groups of interest. These excitation functions were measured at elab = 10° with the array, and the various slit settings are given in Table I, column e. The 0 target consisted of ZnS containing natural sulfur on a 2500 ANi foil. Figure 27 shows the results. at every 200 keV from 8 to 12. 2 MeV. Measurements were made The arrows indicate the beam energies selected for the correlation and branching ratio 31 measurements. For s(2) the correlation and branching ratio were measured before the excitation function was measured, and the beam energies were not optimum. 2. Experimental Setup for the Correlations A schematic diagram of the setup is shown in Fig-ure 28. The alpha particles were detected in the magnetic spectrometer at 0° with a silicon surface barrier detector. The detector was masked 31 31 31 by a slit (1. 27 em wide for s(1. 25), s(2. 23), and s(3. 08) and 31 31 31 . 635 em wide for s(3. 29), s(3. 35), and s(3. 44)) and covered 2 with an aluminum foil which presented a thickness 1. 7 mg/ em to the particles passing through the spectrometer. For the correlations of the levels at 3. 29 and 3. 35 MeV excitation, the beam was caught in a cup of diameter 0. 635 em placed at a distance of 25 em from the target. The half-angle subtended by this cup was 0. 72°. The outer aperture was a hole of 1. 676 em diameter also placed at a distance of 25 em from the target. The half-angle subtended by this 0 aperture was 1. 85 • For the correlations of the other l evels an older, dirtier beam catcher which produced more gamma-ray background was used because completion of the newer beam catcher was unexpectedly delayed on three occasions by other experiments 38 immediately before scheduled runs. The cup in the old system was 0 48 em from the target and subtended a half-angle of 1. 1 . The entrance slits to the spectrometer defined the outer aperture and subtended a half-angle of 2. 0°. The correlation from the 2. 23 MeV level was measured with both systems and the results agreed within the experimental uncertainties. The gamma rays were detected in a 12. 70 em diameter x 10. 16 em long Nai(Tl) crystal which could be moved from 90° to 150°. The distance from the target to the front face of the crystal was 13. 7 em. This spacing could easily be reproduced by means of a spacer between the crystal and the outside of the target chamber. The crystal was supported on a wooden table clamped to a target chamber support. The angles were set by means of lines drawn on this table. A diagram of the electronics is shown in Figure 29. The internal lower level discriminator gate in the RIDL 400-channel analyzer was disconnected from the input and the gating pulses from the diodes were fed to this gate rather than to the coincidence gate supplied by the company. This modification suggested by Dr. R. W. Kavanagh greatly reduced the dead time in the analyzer when there was a high count rate at the input. The two diodes prevented cross-talk between the two coincidence units (RIDL 32- 3). The high voltage stabilizer sampled the counting rates in two windows-- one on each side of a peak-- and adjusted the high voltage to keep these two counting rates equal. The rest of the .circuit is standard. Due to the complexity of the setup and the fact that most of the equipment was used for other experiments, it was difficult to set up the experiment quickly enough so that there was enough 39 time remaining in the 24-hour run to measure the correlation. A standard arrangement for everything used in this experiment was developed, and special length cables reserved for this experiment were made for connecting the electronics. Careful scheduling of the day for the run was necessary in order that all of the required equipment be available. In spite of this diligence, on several days the correlation was not completed even though the beam was available most of the day. Mter the equipment was assembled, the next step was to set the gains and the single channel analyzer (S. C. A. ) windows. The gain for the gamma rays was set by lowering the coincidence level tn one of the coincidence units so that it triggered on singles. The gain could then be adjusted so that the spectrum was spread over the desired number of channels. The gain for the alpha particles was set so the pulses reaching the S.C. A. were between 5 and 10 volts because this was the best operating region for the S.C. A. The gamma-rayS. C. A. was used in the integral mode and set to discriminate against low energy gamma rays. · Raising this discriminator decreased the number of randoms. The S. C. A. window for the particles was set on the alpha particles after identifying them with the usual techniques of placing foils in front of the detector and changing the bias. This procedure was 3 complicated by the fact that there were some He particles scattered around the spectrometer, but their energy was always lower than the energy of the alphas. The magnetic field was varied to find the setting at which the peak was centered on the slit in front of the detector. The next step was to set t¥Ie various pulse widths and delays. Groce (1963) gives the formula 40 t(nanoseconds) = 202. 0 ./Al'ff for the time required for a particle to travel the distance from the target along the mean orbit to the detector, where A is the atomic weight and E is the energy in MeV. The times for the extreme outer and inner orbits are approximately 10% longer and shorter, respectively~ For an alpha withE = 14 MeV, t = 108 ± 11 ns. Because of this time spread, because of the walk in the S.C. A. 's, and because it was difficult to set the rather coarse delay controls accurately, a resolving time of 2T = 120 ns was used, that is, the widths of the logic pulses to the coincidence circuit were 60 ns. To set the appropriate delays for these logic pulses, a measurement of the counting rate versus delay was made and the delay with the maximum counting rate was selected for the "reals" channel. An additional 2 f.l.S was added to the "randoms" channel. The delay on the linear gamma- ray pulses was set by calculating the required delay from the other delays in the circuit and then checked by observing whether every coincidence was stored in the RIDL 400channel analyzer. 3. 31 Spectra s(l. 25) Figure 30 shows the gamma- ray spectrum at e = 120° from the decay of the level at 1. 25 MeV excitation energ/ in 31 s. The gamma-rayS. C. A. was set so that pulses were stored only above channel 34. In Figure 30 the randoms spectrum multiplied . ..number · by the rabo . . b · of . f reals . d has already been subtracte d . T lns nu1n e-r o ran oms ratio was measured by feeding uncorrelated pulses into both channels 41 and counting the number of coincidences in both the real and random channels. This ratio was approximately one for the spectra from · all of the levels. In the spectra from the 1. 25 MeV level, the randoms spectrum typically contained one- third as many counts as the reals spectrum with most of the counts in channels below the photopeak. or 130 keV. The resolution (FWHM) of the photopeak was 10% The gamma-ray singles rate was approximately 50K per sec and the alpha particles singles rate was approximately 75 per sec. · A gamma ray was detected in coincidence with about 2% of the alpha particles detected. Each angle required about three 3 hours with a beam of 0. 15 ~-tA of 11. 2 MeV He ++. Figure 31 shows the angular correlation of the gamma rays in the photopeak normalized to the number of alpha particles detected. 31 The error bars represent the statistical uncertainties. 8(2. 23) Figure 32 shows the gamma-ray spectrum at e = 135° 31 from the decay of the level at 2. 23 MeV excitation energyy in 8. The randoms spectrum which have already been subtracted in Figure 32 contained approximately one-third as many counts as the real spectrum with most of the counts in channels below the photopeak. .k eV. The resolution (FWHM) of the photopeak was 8% or 180 The gamma-ray singles rate was approximately 42K per sec and the alpha particles singles rate was approximately 80 counts per sec. A gamma ray was detected in coincidence with about 2. 6% of the alphas. Each angle required about three hours with a beam of 0. 18 ~-tA of 8. 5 MeV 3 He++. The gamma-ray energy calibration was established with gamma- ray sources. 42 Figure 33 shows the angular correlation of the gamma rays in the photopeak normalized to the number of alpha particles detected. 31 The error bars represent the statistical uncertainties. 8(3. 08) Figure 34 shows the sum of the gamma-ray spectra at all angles from the decay of the level at 3. 08 MeV excitation energy 31 in 8. The random spectra which have already been subtracted in Figure 34 contained approximately one-third as many counts as the reals spectra with most of the counts in channels below the photopeak. The resolution (FWHM) of the photopeak was 6% or 190 keV. The gamma-ray singles rate was approximately 50K per sec and the alpha particle singles rate was approximately 6 counts per sec. A gamma ray was detected in coincidence with about 3. 2% of the alphas detected. Each angle required about four hours with a beam 3 of 0. 2 f...l.A of 8. 4 MeV He++. The gamma-ray energy calibration was established with gamma-ray sources. Figure 35 shows the angular correlation of the gamma rays in the photopeak normalized to the number of alpha particles detected. 31 The error bars represent the statistical uncertainties. 8(3. 29) Figure 36 shows the gamma- ray spectrum from the decay 31 of the level at 3. 29 MeV excitation energy in 8 at ey = 90°. The random spectrum which has already been subtracted in Figure 36 contained approximately one-fifth as many counts as the reals spectra with most of the counts in channels below channel 60. The 43 gamma-ray singles rate was approximately 65K per sec and the alpha particle singles rate was approximately 1 count per sec. A gamma ray was detected in coincidence with about 5. 3% of the alpha particles detected. Each angle required about six hours 3 with a beam of 75 nA of the 12. 0 MeV He ++. The gamma-ray energy calibration was established with gamma-ray sources. Figure 37 shows the angular correlation of the photopeak of the 2. 04 MeV gamma ray. The error bars represent the statistical uncertainties. 31 8(3. 35) Figure 38 shows the sum of the gamma-ray spectra at all angles from the decay of the level at 3. 35 MeV excitation energy 31 in 8. The random spectra which have already been subtracted in Figure 38 contained approximately one-f:ifth as many counts as the reals spectra with most of the counts in channels below channel 30. The gamma-ray singles rate was approximately 60K per sec and the alpha particles singles rate was approximately 0. 5 counts per sec. A gamma ray was detected in coincidence with about 4. 5% of the alphas detected. Each angle required about four hours with a beam 3 of 80 nA of 9. 0 MeV He++. The gamma-ray energy calibration was established with gamma-ray sources. Figure 39 shows the angular correlation of the photopeak of the 2. 11 MeV gamma ray. statistical uncertainties. The error bars represent the 44 31 s(3. 44) Figure 40 shows the sum of the gamma-ray spectra at all -angles from the decay of the level at 3. 44 MeV excitation energy 31 in s. The random spectra which have already been subtracted in Figure 40 contained approximately one- third as many counts as the reals spectra with most of the counts in channels below channel 80. The gamma-ray singles rate was approximately 50K per sec and the alpha particle singles rate was approximately 3 counts per sec. A gamma ray was detected in coincidence with about 3. 1% of the alphas detected. Each angle required about five hours with a beam 3 of 70 nA of 12. 2 MeV He ++. The gamma-ray energy calibration was established with gamma-ray sources. Figure 41 shows the angular correlation of the photopeak of the 3. 44 MeV gamma ray. The error bars represent the statistical uncertainties. 4. Analysis of the Data · The attenuation factors Qk in Formula (6), Section ill. B., were calculated with the formulas Jk ::: 2rr JY sin 13 d[3 Pk(cos e)(l - e -TX(f3) ) 0 where 45 = X(~)= T = angle with respect to the crystal axis the distance through the crystal gamma attenuation coefficient (from Grodstein, 1957). (See Figure 42 for the notation as given by Rose (1953)). These results are given in Table XII. 2 With cr = 0 in Formula (4), Section ill. B. , Q was minimized with respect to I (1/2) for all possible combinations of J d and J e and a discrete set of values for x. Then for each combination of J d and J e a plot was made of these minima versus arctan x as shown in Figure 43 for example. The dips in these plots correspond to possible solutions. The probability that a 2 given dip is the correct one can be found by referring to x probability tables (see Nijgh et aL ,1959). The 0. 1% confidence limit is shown and only points on these curves which lie below this limit are assumed to be possible solutions. The values of the mixing ratio x and its error at the minimum were found with an adaptation of a procedure given by Smith (1964) for the analysis of triple correlations. value of the mixing ratio near a minimum. Let Let x 2 be the 46 . where d is much less than the width (FWHM) of the dip. Then to a good approximation the center of the dip is x + t::.x where 2 t::.x = Ad 2B A = Q (xl) - Q (x3) B = Q2(xl) + Q2(x3) - 2Q2(x2) 2 2 2 Q at the minimum is furthermore, This process was iterated and found.to converge very rapidly. The uncertainty in the mixing ratio is given by cr where H = X J 2 2d B(H- P- 1) = number of angles P = number, of > 0. . magnetic substates with m zThe program for these calculations is given in Appendix D. >I 47 31 s(l. 25) Level 31 s(1. 25) decays only to the 1/2+ ground state (see Section ill. C. 5) and therefore only JTTe = 1/2+ must be considered. . The coincidence requirement limits the possible lifetime of the level 31 10 s(1. 25) to T < 1 i-!S and therefore r > 7 x 10ev. This limit y~ y~ on r Y limits the possible values of J d which must be considered in the analysis. The general surveys by Wilkinson (1960) and Skorka et al.(1966) of the measured transition strengths in light nuclei give some guide to the maximum transition strengths for various values of J d" For electric transitions, which are usually stronger than magnetic transitions, the limits on r Y for various values of J d are: Jd Transition r y (ev) 1/2 E1 2 .:5 10- 3/2 E1 ;S 5/2 E2 _ r-J . 7/2 E3 9/2 E4 Since for this level r Y > 7 x 10- 10 10- 2 4 < 109 < 10- r-J < 10-17 r-J ev , only values of J d.::;; 7/2 must be considered. 2 Figure 43 shows the minimum of Q with respect to 1(1/2) as a function of arctan x for all allowed combinations of J d and J e· All of these curveswere calculated with a = 0 in Formula (4), Section ill. B. values. Only J d = 3/2 gives a fit and xis restricted to two Fou and Zurmuhle (1966) found .e, = 2 for this level and · n 48 therefore the parity is positive and the gamma-ray transition is an M1, E2 mixture which is consistent with cr == 0. given in Table XII. The results are The fit to the correlation data is shown in Figure 31. 31 s(2. 23) Level 31 S (2. 23 ) decays only to the 1/2+ ground state (see Section m. C. 5) and therefore only fT = 1/2+ must be considered. e The limits on r Y for various values of J d are: Jd Transition r y (ev) 1/2 E1 1 < 10- 3/2 E1 5/2 E2 1 :5 1010- 2 7/2 E3 7 < 10- 9/2 E4 < 10-14 < "' Since the coincidence requires r Y > 7 x 10- 10 ev , only values of J d .:5 7/2 must be considered. Figure 44 shows the minimum of Q 2 with respect to I(l /2) as a function of arctan x for all allowed combinations of J d and J e. All of these curves were calculated with cr = 0 in Formula (4), Section m. B. values. Only J d = 5/2 gives a fit and x is restricted to two Fou and Zurmuhle (1966) found t n = 2 for this level and therefore the parity is positive and the gamma- ray transition is an E2, M3 mixture which is inconsistent with cr == 0. To correct this, 49 it is only necessary to change the signs of the mixing ratios calculated from Figure 44. -2. 411 ± • 243. Thus, the values are x = -. 053 ± • 036 and The results are given in Table XII. The fit to the correlation data is shown in Figure 33. 31 s(3. 08) Level 31 S (3. 08 ) decays only to the 1/2+ ground state (see Section ill. C. 5) and therefore only Jrr = 1/2+ must be considered. e The limits on r Y for various values of J d are: r y (ev) Jd Transition 1/2 E1 < ......, 10- 1 3/2 E1 < ......, 10- 1 5/2 E2 2 .:5 10- 7/2 E3 < ......, 10- 6 9/2 ' E4 < ......, 10-13 Since the coincidence requires r Y,2: . 7 x 10- 10 ev , only values of Jd .S 7/2 must be considered. Figure 45 shows the minimum of Q 2 with respect to I(l/2) as a function of arctan x for all allowed combinations of J d and J e· All of these curves were calculated with cr = 0 in Formula (4), Section III. B. It was found that .e, n Both J d ::; 1/2 and J d = 3/2 give fits. ::; 0 for this level (see Section II. C.) and therefore J~ = 1/2+. The results are given in Table XII. correlation data is shown in Figure 35. The fit to the 50 31 s(3. 29) Level 31 S (3. 29 ) decays to both the 3/2 + level at 1. 25 MeV and the 5/2+ level at 2. 23 MeV (see Section III. C. 5). the transition to the 3/2+ level at 1. 25 MeV, J limits on r y e For = 3/2+. The for this transition are: Jd Transition r y (ev) 1/2 E1 1 :5 J.o- 3/2 E1 ,.._,. 5/2 El 1 :5 10- 7/2 E2 3 :5 10- 9/2 E3 ,.._, 11/2 E4 ,.._, Since the coincidence requires r Y,2: 7 x 10- 1 < 10- 8 < 10< 10-14 10 ev , only values of Jd.::; 9/2 must be considered. Figure 46 shows the minimum of Q 2 with respect to 1(1/2) as a function of arctan x for all allowed combinations of J d and J e· All of these curves were calculated with a = 0 in Formula (4), Section Ill. B. but Jd = 5/2 is favored. Both J d = 3/2 and J d = 5/2 give fits, It was found that -t = 2 for this level n (see Section Il C.) and therefore the parity is positive and the gamma-ray transition is art Mi, E2 mixture which is cons istent with a = 0 for both J~ = 3/2+ and J~ = 5/2+. in Table XTI. 37. The results are given The fits to the correlation data are shown in Figure 51 For the transition to the 5/2+ level at 2. 23 MeV the statistical uncertainties in the data were so large that nothing useful was found from the correlation analysis. For both the cascade through the 3/2+ level at 1. 25 MeV and the cascade through the 5/2+ level at 2. 23 MeV, an extension of the analysis was made to analyze the angular correlation of the second gamma- ray transition. The parameters in these cases were very insensitive to the present data, and nothing useful was found. 31 s(3. 35) Level 31 s(3. 35) decays only to the 3/2+ level at 1. 25 MeV (see Section III. C. 5) and therefore only JTT ::: 3/2+ must be e considered. The limits on r Y for various values of J d are: Transition r (ev) 1/2 El :5 10-l 3/2 El 5/2 El 7/2 E2 9/2 E3 11/2 E4 J d Since the coincidence requires r Y,2: 7 x .l0of Jd.::;;: 9/2 must be considered. y 1 < 10- ~ 1 < 10- "-' 3 < 10< 10- 7 ~ < 10-14 10 ev , only values 52 2 Figure 47 shows the minimum of Q with respect to I(l/2) as a function of arctan x for all allowed combinations of J d and J e· All of these curves were calculated with cr == 0 in Formula (4), Section ID. B. Fits were obtained for Jd == 7/2, 3/2, 9/2, and 5/2 in the order of. preference. Since there is only a 1% probability that Jd == 9/2 is a fit and only a 0. 3% probability that J d == 5/2 is a fit, these two values are not considered further. The parity is assumed positive because 31 the paritiesofallofthe levels in the analog P up to 4. 3 MeV excitation energy are positive (see Section IV. A). For J~ == 7/2+, the gamma-ray transition is an E2, M3 mixture which is inconsistent with cr == 0. To correct this it is only necessary to change the signs of the mixing ratios calculated from Figure 47. Thus, the values are x == -. 467 ± • 521 and -2. 204 ± 2. 920 for J~ == 7/2+. For J~ == 3/2+, the gamma-ray transition is an M1, E2 mixture which is consistent with cr == 0 and no correction is necessary. The results are given in Table XII. The fits to the correlation data are shown in Figure 39. The second gamma-ray transition of the cascade through the 3/2+ level at 1. 25 MeV was analyzed, but again the parameters were insensitive and nothing useful was found. 31 s(3. 44) Level 31 + S(3. 44) decays to the 1/2 ground state and to either the 3/2+ level at 1. 25 MeV or the 5/2+ level at 2. 23 MeV or both (see Section ffi. C. 5). For the decay to the ground s tate, Jrre = l/2+ . The limits on ry for various values of Jd are: 53 r y (ev) Jd Transition 1/2 E1 < ,...., 10- 1 3/2 E1 ;S 10- 1 5/2 E1 ;S 10- 2 7/2 E2 < ....... 10- 6 9/2 E3 < ....... 10-13 Since the coincidence requires r Y;:: 7 x 10- 10 ev , only values of J d.:::;; 7/2 must be considered. 2 Figure 48 shows the minimum of Q with respect to 1(1/2) as a function of arctan x for all allowed combinations of J d and J e. All of these curves were calculated with a :::: 0 in Formula (4), Section III. B. Only the curve for Jd = 3/2 fits. It was found that .t = (2) for this level (see Section II. C) and therefore n the parity is tentatively positive and the gamma- ray transition is tentatively an M1, E2 mixture which is consistent with a :::: 0. The results are given in Table XII. The fit to the correlation data is shown in Figure 41. The photopeak yields were also fitted with a series of Legendre polynomials L k even ~QkPk(cos e) 54 "' where k :s 2J d for simple decay or k :s min (2Jd' 2Je) for the second gamma ray in a cascade. The uncertainties were assigned in the standard manner as described in Nijgh et al. (1959). The normalized coefficients, that is y a , and their 0 uncertainties are given in Table XII. 5. Branching Ratios To measure branching ratios, the lucite target chamber top was replaced with an aluminum cup covered with tantalum into which a 10. 16 em x 10. 16 em Nai(Tl) crystal could be inserted (see Figure 49). This allowed the front face to be placed at 3. 556 em from the center of the beam spot and thus increased the efficiency. It was necessary to make separate runs for the branching ratios because there was not enough electronic equipment available to measure the branching ratios and the correlations simultaneously. In some cases, runs with the aluminum cup were not taken and only the correlation spectra were used to determine the branching ratios. Except for the aluminum cup the setup was the same as that u&ed for the correlation measurements. 31 8(2. 23) The gamma-ray decay spectrum taken with the aluminum 31 cup of the level at an excitation energy of 2. 23 MeV in 8 is shown in Figure 50(a). Figure 50(c) shows a standard gamma-ray line 12 3 14 shape obtained by observing the reaction c( He, p) N to the 14 level at 2. 311 MeV excitation in N and observing the gamma rays from the decay of this level in coincidence with the protons. Figure 55 50(b) shows a line shape for a 1. 25 MeV gamma ray obtained by 32 3 obserying the reaction s( He, cx.) 31 s to the level at 1. 25 MeV 31 excitation energy in s and observing the gamma rays from the decay of this level in coincidence with the alphas. To calculate a branching ratio limit to the state at 1. 25 it was assumed that the line shape for a 2. 23 MeV gamma ray was well approximated · by the line shape for the 2. 311 MeV gamma ray. The gain and normalization of the 2. 31 MeV line shape spectrum were adjusted with the computer so that the 2. 31 MeV photopeak matched the 2. 23. Then various amounts of the 1. 25 MeV line shape with appropriate gain were added to the 2. 31 line shape until the composite just exceeded the statistical uncertainties in the region of the 1. 25 MeV photopeak in the spectrum from the decay of the 2. 23 MeV level. In this mixture if Y(90°) 1. 25 p h ot opeak is the number of counts in the 1. 25 MeV gamma-ray peak and Y(90°)2. 23 ph ot opeak is the number of counts in the 2. 31 MeV gamma- ray peak, then 0 J 2.23 Y( 90 >1.25 photopeak PF 2.23 0 N-- < - . -o· )__:.__---.::_---.::__ PF J 1.25 2. 23 Y(90 2. 23 ph ot opeak 1.25 0 Nl. 25 (a 2. 23 + a 2 2. 23 Q 2 2. 23 p 2 ( cos 90().,) J 0 p ( 900)) (ao 1. 25 + a2 1. 25 Q 2 1. 25 . 2 cos min where (10) 56 = number of events in which the 2. 23 MeV level Nl. 25 cascaded through the 1. 25 MeV level and an a. was detected. = number of events in which the 2. 23 MeV level N . 2 23 decayed directly to the ground state and an a. was detected. PF . = photofraction for a 2. 23 MeV gamma ray (from 2 23 Weitkarp.p, 1963). PF 1. 25 = photofraction for a 1. 25 MeV gamma ray (from Weitkamp, 1963). J 0 2 23 · J 1. 25 0 (a 0 = total efficien~y for a 2. 23 MeV gamma ray. = total efficiency for a 1. 25 MeV gamma ray. 2 23 • +•.. ) = relative angular correlation yield (a 0 = 1) of 2. 23 MeV gamma ray for the parameters 2 found with the x analysis. (a 1. 0 25 f . . . w1"th .respect t o x- . +•.. ) = mm1mum 2 23 ... 1. 25 o the relative angular correlation yield (a 0 = 1) for the 1. 25 MeV gamma ray in the cascade. This formula yields Nl. 25 .$. • 029 and therefore N2. 23 Nl. 25 branching to 1. 25 MeV level = to groun~ state;::: 97%. N2 23 ·N .::; 3% , 1 + 1. 25 N2. 23 (See Figure 53.) 57 31 8(3. 08) The analysis of branching of the decay of the 3. 08 MeV level was very similar. The line shape of a 3. 08 MeV gamma ray was obtained by observing the gamma rays from the decay 11 3 13 of B( He, p) c(3. 09). The 2. 311 MeV line shape was used as an approximation to the line shape of a 2. 23 MeV gamma ray in the 3. 08 .... 2. 23 ... 0 cascade. The 1. 25 MeV line shape was used for the 1. 25 MeV gamma ray in the 3. 09 ... 1. 25 ... 0 cascade. Using a formula similar to Formula (10) above yields N2. 23 ~ .09 N3. 08 Nl. 25 < • 15 N3. 08 .. and therefore branching to 2. 23 level ~ 8% to 1. 25 level < 13% to ground state > 85% • 31 8(3. 29) The branching ratios for the decay of the 3. 29 MeV level were extracted from the correlation spectra because no spectrum with the aluminum cup was taken. To calculate a limit on a possible branch .to the ground state the counts in 58 channels 170 through 180 corresponding to the photopeak of a 3. 29 gamma ray were summed at each angle. The yields were normalized to the number of particles detected in coincidence. ':('he resulting correlation was fitted with an expansion in Legendre polynomials. I ~Pk(cos e) k even where k ,::5 4 because the spin of the 3. 29 level was found to be 5/2+ (see Section ill. C. 4). Similarly, the angular correlation of the 2. 04 MeV gamma ray after subtracting the contribution from the 2. 23 MeV gamma ray, emitted in the cascade of the 3. 29 to 1. 25 MeV level was fitted with an expansion in Legendre polynomials. Then PF 2. 04 J 2. 04 a 3. 29 0 0 PF 3. 29 J 3. 29 a 2. 04 0 0 where N . 3 29 = number of events in which the 3. 29 MeV level decays directly to the ground state and an ex. was .detected. N . 2 04 = number of events in which the 3. 29 MeV level cascades through the 1. 25 MeV level and an ex. was detected. 59 PF 2. 04 = photofraction for a 2. 04 MeV gamma ray (from Weitkamp, 1963). PF 3. 29 = photofraction for a 3. 29 MeV gamma ray (from Weitkamp, 1963). J 2.04 0 J 3.29 0 = total efficiency for a 2. 04 MeV gamma ray. = total efficiency for a 3. 29 MeV gamma ray. This gives N3. 29 N S • 184. 2.04 Similar analyses were done to obtain branching ratios for branches to the level at 3. 08 MeV and the level at 2. 23. These gave N3. 08 N < • 227 2.04 N2. 23 N = • 326 ± • 049. 2.04 These results were combined to give 60 branching to ground state 31 12% +3 OJ to 1. 25 MeV level = 75-12 /0 to 2. 23 MeV level = 25+ to 3. 08 MeV level < 3% -6 15% . s(3. 35) Figure 51 shows the gamma-ray spectrum for the decay of the level at 3. 35 MeV excitation obtained with the aluminum cup. 31 The analysis was similar to that for s(2. 23). The results were < 6% to 1. 25 MeV level > 78% to 2. 23 MeV level < 21% to 3. 08 MeV level < 6% • branching to ground state 31 s(3. 44) The branching ratios for the decay of the level at 3. 44 . MeV were extracted from the correlation spectra because no spectrum was taken with the aluminum cup. similar to that for the level at 3. 29. The analysis was The results were branching to ground state = .11.6+3 -4 4 to 1. 25 MeV level}= to 2. 23 MeV level to 3. 08 MeV level 54~!% < 2% . 61 IV. A. DISCUSSION OF Comparison with 31 31 s LEVELS P 31 31 Figure 52 shows the energy level diagrams for P. s and 31 All of the information on s was determined in the present experiment except the t -values for the levels at 1. 25, 2. 23 and 7. 04 n 31 (see Section II. C. 6). The information on P published since the compilation by Endt and van der Leun (1962) was completed comes 30 31 from studies of the reactions Si(p, y ), P (Harris and Seagondollar, 1962; Harris and Seagondollar, 1963; Harris and Hennecke, 1964; van Rinsvelt and Smith, 1964; Harris and Breitenbecber, 1966; van Rinsvelt and Endt, 1966; Willmes and Harris, 1967), and 30 31 si(d, n) P (Cujec et al., 1965; Davies et aL, 1965). Figure 53 shows the gamma-ray decay schemes and Table XIII compares the mixing ratios. A comparison of the signs of the mixing ratios for 31 31 s and P is meaningless because different phase conventions 31 were used for the mixing ratios in P. These phase conventions are given in the references cited in the footnotes to Table XIII. 31 The levels at 1. 25, 2. 23, and 3. 08 MeV in s have, respectively, the same spin, parity, and decay scheme as the 31 levels at 1. 25, 2. 23, and 3. 13 MeV in P. These levels are assumed to be isobaric analogs. For the 5/2+ level at 3. 29 MeV in 31 P, the only possibilities for an analog arc tho 5/2+ (3/2)+ level at 3. 20 MeV ~md tho (7/2, 31 3/2) level at 3. 35 MeV in s. The decay scheme of the 3. 29 MeV 31 level in P ~atches the decay scheme of the 3. 29 MeV level in 31 s but does not match the decay scheme of the 3. 35 MeV level. 31 P is assumed to be the isobaric Therefore the 3. 29 MeV level in 31 analog of the 3. 29 MeV level in s. 62 For the 7/2+ level at 3. 41 MeV in 31 P the only possible 31 analog is the (7/2, 3/2) level at 3. 35 MeV in s because this is the only level in this excitation region which can be fitted with J . = 7/2. Furthermore, the decay schemes match. 31 For the 3/2+ level at 3. 51MeV in P the only remaining 31 s at 3. 44 MeV. Again the possibility is the 3/2(+) level in decay schemes match. For the higher levels one can only speculate on which levels are analogs on the basis of the present information. If the order 31 31 of levels is the same in P and s, then one might propose the following analogs. 31p 31 4. 19 MeV, 5/2+ 4. 08 MeV, (5/2+) 4.26 4.43 4.59 4.63 4.78 5.01 3/2+ 4.21 ' 7/25/2+ 4.46 -e, 4.52 -e, ' ' 3/2 ' 5/2, (7/2) ' 3/2' 5. 12 5. 25 8 ' (1/2) n n ::: 3 = 2 4. 58 4 .. 72 -e, 4.87 ' -e, n 4. 97 -e, n 5. 15 = 2 ' (3) = 1 = 1 n 1/2+ The only inconsistency is the lack of an analog for the (5. 03) MeV level in 31 s. This is not unexpected since the experiments with the reaction 30 si(d, n) 31 P may not have resolved this level and the experiments with the reaction it. 30 si(p, y) 31 P may not have populated 63 B. Comparison with Models The low-lying 1/2+ level and 7/2+ level in 31 P and predicted by Broude et al. . (1958) and Glaudemans et al. 31 s (1964) (see Figure 2) and mentioned in the Introduction (Section I. A. ) 31 have been located. In P van Rinsvelt and Endt (1964) located the 1/2+ level at 3. 13 MeV excitation and van Rinsvelt and Smith 31 (1964) located the 7/2+ level at 3. 41 MeV excitation. In s the 1/2+ level has been located in the present experiment at 3. 08 MeV excitation and the 7/2+ tentatively at 3. 35 MeV. The Nilsson model calculation by Broude et al. (1958) was based on the incorrect assignment of i' = 3/2+ to the level at 31 3. 13 MeV excitation in P. Broude et al. (1958) assumed that the level was the second member of a rotational band based on Nilsson orbit number 9 (1/2+, ground state; 3/2+, 3. 13 MeV; 5/2+, 2. 23 MeV) while the other low-lying levels were obtained by coupling two bands based on orbits 8 and 11. Subsequently, BE2(0 _, 2. 23 MeV) Kossanyi-Demay et al. , (1965) found that BE 2 (o _, 3 . 13 MeV)~ 9 from inelastic electron scattering which disagrees with the expected value of 3/2 for levels of the same band. Also van Rinsvelt and 31 Endt (1964) assigned JTT = 1/2+ to the 3. 13 MeV level in P by means of a polarization measurement, and the analog at 3. 08 MeV 31 in s was assigned JTT = 1/2+ in the present experiment. On the 31 basis of the information for P, Bishop et al. (1965) identified the 3. 13 MeV level with Nilsson orbit num ber 11 and repeated the calculations. Couplings between the three rotational bands based on the Nilsson orbits 8, 9, and 11 were allowed. A range of values for the parameters ~' x., and Tl (standard notation) were chosen from considerations of neighboring nuclei. Figure 54, column 1, shows 64 the results for 1-J. = 0. 167, x = 0. 05, and Tl = -3. There is a serious disagreement with experiment, and similar disagreements were obtained for other choices of these parameters. No computed electromagnetic properties were reported., Bishop et al. (1965) concluded that it was rather difficult to explain the level scheme of 31 p with the Nilsson model. 31 P Kamavataram (1966) generalized the Nilsson model for 28 to take into account three nucleons outside of a si core. The 31 P has two neutrons and a proton in Nilsson orbit · ground state of 9. For the low-lying 1/2+, 3/2+, and 5/2+ excited states, Kamavataram considered the excitation of one of these three nucleons into higher Nilsson orbits of positive parity and the different possible parent states of the other two nucleons in constructing properly anti-symmetrized T = 1/2 wave functions. Kamavataram (1966) tabulated the configurations of three particle 31 states of P. The Hamiltonian consisted of a collective part and a part which took into account two- body residual interaction (see Brink and Kerman, 1959). The parameters were selected from a consideration of neighboring nuclei. Calculating the matrix elements of this Hamiltonian with the wave functions described above and diagonalizing yielded the results shown in Figure 54, column 2. Here TJ = -2 and 1-J. = 0. 3 and the residual inte!action is 0. 5 MeV. No computed electromagnetic properties were reported. This more complicated model is in better agreement with experiment than the simple Nilsson model is, but it fails to predict a low-lying 7/2+ level. Chi and Davidson (1963) proposed a modification of the Nilsson model in which the extra nucleon was coupled to an asymmetric core rather than the usual symmetric core. The Hamiltonian consisted of 65 two parts: HR, the Hamiltonian for a rotating core of fixed shape with quadrupole moments of inertia, and Hp, the Hamiltonian for the single particle moving in an asymmetric oscillator potential .... ..... .... 2 with -e.. • s and -e.. terms. The energy eigenvalues were obtained by an exact diagonalization of this Hamiltonian using an appropriate core-particle basis. The model was applied throughout the 2s-ld shell, and for all nuclei for which there was sufficient experimental information, the three model parameters (P, a core strength parameter, and the usual f3 and y parameters) were determined. 31 For P, P = 0. 180, J3 = 0. 205, andy= 31. 0°,and the predicted energy levels are shown in Figure 54, column 3. This model also is in better agreement with experiment than the simple Nilsson model is, but it fails to predict a 1/2+ level other than the ground state below 5 MeV. The computed mean life of the 1. 27 MeV state 31 in P is 11. 1 ps which disagrees with the value of 0. 5 ps measured by Levesque et al. (1962). Glaudemans et al-. (1964) assumed an inert 28 Si core and performed a shell-model calculation for the nucleons outside of this core. Fifteen interaction energies and two binding energies of 28 2s and 1d nucleons to a Si core were determined by a 112 312 least-squares fit to 50 well established levels in the nuclei from 29 40 si to ca. From the best values of the 17 parameters thereby obtained, the energies and wave functions of 377 levels in this mass region were calculated. in Figure 54, column 4. The results for A = 31 are shown The agreement with experiment is fairly good except that the 5/2+ level at 2. 23 MeV is not reproduced. The authors concluded, therefore, that it probably arises from 28 excitation of the si core. Wiechers and Brussaard (1965), using the wave functions obtained with this model, calculated the level 66 widths for Ml transitions to the ground state of 31 P from the 1. 27 31 and 3. 13 MeV levels and to the ground state of s from the 1. 25 31 MeV level. For the 1. 27 MeV level in P the calculated width 3 P(M1) = 0. 0460 x 10- ev is too small compared to the experimental 3 width r(M1) = 2. 8 x 10- ev, (Booth and V/right, 1962). For the 31 2. 23 MeV level in P the calculated width r(M1) :::: 86. 0 x 10- 3 ev is in good agreement with the experimental width r(M1) : : : : 60. 0 x 3 31 s 10- ev, (Booth and Wright, 1962). For the 1. 25 MeV level in 3 the calculated width r(M1) = 0. 0589 x 10- ev has not been checked experimentally. 31 Thankappan (1962) proposed a model for P in which the odd 30 proton was coupled to a vibrating si core. Core vibration modes through three phonons were included. The first excited state of 30 si at 2. 24 MeV was interpreted as the first excited state of the core, which gives fz w = 2. 24 MeV. Two other parameters of the model, namely, the separation energy 6. of the single particle states 2s and 1d ; and the constant q indicating the strength of the 3 2 112 coupling of the odd particle to the collective oscillation of the core, were considered as free parameters and adjusted to obtain the best agreement of the calculated and the observed energy levels. The level spectrum, shown in Figure 54, column 5, is in fairly good agreement with experiment. A fourth parameter k was introduced in the calculations of the electromagnetic transition probabilities. For k = 10 MeV, Thankappan calculated that the second 3/2+ level in 31 P which was thought to be the 3. 13 MeV level, decays in the ratios 55; 18; 27 to the 0, 1. 27, and 2. 23 MeV levels, respectively. However, experimentally the 3. 13 MeV level decays by at least 99% to the ground state (van Rinsvelt and Endt, 1966). Subsequent to these calculations, it was shown, as mentioned above, that the 67 . 'IT + + 3. 13 MeV level has J == 1/2 , and therefore the second 3/2 level 31 in P should be identified with the 3. 51 MeV level. The experi- ment branching ratios from the 3. 51 MeV level to the 0, 1. 27, and 2.23levels are 64: .20: 16, respectively (Harris and Breitenbecher, 1966) in good agreement with the calculated ratios. The calculated mixing ratios for these transitions are also in good agreement with experiment. For k == 10 MeV, Thankappan calculated that the 5/2+ 31 P decays in the ratios 47: 53 to the 0 and 1. 27 level at 2. 23 in MeV levels, respectively. However, experimentally the 2. 23 MeV level decays by at least 97% to the ground state (Endt and van der Leun, 1962). For k == 10 MeV the mixing ratio for the decay of the 1. 27 MeV level is x == 7. 8 which disagrees with the experimental value of 0. 28 (van Rinsvelt and Smith, 1964). 31 Crawley (1965) proposed a model for P in which a 2s 112 32 hole was coupled to s core excitations. The dashed lines in Figure 54 indicate the proposed coupling scheme. This was based 32 31 P and on the inelastic scattering of 17.5 MeV protons from s. Strongly excited levels with similar angular distributions were assumed to correspond. This model incorporates the 7/2- level at 4. 43 MeV and predicts a 5/2- level at 5. 66 MeV. The model also predicts a 5/2+ and 9/2+ for levels at 4. 78 and 5. 34 MeV, respectively. Subsequently Cujec et al. (1965) found Jrr == 1/2+ for the 5. 25 MeV level which is probably the 5. 34 MeV level of Crawley. model. No electromagnetic properties were reported for this This model had been proposed earlier by Clegg and Foley (1961) but there was not enough experimental information available at that time for meaningful conclusions. Of the several models summarized here Thankappan' s model with the vibrating core seems to give the best fit to experiment. 68 The well established rotational structure near A== 25 (see Litherland et al., 1958) gives way to a vibrational structure near Many more measurements are needed to test this. In 30 30 particular, il si and its analog s have a vibrational structure, A== 30. there should be an approximately degenerate o+' 2+' 4+ triplet 30 near 4 MeV excitation. There are three levels in si at 3. 51, 3. 77, and 3. 79 MeV. For the 3. 51 MeV level Jrr == 2+, but for the 3. 77 and 3. 79 MeV levels, values for Jrr have not been deter30 s two levels have been located at 3. 43 and 3. 71 MeV mined. In excitation (McMurray et al. , 1967) but values for Jrr for these levels have not been determined. 69 A. Excitation Energies of Levels in 33 c1 1. Introduction This section describes the results from the deuteron 32 3 33 \Spectra from the reaction s( He, d) cl which were obtained as a by-product of the alpha particle spectra from the reaction 32 3 31 s( He, a) s described in Section II. B. In addition, some information obtained by extensions of the deuteron spectra to 33 higher excitation energies in c1 is presented. It was useful to analyze the deuteron spectra because, of the reactions listed by Endt and van der Leun (1962) ._ 1) 32S( p,y )33Cl 2) 32s(p, P')328 32 Q= 2.285 2.285 S(d·, n) 33 cl • 060 4) . 33 s(p, n) 33Cl -6.358 3) 5) 6) 7) 3 33 P( He, n) Cl 3.430 33 32 3 s( He, d) cl -3.208 31 32 33 Cl 33 33 3 8) s( He, t) Cl 9) 10) 35 36 s(a, t) cl(p, t) 33 Ar(p, a) Cl 33 Cl -17.528 -5. 593 -15.663 -4.355 70 reaction 6) is the most suitable for locating low-lying levels in 33 c1. In previous studies of reaction 1) (see Endt and van der Leun, 1962) not all of the low-lying levels predicted from the 33 mirror nucleus S were populated. Reaction 2) does not populate low-lying levels. Reactions 3), 4), and 5) emit neutrons. Reactions 7) and 9) have large negative Q-values and reaction 8) is not suitable because it is difficult to distinguish between low- · 3 energy tritons and He+ particles in the spectrometer. Reaction 10) is also suitable, and a study of the reaction is described in Section VI. The description is divided as follows: Section 2 32 3 33 describes the deuteron spectra from the reaction s( He, d) cl obtained as a by-product of th.e alpha particle spectra from the 31 32 3 reaction s( He, a.) s. Sections 2 and 3 describe, respectively, single detector spectra and four detector array spectra corre33 sponding to higher excitations in c1. The single detector, and later a four detector array, was used when it was discovered that the sixteen detector was temporarily unusable for deuterons of energy< 5 MeV. 2. Sixteen Detector Array Spectra (i) Experimental details Since the deuteron spectra from the reaction 32 s( 3 He, d) 33 cl were taken simultaneously with the alpha spectra 31 32 from the reaction s( 3 He, cx) s described in Sectio'n II. B., the experimental details were identical. With a bias of 20 volts on the detectors the pulses from the protons were smaller than those 71 from the deuterons. The same program described in Appendix C was used to reduce the data to spectra. (ii) Discussion of spectra The deuteron spectra are shown in Figure 55. As before, the peaks were first identified by a non-relativistic kinematics program which calculated the mass of the target nucleus and the Q-value of the reaction from the frequencies at two or more angles after correcting for the target thickness. Masses were typically determined to ±1 AI'v1U. Then a relat i- vistically correct program was used to chec.k the identification. Since some levels were seen at only two angles, the spectra were 12 carefully checked for levels from the expected contaminants c, 13c , 16 0 , 28 8 1, . 33s , and 34s . P eak s f rom t 'ne reaction . 12c (3He, 13 16 3 17 d) N and o( He, d) F are labeled in Figure 55. The identifi35 34 3 cations of the peaks from the reaction s( He, d) cl were facilitated by some spectra of this reaction taken by Dr. J. Dubois 13 34 under similar conditions with s targets. No levels from c, 28 . 33 S1, or S were observed. As a further check on these identifications the yields from natural and enriched targets were compared. · Levels (2) and (7) are only weakly populated in this reaction. Level (2), most readily seen in Figure 50(e), was tentatively located in these spectra by calculating its position 33 36 from its excitation energy measured in the reaction Ar(p, cx.) cl (see Section VI) and by comparing the natural and enriched target spectra at 45°. The identification was made more difficult by the . fact that one or more peaks from the reaction not resolved from level (2). 34 3 S( He, d) 35 Cl were 72 The known doublet (Endt and van der Leun, 1962) at 2. 848 - 2. 856 MeV excitation energy was not resolved and no attempt has been made to determine the relative intensities of these levels. The contributions to the resolution of a typical peak in the spectra shown in Figure 55 are listed in Table XIV, and the observed resolution was 10 keV (FWHM). (iii) Calculations of excitation energies The excitation energies and Q-values for l evels in 33 c1 were calculated with the program described in Appendix A after suitable modification to account for the fact that deuterons and not alpha particles were being emitted. Table XV lists the results for the excitation energies for the spectra shown in Figure 55. As before, to obtain final excitation energies, an average of the excitation energies calculated from selected peaks was taken 33 and the results are shown. Q-values for the ground state of Cl . are given in Table XVI. . 34 3 35 Q-values for the reaction S( He, d) Cl were also calculated with this program and then combined with QGS = . 8764 ± . 0030 (Maples~ al., 1966) to find the excitation energies which are listed in Table XVII. (iv) Results Table XV compares the present results for with those reported previously. 33 Cl The present experiment obtained accurate excitation energies for levels (2) and (3) and located levels (4) and (7). For the ground state, the present experiment found 73 QGS = - 3. 217 ± 5 . Using this value and the 1964 Mass Table (Ma.ttauch et al., 1965) for the mass excesses -26012.7 D ± 0. 9 keV 14931. 34 ± • 21 13135. 91 ± • 13 yields -21000. ± 5 This is to be compared with the mass excess quoted for 33 c1 in the 1964 Mass Table; -2101 .4 ± 12 . Table XVII compares the present results for 35 c1 with those reported previously. The Q-value for the ground state 35 of c1 is known to± 3 keV (Ivlaples et al., 1966) and the excitation 35 energies of the levels in c1 at 4. 058 and 4. 174 MeV are kilown to± 5 keV (Endt and van der Leun, 1962). The good agreement of the excitation energies found in the present experiment for these levels with the excitation energies given by Endt and van der Leun (1962) is a check on the ground state Q-value for the reaction 32 3 33 s( He, d) cl and a further check on the ground state Q-value 74 for the reaction 32 s( 3 He, a) 31 s, because all of these groups occur at approximately the same frequency (see Figures 11 and 55). 3. Single Detector Spectra (i) Experimental details 2 The target consisted of 579 ± 174 ~g/cm of Sb s 2 3 2 on 1255 ± 377 ~ gm/cm of gold. The beam of 0. 2 ~A of 12. 0 MeV 3 He ++ was incident on the Sb S side. The normal to the target 2 3 always bisected the angle between the beam direction and the spectrometer. Previous experience with this kind of target s howed that with this beam current, the target depletion was slow (;S 5% in six hours). This target was used rather than a CdS target because it was the thickest available at the time of these measurements. A high yield was needed to comp.::msate for the low efficiency of the single detector. The pulses from the silicon surface barrier detector were fed to a Tennelec (Model lOOA) preamplifier and ·then into the internal amplifier of a RIDL 400 -channel analyzer. The spectra were read out on punch tape and then read back into another RIDL 400-channel analyzer, which was equipped with a device for integrating peaks. One run could be analyzed while the next run was in progress. Background subtractions, dead time corrections, and plotting were done manually during the experiment. The same calibrations used for the measurement of 32 3 the ground state Q-value of the reaction s( He, a) 31 s (Section IL A. 5) was used for the beam analyzing magnet (k = . 0199062 ± 2 a . 0000033 MeV /(Me/sec) ) and for the spectrometer (ksa = • 0113934 2 ± • 0000013 MeV /(Mc/sec) ). 75 The slit settings are given in Table I, column h. (ii) Discussion of spectra Figure 56 shows the deuteron spectra at 20° and 45°. The gaps in the spectl'a corre spond to regions of severe elastic scattering fro m the gold foil. The observed resolution of 83 keV (FW) is due mainly to the target thiclmess and the collector slit width. The alpha particle s pe ctra and proton spectra obtained simultaneously were of little interest because of the poor resolutions and the high level densities. The peaks were again first tentatively identified from the shifts with angle. Level s (5) and (6) were expected from the sixteen counter array spectra (see Section V. A. 2) and from previous work (see Endt and van der Leun, 1962). The le vel fro m 13 N(2. 367) was uniqu ely identified from its kinematic shift. The 35 identification of the Cl(7. 56) was confirmed by a deuteron 0 4 3 °5 spectrum from the reaction v -s( He, dr' Cl taken under similar conditions by Dr. J. Dubois which showed that this level is strongly 33 populated. Level (9) was attributed to c1 on the basis of its kinematic shift and intensity. The spectra of J. Dubois do not show the region containing this level. (iii) Calculation of excitation energies The Q-values at 20° and 45° for levels (5) + (6) and (9) were calculated with a modified version of the program given in App,::mdix A. For each group Q-values at the two angles were averaged and then combined with QGS = -3 . 217 ± 5 (see Section V. A. 2) to find the excitation energies. Table XV. The results are given in 76 The Q-value to the level in 35 c1 was also calcu- lated with a suitably modified version of the program given in Appendix A. Again the Q-values at the two angles were averaged and then combined with QGS = • 8764 ± • 0030 (Maples et al., 1966) to find the excitation energy. These results are also given in Table XVII. (iv) Results Table XV compares the se results for previously reported results. 33 c1 to the The agreement for the level at 4. 12 MeV excitation energy is quite good. The level at 3. 986 ± 12 32 33 which has been seen in the reaction s(p, y) cl (Lonsjo, 1962; and Prosser and Gordon, 1967) was not seen here. 35 The level in c1 at 7. 559 MeV excitation energy 34 35 is probably the level reported at 7. 559 from the reaction s(p, y) c1 (see Table XVII). 4. Four Detector Spectra (i) Experimental details 2 The target consisted of 97 ± 29 !J.g/cm of CdS 32 containing sulfur enriched to 98.1% s on 287 ± 86 f..l.g/cm 2 of go~d. ..., .J..' The beam of 0. 2 !J.A of 12. 0 MeV .:>He'' was iilcident on the CdS side. The tar get was oriented so that the angle between the incident particles and the target normal was equal to the angle between the emerging particles and the target normal. 77 Four adjacent detector (9 through 12) in the 16 detector were used. The others were masked off. The pulses from each counter were fed into a Tennelec (Model 100A) pre amplifier, then to a RIDL single delay line amplifier (Model RIDL 30-23), and then into the routing system of a RIDL 400- channel analyzer. There was little dead time (typically.:::; 5%) with this system. The peaks were integrated with the L11tegrating device on the analyzer, and then read out on punch paper tape for a permanent record. Background subtractions, dead time corrections, and plotting was done manually. the reaction 36 The same calibrations used for the spectra from 33 Ar(p, a) cl (see Section VL C.) were used for the beam analyzing magnet (k 2 = . 0199062 ± • 0000033 MeV/(Mc/sec) ) a 2 and for the spectrometer (k =. 0113844 ± .0000013 MeV/(Mc/sec) ). s The slit settings are given in Table I, column i. (ii) Discussion of spectra Only the regions about the peaks found in the single detector spectra were re-investigated with the four detector array. This re-investigation was made because narrower detector slits 6r were feasible with the four detector array than with the c,sp single detector and therefore better resolution could be obtained. The peaks were again identified from the shifts with angle, and t he results confirm the single detector results. (iii) Calculation of excitation energies The Q-values and excitation energies for the levels 35 33 in c1 and c1 observed in these spectra were calculated in the 78 same way as were those for the single detector spectra and the r esults are given in Tables' XV and XVII. (iv) Results The results are compared with other measurements in Tables XV and XVII. B. Angular Distributions of 33 c1 States 1. Introduction This section describes the results from the deuteron 32 3 angular distributions from the reaction s( He, d) 33 cr which were obtained as a by- product of the alpha particle distributions from 32 3 31 the reaction s( He, a.) s described in Section II. C. Only the distributions from the levels at 0, 2. 35, and 2. 69 MeV excitation 33 in c1 were obtained as by- products. The distributions from the 2. 35- and 2. 69- MeV levels were interesting because the spins and parities for these levels were not known. It was hoped that comparisons with theoretical predictions would determine t - values p for these levels. Measurements of the distributions from the levels at 0. 81, 2. 85, 2. 86 and 4. 12 MeV excitation were not made because the spins and parities of these levels were known. Measurements of the distributions from the levels at 1. 98 and 2. 98 MeV were not made because these levels were so weakly populated that measurements of their distributions would have required an excessive amount 32 33 of machine time. An extensive study of the reaction s(p, y) cl in progress at the University of Kansas with higher proton energies 79 than used previously s hould yield the spins, parities, miXmg 33 ratios, and branching ratios for the low-lying levels in c1. 2. Experimental Details Because these deuteron angular distributions were measured simultaneously with the alpha particle angular distributions, the experimental conditions were identical to those described in Section II. C. 2. Exactly the same procedure described in Section II. C. 3 was used to analyze these distributions. 3. DWBA Predictions For these calculations it was assumed that the reaction mechanism was simple stripping. The zero-range approximation was used and spin-orbit coupling was neglected. The three sets of optical model parameters for the 3 He particles described in Section II. C. 4 and listed in Table XVIil were also tried for this reaction. Again the predicted distribution for each set were very similar and the Set I parameters of Table XVIII were selected. The optical model parameters used for the deuterons were those found by Perey and Perey (1963) at Oak Ridge for the elastic scattering of deuterons from aluminum at 11. 8 MeV and are given as Set IV in Table XVID. given by The shap2 of the potential is 80 U(r) - v - - - + i W' d dx' ex+ 1 X = r-R a R = r (M) 1/ 3 0 x' = 1 ( x' ) e + 1 r- R' a' 1 R' = r '(M) / 3 . 0 The distributions were again calculated with the code TSALL Y. The same procedure described in Section IT. C. 4 was used to plot the results. Attempts to improve the fits by varying the parameters met with little success. 4. Discussion Figure 57 shows four points on the angular distribution for 33 Cl(G. S.) whiCh must have ,e_P = 2 because for this state fT = 3/2+. The theoretical prediction for ,e_P = 2 is consistent with the data. 33 Figure 58 shows the angular distribution for cl(2. 35). . 0 0 17 The pomts at 8CM = 6 and 11 were obscured by F(. 500). 33 Since c1(2. 35) is unbound by approximately 60 keV and since the TSALL Y code is not suitable for unbound levels, it was assumed that the level was bound by 100 keV. Varying this binding energy by less than 1 MeV had little effect, a result in agreement with Goosman's observation (1967) for a similar case 33 37 3 36 in the reaction Ar( He, d) K. Level Cl(2. 35) is assigned ,e_P = (2) which implies Jrr = (3/2+) or (5/2+). 81 <:{0 Fig·ure 59 shows the angular distribution for vVCl (2. 68) . This level was also assumed bound by 100 keV. The theoretical distributions for t p ~ 2 fail to dip as much as the experimental distribution near eCM = 0°. = 3 p agrees best with the experimental distributions, but no assignment 1 The t heoretical distribution for t is made. 5. Results Table XIX sun1.marizes the results of this and previous work. The values listed. in columns b and c are for the reaction 32 33 s(d, n) cl. Column d gives the known values of JTT or the values of JTT implied by these t -values. p 82 VI. 1. 36 Ar(p, a) 33 cl Introduction Since an initial analysis of the dat a from the reaction 33 33 s( He, d) cl failed to locate the second excited state in c1 33 predicted from the mirror nucleus s the second most suitable 36 33 reaction Ar(p, a) Cl (Q = - 4. 355) was studied with the magnetic 32 3 spectrometer to find this level as described in this section. 2. Target A diagram of the gas cell used in this experiment is shown in Figure 60. This cell was d ;;signed by Dr. D. R. Goosman. The beam was first collimated by the slits (1. 016 mm (F\V)) in both the horizontal and vertical directions immediately in front of the target chamber. Following this, the beam was collimated by a hole 4. 8 mm in diameter in a sheet of tantalum of 0. 38 mm thickness at a d~stance of 3. 8 mm in front of foil A. This second collimator, which was attached to the gas cell but electricall y insulated from it, was aligned by moving the gas cell to find a minimum in the beam striking the collimator. An optical al ignment procedure using the target chamber protractors gave the same result to better than 30 '. The firs t exit aperture was 1. 59 mm (FW) in the 8 direction by 3. 81 mm (FVI) in the 8 direction. At the center of the target it subtended 3. 73° (FW) in the 8 direction and 8. 95° (FVV) in the ¢ direction. The second exit aperture was 1. 59 mm (FW) (= 2. 43°) in the e direction by 4. 57 mm (FW) (= 7. 01 °) in t he 83 ¢ direction. By placing the spectrometer at 0° it was also possible to align these apertures with the beam by measuring the beam striking them. Again this setting agreed with a setting made with the target chamber protractors. Because the reaction was observed only at 20°, 40°, and 60°, the beam entered through foil A and the ex. particles emerged through foil C as shown. Foil A was a 5000 J?.. nickel foil. Both were supplied by the Chromium Corporation of America.. They were glued to the staiP~ess steel walls with epoAry. The target gas obtained from Monsanto Research 36 Corporation by Dr. David Goosman contained 99. 94% Ar and 38 . 06% Ar. The cell was pumped for 24 hours before it was filled with argon to a pressure of 14. 0 em of mercury. 3. Supplementary Data The calibration constant for detector eight in the array with the 3. 18 mm detector slits was determined in the same way as the constant for the single detector was determined as described in Section II. A. 5. used. Again the electronics shown in Figu.re 6 were The result was k sex. = 0. 0113844 ± 0. 0000013 MeV/(Mc/sec) 2 , (f = 27700 ± 1 kc/sec). The yield factors were again measured with the procedure described by McNally (1966). The same s lit settings used for the 36 33 alpha spectra from the reaction Ar(p, cx.) Cl described in Section VI. 5 . were used for the slits immediately in front of the target chamber (vertical, 1. 02 mm (FW); horizontal, 1. 02 mm (FW)), the angul?.r acceptance slits of the spectrometer (8 = 2° (FW), ¢ = 6. 6° (FW)) ' and the detector slits (or c,sp = 3. 18 mm (FW)). The exit 84 apertures were not used in the measurements of the yield factors, and furthermore the elastic scattering was from a sheet of tantalum rather than from a column of gas. However, since only peak positions and not absolute yields were required from the spectra, these two differences were unimportant. Table II, column c, lists the yield factors. 4. 36 Ar(p, cx.) 33 cl Spectra Collection Details = 24643 kc/sec) a Neither the beam analyzing magnet A beam of 0. 2 ~A of 12. 011 ± • 014 MeV (f protons bombarded the target. nor the magnetic spectrometer were cycled because low accuracy was expected because of the energy losses in the gas cell. The slit settings not associated with the gas cell and detector foil thic.kness are given in Table I, column j. An electron suppressor upstream from the target was placed at- 300 v, and the gas cell and the Faraday cup were placed at +300v relative to the chamber walls. With 55 volts bias, most of the detectors completely s topped the alphas and the protons. In those cases where the protons were not stopped, the data were not analyzed. At 20° two steps of the magnetic field corresponding to a displacement of approximately 2. 90 mm of the spectrum relative to the detectors were made for each of the regions of the spectrum. adjacent regions were overlapped. As a check the ends of At 40° and 60° only one setting of the magnetic field was made in each region because of a lack of machine time. The data were read out on the Nuclear Data Optikon (Model ND 307), and reduced to spectra in exactly the same way as described in Section II. B. 5. 85 5. Discussion of Spectra Figure 61 shows the spectra. Only a small range excitation ( < 3 MeV) was scanned because of the unfavorable Q ~alue (Q :::: -4. 355). The peaks here from levels in 33 c1 at 0, . 810, and 2. 35 1 MeV excitation (see Section V. A) and from 13 N(G. S.) (Ajzenberg-Selove and Lauritsen, 1959) were identified from their positions predicted by a relativistic kinematics program after appropriate corrections for the various energy losse so Level number (2) was identified by its kinematic shift with angle. C he cks 12 were made for contributions from the reactions c (p, a) 9 B, 13 10 14 11 14 3 - 12 C (p, a) B, N(p, a) C, and N(p, He) C. 6. Calculation of Excitation Energy The spectra shown in Figure 61 were used to calculat e 33 the excitation of level (2) in c1. Table XX gives the various energy losses for a typical peak. Since only a nominal value of 0 10000 A for the thickness of the exit foil was available and since the alpha particles lost approximately 400 keV in this foil, it was necessary to determine the thickness more accurately. At each angle the stopping power curves of Demiolioglu and Whaling (1962), 32 s( 3 -w -) 33 c , · · 33 c 1-"1rom th e reacnon ·· m .ue, d · 1. the exc1·ta t·wn energies 33 (see Section V), and the mass excesses for c1 (see Section V), 36 Ar, protons, and alpha particles (Mattauch etal.,1965)wereusedto calculate the exit foil thiclmess for each peak except those from level (2). The average of the resulting exit fo il thiclme ss at each 0 angle (typically 11400 A) was used to calculate the excitation energy of level (2). The excitations at the three angles were then averaged too btain the final excitation energy of 1. 999±. 020 MeV for level (2) in ~3 v Cl. 86 VII. A. DISCUSSION OF 33 c1 STATES . . " 33s C ompar1son wun 33 Figure 62 s hows the isobaric level diagram for s and 33 c1. 33 The information summarized here for s was taken from the compilation of Endt and van der Leun (1962) as well as from more recent work by Becker et al.(1966), O'Dell et al.(1966), and Moss 33 (1967) (see Appendix G)-:- The information for c1 was taken from Endt and van der Leun (1962) and the present work. 33 The levels in c1 at 0, . 810, 1. 978,and 2. 351 MeV corre 33 s at 0, s pond quite well in excitation energies to the levels in . 841, 1. 965, and 2. 313 MeV, respectively. Furthermore , if it 32 32 3 33 33 is assumed that the reaction s s(d, p) s and s( He, d) c! are s imple stripping reactions, then the relative reduced widths to corresponding levels should be similar. Table XXI gives the 2 values of (2J + 1) en . quoted by Endt and van der Leun (1962) 33 for the reaction 32s(d, p) s, and the relative intensities at e L , = 45° of the deuteron groups corresponding to the levels in ao 33cl. For the first four levels these two quantities are qualitatively similar. In particular, the level at 2. 0 MeV excitation is weakly populated in both. It is highly probable that these levels are isobaric analogs. On the basis of the present information one can only speculate 33 s on the correspondences of the next four higher lying levels L11 33 a nd c 1. We s uggest the following correspondences : 87 2. 869 MeV, ,e, n == 2 2. 848 MeV, 2. 937 2.686 2.970 2.980 3.224 2. 856 5/2+ These correspondences are consistent with the values of (2J + 1) 2 8 and the intensities given in Table XXI. In particular, the n 33 33 level at 2. 970 MeV in s and the level at 2. 980 in c1 are weakly populated. As pointed out in Section V. B. 5, the theoretical angular distribution for ,e, == 3 agreed best with the exparimental distri33 p bution for Cl(2. 686). However, the agreement was not good enough to make an assignment. B. Comparison with Theory A refinement of the Nilsson Model for discussed by Bishop (1959). 33 s and 33 c1 has been He assumed that the 3/2+ ground state and the 5/2(+) level at 2. 0 MeV formed the first two members of a K = 3/2 band. Then the formula EJ, K = eK + ;; [J(J+l) - 2il + l\c,(l/2f(-)J+(l/2)(J+l/2)] 2 (see Preston, 1962) gives ~I= +396 keV and predicts a 7/2+ level at 4. 8 MeV. He further assumed that the 1/2+ level at 0. 8 and the· 3/2+ level at,...., 2. 3 MeV formed the first two members of a K = 1/2 88 band. ;,2 If it is assumed that ;I= 396 .k eV for this band also, theri the formula gives a = 0. 30 and predicts a 5/2+ level at 3. 74 (see Figure 63, column 1). Experimentally if one assumed the iso baric correspondence suggested in Section VII. A. , then the second 5/2+ 33 level is at 2. 848 MeV in c1. The location of the first 7/2+ level is not known. The results for 33 c1 of the shell model calculation by Glaudemans et al.(1964) which was described in Section IV. B. are shown in Figure 63, column 2. If the isobaric correspondence suggested in Section VIL A. is again assumed, then the predicted sequence 3/2+, 1/2+, 5/2+, and 3/2+ agrees with experiment. However, the excitation energies do not agree very well with experiment. The second 5/2+ level is predicted to lie at 3. 8 MeV which is well above the second experimentally observed 5/2+ at 33 2. 848 MeV in c1. This model predicts a 7/2+ level at 2. 9 MeV which suggests the possible identification of this level with the 33 experimentally observed level at 2. 980 MeV in c1. The fact that the wave function given by Glaudemans et al. (1964) for the ...1.. first 5/2' state does not look like the wave function for the ground 32 state of s plus a proton could explain the weak population of this 32 3 level in the stripping reaction s( He, d) 33 cr. A similar shell model calculation for odd- parity levels of nuclei in the region 33 ~ A~ 41 has been done by Erne (1966). 32 An inert s core was assumed and one nucleon was considered to be in the lf shell while the others were in the ld shell. 312 712 Values for the twelve two-particle interaction energies and the 32 binding energies to the s core of ld 312 and 1£712 nucleons were determined by a least- squares fit of the computed energies to the energie s of sixty states in the region 33 .:5 A~ 41 with known spin 89 and isospins. Then from these fourteen parameters, the energies and wave fW1ctions of 240 states in this region were calculated. For A= 33 only a 7/2 level at 2. 94 MeV is predicted. This is shown in Figure 63, column 3. Experimentally there is a 7/2 33 level in s at 2. 937 MeV. The suggested analog in 33 c1 occurs at 2. 686 MeV (see Section VII. A). The good agreement of the 33 predicted excitation with the observed excitation in s is not 33 surprising since this 7/2- level in s was one of the levels fitted. 33 The 3/2- level at 2. 856 in c1 is not predicted. 90 APPENDIX A: PROGRAM FOR CALCULATING THE Q- VALUES 31 AND EXCITATION ENERGIES OF LEVELS IN s The Q-value for the ground state is given by the relativistically correct formula where M , M , M = nuclear masses not including the electron 2 1 3 masses ElGS' E 3 GS = kinetic energies after corrections for the target thickness C AVO TTGT 2 Mp - (l + CCDSHE3) W CDS 2cos ein 2 1 8 CDS ( M ElGS) • 1 ,) 91 (The beam is assumed incident on the side with the CdS.) = position of the beam in the beam analyzing magnet slits, normally 0. = radius of the orbit in the beam analyzing magnet. = mass of the proton. = calibration constant of the beam analyzing magnet. F = beam analyzing magnet frequency. 108 CCDSHE 3 = fractional error in the stopping power for 3 He particles in CdS, normally 0. CAVO = Avogadro constant. WCDS = atomic weight of CdS • . TTGT = thickness of CdS in a direction normal to the target. e. ill = THIN = angle between the beam and the normal to the target. = stopping power of CdS for protons, a function of energy. C T M T.1" (1 ) A VD _BACK z 2 8 ( _E E" ) ~GS = .c.3GS + + C AUHE4 W AU cos eout 3 AU M3 3GS , ''-:' 92 C FACTOR = magnification of the spectrometer times 6E/E per unit length perpendicular to the mean orbit. YGSTGT = vertical position of the beam spot, normally 0. REK3GS = fractional error in the ratio K3 G8 /K30 , normally 0. K3GS - calibration "constant" for the spectrometer, a function of F GS and K30 . 3 = magnetic spectrometer frequency. = calibration "constant" for the spectrometer at a frequency corresponding to the energy of the alpha particles (8785. 0 ± 0. 8 keV (Wapstra,l964)) from a 212 Po source. C AUHE4 = fractional error in the stopping power for alpha particles in Au, normally 0. WAU = atomic weight of gold. TBACK = thickness of gold in a direction normal to the target. = THOUT = angle between the emerging particles and · the normal to the target. 8 AU = stopping power of gold for protons, a function of energy. = fractional error in the stopping power for alpha particles in gold, normally 0. 93 The Q-value for the N-th excited state is given by a similar set of equations and definitions with "GS" replaced by "N". The excitation energy for the N-th excited state is given by To calculate the error in a Q-value, errors are assigned to the arguments of Q which have a significant error. Let Q be a function of the arguments x. and suppose the error in x. is 6x .. 1 1 1 Then the error in Q due to this error in x. is 1 and the total error in Q due to all of the x. is 1 Table VIII gives the values of the arguments, their errors, and the errors introduced in Q for two typical cases. The error in the excitation energy is calculated in a similar way. Since the ground state and the N- th excited state are not observed simultaneously, there are separate arguments for the ground state and the N-th excited state in some cases. reason for the subscripts "GS" and "N" above. This is the Table VIII also gives the errors introduced in the excitation energy for the same two cases. The input for this program consists of the following cards: 94 Argument Error Card 1 Kl, ERR(1) Card 2 FIGS, EKK(2) 3 XGS90 3 4 TTGT 4 5 CDSHE3 6 CDSHE4 7 AUHE4 8 THIN 9 'TROUT 10 FIN 11 XN90 12 K30 13 EK3GS 14 EK3N 15 F3GS 16 YGSTGT 17 TBACK 18 YNTGT 19 TH3 20 F3N 20 blank card Card 20 may be repeated indefinitely to analyze other levels observed under identical conditions. 95 If the conditions are not identical, a blank card is placed after the last card in this first group which has F3N and ERR(20) and cards 1 through 20 are repeated. This procedure may also be repeated indefinitely. A listing of the program is given below. 96 1;!FIFTC Dt.T c c c DFCK Dt.TA FOR 532CHF3,HE4lS31t CDS BLOCK DATA COMMON/TEX/MltM2,M3,M4,ZltZZ,z3,z4,NPARTl•NPART3,NMATl,NMAT2 DOUFILE PRECIS!ON.Ml,MZ,M3,M4 DATA MltM2,M3tM4,Zl,ZZ,z3,Z4,NPARTltNPART3,NMATl,NMAT2/ 1 2808.343300t29773.1073D0,3727.3147D0•28848.650DOt2o•l6.•2••16.,5, 2 4.1.2/ ENf'l $!AFT(" MEX J')FCK ( c (" c c c MAIN °ROGRAI-A PROGRAM FOR THE ERRORS IN THE EXCITATION ENERGIES AND Q-VALUES OF LEVELS IN 531 D 1 MENS I ON X( 20 l , ERRX ( 20 l , SERR EX C20 l • ERRQGS ( 20) • E RRQN ( 2 0 l , A ( 20 l REAL K1tK30tK3GStK3N DOUFILE PRECISION Ml,MZ,M3.M4,QGS,QN EQUIVALENCE CKl,XClll COMMON/TEX/MltMZ,M3 , M4tZl , zZ,Z3 , z4 , NPARTltNPART3.NMATl , NMAT2 COMMON/ARG/Kl , FlGS,XGS90,TTGT , CDSHE3•CDSHE4tAUHE4,THIN,THOUT , FlN• 1 XN9(ltK30,FK3GS,EK3N,F3GS,YGSTGT,TBACK,YNTGToTH3tF3NoOGS•ON t EX 10 RF ADC5,201 CXCJJ,ERRXC llt!=l•l9l ;>n FORMAT(2Fl0.0) DATACA(IJ,!=l•19l/2HK1•4HF1GS , 5HXGS90,4HTTGT,6HCDSHE3 o6HCDSHE 4• 1 5HAllHE4,4HTHINt5HTHOUT,3HFlN,4HXN90t3HK30t5HEK3GSt4HEK3N,4HF3GSt 2 6HYGSTGT,5HTRACK,5HYNTGT,3HTH3/ WRITEC6,30l 30 FORMAT(lHll WRITEC6,40l CACiltXCil,ERRXC lltl=ltl9) 4(1 FORMATCA6,4Xt2Fl5.8l READC5t20lF3NtERRXC20l 45 IFCF3N.EO.Ool GO TO 10 INSERT PLANK CARD IF ANYTHING BUT F3N CHANGES CALL OFX EXO=EX OGSO=OGS QNO=<QN DO 60 !=<1,20 XCil=<XCil+ERRXC!l CALL OEX SERREX (I l =EX-EXO ERRQGSC!l=OGS-OGSO ERRONCil=QN-ONO X(Il=X(Il-ERRXCil 60 CONTI NUF SIIMEX=O • Sli MOGS=O. StJMON=O. DO 70 I=lt20 SU MEX"'SUMEX+ CSERREX (Ill* ( SERREX CIll SUMOGS=SUMOGS+CERROGSC!ll*CERROGSCill SlJ MON=SUMON+IERRQNCill*IERRONCill 70 CONTINUE TF X:oSORTCSlJMEXl TQGSsSQRTCSUMOGSl TON=SORTCSlJMQN) WR!TEC6,80l sn FORMAT(1Hl,66X,36HERRORS IN EX INTRODUCED BY ERRORS IN> 97 9() 1 2 3 4 5 WPITEC6o9()) F3N,ERRXC20l ,EXQ,(SERREXCI l ,!=lt20l ,TEX FORMAT(JH(),2Xo3HF3N,4 Xt6HERR F3 Nt5X ,2HEX,1 3Xt2HKl, 7 X,4HFlGSo6X, 5HXGS9n,5X,4HTTGT,5Xt6HCDSHE3,4X,6HCDSHE4,5Xt5HAUHEL••5X•4HTHIN, 6X,5HTHOlJT,6X,3HFlN/lX,F7.3,F9.4,Fl0.6,5X•lOFl0.6/lH0•34X. 4HXN90 0 7X,3HK30,6X,5HEK3GS,5X,4HEK3No6X,4HF3GS,5X,6HYGSTGTt5Xo 5HTRACKo5X,5HYNTGT,6X•3HTH3,7X,3HF3N/32XolOFl0.6/lHOo35Xo3HTEX/ 3;>X,Fl0.6//ll ~IRITEC6.11'l()l FOR~ATC1HI'l,66Xt37HERR ORS IN QGS INTRODUCED BY ERRORS INl 'IIRTTfC6,ll()l F3N,ERRXC2nJ ,QGSn• <ERRQGSCil•l=l t20ltTQGS FOR~ATC!H0,2Xt3HF3N,4Xo6HERRF3N,4Xo3HQGS,l3Xo2HKlo7X,4HFlGSo6Xt 4 5 12('\ 1'3() 1 2 3 4 5 ,:JBFTC 5HXGS90,5X,4HTTGTt5Xt6HCDSHE3,4X,6HCDSHE4,5Xo5HAUHE4,5X•4HTHINo 6Xo5HTHOUT,6X,3HFlN/lX,F7.3tF9.4,FlOo6o5X,lnFl0.6/lHOt34X, 4HXN9n,7X,3HK30,6X,5HEK3GS,5X,4HEK3N,6X,4HF3GS,5X o6HYGST GTo5X o 5HTRACK,5X,5HYNTGT,6X•3HTH3,7X,3HF3N/32X,l0Fl0.6/lH0,35X,4HTQGS/ 3?X,Fln.6//ll WRITEC6.J20l FORMATC1Hn,66X,36 HERRORS IN QN INTRODUCED BY ERRORS INl WR!TEC6.130l F3N,ERRXC2Q),QNO ,CERRQN Cil,I=lt20l •TQN FORMATC1Hn,2Xt3HF3N , 4Xt6HERRF3N,5X,2HQN,l3 X,2HK 1,7X ,4HF lGS t6Xt 5HXGS90,5Xt4HTTGT,5Xt6HCDSHE3,4X,6HCDSHE4t5X,5HAUHE4t5Xt4HTHINt 6 X, 5H THOIJT, 6 X • 3HF 1 N /1 X, F 7. 3, F9 • '•, F 10 • 6, 5X, lOF 10. 6/lHO, 34X, 4HXNOI'l,7Xt3HK3(),6X,5HEK3GS,5X,4HEK3Nt6X,4HF3GS,5X o6HYGSTGTt5Xo 5HTRACKt5X,5HYNTGT,6Xt3HTH3t7X,3HF3N/32X,lOF10.6/lH0,35X,3HTQN/ 3?Xtflf''.6//ll GO Tl"l 45 END OfX DECK SUBROUTINE QEX c C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C Kl=CAL!BRATION CONSTANT FOR 90 DEGREE ANALYZER IN MEV*CSEC/MCl**2 Fll,S=TNCIDENT REAM FREQUENCY FOR GROUND STATE PEAK TN MC/SEC XGS9()=REAM POSITION IN 9n DEGREE ANALYZER SLITS IN MI LS FOR GS. ENTRANCE AND EXIT SLITS ARE ASSUMED EQUAL. + OR - SLIT SETTING ARE TREATfD AS ERRORS. ERROR CALCULATED=l/2 MAX POSSIBLE ERROR. TTGT=TARGFT TH!CKNFSS TN MICROGRAMS/(CMl**2• BEAM IS ASSUMED INCIDFNT ON TARGET SIDE. CDSHE3=FRACTIONAL ERROR IN THE STOPPING POWER FOR HE3 IN THE TARGET MATERIAL• NORMALLY 0 CDSHE4=FR~CTIONAL ERROR IN THE STOPPING POWER FOR HE4 IN THE TARGET MATERIAL• NORMALLY 0 AUHE4=FRACTIONAL ERROR IN THE STOPPING POWER FOR HE4 IN THE BACKING FlN•FRF.~JENCY FOR NTH EXCITED STATE IN MC/SEC XN9n=RFAM POSITION IN 90 DEGREE ANALYZER SLITS IN MILS FOR NTH FXCITED STATF. K~()=(ALIBRATION CONSTANT FOR MAGNETIC SPECTROMETER IN MEV*CSEC/ MCl**~ AT THF ALPHA SOURCE ENERGY 8.785 MEV K3GS=CALTRRATTON CONSTANT FOR MAGNETIC sPECTROMETER IN MEV*CSEC/ M()**2 AT F3GS F3GS=MAGNETIC SPECTROMETER FREQUENCY FOR GROUND STATE PEA K IN MC /SEC YGSTGT~AEAM POSITION IN VERTICAL TGT SLITS IN MILS FOR GS. ERROR CALCULATED =1/2 MAXIMUM POSSIBLE ERROR. YNTGT=AEAM POSITION IN VERTICAL TGT SLITS IN MILS FOR NTH EXCITED STATE. ERROR CALCULATED = l/2 MAXIMUM POSSIBLE ERROR TRACK=RACKTNG THTCKNFSS IN MICROGRAMS/CCMl**2 F3N=MAGNETIC SPECTROMETER FREQUENCY FOR NTH EXCITED STATE PEAK IN MC/SFC TH3•SPFCTROMETER ANGLE TN DEGREES 98 C C C C C K1N=CALIRRATION CONSTANT FOR MAGNETIC SPECTROMETER IN MEV*CSEC/ MCl**2 AT F3N THIN=ANGLF BETWEEN NORMAL TO TARGET AND INCIDENT BEAM IN DEGREES THOUT=ANGLE BETWEEN NORMAL TO TARGET AND EMERGENT PARTICLES IN DEGREES C REAL KltK30tK3GS,K3N DOUBLE PRECISION Ml,M2,M3,M4 DOURLF PRECISION ElPGS,ElPNtDElGStDElN , DE2GS,DE2N , DE3GS•DE3 N, l ElGStE1NtF3PPGS,E3PGStF3PPN,E3PN , E3GS,E3N,E M4,ETGS,ETN oPlSOGS, 2 PlSON,COSTH,PlGS,P1NoP3GS,P3N,W,WWtXGS t XNtOGSoON t P3SOGStP 3 SO N COMMON/TFX/Ml,M2 , M3oM4tZl,Z2,Z3tZ4oNPARTltNPART3,NMATl,N MA T2 COMMON/ARG/Kl,FlGS,XGS90,TTGT,CDSHE3oCDsHE4,AUHE4,THIN , THOUT,FlN, 1 XM90,K30,EK3GS,EK3N,F3GS,YGSTGT,TBACK,yNTGT,TH3,F3NtOGS•ON,EX DATA RAD,R/57.2957795•34000o/ M1 S ARE NUCLEAR MASSES NOT INCLUDING ELECTRON MASSES ElPGS•DS0RTCMl*Ml+2o*938.256 * Zl*Zl * Kl*FlGS*flGSJ-Ml ElPN=DSORTIMl*Ml+2.*938.256*Zl*Zl*Kl*FlN*flNJ-Ml TKNSSl=TTGT/C2o*COSITHIN/RADlJ DElGS=Clo+CDSHE3l*ENL0SSCNPARTltElPGSoNMATltTKNSSltlt3) DElN=Cl.+CDSHE3l*ENLOSSCNPARTltElPNtNMATltTKNSSltl•3l ElGS=FlPGS*(1o+XGS90/Rl-DElGS E1N•ElPN*Ilo+XN90/Rl-DElN K1GS=Il.+FK3GSl*CK3(F3GS,K30l K3N=Cl.+EK3Nl*CK3CF3NtK30l c E3PPGS~Clo+FACTOR*YGSTGTl*CDSQRTCM3*M3+2o*938o256*Z3*Z3*K3GS* 1 F3GS*F3GS)-M3l E3PPN=Clo+FACTOR*YNTGTJ*IDS0RTIM3*M3+2o*938o256*Z3*Z3*K3N* 1 F3N*F3NJ-M3) TKNSS3=TBACK/COS(THOUT/RAD) DE3GS=(lo+AlJHE4l*ENLOSSINPART3,E3PPGS,NMAT2,TKNSS3,1,3J DE3N=Ilo+AUHE4l*ENLOSSCNPART3,E3PPN,NMAT2tTKNSS3,lt3l E3PGS=E3PPGS+DE3GS E3PN=E3PPN+DE3N TKNSS2=TTGT/I2o*COSITHOUT/RADJ J DE2GS=Clo+CDSHE4l*ENLOSSINPART3tE3PGS,NMATl,TKNSS2tl•3J DE2N=Ilo+CDSHE4l*ENLOSSCN~ART3,E3PN,NMATl•TKNSS2,1,3l FACTOQ=o84/C125.*360o*2.J E3GS=E3PGS+DE2GS E3N=E3PN+DF2N EM4=Ml+M2-M3 ETGS=Ml+M2+FlGS • ETN=Ml+M2+ElN PlS0GS=E1GS*CE1GS+2.0DO*Ml) P1SON=ElN*IElN+2.0DO*MlJ P~SOGS=~3GS*IF3GS+2o0D0*~3) P~SON=F3N*IE,N+2.0DO*M3) COSTH=DCOSITH3/RADl PlGS=DSORTCPlSOGSl PlN=DSORTIPlSONJ P3GS=DSORT(P3SOGSJ P3N=DSQRTCP3SQNJ W=ETGS-M3-E3GS WW=ETN-M3-E3N XGS=W*W-PlSOGS-P3SOGS+2.0DO*COSTH*PlGS*P3GS XN=WW*WW-PlSON-P3SQN+2oODO*COSTH*PlN*P3N 0GS=FM4-DSORT(XGS) ON•EM4-DSQRT.(XNJ EX=OGS-QN RFTURN END 99 $!AFTC LOS OF.CK FUNCTION ENLOSS(NPART,ENERGY,NMAT,TKNESs,NUTSTK,NUTSESl c C C C C C C C THIS PROGRAM CALCULATES THE ENERGY LOSS OF PARTICLES IN CDS OR AU NPART=PARTICLE OPTION NUMBER l=PROTON 2=0EUTERON 3=TRITON 4=HELIUM 4 5 o:HEL!lJM 3 C C C NMATo:MATERIAL OPTION NUMBER 1 =CDS 2=AU C TKNESS=THICKNESS C C C C ( C C NlJTSTKcTHICKNESS UNITS OPTION NUMBER 1=MICROGRAMS/CM**2 2=MILLIGRAMS/CM**2 3:(M 4=ANGSTROMS 5=MILS 6ziNCHES C C C C NUTSES=ENERGY LOSS UN ITS OPT ION NUMBER l=EV 2=KEV 3=MEV c c c c c 10 20 30 40 ~0 60 70 110 120 130 140 DIMENSION ATWT(2J,RH0<2J,UEV(3) DATA AV0/.602252E 24/ DATA !ATWT(Il•I=l•2l/72.24t196.967/ DATA !RHO(Il.T=1t2l/4o82.19.3/ DATA CUEVCTlti=1t3l/1ot.1E-02t.1E-05/ A=AVO/ATWT!NMATl GO TO (10t20,30,40t50t60l, NUTSTK B=0.1E-05*TKNESS GO TO 70 B=O.lE-02*TKNESS GO TO 70 B=RHO(NMATl*TKNESS GO TO 70 B=OolE-07*RHO(NMATl*TKNESS GO TO 70 R=0.254E-02*RHO(NMATl*TKNESS GO TO 70 R=2o54*RHO(NMATl*TKNESS GO TO (110t120tl30t140,150l• NPART EP=ENfRGY ZSQ=l• GO TO 160 EP=ENERGY/2o ZSQ=l• GO TO 160 EP=ENERGY/3o Z.<;O=l• GO TO 160 EP=ENERGY/4. ZS0=4o GO TO 160 100 150 EP=ENERGY/oo ZSQ=4• 160 GO TO ( 2 10o220lo NMAT 210 C=ZSO*ECDS<EPl GO Hl 230 220 C=ZSO*EAtl ( FP l 2'H) D:tJFVCNUT.SESl ENLOSS=A*R*C*D RFTlJRN END $JRFTC CFCDS DFCK . FUNCTION ECDS<EPl DIMENSION FC29ltDELC29l DATA F/22o1,19.8o17o8tl6o2ol4.9ol3.93ol3ol0ol2o38ollo74tl2.38 t 1 9o78t8o27t7o19t6o40o5•8lo5o34,4o93t4o58,4o29o4o04t3o83o3o65t3o48t 2 3o32t3ol7o3o04t2.93t2o83o2o72/ DATA DEL/-0.2,o.3,0.4,0.3,o.33,0.l4,0.11,o.oa,o.o7,2.82,l.o9,o.43, 1 Oo29,0.20,0.12t0.06,0.06o0.06,0o04o0•04,0.03,0.0loO.OloO.OltOo02o 2 o.o2,0.01,-o.ol.-O.o1t !F(EP.LToOo3l GO TO 44 !F(FP.GT.1.0l GO TO 27 f1026I=lo'l TRY= ~.1*FLOAT(I+2l JF(fP.LT.TRYl GO TO 32 26 CONTINUE 27 JFCEP.GE.5.0l GO TO 29 DO 30 !=10.18 TRY= Oo5*FLOAT<I-8l !F(EP.LT.TRYl GO TO 33 31'\ CONTINUE "12 ROT 0.1 XI'\= Ool*FLOAT<I+ll GO TO 28 29 DO 31 I=19o29 TRY= Oe5*FLOATCT-8l JF(EPeLT.TRYl GO TO 33 31 CONTINUE 33 ROT • 0.5 XO = Oo5*FLOAT<I-9l 28 P CEP-XOl/BOT E2 = -P*(P-l.)*(P-2.!/6. F2 = -<1.-Pl*P*CP+1el/6. FCDS"' Cl.-Pl*F<T-11 + P*F(Jl + E2*DEL<I-ll + F2*DEL<Il FCDS ECDS*l.OE-15 RETURN 44 ECDS = 22•1*1.0E-15 RETURN END $IB.F_TC CEAU DECK FUNCTION EAU(EPl DIMENSION FC29loDELC29l DATA F/36o3o32o4o29o5t27olo25olo23o5o22o1o20.9ol9o9o20o9•l7o0 1 ol4o7ol3o26t12o12o1lol6,lOo35,9o67,9o09o8o58,8ol3,7o73o7o37 t 2 7.04,6.75,6.50.6.28.6.07.5.88,5.71/ DATA DELI-1.3t1o0,0.5o0.4,0.4,Q.2,0o2t0.2oOo2o4o7ol.6oOo86,Q.30 , 1 Oo18o0ol5t0o13oO.l0oOo07ol'\o06o0o05oOo04oOo03oOo04tCo04o0o03oCoOl, 2 o.o2,0.02,0.02/ !F(EP.LT.0.3l GO TO 44 IF(EP.GT.1.0l GO TO 27 DO 26 I•lo9 TRY= Co1*FLOATCI+2l = = = 101 !FCFP.LToTRYl G0 TO 32 26 CONTINUE 27 !FCFP.GE.5.0l GO TO 29 DO 3 0 I =1 0 t 1 8 TRY= Oo5*FLOATCI-8l !FCFPoLT.TRYl GO TO 31 31) CONTINUF 32 ROT = 0.1 XO = 0.1*FLOATCT+ll GO TO 28 29 DO 31 !=19,29 TRY= 0.5 *FLOAT(l-8l TFCEP.LT.TRYl G0 TO 33 31 CONTINUE 33 FlOT "' 0.5 XO = O.S*FLOAT(l-9) 28 P z CEP-X O !/BOT F? = -<1.-Pl *P* CP+1ol/6o FAtl = <1.-Pl*FCI-ll + P*FCil EA U = EAU*1.0E-15 RE TURN 44 EAU a 36.3*1oOE-15 RETURN , FND $!BFTC CK3 DECK FUNCTION CK3CFtCK30l c C C + E2*DELCI-1l + F2*DEL<Il CK3 AS A FUNCTION OF FREQUENCY IN MC/SEC THE FUNCTION INTERPOLATES OR EXTRAPOLATES THE EXPERIMENTAL POINTS c DIMENSION XXC16l ,YY<l6l,XXPC3l•YYPC3l DATA XX/l4o0t16o0t18o0t20o0t22•0t24o0t26o0t28o0t30o0t32•0t34.0t 1 36o0t38o0t40o0t42o0t44 o0/ DATA VY/1.00025tlo00000to99975,.99950t•99936,.99945,.99969, 1 lo00 002tl o00 0 63tlo00130tlo00204tlo00291,lo00376,lo00478tlo00590t 1 1.00700/ DO 100 I=ltl4 I I• I IFCXXC!loGEoFl GO TO 200 CONTINUE KMIN=14 GO TO 300 2!ln KMIN=I!-1 IFCKMINoLF.Ol KMINsl 300 KM AX= KM!N +2 DO 400 J=KMINtKMAX N"'J-KMIN+l XXPCNl=XXCJl YYPCNl>=YY(J) 400 CO NTINUE N"2 CK3=CK30*AITKENIXXP,YYPtFtNl RFTURN END $IRLDR*MGHAIT lOI'l 102 APPENDIX B. PROGRAM FOR 8Effec t·Ive Let 8 = THETA = the spectrometer angle (track reading). 68 = DTHT = the half angle of the spectrometer aperature in the 8 direction. 6¢ = DPffi = the half angle of the spectrometer aperature in the ¢ direction. Figure 64 shows the notation. Then 8e ff ec t·Ive = TEFF 1 = 4 Tan 6 8 Tan 6¢ 'l = Tan 6¢ s = Tan 6 8 fYl = -Tan 6¢ 'sf. = -Tan 68 . 2 2 1/2 Tan-l(((sm 8 + scos ~) + Yl ) ) dsd • cos 8 - ssm 8 Yl The program listed below calculates this integral from THETA= TlVliN to THETA= TM.AX in steps of DTIIT. the present work NSTEPS = 51. In all of 103 $IRFTC TEF DECK c c c c COMPUTES THETA EFFECTIVE 6 101 DIMENSION Tlll0ll,T2110ll READ15,1011TMIN,DELT,TMAX,DTHT•DPHI•NSTEPS FOR~AT15F10oO,I5l NOTATION TMIN DEL T TMAX DTHT DPHI NSTEPS INTEGRATION (" c c c c c c c c THETA MIN STEP FOR THETA THETA MAX DELTA THETA DELTA PHI = NUMBER OF TABULATED VALUES FOR INTEGRAND WILL BE DONE BY SIMPSON$ RULE WRITEI6•2001DTHT,DPHI , NSTEPS FORMATI35HlTHETA EFFECTIVE FOR DELTA THETA F4o2 9 J 14Ht DELTA PHI = F4.2• I ?46H0THE NUM8ER OF POINTS TAKEN FOR INTEGRATION • I5, I 3 1H0 15X 5HTHETA 3X 9HTHETA EFF l TDTHT = TAN(DTHTI57o295779l TDPHI = TANIDPHII57o295779) DENOM = 4o * TDTHT*TDPHI DXI = 2o*TDTHTIFLOATINSTEPS-ll DETA = 2·*TDPHIIFLOATCNSTEPS-ll NN = (NSTEPS-1112 - 1 THETA = TMIN 5 TRAD = THFTAI57o295779 CT COSITRADl ST = SINCTRADl FTA ,. -TDPHI DO 1 I = ltNSTEPS XI -TDTHT DO 2 J = l,NSTEPS ARG = SORTCIST+XI*CTl*IST+XI*CT!+ETA* ETA)IICT-XI*STl TliJl = ATANIARGl IFIT11JloLToO•lT11J l = TliJl + 3.1415927 2 X I • X I + DX I SUM O. DO 3 J ltNN 3 SUM~ SUM + 4o * Tli2*Jl + 2o*Tli2 * J+ll T21Il = DXII3o*CSUM+T1111+4o*T11NSTEPS-ll+TliNSTEPSll 1 ETA • ETA + DETA SUM O. DO 4 J = 1•NN 4 SUM • SUM + 4o*T212 * Jl + 2o*T212*J+ll TEFFR =DE TAI3o*CSUM+T2C1l+4o*T21NSTEPS-1l+T2CNSTEPSll TEFF TEFFR * 57.295779 TEFF TEFFIDENOM WRITEC6.201)THETA,TEFF 201 FORMATC1H lOX FlO.O,Fl2o4l THETA • THETA+ DELT IFCTHETAoLEoTMAXlGO TO 5 GO TO 6 END = 200 = = = = = = = 104 APPENDIX C. ARRAY DATA REDUCTION PROGRAM For each run the frequencies for the detectors are calculated from the frequency for detector eight. The sixteen sums corresponding to the yields in the sixteen detectors are multiplied by the sixteen yield factors. The resulting corrected yields are then plotted against frequency. Other runs may be plotted on the same sheet(s) of graph paper. The input consists of the following cards: Card 1 DD Card 2 NPLOTS, YMiv( Card 3 (XMN(I), I = 1, NPLOTS) Card 4 (XMX(I), I= 1, NPLOTS) Card 5 RUN, F8 Card 6 SUM Card 7 RUN, F8 Card 8 SUM Blank Card where DD = title of :S. 12 characters NPLOTS = number of sheets of graph paper YMAX =number of counts at the top edge of the graph paper 105 Xl\IIN = array of frequencies at the left edge of the NPLOTS sheets of graph paper. XMX = array of frequencies at the right edge of the NPLOTS sheets of graph paper. RUN F8 = arbitrary run number SUM = array of 16 sums corresponding to the = frequency of detector 8 yields in the 16 detectors. Cards 5 and 6 contain the data for one run. Cards fo r other runs which are to be plotted on the same sheet(s) of graph paper are placed after card 6 as illustrated by cards 7 and 8. blank card must be placed after the last run for this plot. sequence of cards may be repeated indefinitely. A listing of the program is given below. A This 106 $TAFTC CMD c c c ARRAY DATA REDUCTION DIMENSION DDC12lt!NNC3l INTEGER RUNtABCD DAT/1 INN 11H( t 6H • 6HF10o0) I Dfi•IENS I ON CORR ( 16 l tFREQ ( 16 l ,x ( 1000 l • Y I 1000 l , Z I 1000 l • E I 1000 l DIMEN~ION TIT1C2l DATA TIT119HFREOUENCYI DATA TIT215HYIELDI DIMEN~!ON XMN(8).XMXI8),SUMI16l c NOT AT ION X IS AN ARRAY OF FREQUENCIES Y I~, AN ARRAY OF SUMS FROM THE 16 COUNTER ARRAY E IS AN ARRAY OF FREQUENCIES TO BE PLOTTED Z IS AN ARRAY OF SUMS TO BE PLOTTED ( c c c c c DFCK DATAIFREQCilti=ltl6ll.98149,.98416••98 b8 9,.9896lto99230, 1 o99494to99749•1otlo00257tlo00502tlo00749t1o00984tlo01222tlo0l453t 2 lo01692,1o019121 DATA<CORRCTl,I=1,16llo879,loOl8,.950to954to949,.995,1o033,1oOOO• 1 1o124tloOn5,1ol09,1.16n,1.171,lo232t1o254,1.2791 1? CONTINUE RFADC5,500lDD 500 FORMAT(12A6l READ(5,102lNPLOTS,YMAX 102 FORMAT(I2tFlOo0) TNN(2) = ABCDINPLOTSl READ15tiNNl(XMNC!lti=ltNPLOTSl READC5,INNl (XMXI!ltl 2 ltNPLOTSl WRITE <6 t210l ( XMN <I l tXMX I I l, I =1,NPLOTS l 210 FORMATI1H02~10o0l L =0 RFADC5t100lRUNtF8 100 FORMATII2tFlOo0l TFCFB.FO.OolGO TO 4 WRITEI6t201lRUN,F8 201 FORMAT(5HlRU N I2t 7Ht F8 = F10o0 I 1 lHO 16X 4HFREQ 7X 8HC0RR SUM 12X 3HSUM L " L + 16 READC5t103lSUM 103 FORMATI16F5o0l DO 1 J = ltl6 F F8*FREQCJl S a SUMCJl*CORRIJl N " <L-16l + J X IN l " F YIN l = S WRITE(6,200)JtXCNltYCNl•SUMCJl 200 FORMATClH llOtFl0.3,F15.3,Fl5o3l 1 CONTINUE GO TO 3 4 CONTINUE WRITEC6t204l 204 FORMAT(lHll DO 10 J = l,NPLOTS XMIN "' XMN(J) XMAX • X,.,.X(J) 3 K s 0 107 1!0 11 I = 1tN !FIXIIl.LT.XMIN.OR.X(Jl.GT.XMAXlGO TO 11 K = K + 1 fiKl =XIII ZIKl Y(ll 11 CONTINUE WRITF.I6t203lJtXMINtXMAX.YMAXtK 203 FORMAT16HOPLOT !lt 9Ht XMIN = F6.0t 9H, XMAX • F6.Q, 1 9Ht YMAX = F6o0t 2H, 13, 7H POINTS l CALL LAAELCO.OtO.O,O.OtYMAXtlOo0t10tTIT2,5t1l CALL LARELCO.o,n.n,xMINtXMAXt15.0,15tT!Tl•9tOl CALL XYPLTIKtEtltXM!N,XMAXtOotYMAXtDDt1t3l 10 CONTJNUF. GO T0 1?. END $JALDR*MLLLAL $!8LDR*MLLXYP = 108 APPENDIX D. PROGRAM FOR THE ANALYSIS OF PARTICLEGAMMA CORRELATIONS The analysis is carried out in the manner described in Sections III. B and ill. C. 4. Only one gamma ray is considered, but only a simple modification is necessary to analyze any member of a gamma-ray cascade (see Appendix E and Poletti and Warburt on, 1965). The program can handle one or two non-negative magnetic substates, that is Md = 0; 1/2; 0, 1; or 1/2, 3/2. Admixtures of the first magnetic substate which is not allowed may be added to observe a possible effect from the finite size of the particle detector. These admixtures are specified as a fraction of the population of the last allowed magnetic substate. Then Formula (9) of Section III. B. becomes W(e) = \ M ,L>M>O dMAX- d- +(ADM) x I(MdMAX)[ I(Md)['\ pk(Jd' Md)Fk(JdJ )QkPk(cos 8) ] L . e . . k even L pk(Jd' MdMAX + l)Fk(JdJe)QkPk(cos e)] k where MdMAX is the maximum allowed magnetic substate and ADM is the admixture of the magnetic substate MdMlvC + 1. The input consists of the following: Q(5) Card 1 Card 2 K, A(K) Card 3 L, B(L) Card 4 H, p 109 Card 5 THT(H) Card 6 Y(H) Card 7 ERR(H) Card 8 MAXADM, ADM(MAXADM) where Q(5) = attenuation coefficients Q , Q , Q , Q , Q 0 2 4 6 8 K = number of values of the spin of the initial state (K ~ 6) A(K) = spins of the initial state L = number of values of the spin of the final state (L ~ 6) B(L) = spins of the final state H = P = number of non-negative magnetic substates number of angles allowed THT(H) = angles Y(H) = ERR(H) = uncertainties in the yields MAXADM yields = number of values for the admixture ADM. (MAXADM~ 3) ADM(MADADM) = admixtures A listing of the program is given below. 110 $TAFT( PGC f)F(K ( c c c c c c c c c c PARTICLE-GAMMA CORRELATION ANALYSIS DIMENSION AC6 l t B C6) , PH I C37 l t QSQR C3 7 • 3 l • PPR C3 7 • 3 • 2 l , PH I MIN C6 t 3) , 1 EPMINC6•3l,EPMAXC6.3ltXMINC6.3l•ERRXC6,3) tCHISOC6.3l• 2 PPMINRC6•?•2ltDXRC6t3l,PHISTPC6•3•11l,QSQSTPC6t3tlll•XTRIALC6l • 3 NMINC3l • DUMMYC2l COMMON/LSQ/P,HtiTHT,KMAX.THTCl6l tKADMtALPHAtAP,ADMC3lti3,QC5l ,sp, SIGMA•X,ATANX.KARG,KCALC.ERRC16ltYC16),PPC2 ),QSQ,NDEG INTEGER PtHtSIGMA 5 READC5t10l0 10 FORMATC5Fl0o3l READC5t20l KtCACiloi•ltKl READC5t20) L.CRCil.I=ltLl 20 FORMATCI2t3X,6F5.2) READC5t30)HtP Ho:NUI-IBER OF ANGLES, HoLEo8 P=NU~BER OF MAGNETIC SUBSTATESt P.LEo2 30 FORMATC2I2l READC5t40l CTHTCilti.,ltHl 40 FORMATC8Fl0o3l READC5t40l CYCilti=1tHl READC5t40l CERPCil.I=1tHl RFADC5,50l MAXADMtCADMC Il•I=1tMAXADMl MAXADM.LE.3 50 FORMATII2t3Xt6F5.2l SIGMA=O IN THE REMAINDER OF THIS PROGRAM, SIGMA HAS BEEN ASSUMED TO BE ARBITRARY • NDEGzrH-P-1 THIS SECTION PRINTS OUT INPUT 100 110 120 130 140 c 1 !Hl WRITEC6t100lHtPtNDEG FORMATC5HlH = I2t4Xt4HP = I2t4Xt7HNDEG = I2l WRITEC6tll0l FORMAT(//1H0,9Xt26HQO 02 04 06 081 WRITEC6t120l0 FORMATI8Xt5F6.3) WRITEC6t130l ITHTCiloi=ltHl FORMATI//9HOANGLES 8Fl3.2/9Xt8F13.2/9X,SF13.2l WRITEC6t140l CYCilti"'ltHl FORMATC//9HOYIELDS 8Fl3o6/9Xt8F13.6/9Xt8Fl3.6l WRITEI6t150l IERRC I) ti=ltHl FORMATC//9HOERRORS 8F13.6/9Xt8F13.6/9X,8F13o6l THIS SECTION BEGINS THE CALCULATIONS ( c 210 205 PHIIll•-90. DO 210 I=2t37 PHTIIlzPHICI-ll+5. ITHT=O DO 760 Il,.ltK AP=ACill DO 760 I2=1 tl TWOA=2e*AP I AP,.TWOA /2 • . FLJAP=IAP IFCFLIAP*2.-TW0Al205t206t205 KMAX•TWOA-1o I \ 111 206 207 2~0 240 250 255 256 257 c c c 261') p,.l GO TO 257 Pm2 DO 260 I4=1o37 ATANX=PHI CI4) CALL O<;PP QSQRCI4oT3l=OSO PPR(I4oi3oll=PPCll PPRCI4oi3t2lsPP(2l FINDS MINIMA OF OSQ-S AS A FUNCTION OF X 265 270 ?80 290 c ALPHA=o5 GO TO 207 KMAX=TWOA ALPHA= eO KCALC=O RP=BCI2l DO 520 I3=loMAXADM KARG"'2 KADM"'O GO TO C230o250loP DO 240 I4=1o37 ATANX=PHICI4l CALL Q.<;PP O.<;QR CI 4, I 3 l "OSO PPR(I4ol3ol):PP(l) GO TO 265 IFCAP-l.Ol255o256o256 300 c IFCAP-lol520t270t270 IXMIIII=l KSTARTsl IF(QSORCloi3loGT.l5.l GO TO 340 IFCOSORCloi3!-0SORC2ti3ll280o340t340 ATANX=-89.9 CALL QSPP IFCOSO-OSORClti3ll290t300o300 XTRIAL(IXMIN!•ATANC-89.9/57.295779) IXMIN=2 GO TO 340 PHIMIN(l,I3l=-90o FIRST INDEX=MINIMUM INDEX SECOND INDEX=ADM INDEX EPMINCloi3l=Oo EPMAXCloi3l=Oo XMINCloi~l=O. ERRX(lol3l=O. CHISOCloi~l=OSORClti3l 310 C C C C C C DO 310 I7=loP PPMINRClti3oi7l=PPRCloi3oi7l FIRST INDEX OF PPMINR=MINIMUM INDEX SECOND INDEX OF PPMINR•ADM INDEX THIRD INDEX=POPULATION PARAMETER INDEX DXRC1ol3l=O• DO 330 !"'loll Ril:I-1 PHISTPCloi3oil=-89o9+.5*Ril FIRST INDFX•MINIMUM INDEX SECOND INDFX=ADM INDF.X THIRD INDFX,.STEP INDFX ATANX=PHISTPCloi3til 112 330 340 350 360 370 380 '390 400 420 430 440 C C CALL OC.PP OC.OSTP!ltl3tll=OSO IXMIN=2 KSThRT•2 DO 360 I5=2t36 I F ! 0 c, 0 R ( I 5 , I 3 l • GT • 1 5 • l GO T0 3 6 0 IF! OSOR! I 5, I 3 l • LT. OSQR ( I 5-l , I 3 l. AND.QSQR ( 15 t I 3 l • L T .OSQR! I 5+1t I3ll GO TO 350 GO TO 360 XTRIAL!IXMINl=TAN!PHIII5l/57.295779l IXMIN=IXMIN+l CONTINUE IF!OSOR!37.I3loGT.l5ol GO TO 430 IF!OSOR!37ti3l-QSOR!36oi3ll 370t430o430 ATANX=89.9 CALL QSPP IF(QC,Q-QC,QR(37ol3l) 380o390o390 XTRIAL!lXM!Nl•ATAN!89e9/57.295779l IXMIN=IXMIN+l GO TO 4'30 PHIMIN!lXMINoi3l=90o EPMIN!IXMINoi3)20. EPMAX(lXMINoi3l=O• XMIN( IXMINoi3l"O• ERRX!IXMINoi'3l=O. CHISQ!IXMINoi3l.,QSQR(37ti3) DO 400 I7=1oP PPMINR!IXMINoi3oi7l=PPR!37oi3oi7l DXR!IXMIN,I3l•O. DO 420 !=loll Ril=I-1 PHISTP!IXM!Ntl3oll=84o9+.5*RI1 ATANX=PHISTP!IXMINoi3oll CALL QSPP QSQSTPCIXMINoi3oil=OSQ KSTOP=IXMIN-1 IXMIN=IXMIN+l GO TO 440 KSTOP=IXMIN-1 NMIN!I3l=IXMIN-1 IF!KSTART.GT.KSTOPl GO TO 520 WILL OCCUR WITH ONLY A MINIMUM AT -90 OR +90 OR NO MINIMUM DO 515 IB=KSTARTtKSTOP KARG=l X2•XTRTAL(I8l DX•O• DO 490 I=lolO X?=X2+DX 450 460 470 DP=AFIS(X2l 1100. IF!DP-.Oll450o450t460 D=.Ol GO TO 470 D•DP Xl=X2-D X3•X2+D X•Xl CALL OSPP OXl•OSQ X•X2 CALL OSPP 113 49n 500 <;11"1 c c c 515 '52 0 OX2:QSQ x,.x3 CALL OSPP OX3,.0SQ Af:c0Xl-OX3 BE,.OX1+0X3-2.*0X2 DX,.AE*D/C?.*REJ IFCABS(X2J.LToo001J GO TO 490 PFR(,.ARSC()X/X2l IFCPFRCoLT •• OOll GO TO 500 CONTINUE XMINCI8tlol=X2+DX ERRXCI8ti3JcSQRTC2.*D**2/CBE*FLOATCH-P-1Jll CHISOCI8ti3J=OX2-AE* * 2/C8.*BEJ PH I MIN ( I 8 , I 3 J =AT AN ( XM INC I 8, I 3 J J *57 • 2 95 779 E PM INC I 8, I 3 J =A TAN CXM IN ( I 8 t I 3 J -ERRX CI 8 • I 3 J l *57 • 2 9 5 779 EPMAXCI8t!3l=ATANCXMJNC I8ti3J+ERRXC I8oi3J 1*57.295779 DXR<I8,I3J=DX DO 510 !7=ltP PPMINRCI8,I'3.I7J=PPCI7l PSMIN=ATANCXMINCI8ti3lJ*57o295779-2.5 IFCPSMlNoLT.-89.9) PSMIN=-89.9 IFCPSMINoGTo84o9l PSMJNc84o9 KARG.,2 DO 515 I=1•11 Rll=I-1 PHISTPCI8tl3tilcPSMIN+RI1*•5 ATANX=PHISTPCI8ol3tll CALL OSPP 0SOSTPCI8,I3oiJsQSQ CONTINUE CONTINUE THIS SECTION WRITES THE OUTPUT WRITEC6o2?0l ACill.BCI2l FORMAT(5HlA = F4.1,3Xo4HB = F4.ll WRITEC6t600) CADMCIJol=ltMAXADMl 600 FORMATC12HOADMIXTURE =ol3XoFl0.3,30XtFlo.3o30XoF10.3J WRITEC6,610J 610 FORMATC4HOPHit16Xt3HQSQ,7Xo4HP!lJo6Xt4HPC2lt16Xt3HOSOo7Xt4HPCllt 1 6Xt4HPC2Jol6Xo3HQSQ,7Xo4HPC1J,6Xo4HPC2!//J GO TO C62no640loP 620 DO 630 1=1,37 WRITEC6t635J PHICI),(QSQRCioJJ,PPRCioJolloJ=ltMAXADMl · 6~0 GO TO 661 635 FORMATClH ,F4o0t10Xt2Fl0.3o20Xt2Fl0o3o20Xt2Fl0o3l 640 DO 650 I=lo37 650 WRITEC6o660JPHICIJ,(QSQRCI,JJoPPR<I•J•l!tPPRCitJt2JoJ=l•MAXADMJ 660 FORMATClH ,F4.0tlOXt3FlOo3olOXo3FlOo3tlOXt3F10.3J 661 DO 750 I3=loMAXADM IFCAP-lol665o669o669 665 WRITEC6o666l ADMCI3J 666 FORMATC16HOFOR ADMIXTURE "oF6.3J WRITFC6t668l 668 FORMATC1HO,l4Xo4HP<llt6Xo4HPC2ll WR IT E C6 t 6 6 7 l CPP R C1 , I 3 • I l , I •1 • P J 667 FORMAT(l1Xo2Fl0o3l GO TO 750 669 NMINP=NMINCI3J IFCNMINP-OJ 750,750,670 220 114 WR l T F ( 6, 6 71 l ADM C!3 l FORMAT(16HOFOR ADMIXTURE =,F6.3,18H MINIMA OCCUR ATl DO 745 !8=1•NM!NP WRTTEC6,680l FORMAT!1HI'l 9 10Xt4X.6HPHIMIN,5X,5HEPMINt5X,5HEPMAX,8X,4HXM!N,l6Xt 680 1 4HFRRX,l5X,5HCHISO,l7X,3HDXRl WRITEC6.690l PH!M!N( !8, l3l tEPMIN( I8,I3l ,EPMAXC I8,I3l ,XMINC I8,!3l • 1 ERRXC IA,I"ll•CHTSO! I8tl3l ,[)XR! T8t T3l FORMAT(]H ,]0Xt3F10.3t4E20o8l 69t'l WR!TFC6,700l 700 FORMAT ( lH () tl4X t 4HP! 1 l •6X, 4HP ( 2 l l DO 702 K=l,P OUMMYCKl=PPMINR!I8,!3•Kl 702 CONTINUE WRITEC6t710l CDUMMYCKltK=ltPl FORMATC11X,2Fl0.3l WRITEC6,720l FORMAT(lH0,7Xt6HPHISTPt4Xt6HQSQSTPl DO 730 I=ltll 7'\l'l WRITE!6t740l PHTSTP!T8ti3.Il,QSQSTPC!8,J3,Il 741'l FORMAT(7XtF7.3,3X,F8.3) 745 CONTINUE 750 CONTINUF 760 CONTINUE GO TO 5 END $lf\FTC QPP DECK 670 671 c c c c c C C C C C C C A SUBROUTINE FOR OSO AND PP THIS SUBROUTINE USES THE FOLLOWING PROGRAMS RKtFAK StJRROUT INF OSPP COMMON/LSQ/P,H,lTHT,KMAX,THTC16ltKADM,ALPHA,AP,ADMC3l•I3,QC5ltBP, 1 SIGMA,X,ATANXtKARG,KCALC,ERRC16l,Y(l6l,PPC2l,QSQ,NDEG DIMENSION PLRC5t16),RKQADRC5t2ltSUMKC16,2l tDC2l,C(2,2l REAL NUMC2l INTEGER PtHtSIGMA KMAXP=KMAX/2+1 IFCITHT-Ol 35t20,35 IF ITHT.EQ.O, CALCULATES A NEW LEGENDRE POLYNOMIAL ARRAY AND SETS ITHT•l IF ITHT.NE.O, USES STORED ARRAY 20 RNDEG=NDEG DO 30 Jl=ltH COSTHT•COSCTHTCJll/57.295779) DO 30 J2=1•5 J2P"2*C J2-ll 30 PLR(J2,Jll=PL!J2P,COSTHTl FIRST INDEX • K INDEX SECOND INDEX • ANGLE INDEX ITHT=l 35 GO TO C40t240ltP 40 IFCKAD M- Ol 70,50,70 IF KAD M.Eo.n, CALCULATES NEW RKOADR-S AND SETS KADM•l IF KADM.NE.Ot USES STORED RKQADR-S 5t'l ALPHAl•ALPHA+lo DO 60 Jl=ltKMAXP RJ1•2*CJ1-1l RKQADR(Jltll=CRHOKCRJltAPtALPHAl+ADMCI3l*RHOKCRJltAPtALPHAlll 1 *OCJll 115 c c c c CONTINUE FIRST INDFX = K INDEX SECOND INDEX = PP INDEX KADM=l 70 DO 80 Jl= l tH SlJM K( Jl t 1 l =0 • DO ~ 0 J2=ltKMAXP AK = 2*CJ?-ll SlJM KCJloll=SUMKCJlol l+RKOADRCJ2oll*FCAK,AP,BP,SIGMAtXtATANXt 1 KARG,KCALCl*PLRCJ2,Jll CONTINUE ~0 FIRST INDEX • ANGLE I NDEX SECOND INDEX • PP INDEX KCALC=l DCll=O. CCltll,.Q. DO 90 Jl=ltH ERRSO = ERR(Jll*ERRCJll DCll•DCll+YCJll*SUM K(Jl,ll/ERRSQ C Clt l l=CC 1 tll+SlJMKC Jl tll*SUMKC Jltll/ERRSQ 90 CONTINUE PPCll=DCll/CCltll IFCo0001-CC1t1ll 120,120•100 100 GO TO C10S,115l, KARG 105 WRITEC6t110lXtDClltCC1 t lltPPCll FOR X = tFl0.4t2H ttl3H NUMERATOR =tE12o4t 110 FORMATC20HOWARNING 1 1SH DENOMINATOR = tEl2o4t8H PPC1l • tF12.4) GO TO 120 115 WRITEC6,116l ATANXtD(l),CC1tlltPPCll FORMAT(28HOWARNING FOR ARCTAN X = ,F10.4,2H ,, 116 oFl2o4l 1 13H NUMERATOR • E12.4o15H DENOMINATOR • ,E12.4o8H PPCll 120 StJMOSO=O. DO 110 JlcloH TERM:CYCJll-PPCll*SUMKCJlolll/ERRCJ1l SUMOSO:SLJMQSQ+TERM*TERM OSQo:SUMOSQ/RNDEG GO TO 380 IFC KADM-Ol270o250o270 240 250 ALPHAl:ALPHA+lo 60 ALPH~2•ALPHA+2o c c DO 260 JlcloKMAXP RJ1:2 * CJ1-ll RKQADRCJloll=RHOKCRJloAP,ALPHAl*OCJll RKQADRCJlo2lo:CRHOKCRJ1oAPtALPHAll+ADMCI3l*RHOKCRJ1oAPoALPHA2ll* 1 Q(Jll CONTINUE '260 FIRST INDEX = K INDEX SECOND INDEX • PP INDEX KADM=l 270 DO 280 J1zloH DO 280 J2=1t2 SUMKCJloJ2l=O. DO 280 J3=1oKMAXP AK = 2*CJ3-1l SIJ MK CJ1tJ?l=SUMKCJ1,J2l+RKQADRCJ3oJ2l*FCAK,APtBP,SIGMAtXtATANXt KARG,KCALCl*PLRCJ3,Jll 280 CONTINUE FIRST INDF.X • ANGLE INDEX SFCOND INDEX • PP INDEX KCALC=l CCloll•O. , c c 116 Cl2tl )=0. Cllt2l"'O• CC2t2)z0. DO "1?0 .Jl=lt2 DO 320 .J2"1•2 DO 32rl .J3=ltH CI.Jl,.J?l=CI.J1t.J2l+SUMKI.J3tJll*SUMKI.J3t.J2J/CERRC.J3l*ERRCJ3ll "120 CONTINUE D(l)=O. Dl2l=O. DO 330 Jl=ltH ERRSO=ERR(Jll*ERRC.Jll Dlll"O(ll+SUMKIJltll*YC.Jll/ERRSQ DC2l=DC21+SUMKCJlt2l*YCJlJ/ERRSQ 330 CONTINUE NUM(ll=DCl l*CC2,2l-0(2l*CC1•2l NlJM ( 2 l zD C2 l *C ( 1 t1 l -D ( 1 l *C C2,1 l DEN,.CC1,1l*CC2t2l-C<2•ll*C(l,zl PPCll=NlJM(ll/DfN PP12l=NUMI2l/DEN TEST=PPI1l*PPI2l IFCTEST-O.l 400,335,335 IFCo0001-0ENl360,360t340 335 "140 GO TO C345t355),KARG 345 WRITEC6,350l XtDEN,NUMClltPP(lltNUMC2ltPPC2l FOR X = tF10.4t2H ,,7H DEN "' ,El2•4t 351"1 FORMATCZOHOWARNING 1 10H NUMI1l = tE12.4t9H PP<ll = tFl2o4tlOH NUMI2l • tEl2•4t 2 9H PPC2l = tF12.4l GO TCl 360 "155 WRITEI6t3561 ATANX,DEN,NUM(l l ,PP(l l tNUMI2) ,PPI2l FOR ARCTAN X " tF10o4t2H tt7H DEN z t 356 FORMAT(28HOWARNING 1 El2o4tlnH NUMCll = ,El2.4t9H PPCll "' tFl2o4/lOH NUMC2l = tE12o4t 2 9H PPC2l = tF12.4l 360 SUMOSQ•O. DO 370 Jl=ltH TERM=CYCJl!-PPill*SUMKCJltll-PPC2l*SUMKCJlt2ll/ERRCJll SUMOSO=SUMQSO+TERM*TERM "170 CONTINUE OSQ=SUMOSO/RNDEG GO TO 380 THIS SECTIONS CONSTRAINS PP-S TO BE NON-NEGATIVE c 41"10 PP2=DC2l/CC2,2l IFCo000l-CC2,2l1460,460t440 440 GO TO C445,455ltKARG 445 WRITEC6t450!X,CC2t2l ,0( 21 ,ppz FOR X = tFlQ.4,2H ,,7H DEN "' ,El2e4t 450 FORMATC20HOWARN!NG 1 lOH NUMill = tE12.4,9H PPCll = ,Fl2o4l GO TO 460 455 WRITEC6t456l ATANX,CC2,2loDC2ltPP2 FOR ARCTAN X = ,Fl0.4,2H ot7H DEN = , 456 FORMATC28HOWARN!NG 1 El2•4ol0H NUMill = ,El2o4t9H PP(ll = tFl2o4) 460 SlJMOC:l•O. DO 470 Jl=ltH TERM .. CYCJll-PP2*SUMKCJ1•2l)/ERRCJll SlJMQS l•StJMQS 1 +TERM*TERM 47() CONT!NUF OSl=SUMQSl/RNDEG PPl,.DCll/CCl,ll !FCoOOOl-CCltlll 560t560,540 540 GO TO (545t555ltKARG 545 WRITEC6,550l XtCCl.lltDClltPPl 117 FORMAT(20HOWARNING F OR X ~ .F10.4•2H ,,7H DEN z .El2•4t 1 l()H NUM(ll"' tE"l2.4,9H PP!ll "tFl2.4l GO TO %0 5 '>5 WRITF.!6.SS6l ATANX,CiltlltDilhPPl FOR ARCTAN X " .F10.4t2H tt7H DEN ~ '>'>6 FORMAT(28HOWARNING tE12.4t9H PP(ll = tFl2o4) 1 E"l2•4•10H NUM(ll S61'\ SUMO!i2c0. DO 570 Jl:ltH TF RM•(Y(Jll-PPl*SUMK(Jltlll/ERR!Jll SU MOS2•SUMOS2+TERM*TERM CONTINUE OS2aSUMOS2/RNDEG IFIOS1-0S2l 600t600t610 600 OSO=OSl 5511 = PP(ll~O. PP(2l=PP2 GO TO 380 0SO=OS2 PP!l)=PPl ;so PP(2l~O. RETURN END $IBFTC FAK c c c c DECK A FUNCTION FOR F SUB K OF AtBt AND X OR ATANX NEW 1/16/67 FUNCTION F!AKtAtB,SIGMA,XtATANXtKARG•KCALCl r ( C RFAL AK,AtRtATANX INTEGER SIGMAtKARG,KCALC ( C ATANX IN DEGREES C C IF KARGzlt X IS USED IF KARG•2tATANX IS USED C C IF KCALC=Ot FK-S ARE CALCULATED IF KCALC=l• STORED FK-S ARE USED c c c c 10 211 311 40 51'\ 60 70 DIMFNSION FKR!5,3) INTEGER SIGMA ARST=O• GO TO !10t20ltKARG XsO =X*X GO TO 40 ARST~ARSIATANXl IFIABST-90ol 30,40,30 X=TAN!ATANX/57.295779) XsO=X*X K•AK/2.+1. IF!KCALC-Ol 100,50,100 EMAX=A+B IFIEMAX-1.) 60t70,70 ICASE•l GO TO 1011 EL,.ARS(A-Al IFIEL.EO.Ool EL•l• ELP,.EL+l• IFIELP-EMAXl90t90t80 t 118 en FKR(K,ll=FKCAKtELtFLtAtAl TCA!;F=? GO TO 10n PH7=C-1.1**SIGMA FKR(K,li=FKCAKtfLtELtAtAl FKRCK•?l=FKCAKtfL,fLPtBtAl FKRCK•'>=FKCAKtFLP,ELPtBtAl !CASE=3 GO TO Cll0tl20t130),ICASE F=O• GO TO 160 F=FKRCKtll GO TO 160 IFCABST-90.) 150,140tl50 F=FI<'RCKt'l G0 T0 160 F:CFKRCKtJ 1-PHZ*?o*X*FKRCKt21+XSO*FKRCK,31l/C1e+XSQ) RETURN END $TRFTC ADC DECK ( c c c c c c A FUNCTION FOR F-KCLtL 1 tBtAlt ANGo DISTRIB. COEFF. RFFot FOUATION C6), LOW LYING LEVELS OF Fl8t POLETTI AND WARBURTON, PHYS REV 137t 8599 C1965) ALL ARGUMENTS IN FLOATING POINT FUNCTION FKCKtLtLPtAtAl RFAL KtLtLP = R-A-1. PHZF =C-1el**N RF = !',QRTCC2.*L+lel*C2o*LP+1.1*C2o*A+1ell N " LP-L PHZ = C-Joi**N R00T = SQRTC2e*K+lol CG =PHZ*ROOT*THREEJCLt1otLPt-1otKt-Ool N " -A-A-L-LP PHZ = ( -1 • l **N W • PHZ*SIXJCA•A•L•LP,K,Bl FK = PHZF*RF*CG*W RFTlJRN END $TRFTC RK DECK N c c c c c c c c A FUNCTION FOR RHOCK,A,ALPHAlt STAT. TENSOR COEFFICIENTS REF. EOUATIONC3l OF LOW LYING LEVELS OF Fl8t POLETTI AND WARBURTON, PHYS REV 137t 8599 (1965) ARGUMENTS FOR THIS FUNCTION MUST BE IN FLOATING POINT FlJN(TION RHOKCKtiltALPHAl REAL K R00T = SORTC2e*K + lol C\.1 = ROOT*THREEJCAtALPHAtAt-ALPHAtKt-Oel R()()T ·" 1 o CG? = R00T*THREFJ(A,ALPHA,A,-ALPnAt0e,-O.J NOTE, BECi\\JSE Jl=J2 MlD M3=0 THE PHASE IS TAKEN AS +1• ( RHOK = C2.- DABCALPHAtOoll*CG1/CG2 RETURN END 119 $lflFTC PLC ( (" DF.CK LFGFNDRF POLYNO~IALS (" 2 3 4 7 6 5 F!INCT!ON PL<LtCTI IF<Liltlt? PL ,. 1. RETURN IF(L-113t3t4 PL " CT RFTURN N • 2 PO a 1.0 Pl a CT AN • N P? s ((2.0*AN-1oOI*CT*P1-(AN-1.01*P0)/AN N ,. N + 1 TF(L-N)5t6t6 PO a PJ Pl " P2 GO TO 7 PL • P2 RETURN END K~ DFCK FUNCTION DAF\(AtBI !F(A-Rilt2tl 2 DA.R "' leO :'\ RFTURN $!flFTC 1 o.o DAR " GO TO '3 END $IF\FTC DEL NOLISTtDECK C FUNCTION DELTACAtRtCI c C ROTENBERG ETo AL. PAGE 13 C2.41 c FUNCTION DELTA(A,RtCI ~1 " A + F\ - C M • Sl F ~ 1 = FACT ( M I 52 • A + C - B M 52 FS2 FACT(MI 53 • B + C - A M S'3 FS3 ,. FACT<MI DFNOM = A+B+C+1.0 = = = M • r,ENOM = FD FACTCMI DFLTA • SORTCCFS1*FS2*FS31/FDI RFTURN END $IBFTC TOR NOLTSTtDECK C CONTAINS FACTORIALS OF NUMBERS UP TO 33 FUNCTION FACTCLI IFCLl55olt50 1 FACT leO RETURN 50 GO TOClt2t3t4t5t6t7t8t9tlOtllt12tl3tl4tl5tl6tl7tl8tl9t20t2lt22t 1 2'3t24t25t26t27t28t29t30t3lt32t33 ltL = DAB DAB DAB DAB DA B DAB DAB 120 Fr-CT = z.n "'FTllRN 'I FAIT "' 6.() OfTtJRN 4 F~CT = ?4. () RFTtiRN 5 Fi\CT "' 12().(') RETliRN 6 FACT = 7?0.0 RETLIRN 7 FACT = 5or'l4f+3 RETURN FACT = 4.0'1?F+4 A RETIIRN FII\T "l.6?88E+5 9 2 . R~Tl/PN lCl 11 12 1"1 14 15 16 17 18 19 zn :?1 ?? 23 24 25 26 27 28 29 3r'l "11 "12 FACT = :'1.6?88F+6 RETURN FACT = 3.9917E+7 RETURN FACT = 4.7900E+8 RETURN Fi\CT = 6o?27E+9 RFTURN FACT = 8.7178E+10 RFTlJRN FACT = J.?,077F+l2 RFTtJRN FACT = 2or'l9:?3F+l3 RETURN FACT = 3.5569E+l4 RETURN FACT = 6.4024E+l5 RETURN FACT = 1o?l65E+l7 RETURN FACT = 2.4329F+18 RFTIJRN FIICT = 5.1091F+l9 PETliRN FACT = 1ol240E+21 RETURN FIICT = 2o585?E+22 RE"TURN FACT = 6o2045E+23 RETURN FIICT = 1.551IE+25 RETURN FACT = 4o0329E+26 PFTtlRN FACT = J.0889F+28 RFTliRN FACT = 3.0489E+29 RETURN FACT = 8o8418E+3() RETURN FACT = Zo6525E+32 RETURN FACT = Ao2228E+33 RETURN FACT " 2o6"113E+3"> 121 "lFTURN ;~ FACT : 8.6833F+36 RFTURN 'i'i WR!TEC6o2()()) 20n FORMATC29HOFACTOR!AL OF NEGATIVE NUMBER /) STOP END $IRFTC 3JS DECK C A FUNCTION FOR THREE ..J SYMBOLS c c c c c ROTENBERG FT. AL. Clo5l PAGE 2 WITH !2.4) FROM PAGE 13 INPUT TS THREF..JI..JloMlo..J2oM2,..J3tM3l FLOATING POINT ROUTINF RFOUIRES FACTORIAL AND DELTA ROUTINES 3 'i 36 1 2 12 14 15 5() 51 '52 FUNCTION THRFE..JCAlo Al, A2, 82• A3• 83) DI MENSION AC3l, BC31 Alll A1 A ( 21 A2 A!3) = A3 8!11 = 81 8(21 A2 A ( 31 " R3 DO 3 5 I : 1 , 3 IFCAC!loNFoOolGO TO 36 IFCRCiloNEoOolGO TO 36 CONTI NlJF THPEEJ • lo RETURN CONTINUE TEST • B1+B2+B3 lFITESTl1o2ol THREEJ "' 0.0 RETURN Sl • Al + A2 - A3 IFCS1)1,12ol2 52 • Al -A? + A3 IFCS2)1,14o14 S3 : A? + A3 - Al IFCS3)1ol5•15 N : Al -A2 - 83 TRA = ABSCBll-Al IFCTBA)50,50,1 TRA = AASCB21-A2 !FCT8A)51,51,1 TRA = AASCB3l-A3 IFCTRA)52o52•1 CONTINUE PHZ = (-l.Ol**N DFL = DELTACAl• A2t A3) X • 1• 0 DO 3 ..J = lt3 S "'A(Jl + BC..Jl M ,. 3 S FS • FACTCM) X • X * FS SM • A(..Jl - fH..Jl M ,. SM FSM ,. FACTCM) X ,. X*FSM ROOT = SORTCXl suM • n.o 122 AK " 0.0 11 = AK+~3-Al-R?. D~l !FIDSll'>•4•4 4 M = DSl FD~l " FACT(Ml 0~2 = AK + 81 + A3 - A2 IFIDS2l5,6t6 6 M " DS2 FDS2 = FACTIMl DS3 " Al - Bl - AK IFIDS"')8,7t7 .7 M = DS3 FDS1 FACTIMl 0~4 • Al + A2 A3 - AK IFIDS4)8,9,9 9 M DS4 FDS4 FACT(Ml DS5 = A2 + 82 - AK IFIDS5)8,10,10 10 M = D 55 FDS5 FACTIMl M = AK FAK ,. FACTIM) N = AK T0P :: (-1.0l * *N DENOM = FAK*FDSl* FDS2* FDS3* FDS4* FDS5 SUM = <;IJM + (TOP /DE NOM) 5 AK AK + 1.0 GO TO 11 THREEJ • PHZ*DEL*ROOT*SUM 8 RETURN END $IAFTC 6JS DECK A FUNCTION FOR SIX J SYMBOLS 2/25/64 c ROTF.NAERG FTo AL. PAGF 13 EQUATION (2o3l c INPUT STXJIJl,J2,L2,Ll,J3,L3l IN FLOATING POINT c RFQUTRF~ DFLTA AND FACTORIAL ROUTINES c FUNCTION STXJ(A,B,C,Dtf,Fl TRTl = A+R-E IFITRI1l2tltl SIXJ = 0.0 2 RETURN TR I1 = A-A+E 1 TFITRI112t3t3 TRTl = -A+B+E 3 IFITRI1l2t4t4 FIRST TRIANGULAR TEST COMPLETED c TRT2 D+C-E 4 IFITRPJ2,5,5 5 TRI2 = D-C+E IFITRT:?l2t6t6 TRI2 = -D+C+E 6 IFITRI2l2•7,7 SECOND TRIANGULAR TEST COMPLETED c 7 TRI3 = A+C-F IFITRI3l2t8t8 8 TRI3=A-C+F IFCTRT3l2•9,9 9 TRI3 = -A+C+F = = = = = = c IFITRT"~l2o10,11'l THIRD TRIANGULAR TF.ST COMPLETED 123 ll'l 11 12 C 1~ TRT4 = D+F\-F IFCTRI4l?ollt11 TRI4 = D-fi+F IFCTRT4l2tl2tl2 TRI4•-D+A+F IFCTRI4l2tl3tl3 FOURTH TRIANGULAR TEST COMPLETED DFLl DfLTACAtBtEl DFL? ~ DELTACDtC,El DFL' DELTAIDtAtFl DFL4 • DFLTACAtCtFl DF.LX = DFL1*DEL2*DFL'*DEL4 N E A+R+C+D PHZ • 1-l.Ol**N suM • n.o 24 16 18 19 20 ~1 AK = 0.0 Sl • A+B-E-AK IFISll22tl6•16 M ~ "1 F<;l "' FACT CMl 52 • C+D-E-AK IFC.<;2)22tl8ol8 M " ~2 F~2 ,. FACT Cl-1) 53 • A+C-F-AK IFIS3)22tl9tl9 M "' S3 F<;3 = FACTCM) 54 • D+B-F-AK IFCS4)22t20t20 M = 54 FS4 " FACTCMl 55 • -A-D+E+F+AK IF(S5)17t2lt21 M "' .<;5 F<;5 ,. FACT(I-1) 56 • -R-C+E+F+AK IF(56)17t23o23 23 M = ~6 = FACTCM) N = AK SPHZ = 1-l.Ol**N TOP = A+B+C+D+l.O-AK M " TOP FTOP ., FACT(Ml TOP = <;PHZ*FTOP M " AK FAK " FACTIM) DENOM • FAK*FS1*FS2*FS3*FS4*FS5*FS6 SUM ., SUM + CTOP/DENOM) 17 AK " AK + leO GO TO 24 22 SIXJ = PHZ*DELX*SUM RETURN END F~6 124 APPENDIX E. PROGRAM FOR THE ANGULAR DISTRIBUTIONS OF GAMMA RAYS FROM ALIGNED STATES a ~ b ------1.~-- c y z Let a be the spin of an aligned state and let b, c, ... y, z be the spins of ·succeeding levels populated in a cascade. Then the angular distribution of the N-th gamma ray in a cascade is given by (Poletti and Warburton, 1965) W(en) = L pk(a)Uk(ab)Uk(bc) .•. Uk(xy)Fk(yz)QkPk(cos en) k even where the sum in Formula E. 1 contains the product of n-1 Uk coefficients. The various factors are given by _ (2 Pk (a, a.) - ) (a a. a - a. - 6 a.O (a a. a - a. I k0 0) 0) (E. 1. ) 125 U (Lab) = W(a b a b; L k) k v:i(a b a b; L 0) Fk(LLba)- (-f 2xFk(LL'ba) + x 2 Fk(L'L'ba) Fk(ab)= 1 +X (E.2.) 2 Fk(LL'ba) = (- )b-a- 1 [ (2L+1)(2L'+1)(2a+1)] 112 x (L 1 L' - 11 k O)W)aaLL', kb) L = max (1, I b - a!) L' '= L + 1 where P(a.) is the population parameter for magnetic substate a., W is a Racah coefficient, Qk is the N-th attenuation coefficient and Pk(cos en) is the k-th Legendre polynomial. The program WOT calculates W(en) for n ~ 3. coefficients are calculated in subprograms. The required The input consists of the following cards: Card 1 H, P, SIGMA, RQ, NPC, NG, NA, NB, NX(l), NC, NX(2), ND, NX(3), CTOA, ALLOUT Card(s) 2 Q(H, 5) 126 Card(s) 3 PC(NPC, P) Card 4 A(NA) Card 5 B(NB) Card 6 X(NX1) Card 7 C(NC) Card 8 X(NX2) Card 9 D(ND) Card 10 X(NX3) Card 11 THETA(H) or (COS(THETA(H)))**2 where H ::: number of angles, ~ 8 . p ::: number of magnetic substates (P .:S 3) with m z =a.>O. - SIG:MA ::: a in Formula (E. 2) RQ ::: 0 if the set of attenuation coefficients Qk is the same at all angles. f. 0 if the set of attenuation coefficients Q { is not the same 1 at all angles. In this case a set must be read in for each of the H angles, and Card 2 is replaced by H cards. NPC = number of sets of the population parameters P(a.) to be read in. If NPC > 1, card 3 is replaced by NPC cards. NG = n, the number of the gamma ray in the cascade. NA = number of values for spin a . NB = number of values for spin b . 127 ~.X(1) = number of values for the mixing ratio x in the transitions a .... b. If NX(1) = 0 then the first entry on Card 6 will be read as D PI-II. The mixing ratio x will be set equal to tan PHI and PHI will be stepped from -90° to 90° in steps of DPHI. NC = number of values for spin c. NX(2) = number of values for the mixing ratio x in the transition b .... c. If NX(2) = 0, then the first entry on Card 8 will be read as DPHI. ND = number of values for spin d. NX(3) = number of values for the mixing ratio x in the transition c .... d. If NX(3) = 0, then the first entry on Card 10 will be read as DPHI. CTOA = · 0, entries on Card 11 will be read as THETA. f 0, entries on Card 11 will be read as (COS(THETA))** 2. ALLOUT = a print out option. If ALLOUT f 0, all components of W(N) will be printed out. Q(H, 5) = array of attenuation coefficients. If RQ = 0, · then Q(1, 5) = Q(2, 5) = Q(3, 5) = ••• Q(H, 5). PC(NPC, P) = array of population parameters. A(NA) = spins for state a. B(NB) = spin~ for state b. X(NXI) = mixing parameters for the transition a .... b if . NX(1) f 0. C(NC) = DPHI J! NX(1) = 0. spins for state c. 128 X(NX2) ::: mixing parameter for the transition b _, c, if NX(2) f. 0. DPHI if NX(2) : : : 0. D(NX3) ::::: spins for state d. X(NX3) ::::: mixing parameter for the transition c _, d if NX(3) f. 0. THETA(H) ::: DPHI if NX(3) : : : 0. angles at which the distribution is calculated. A listing of the program is given below. 129 $TRFTC WOT ( (" (" c c c c c c c ( ( ( c c c c c c c c ( ( ( c c c c c c c c c ( c ( c c c c ( c c c c c ( c c c c c TO TAR\JLATE W(THFTA) FROM POLETTI AND WARBURTON, LOW LYING LFVEL~ OF F18o PHYS REV 137, B600 !1965), EQUATION !10l TO RE RF/>D IN THF FIR~T D/>TA CARD IS TO CONTAIN THE FOLLOWING 15 INTEGERS FORMAT!l5I2l HoPo<;JGMA IF RO.NE.O THE ENTIRE 0 AR RA Y WILL BE READ IN BY ROWS RO THE NUMBER OF ROWS OF THE PC MATRIX TO BE READ IN NPC THE NUMBER OF GA~MA TRANSITIONS 1o 2o OR 3 NG NUMRER OF VALUFS FOR SPIN A !F5 .0 LIMIT 16 PER CARD NA. IF NA=O AM!NoAMAX WILL BF RFAD TN (2F5 o0 ) NUMRFR OF VALUES FOR SPIN R CF5.0 LIMIT 16 PER CARD l NR IF NR=O BM!NoBMAX WILL AE READ IN C2F5.0l THE NUMBER OF X VALUES FOR A-B NX ( 1 l IF NX!ll=O DPHJ WILL AE READ !F10.0l NUMBER OF VALUES FOR SPIN C CF5.0 LIMIT 16 PER CARD l NC IF NC=O CM!NtCMAX WILL BE READ IN <2F5o0l NX ( 2 l X VALUES FOR B-C IF NXC2l=O DPHI WILL Bf READ IN !FlO.Ol NUMBER OF VALUES FOR SPIN D CF5.0 LIMIT 16 PER CARD l ND IF ND=O DM!NtDMAX WILL BE READ IN !2F5o0l THE NUMB>R OF X VALUES FOR C-D NXC3l IF NXI,l=O DPHI WILL RE READ IN !F10.0l CTOA IF = 0 PROGRAM EXPECTS ANGLES IN DEG. TO BE READ IN IF .NE.o PROGRAM EXPECTS COS!THETA!Hll **2 A PRINT OUT OPTION, IF .NE. 0 ALL COMPONENTS OF W(Nl ALL OUT WILL BE PRINTED OUT THE PROGRAM THEN EXPECTS THE FOLLOWING CARDS IF NG = 3 5 PER CARD F10 .0 ATTENUATION COEFFICIENTS 0CHo5l POPULATION PARAMETERS PC!NPCoPl 3Fl0o0 NPC CARDS SPIN~ OF INITIAL STATE ACNAJ F5.Q ONE OR MORE ON A CARD ~PINS OF INITIAL STATE BCNRl F5 . 0 ONE OR MORE ON A CARD MIXING PAR AM ETERS FOR A-8 XCNXll F10o0 ONE OR MORE ON A CARD 5PIN~ OF INITIAL STATE CINC) F5eO ONE OR MORE ON A CARD MIXING PARAMETERS FOR B-C X!NX2 l F10o0 ONE OR MORE ON A CARD SPIN~ OF INITIAL STATE D!NDl F5.0 ONE OR MORE ON A CARD MIXING PARAMETER~ FOR C-D X!NX3l F10.0 ONE OR MORE ON A CARD THETACHl OR COSCTHF.TACHll**2 F5oO ONE OR MORE PER CARD . 11 VALUES MAXIMUM IF NG = ?. OMIT SPIN D CARD AND XINX3l CARD IF NG=l OMIT SPIN Co SPIN Do XCNX2lo AND X!NX3l CARDS IF ALLOUToNF..O AND NG.E0.3 OUTPUT WILL BE l( FCX31 U!X2l X3 X2 U!Xll RHOCKoAl QCTHETA,Kl PCK oCOSCTHETAll FCX3l*UCX2l * U!Xll *RHOCKtAl FCX3l*U!X2l*UCXll*RHOCKoAl*O!NoKl Xl Wtll W(2) W!Hl c c c c INTEGER SIGMAtP,H,ABCDoROtCTOAtALLOUT DIMFNSION OCllo5loXAR!50o3lt AC16lo B<l6ltCC16lo DC16lo CSQT<lll 1 IN1C3lt TN2t3lt WClllo NX!3lo PC(20o3) f)IMEN<;I(')N I~0(3loTW0(4lo t\oi2C5lo IW1!5lt!THOC6) • 130 ~TMFN~T0N KW0(4) , 6HF5o OJ I DATA TN?I1HC• 6H t6HF10o0l I DATA TN 111 H C, 6H , 6HF5.ll I DATA ISO I 4HC1H , 6H OAT.~ TWO I 4HC1H , 6H3F7.4., 6H , 6HFlOo4l I DIITI\ !Wl I 4HC1H , 3H14Xt 5HF7.4., 6H , 6HFlOo4) I DATA TW?. I 4HC1H , 2H7X, 6H2F7.4,, 6H , 6HFlOo4l I DATil KW014HC1H t 3H21Xt 6H , 6HF1Q.4) I DATA TTHO 16HC1H05X, 6H2HX35X, 6H2HX25X, 6H2HX1 t 6H 1 6HF1"•?l I COMMONIWTHTIALMTN,KMAX ( c 91 READC5• 99) H, Po SIGMA, ROt NPC, NG• NA, NB,NXClloNC,NX(2)oNDt 1NXl3ltCTOAtALLOUT 99 FO"?r-<ATC15T2l KWOC3l = ABCDCHJ TTHOI~l = A8CDCHJ NX 1 = NX ( 1 l NX2 "' NX(2) NX"l = NXC3l WRITEC6.6523lNXltNX2•NX3 6523 FORMATC1H02X3HNX1 2X3HNX2 2X3HNX3 I lH 3I5l !FCRO.FQ.O) GO TO 1 oo ? r =1 ,H ? READC5tl00J CQCI,JloJ•1o5l 100 FORMATC5F10.0l GO TO 3 1 READC5o100) (Q(1oJlo J~lo5l DO 4 1=2tH DO 4 J=lo5 4 QCioJl "'Q(l,J) 3 CONTINUE DO 5 I = loNPC ') RF.ADC5o150JCPC(I,JloJ•<lo3l 150 FORMAT(3F10o0l 6 CONTINUE TFCNA.EQ.O) GO TO 8 TN2C2l = ARCDCNAl REA0(5,TN2l CAC!l, I=1oNAl GO TO 9 8 READC5t105l AMIN, AMAX 105 FORMATC2F5.0l NA = CAMAX-AMTNl+1• DO 10 I., 1, NA 10 A(ll = AMIN + FLOATCT-ll 9 CONT!NUF. !F(NR.EQ.O l GO TO 11 TN? • ARCDCNBl READC5t!N2) CBCil t I• loNAl GO TO 12 11 REA0(5,105lBMINoBMAX NR = CBMAX -BMINl + 1• DO 13 I =1.NB 13 RCil • FLOATCI-ll + BMIN 12 CONTINUE NXl., NXCll IFCNXl.EQ.OJGO TO 21 IN 1 • AACD CNX 1 l READC5o!Nll CXARC!ollt !=loNXll 131 c c PROGRAM FXPECTS TANGENTS OF PHI TO BE READ IN I901 .. 0 GO TO 22 21 RF.AOC5t106lOPHI 106 FORMATCF10.0) NX1 = 180./DPHI + 1. NXC1 l = NX1 I901 .. 2 DO 2"1 I• 1tNX1 2"1 X~RCTtll • -90o + FLOAT(I-ll*DPHI 00 4 () I = 1 • NX1 lFCl.EQoloOR.I.EO.NXl.AND.I90l.NE.OlGO TO 40 X.I \RCitll = TA"lCXARCitll/57.2957791 4() CONTINUE 22 CO~tTINUE TFCNG.LEo 1l GO TO 14 !FCNC.EQ.Ol GO TO 15 TN2C2l • ARCDCNCl READC5tiN2l CCCII , I• ltNCl GO TO 16 15 READC5,105lCMINtCMAX NC z CCMAX-CMTNl + lo IJO 17 I., 1 , NC 17 CCI> = FLOATCT-11 +CMIN 16 CONTINUE NX2 = NXC2l !FCNX2oEOoOlGO TO 24 IN1 ,. ABCOCNXll READC~t!N1l (XAR!It2lt I•ltNX2l 1902 = 0 GO TO 25 24 READC5t106lOPHT NX2 = 180 •./0PHT + 1o NXC2l z NX2 !902 • 2 DO 26 I= ltNX2 26 XARCit2l • -90o + FLOATCI-1l*DPHI DO 41 I = 1tNX2 !F(loEOo1oOR.I.EO.NX2oAND.I902oNEoOlGO TO 41 XARCit2l = TANCXARCit2l/57o295779l 41 CONTINUE 25 CONTINUE TFCNG.LF.. 21 GO TO 14 TFCND.EQ.O) GO TO 18 TN2C2l ., ND READC5t!N2l (DCilt I=1tNDl GO TO 140 18 READC5t105lDMINtDMAX ND = DMAX- DMIN + 1o DO 20 I= ltND 20 DCil = FLOATCI-11 + DMIN 140 CONTINUE NX3 = NXC3l TFCNX3oEOoO)GO TO 27 IN1 = ARCDCNXll READC5tiN1l (XARCTt3lt I•ltNX3) I903 .. 0 GO TO 28 27 READC5t106lDPHI NX3 • 180o/DPHI + 1o 132 29 '•2 ?B )4 103 30 32 "11 20~ 201 NX(3) "'NX3 DO 29 I• ltNX3 190:'1 .. 2 XAR(lt3l = -90o + FLOATCI-ll*DPHI DO 42 I = ltNX3 IF(loE0.1.0RoloEO.NX3.AND.I903oNEoOlGO TO 42 XARCit3l = TANIXARI!t3l157.295779) CI)NTINUF C0NT!NUF CONTINUF IFCCTOA.FOoOlGO TO 30 READ (5,103! <CSOTCilt I• ltHl FORMATC11F5.01 GO TO 31 IN2 ABCDCHl READC5t!N21 CCSOTCll • I: ltHI DO 32 Ia ltH CSOTCI l •<COSCCSQTCIJI57o2957791**21 CONTINUE WRITEC6t2001 FORMAT(21H10UTPUT OF INPUT DATA I 7HOSPIN A l 1~0(21 = ABCDCNAl WRITE ( 6 • I SOl ( A( I I • I •1 • NA) WRITEC6t2011 FORMAT(7HOSPIN B I ISOC21 = ABCDCNBI WRITE C6 • I SOl CB CI I ol•l • NB I IFCNG.LE.llGO TO 51 = ~.'RITEC6t203l 203 2fl4 51 202 51') 2M 206 207 c c c 273 FORMAT(7HOSPIN C I IS0(2) = ABCD(NCl WRITE ( 6 • I SOl CCC I l , I •1, NC I IF(NG.LE.2JGO TO 51 WRITFC6t2041 FORMATC7HOSPIN D I ISOC21 = ABCDCNDI WRITEC6tiSOJCDCiltl•loNDl CONTINUE WRITEC6t202l FORMAT(13HO THE X ARRAY l NMAX • NXCll DO "'O I = loNG IFCNXCIJ.GT.NMAXlNMAX•NXCil CONTINUE IWOC2) = ABCD(NGI WR IT E ( 6 , I WO l C( XAR CI , J I • J =1 , NG l , I •1 • NM AXl WRITE(6,2051 FORMATC21Hl0UTPUT OF INPUT DATA I 112HOTHE Q ARRAY l WRITE ( 6, 2 06 l I ( Q (I ,J I • J= 1 t 5 l • I= 1 tH I FORMAT(1H 5Fl0o4) WRITEC6.207l FORMAT(l8HOTHE VALUES FOR PC I WRITE< 6, 2731 ( CPC CI oJ I , J=1, 3 I , I= 1• NPC I FORMATC1H 3Fl0o41 COMPLETES OUTPUT OF INPUT PARAMETERS IA • 1 61 CONTINUF AP = ACIAl WRITEC6t210l AP 133 21~ FORMATI10H1SPIN A = F4o1l IAP ,. AP IF(FLOATIIAPloEO.APlALMIN = 0 IFIFLOATCIAPloNE.APlALMIN Oo5 ' TWOA" 2o*AP IAP = TWOA/2• IF(FL0ATI2*IAPl.EO.TWOAlKMAX TWOA IF(FLO~TC2*IAPl.NE.TWOAlKMAX ,. TWOA-lo I<1 " 1 -67 CONTINUE AP = A<IAl WRYTEC6,2lll BP 211 FORMATI10H SPIN 8,. F4oll GO TO 163t64t64l , NG 64 IC " 1 66 CONTINUE CP = C I I C l WRTTE16t212l CP 212 FORMAT<lOH SPIN C • F4oll GO TO 163,6~t86ltNG 86 CONTINUE ID = 1 6':> CONTINUE DP,. DIIDl WRITE16,213l DP 21! FORMATt1bH SPIN D • F4o1l 63 CONTINUE IPC 1 7 CONTINUE WRITE16tiTHOl ICSQT(Il•I=1tHl GO TO 183t67t68l t NG 6A IX~ ,. 1 69 CONTINUE' WRITE16t6526lNX3 6526 FORMAT(1HO 5X3HNX3 1X I5l X3 • XARIIX3• 3l El = ABSCD-Cl IFIEL.EO.OolEL" 1• ELP " EL + 1• EMAX " CP+DP K903 = 1 IFII903.EOo0lGO TO 87 IF IIX3.E0.1.0R.IX3.EO.NX3l X3 • 1o IFI IX3.NE.1.0RoiX3.NEoNX3 .ANDoELP.LE.EMAXlK903=1 IF( TX3.EOo1oOR.IX?.EOoNX3 oAND.ELP.LE.EMAXlK903=2 87 IFIELP.GT.fMAXlK903=3 67 IX2 = 1 70 C0~1 TINUE WRITEC6t6525lNX2 6':>25 FORMATI1HO 5X3HNX2 lX 15) X2 = XAR(IX2t2l EMAX • BP+CP EL "' ARSIC-Bl IFI~L.FO.OolEL • 1. ELP = EL + lo 1(90? a 1 IF(I902oEOoOIGO TO 88 IF( IX2oEOo1oORoiX2.EOoNX2lX1=1• IF( IX2oNEo1oORoiX2oNE.NX2 .ANDoELP.LE.EMAXlK902=1 IFI IX2oEOolo0RoiX2.EO.NX2 .ANDoELP.LE.EMAXlK902m2 88 IF!ELPoGT.EMAXlK902•3 = 134 83 !Xl "' 1 WRITE(6t6523lNXltNX2oNX3 71 CONTINUE Xl = XAR<IXltll EM/'.X = AP+BP El " ARS(R-Al !F(EL.FO.O.)EL • lo FLP = Fl + 1• K901 = 1 lF(I901·EO.OlGO TO 89 IF( IXloEO.l.OR.IXl.EO.NXllXl = 1. IF( !Xl.NE.l.OR.IXl.NE.NXl .AND.ELP.LE.EMAXIK901=1 IFC !Xl.E0.1.0RolX1oEO.NX1 .AND.ELP.LE.EMAXlK901=2 89 IFCELP.GT.EMAXlK901•3 DO ')0 KN a ltH 90 W CKN) " 0 • DO 72 N"ltH W(N) = OoO <T • SORTCCSQT(Nll K • 0 NK " 1 T1 • 1• T2 • 1 • T3 • 1• T4 • 1. T5 • 1. 73 PK = PLCKtCTl .1\K ,. K TR = RHO(AKoAPoPoiPCtPCl TERM • TR*PK *OCNtNKl GO TO (74o75t76 loNG 74 T1 = f(AKoAPoBPoSIGMAoXloK901) T4 ., Tl*TR T5 • Tl*TR*O(NoNKl WCNI • W<Nl +Tl*TERM GO TO 77 75 T2 " f(AKoBP,CPtSIGMAtX2oK902) Tl • UCAKoAPoBPoXloK90ll T4 ., Tl*T2*TR T5 " Tl*T2*TR*OCNoNKl W(Nl • WCNI+TERM*Tl*T2 GO TO 77 . 76 Tl ., UCAKoAPo8PtXloK901) T2 UCAKt8P oCP,X2oK902) T3 = FCAKoCPtDPoSIGMAtX3tK903l i4 = Tl*T2*T3*TR T5 = Tl*T2*T3*TR*O(NoNKl W(Nl = W<Nl+TERM*Tl*T2*T3 77 IFCALLOUT·EO.Ol GO TO 78 WRITEC6,214 l Kt T3o T2t Tlt TRo Q(NoNKlo PK,T4t T5 214 FORMATClH 14X 4HK ,. Ilo2X/ lH 3F7o4t/lH 14X F7.4, I lH 14XF7.4t/ 1 lH 14X F7o4t/1H 14X F7.4o I 1H 14X F7.4 l WRITEC6oKWOl(W(KNloKN~loHl 7A CONTINUE K • K + 2 " NK + 1 IF<K.LF.oKMAXl GO TO 73 ~'K c C c W(N) FOR ONE SET FINISHED 72 CONTINUE 135 GO TO C79t80t81) , NG IW1(4) = ABCDIH! WR!TEC6tiWll Xlt CWCNW!,NW=ltH) GO TO 8?. 8~ TW?.(4) = ARCD(Hl WR!TfC6tiW2l X2t Xlo CWCNW!tNW•ltHl GO TO 8? R1 TWOC~l • ARCDCHJ WRTTEC6.TWO! X3o X2, Xlt CWCNWJ,NW=ltH) 82 CONTINUE WRITE(6,6524!NXltNX2tNX3oiX1tTX2tiX3 6524 FORMATC1H02X3HNX1 2X3HNX2 2X3HNX3 2X3HIX1 2X3HIX2 2X3HIX3 /lH 615 79 1 ) IXl = IXl + 1 IFCIX1.Lf.NX1!GO TO 71 IX2 = IX2 + 1 IFCTX?oLFoNX2!GO TO 70 IX'I = IX~ + 1 IFCIX3.LE.NX3!GO TO 69 IPC " IP( + 1 IFCIPCoLF.NPC!GO TO 7 ID = ID + 1 IFIID.LE.ND!GO TO 65 IC + 1 IC IFCTC.LE.NClGO TO 66 IB = TR + 1 IFCTB.LE.NB!GO TO 62 IA = IA + 1 TFCIAoLEoNA!GO TO 61 GO TO 91 END $I AFTC UAK DFCK . ( C A FUNCTION FOR U SUB K OF A• Bt AND X c FUNCTION UCAKtAtBtXoK90) X50"X*X EL•ABSCB-Al IFCFI oEO.O.! EL•1• ELP•EL+1• GO TO Cl0olltl2ltK90 1tl U=CUKCAK,FLoAoBl+XSO*UKCAKoELPoAtBI!/(1.+XSOl RETURN 11 U•UKCAKtELPtAtBl RETURN 12 U=UKCAKoELoAoBl RETURN END $I8FTC UKL DECK c C THE ANGULAR DISTRIBUTION COEFFICIENT UKCLAB! c 2 1 FUNCTION UKCAKtELoAoAl N = -A-8-A-FI PHZ = C-l.l**N Wl • PHZ*SIXJCAoB,AoBoELoAKl W2 = PHZ*SIXJCAtBtAtBoELoOol IFCW?.EO.Oo!GO TO 1 UK "' Wl/W2 RETURN WRITEC6o200) 136 FORMATC37HOTHE FUNCTION UKCKoLoAoBl GO TO 2 END DFCK !.TAFTC Af'lC 7.0() c ( c c c IS INFINITE l A FUNCTION FOR F-K(L t L'tAoAl , ANG.DISTRIB. COEFFo REF., EQUATION C6loLOW LYING LEVELS OF Fl8o POLETTI AND WARBURTON, PHYS REV 137, 8599 (1965) ALL ARGUMENTS IN FLOATING POINT \ FUNCTION FKCKoLoLPoBoAl REf\L KoLoLP N "' B-A-1. PHZF a(-lol**N RF = S0RTCI2o*L+1ol*C2o*LP+1.l*(2o*A+loll N "' LP-L PHZ = (-l.l* * N ROOT • SORTC2o*K+lol CG •PHZ*ROOT*THREEJCLo1ooLP,-l.,K,-O.l N ., -A-A-L-LP PHZ = 1-l.l**N W • PHZ*SIXJCAoAoloLPoKoBl FK • PHZF*RF*CG*W RETURN END $JAFTC FAK DECK c C A FUNCTION FOR F SUB K OF A, Bo AND X c FUNCTION FCAKoAoAoSIGMAoXtK90l INTEGER SIGMA XsQ = X*X EL = ABSCB-Al IFCEL.EO.OolEL=l• ELP = EL + 1• PHZ = 1-l.l**SIGMA GO TO Cl0ollol2loK90 1n F =<FKCAKoELoEL, BoAl-PHZ*2•*X*FKCAKoELoELPoBoAl + XSO* 1 FKCAKoELPoELPoRoAll/Cl.+XSQl RETURN 11 F=FKCAKoELPoELPoRoAl RFTURN 1? F=FKCAKoELoELoBoAl RETURN END $IBFTC STR DECK c C c STATISTICAL TENSOR RHO-K(Al FUNCTION RHOCAKoAoPoiPCoPCl TNTFGER P DIMENSION PCI20o3l COMMON/WTHT/ALMINoKMAX <;UM = O. AL " ALMTN DO 1 I = 1 o P SUM • SUM+ RHOKIAKoAoALl*PCIIPCoil 1 AL = AL + 1• RHO = SUM RETURN END 137 DECK 1;IAFTC RK c c c c A FUNCTION FOR RHO(K,A,ALPHAl• STAT. TENSO R CO EF F I CIE NT S REF. FOU ATI ONC 3 1 OF LOW LYTNG LEVELS OF Fl8t POLETTI AND WARBlJRTC1N• PHYS REV 137, B599 (19 6 51 ARGUMFNTS FOR THIS FUNCTION MUST BE IN FLOATING POINT ( c FUNCTION RHOKCKoAoALPHA) RFAL K ROOT • SQRTC2• * K + l•l CGl = ROOT*THREEJCAtALPHAoA,-ALPHA,Ko-O•l ROOT • lo CG2 = ROOT*THREEJCAtALPHAoA,-ALPHAoOoo-Ool c NOTE, AECAIJSF. JlcJ2 AND M3cQ THE PHASE IS TAKEN AS +1• C c RHOK a C?. - DAACALPHAoO.)l*CG1/CG2 Rf'TURN FND $IAFTC PLC DECK c C LEGENDRE POLYNOMIALS c 2 3 4 F\liiiCTfON PL( L oCT l IFCLllol•2 PL "' 1. RETURN IFCL-1)3o3o4 PL = CT RFTURN N • 2 PO = 1o0 Pl • CT 7 AN '"' N P2 • CC2.0*AN-l.Ol*CT*Pl-CAN-l.Ol*P0l/AN N =N + 1 IF<L-Nl5o6t6 6 PO '"' Pl Pl '" P2 GO TO 7 5 PL ,. P2 RETURN END $IBFTC KD DECK FUNCTION OABCAtBl IFCA-Bllt2tl 2 DAB = loO 3 RETURN 1 DAR " 0.0 GO TO 3 FND $IAFTC DEL NOLISTtOECK FUNCTION DfLTA(AoA.Cl C c C c ROTENAFRG ET. AL. PAGE 13 12.41 FUNCTION DF.LTA(AoBtCl Sl • A + fl - C M • S1 FSl • FACTCMl 52 • A + C - B DAB DAB DAB DAB DAB DAB DAB 138 M " S2 FC.2 • FACTCI-1) S3 • B + C - A M ., S3 FS'3 "' FACTCMl DENOM m A+B+C+1o0 M " DfNOM FD • FACTCMl DELTA • SQRTCCFS1*FS2*FS3l/FDl RETURN END $TAFTC TOR NOLISTtDECK C CONTAINS FACTORIALS OF NUMBERS UP TO 33 FIINCTION FACTCLl IFCLl55t1t50 FACT= 1.0 RFTIJRN 50 GO TOI1t2t'3t4t5,6,7t8t9t10t11t12tl3t14t15tl6.17tl8t19t20,2lt22t 1 23t24t25.26t27t28t29t30t3lt32t33 ltl 2 FACT = 2.0 RETURN 3 FACT = 6.0 RETURN 4 FACT = 24.0 RETURN 5 FACT = 12 o. 0 RETURN 6 FACT = 720.0 RETURN FACT "' 5o04E+3 7 RETURN 8 FACT = 4o032E+4 RETURN 9 FACT 3o6288E+5 RETURN 10 FACT "' 3.6288E+6 RETURN FACT = 3o9917E+7 11 RETURN 4.7900E+8 12 FACT RETURN 6.227E+9 13 FACT RETURN 8.7178E+l0 14 FACT RETURN 15 FACT = 1.3077E+12 RETURN 2o0923E+l3 16 FACT RETURN 3.5569E+14 17 FACT RETURN 6.4024E+15 18 FACT RETURN 1o2165E+17 19 FACT qETURN 2o4329E+18 FACT 20 RETURN 5.1091E+l9 FACT 21 RETURN ., lol240E+21 FACT 22 RETURN . .. .. . .. .. .. . . . 139 FACT = 2.5B52E+22 RFTIIRN 24 FACT = 6.?045E+2'3 RETIJRN 25 FACT = 1.5 511E+25 RETURN 26 FACT = 4.0329E+26 RETURN 27 FACT = l.0889E+28 RETURN 28 FACT = 3o0489E+29 RFTliRN 29 FACT = 8.8418E+30 RFTlJRN ''I() FACT = ?.6525f+32 RETURN '31 FACT = 8o2228E+33 RETURN FACT = 2o6'313E+35 RETURN 33 FACT = 8o6833E+36 RETURN 55 WRITEC6t200l 20() FORMATC29HOFACTORIAL OF NEGATIVE NUMBER /) .STOP END $TFIFTC 3J~ DFCK C A FlJNCT TON FOR THREE J SYMBOLS 2'3 c c c c c ROTENRERG ET. AL. Clo5l PAGE 2 WITH C2.4l FROM PAGE 13 INPUT IS THREEJCJltMltJ2,M2oJ3oM3l FLOATING POINT ROUTINE REQUIRES FACTORIAL AND DELTA ROUTINES 35 '36 2 12 14 15 FUNCTION THREEJCAlo Blt A2t B2o A3t 831 DIMENSION A(3lt AC3l ACll Al AC2l A2 A ( 3) A3 A Cl l = B 1 RC;>l = R2 AC3l = B3 DO 35 I = lo3 IFCAIIloNEoOolGO TO 36 IFCACtl.NEoOolGO TO 36 CONTINUE THREEJ = lo RETURN CONTINUE TE~T " Bl+B2+A3 JF<TESTllt2tl THREEJ " o.o RETURN 51 " AI + A2 - A3 IFCS1)1,12t12 52 • A1 -A2 + A3 IFIS2Jl•l4tl4 53 = A2 + A3 - Al IFCS3llol5t15 N • Al -A2 ~ 83 TRA,. AB~CBll-Al IFCTAA)50t50tl 140 5~ 51 52 TPA = ARSCR2l-A2 JFCTRAl5lt5lol TRA = AR~CR3)-A3 JFCTRAl52o52tl CONTINUE PHZ = C-1.0l**N DEL= DELTACAlt A2t A3l X • 1. 0 DO 3 J • lt3 S • ACJl + BCJl M • S FS • FACTCMl X " X * FS SM • A ( J l - R CJ l "1 SM FSM " FACTCMl X "' X*FS'-1 ROOT = SORT(Xl SUM " 0.0 AK • 0.0 Ds1 AK+A3-A1-B2 ll IFCDS1l5t4t4 4 M 051 FDSl " FACT(Ml OS? = AK + Bl + A3 - A2 IF CDS? ·l 5 t6t6 6 M OS? FDS2 " FACT(Ml 053 A1 - Bl - AK JF(053l8t7t7 7 M 053 FDS3 ,. FACTCMl DS4 " A1 + A2 - A3 - AK JFIDS4)8,9t9 9 M 054 FDS4 = FACT!Ml DS5 A2 + A2 - AK JF(DS5l8t10tl0 10 M DS5 FDS5 = FACT(M) M = AK FAK FACTCM) N "' AK TOP • (-l.Ol**N DENOM "' FAK*FDSl* FDS2* FDS3* FDS4* FDS5 SUM = SUM + (TOP/DENOM) AK = AK + lo 0 5 GO TO 11 THREEJ = PHZ*DEL*ROOT*SUM 8 . RETURN END $IAFTC 6JS DECK A FUNCTION FOR SIX J SYMBOLS 2/25/64 c ROTENBERG ETo AL. PAGE 13 EQUATION (2.31 c INPUT SIXJCJloJ2oL2tLltJ3tL3l IN FLOATING POINT c REQUIRES DELTA AND FACTORIAL ROUTINES c FUNCTION SJXJCAtBtCtDtEtFl TRil = A+B-E IFCTRI1l2tlt1 SIXJ 0.0 2 RETURN = = = = = = = = = = = 141 3 c 4 5 6 c 7 8 9 c 10 11 12 c 13 TRil = A-R+F TFCTRI1l?,3,3 TRil = -A+R+E TFCTRil l2t4t4 FIRST TRIANGULAR TEST COMPLETED TRI2 = D+C-E TFCTRT2l2t5t5 TRI2 = D-C+E IFCTRI2l2t6 • 6 TPI2 = -D+C+E IFCTRI2l?t7t7 SFCOND TRIANGULAR TFST COMPLETED TRI3 = A+C-F TFCTR!3l2t8t8 TR!3=A-C+F TF!TRT3l2•9•9 TRI3 = -A+C+F IFCTR!3l2tl0tl0 THIRD TRIANGULAR TEST COMPLETED TRI4 = D+B-F TFITRI4l2•ll•ll TRT4 = D-R+F TF!TRI4l2t12tl2 TR!4=-D+R+F IF !TR I 4 l 2 t13 tl3 FOURTH TRIANGULAR TEST COMPLETED DELTA!AtBtEl DELl DELTACDtCtEl DfL2 DEL3 = DELTACDtBtFl DELTA!AtCtFl DEL4 DELl*DEL2*DEL3*DEL4 DELX N = A+B+C+D PHZ C-l.Ol**N o.n SUM n.o AK A+R-E-AK Sl IF!Sll22t16tl6 M ,. .<;1 Fsl = FACTCI-1l C+D-E-AK S2 IF!S2l22tl8t18 M = S2 FS2 = FACTCMl A+C-F-AK 53 IF!S3l22tl9tl9 M 53 F$3 = FACTCMl D+R-F-AK 54 !F(S4)22t20t20 ,. M 54 FS4 FACTCMl -A-D+E+F+AK 55 IFCS5ll7t2lt21 M 55 FS5 " FACTCMJ -R-C+E+F+AK 56 IFCS6l17t23t23 M 56 Fs6 " FACTCMl AK N SPHZ 1-l.Ol**N .... 24 16 18 .... .. . .. 19 . . 21'l 21 23 . .. .. .. . .. . 142 = 17 22 TOP A+R+C+D+l.O-AK M "' TOP FTOP " FACTCMl TOP = ~PHZ*FTOP M "' AK FAK " FACTCMl DFNOM "' FAK*FS1*FS2*FS3*FS4*FS5*FS6 SUM = ~UM + CTOP/DENOM) AK c AK + loO GO TO 24 ~TXJ = PHZ*DELX*~UM RFTlJRN END 143 APPENDDC F. ARRAY ELECTRONICS Because the array electronics as built and maintained by Mr. L. J. Graham have been modified since McNally (1966) described them and because a subtlety in the operation of the electronics has become apparent in the course of this experiment, a new discussion of the electronics is desirable. For completeness. some of the things discussed by McNally will be repeated. Figure 65 shows a block diagram of the present (May, 1967) system. Each of the sixteen detectors has its own charge sensitive preamplifier and linear amplifier. The outputs of the sixteen amplifiers are fed into a summing amplifier which, in turn, is fed into the F input of the Nuclear Data 160 pulse- height analyzer. The outputs of the sixteen linear amplifiers are also fed into a logic section which routes the pulses to the appropriate ch"¥lnels in the Nuclear Data analyzer. The analyzer is operated in a 16 x 64 mode so that the pulses from each detector are analyzed into 64 channels. The charge-sensitive preamplifiers, designed by R. Y. Cusson, have a conversion gain of 7 mv/MeV. They are contained in a box mounted on the brass plate on which the array is mount ed. Inside this box the preamplifiers are shielded from each other. Originally the preamplifiers were contained in the box containing the other array electronics and mounted in the spectrometer electronics rack. The detectors were connected to the detectors by one meter coaxial cables. However, a severe noise problem caused the adoption of the present system. The pulse shaping amplifier is an adaptation of the RID L 31-17 amplifier with a nominal gain of x 10. A toggle switch 144 provides two gain settings. In the LO position with the potentio- meter between the pulse shaping amplifier and the linear amplifier at maximum, the linear amplifier saturates at 15 MeV. In the HI position it saturates at 45 MeV. The linear amplifier is an adaptation from the RIDL 31-12 with a nominal gain of x 10. A helipot at the input control s the size of the output of the amplifier which saturates at 10 volts. The routing trigger pair designed by Mr. L. J. Graham is set so that with the switches on LO and helipots at maximum, it triggers at approximately 750 keV. goes to a binary encoder. The 5 ~sec pulse produced In the four bit code used, det ector 1 is 0000, detector 2 is 0001, detector 3 is 0010, and so on. These four pulses are fed directly into the address scalers of the Nuclear Data analyzer to route the linear pulses to the proper group of 64 channels. The analyzer generates a pulse (ca lled Linear Gate Open) 4 ~sec after the arrival of a pulse at the F ADC input. The LGO pulse is fed bac.k to the binary encoder to suppress further routing pulses during the time the analyzer is processing a pulse. A common bias is applied to all of the detectors by means of a control located on the Nuclear Data analyzer rack. The overall conversion gain of the array in 700 mv/ MeV with the switches on LO and all of t he helipots at maximum. The noise is less than 50 keV, and the system is limited by the noise of the silicon surface barrier detectors. The subtlety that has caused difficulty is the fact that the address scalers are not reset unless the ADC receives a pulse. This situation can arise if the Nuclear Data analyzer threshold is set too high. Even if the threshold control reads zero there / 145 is still a threshold of approximately 400 mv at the 0-10 volts input. The effect is to misroute some of the data. In the present work this difficulty was always avoided by setting the routing threshold above the linear pulse threshold for every detector. The threshold control on the analyzer was always set as low as possible (usually 000) without significant dead time ( < 2%). The routing threshold is controlled by the 16 switches and helipots. The linear threshold is controlled by the 16 switches and helipots, the helipot at the F P..DC input, and the analyzer threshold. When the routing threshold lies higher, a pulse fed into the array will route into the correct group of 64 channels, and then as the pulse height is decreased it will suddenly route into the first group of 64 channels corresponding to no routing pulse. Storage will stop when the linear threshold is reached. When the linear threshold lies higher, storage will stop before the transition to the first group of 64 channels occurs. this should be checked for all 16 detectors. Obviously, 146 APPENDIX G l.E.l Nuclear Physics A96 (1967) 1-5 ; © North -Holland Pub/is/zing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher NON-EXISTENCE OF A LEVEL AT 1.35 MeV IN 33 S C. E. MOSS California Institute of Technology, Pasadena, California t Received 27 December 1966 Abstract: A natural sulphur target has been bombarded with 2.541 MeV deuterons and the emitted protons have been observed with a magnetic spectrometer. The peak tentatively attrib uted earlier to a level at an excitation energy of 1.35 in 33S is shown to be due to levels in •·•s at excitation energies of 4.08 and 4.12 MeV. NUCLEAR REACTIONS 32 S(d, p), E = 2.541 MeV; measured a(£p,8). 33 S deduced levels. Natura l target. 1. Introduction A shell-model calculation by Glaudemans et a!. 1 ) predicted a J + level in 3 3 S at an excitation energy of 1.38 MeV. If this level consists of a n inert 28 Si core and two protons and three neutrons in the (2st d,_) shell coupled to give a total spin of 1- +,then it should not be populated in the stripping reaction 32 S(d, p) 33 S. A recent study of this reaction by O'Dell et al. 2 ) produced evidence which was tentatively interpreted as a weakly populated level in 33 S at an excitation energy of 1.35 MeV. The peak attributed to the "1.35" MeV level is shown in the present experiment to be due to levels in 34 S at 4.08 and 4.12 MeV which can be formed by the reaction 33 S(d, p) 34 S on the 0.76% abundance of 33 S in naturalS. 2. Experimental procedure Deuterons were accelerated by the ONR-CIT tandem accelerator. The target was prepared by evaporating BaCl2 , Au(~ 290 Jlg/cm 2 ), and CdS (~ 90 Jlg/cm 2 ) containing natural S, onto a glass slide and then floating off the Au and CdS in distilled water. The protons were detected in an array of 16 Au-Si surface barrier detectors 3 ) in the focal plane of a 61 em d:>uble-focussing magnetic spectrometer 4 ). Since the (He 4 )+ + and protons which are focussed by the spectrometer at a given magnetic field have the same energy, an aluminium foil of thickness 1.7 mg/cm 2 was placed in front of the counters to degrade the energy of the (He 4 )++ relative to the energy of the protons. Slits in front of each counter defined a momentum window LJP = P/720. The total instrumental resolution (FWHM) was ~ 30 keV. t Work supported in part by the Office ofNava1 Research [Nonr-220(47)]. 1 April 1967 147 2 C. E. MOSS 3 .... std,pl:-.:'s "'....z {o) ::> 0 ~~372.869 2K u 0 5.0 G.S. E, • 2.541 BL. 130• 3.224 4K "1.35'' ~ 2.313 1.965 ~A A "stG.S.l I I 0.841 II I I 7.0 6.0 8.0 E, {MeV) 29 100 Si ( 1.277} t {b I 7.2 6.6 09Si{t.277l "stG.S.) 100 I (c) I 14 C {G.S.) 'r I >< 5{4.081 X 1/3 0 (j) f- z 6.6 7.2 100 ::::> 0 0 (d) 0 7.4 100 {el 0 68 100 " {f) 0 7.0 7.6 Fig. 1. Proton spectra from bombardment of a natural sulphur target with 2.541 MeV deuterons. {a) a spectrum at OL = 130° with each point corresponding to !50 fiC of incident deuterons. (b)(i) expanded plots of the spectra in the region of the "1.35" level at various angles with each point corresponding to 750 fiC of incident deuterons. The peaks are labelled by the corresponding residual nucleus and its excitation energy. The scale factor applies only to the 36S(G.S.) peak. 14.R NON-EXISTENT LEVEL IN 33S 3 100 (g l 34 "1 35" . t 0 5 ( 4.12 ) 34 514 ' 08 ) . II i '\1(1 .1 64) 7.6 7.0 100 <f) 1- z ::> 0 (h) (.) 0 7.8 100 34 (;) 1.35" 0 I ,. 5(4.08) 1 ,.f'11.164) 7.8 7.4 7.2 5(4 .12) Ep(MeV) Fig. 1. (continued). 3. Results Fig. 1 shows the proton spectra. The number of counts in a momentum window .t1P = P/720 is plotted against the proton energy. Fig. l(a) shows the proton spectrum obtained at a lab angle of 130° with a bombarding energy of 2.541 MeV. Each point corresponds to 150 11C, of incident deuterons. The spectrum is to be compared with the one shown in fig . 1 of ref. 2 ) which was taken at the same angle and bombard ing energy. The peaks attributed to levels in 3 3 S are labelled by their corresponding excitation energies. The position of the proton peak from the 35 S ground state which can be formed by the reaction 34 S(d, p) 35 S and the position of the peak from a "1.35" level in 3 3 S are shown. Fig. l(c) shows a proton spectrum in the region of the "1 .35" level at 130°, and figs . 1(b )-(i) give the kinematic shift of the levels in this region with angle at 20° intervals. In these spectra each point corresponds to 750 11C of incident deuterons. The 35 S(G.S.) peak is scaled down as indicated; all other peaks are full size. The identification of the peaks was made with a non-relativistic kinematics program which calculated the mass of the target nucleus and the Q-value of the reaction from the energies of the protons at two or more angles and the incident beam energy. A relativistic kinematics program was then used to calculate the positions of the peaks. Masses in the program from the 1961 mass table 5 ) were used. The excitation energies for the 29 Si(l.277) level and the 36 01(1.164) level were taken from Endt and van . -;-· ~ - - 149 4 C. E. MOSS der Leun 6 ). For the 34 S(4.12) level, the excitation energy of 4.120±0.008 MeV reported by Brenner 7 ) in the reaction 33 S(d, p) 34 S was used. Brenner's value differed by 6 keY from the value of 4.114±0.008 MeV reported by Endt eta!. 8 ) in the reaction 37 Cl(p, &) 34 S. Since Brenner did not see the 34 S(4.08) and Endt et a!. did, the latter's excitation energy of 4.073±0.008 MeV for this level was raised by 6 keY to yield an excitation of 4.079 MeV. Finally, to correct for energy loss in the target, errors in the calibration of the 90° beam analysing magnet, and errors in the calibration of the spectrometer, the peak positions predicted by the relativistic kinem atics program were shifted down in energy at each angle by a constant amount equal to the energy difference between the peak position predicted by the relativistic kinematics program for 35 S(G.S.) and its observed position. The shift was never more than 13 keY. In effect, the proton energies are measured relative to the energy of protons in the 35 S(G.S.) peak. The resulting final predictions for the peak positions are shown by arrows in figs. l(b)-(i). The fact that the predictions for the position of the 29 Si(l.277) peaks at GL ~ 70° are higher than the observed ones can be explained by assuming that the 28 Si contaminant was on the front and back of the target. At GL ~ 90°, the beam was incident on the CdS side of the target and the protons were detected on the same side. The peak nearest the 29 Si(1.277) arrow was produced by 28 Si on the incident side of the target, and the peak at slightly lower energy was produced by 28 Si on the back side of the target. The latter was shifted down in energy relative to the other 29 Si peak by an amount equal to the sum of the energy lost by deuterons and protons in passing through the target. This peak is larger at f)L = 150° because the spectrum at this angle was taken after the spectra at f)L = 130° through 10° had been taken and more 28 Si had been deposited on the gold side. At f)L ~ 70°, the beam was incident on the CdS side and the protons were detected on the opposite side. The 29 Si(1.277) protons from the 28 Si on the CdS side were shifted down by approximately one-half of the energy loss in passing through the CdS. The 29 Si(1.277) protons from the 28 Si on the gold side were shifted down by approximately an amount equal to the difference in energy lost of the deuterons and protons in passing through one-half of the CdS and the full thickness of gold. The result was an unresolved doublet shifted down in energy relative to its predicted position. Similarly, 13 C was also probably present on both sides of the target. The peak at 110° labelled 36 Cl(l.l64) and the peak at 130° labelled 34 S(4.12) may be partly due to 14 C(G.S.). From a comparison of the spectra at f)L = 150° and f)L = 10° it is apparent that the peak near the arrow labelled "1.35" is due mainly to the level in 34 S at an excitation energy of 4.12 MeV. The small discrepancy between the predicted position and the observed position is within the error and is essentially independent of angle. The level in 34 S at an excitation energy of 4.08 MeV is also seen. 150 NON-EXISTENT LEVEL IN 3>s 5 4. Conclusions No evidence was seen in this experiment for a level in 33 S at an excitation energy of 1.35 MeV. The peak observed by O'Dell eta!. 2 ) was probably due to the levels in 34 S at excitation energies of 4.12 and 4.08 MeV. Some of the gamma rays they observed in coincidence with the protons in this p eak were probably from the gamma . decays of the 4.12 and the 4.08 MeV levels (see ref. 6 )) . References I) P. W. M. Glaudemans, G. Wiechers and P. J. Brussaard, Nuclear Physics 56 (1964) 548 2) J. M . O'Dell, R. W. Krone and F. W. Prosser, Jr., Nuclear Physics 82 (1966) 574 3) J. H. McNally, thesis, California Institute of Technology (1966) 4) D. E. Groce, thesis, California Institute of Technology (1963) 5) L.A. Konig, J. H. E . 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Prosser, F. W., Jr., .and Gordon, J. W., 1967, Bull. Am. Phys. Soc. 12, 572. Ramavataram, K. , 1966, Physics Letters 21, 690. Rose, M. E. , 1953, Phys. Rev. 91, 610. Seidlitz, L., Blueler, E., Tendam, D. J., 1958, Phys. Rev. 110, 682. Skorka, S. J., Hertel, J., and Retz-Schmidt, T. W., 1966, Nuclear Data A~' No. 4, 347. Smith, P. B., 1964, Can. ~· Phys. 42, 1101. Thankappan, V. K. , 1962, Physics Letters~' 122. van Rinsvelt, H. A. , and Endt, P. M. , 1964, Physics Letters .Q, 266. 156 van Rinsvelt, H. A., and Endt, P. M., 1966, Physica 32, 529. van Rinsvelt, H., and Smith, P. B., 1964, Physica 30, 59. Wa,pstra, A. :H. , 1964, Nucl. Phys. 57, 48. Weitkamp, C., 1963, Nucl. Inst. and Meth. 23, 13. Wiechers, G., and Brussaard, P. J., 1965, Nucl. Phys. 73, 604. Willmes, H., and Harris, G. I. , 1967, Bull. Am. Phys. Soc. 12, 91. Wilkinson, D. H., 1960, in "Nuclear Spectroscopy Part B", Ajzenberg-Selove, F., Academic Press, New York, 859. c,a s,sp 6z a 0. 761 mm 2.0° 9. 0° 0. 794 mm 0 1. 016 mm 0. 508 mm 2.0° 9.0° 0. 794 mm 0 2. 03 mm 2. 03 mm 1.5° 11. 6° 3.18 mm 63 b¢ g h f a b c d c 0 3. 18 mm 3.18 mm 3.18 mm 1. 84 mm 3, 18 mm 2 2 1. 7 mg/cm 1. 7 mg/ cn? 1. 7 mg/cm 1. 7 mg/cn? 0 1. 84 mm mm 6. 6° 11. 6° 9. 0° 11. 6° 7.4° 5.2° 7, 4° 12. 7 2.0° 4. 2° 2.0° 1. 50 0.64° 4. 2° 0 1. 7 mg/cm 1. 01 6 mm 1. 016 mm 1. 01 6 mm • 761 mm 1. 01 6 mm 1. 016 mm 1. 016 mm 1. 016 mm 1. 016 mm 1. 016 mm 1. 016 mm 0.64° • 761 mm 1.016 mm 1. 016 mm 2. 54 mm _2. 54 mm 3. 81 mm 3. 81 mm 3. 81 mm 2. 03 mm 2.54 mm 2. 54 mm 3. 81 2. 54 m m h 2. 54 mm g 3.81 m m mm f 3. 81 mm e 2.03 mm d Used for the thin target spectrum shown In Figure 5(a) (see page 4 ). Used for the th ick ta rget spectrum s hown in Figure 5(b) (see page 4) . Used for the calibrati0n s r ectrum s hown In Figure 7(b) (see page 10 ). Used for the spectra shown in Figure 11 (see pa ge 18) and Figure 55 (se e page 70) . Used for the excitat ion fu nctions shown in Figur e 27 (see page 37). Used for all of the angular di st ributi:ms except th ose for le vel s 3, 4, and 6 in 3 1S (sec page 24). 31 Used for the angular distributions for le vels 3, 4, and 6 in s (see page 24). Used for the s in gle detector deuter on spect r a shown in Figure 56 (see page 75). Used for the four detector deuteron spectra (sec page 77). Used for the ~pcctra shown in Fib'Ure 61 (s ee pa[:e 84) . t(Al) c,sp s,sp br br s,sp 6z 1. 016 mm 0. 381 mm 1. 916 mm c,a 6r 3. 81 mm 3. 81 mm s, a br 0. 38 1 mm c 1. 916 mm b Thickness of the foil in front of the detector(s) measured normal to the foil surface FW measured perpendicular to the mean orbit of the slit in front of the detector(s) c,sp FW of the angular acceptance slit in the ¢ direction 6¢ FW of the angular acceptance slit in the a direction FW of the slit 46 em in front of the ta rget which defines the vertical dimension of the beam spot FW of the slit 42 em in front of t he target which defines the horizontal dim ens ion of the beam spot FW of the image slit of the beam analyzing magnet FW of the object slit of the beam analyzing magnet 6r s, sp 69 6r s,a 6r 6r Notation TABLE I Slit Settings and Detector Foil Thickn ess 2 -J t--1 CJl 158 TABLE II Frequency Factors and Yield Factors Detector Number Frequency Factor a Yield Factor b c 1 . 98149 .8 79 . 939 . 883 2 . 98416 1. 018 1. 056 1. 068 3 . 98689 . 950 . 976 . 924 4 . 98961 . 954 . 954 . 918 5 . 99230 . 949 • 986 • 934 6 • 99494 . 995 1. 010 . 968 7 . 99749 1. 033 1. 054 . 982 8 1. 00000 1. 000 1. 000 1. 000 9 1. 00257 1. 124 1. 171 1. 017 10 1. 00502 1. 005 1. 052 1. 030 11 1. 00749 1. 109 1. 179 1. 063 12 1. 00984 1. 160 1. 225 1. 056 13 1. 01222 1. 171 1. 298 14 1. 01453 1. 232 1. 448 1. 078 1. 121 15 1. 01692 1. 254 1. 473 1. 119 16 1. 01912 1. 279 1. 479 1. 135 a Used for the spectra shown in Figure 11 (see page 18) and Figure 55 (see page 70) and for all of the angular distributions except those for levels 3, 4, and 6 in 31s (see page 24). b Used for the angular distributions for levels 3, 4, and 6 in 3ls (see page 24). c Used for the spectra shown in Figure 61 (see page 84 ). 159 TABLE III Input for the Calculation of the Ground State Q-value of the 32 3 Reaction s( He, a.) 31 s The notation is given in Appendix A. 2 K1 = . 0199062 ± • 0000033 MeV/(Me/sec) F1GS = 17. 897 ± • 001 Me/sec XGS90 = 0 ± 20 mils (position of the beam in the beam analyzing magnet slits) K3GS F3GS ::;; • 0113934 ±. 0000013 MeV /(Me/sec) ::;; 29. 694 ± • 004 Me/sec 2 YGSTGT = 0 ± 10 mils (vertical position of the beam spot) 83 ::;; 149. 898 ± • 05° Result Q = 5. 538 ± • 006 MeV 160 TABLE IV Target Thickness Target a a 2 2 Au(!..Lg/cm ) CdS(!..Lg/cm ) CdS 1 (natural) 282 ± 60 78.4 ± 16 CdS 2 (natural) 282 ± 30 78.4 ± CdS 7 (enriched) 323 ± 30 141 8 ± 10 Targets used for spectra shown in Figures 11 and 55. 161 TABLE V Contributions to the Resolution of Peak (9) in Figure ll(b). All FVlHM 1) Variation of the beam intensity across the beam analyzer slits 0 2) Variation of the beam magnet analyzer current 0 3) Vertical dimension of the beam spot, or = · s,sp 0. 762 mm 7. 1 keV 4) Energy dependence of the reaction cross section 0 5) Homogeneity of the target material and the backing foil 0 6) Target thickness 3. 0 keV 7) Energy straggle in the target material :5. 13. 0 ke V 8) Energy straggle in the supporting gold foil 25. 2 keV 9) Energy dependence of the stopping cross section in the target and supporting foil 0 10) Aberrations in the spectrometer < 3 keV 11) The e angular acceptance of the spectrometer and the variation of do/dO over this angular range 12) The variation of the spectrometer current 22. 5 .k eV .:::; 2 keV 13) The width of the slit in front of the detector in the focal plane of the spectrometer, or c,sp = 1. 84 mm 19.7 keV Level 20° 7.731 • 22 41 4.210 ± 22 4.462 ± 22 4. 526 ± 22 4.588 ± 22 4.722 ± 21 4.877 ± 22 ·4.972 ± 23 5.024 ± 23 5.156 ± 22 5.307 ± 22 5.414 ± 22 5.451 ± 22 5.519 ± 22 5.685 ± 22 5.772 ± 22 5.842 ± 22 5.887 ± 22 5.991 ± 22 6.160 ± 22 6.269 ± 22 6. 353 ± 12 6.409 ± 22 6.539 ± 22 6. 590 ± 22 6.628 ± 22 6.718 ± 22 6. 750 ± 22 6. 837 ± 22 6.868 ± 22 0 1.254 ± 23 2.2 37 ± 22 3.084 ± 22 3.292 ± 22 3.3 50 ± 22 3.439 = 22 natural 7.039 ± 22 7.167 ± 22 7.1 96 ± 22 7.3 12. 22 5.155 ± 21 5.300 ± 21 0 1.248 ± 21 2.237 ± 21 3.070 ± 22 3.284 ± 21 3.357 =22 3.436 = 21 4.084 ± 21 4.206 ± 21 4.450 ± 21 4.521 ± 21 4.579 ± 21 4.720 ± 21 4.866 ± 21 4.972 ± 21 10° natural 37 38 39 40 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 .17 0 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number TABLE VI 22 22 22 22 22 22 22 22 22 22 22 22 22 4.58 5 4.727 4.872 4.973 5.305 5.407 5.456 5.51 5 5.6 81 5. 774 5.819 5.890 5.978 22 22 22 22 22 22 22 22 23 0 1.245 2.235 3.071 3.289 3.343 3.447 4.089 4.228 4.460 na tu ral 45° 7.720 ± 21 7.031 = 21 7.1 54 ± 21 7.1 96± 21 7. 293 ± 21 5.889 =21 5.977 ± 21 6.152 ± 21 6.267 ± 21 6.346 ± 21 6.389 ± 21 6.541 ± 21 6.595 ± 21 6.628 ± 21 6.704± 21 6.736 ± 21 6.836 ± 21 6.861 ± 21 4.199 ± 22 4.453 ± 21 4.520 ± 21 4.583 ± 21 4.718 ± 21 4.868 ± 21 4.970 = 21 5.027 ± 21 5.152 ± 21 5.298 ± 21 5.408 ± 21 5. 434 =21 5.514 ± 21 5.676 ± 21 5.773 ± 21 0 1. 248 ± 21 2.234 ± 21 3.079 ± 21 3.2 85 ± 21 3.343 ± 22 3. 442 ± 22 20° enriched 31 s. 5.141 ± 23 0 1.237 ± 21 2.229 ± 21 3.069 ± 21 3.278 ± 20 3. 342 ± 21 3.420 ± 21 4.075 ± 21 4.201 ± 21 4.444 ± 21 4.506 ± 21 4.579 ± 20 4.712 ± 20 4.863 ± 21 4.966 ± 21 45° enriched Excitation Energies of Levels in 7.737 . 23 7.035 ± 22 7.165 ± 22 7. 204 ± 22 7.325 = 22 5.309 22 5.411 22 5.449 22 5.5 35 22 5.685 22 5. 788 22 5.829 22 5.904 22 5.9 91 22 6.161 22 6.269 22 6.344 23 6.397 22 6.570 22 6.58 1 22 6.6 35 ± 22 6.711 ± 22 6.74 2 =22 6.839 ± 22 6.878 ± 23 0 natural 45° 7. 037 = 20 7.1 57 ± 21 7.1 83 = 21 7.310 =21 6.823 ± 21 6.857 ± 21 4.202 ± 21 4.410 ± 20 4.506 ± 21 4.574 ± 21 4. 704 = 21 4. 856 ± 21 4.962 = 21 5.006 ± 22 5.138 ± 22 5.300 ± 21 5.393 ± 21 5.425 ± 20 5.508 ± 21 5.673 ± 21 5.773 ± 22 5.824 ± 21 5.897 ± 21 5.978 ± 21 6. 150 ± 20 6.267 ± 21 6.353 ± 21 6.336 ± 21 6.540 ± 21 6.572 ± 20 6.636 ± 21 6.724 ± 21 0 45° enriched Units: MeV:: keV 0 1.242 ± 20 1.246 ± 10 2.2 34 ± 10 2.232 = 15 3.075 ± 10 3.287 ± 15 3.286 ± 10 3.347 ± 10 3.35 9 ± 15 3.435 ± 15 3.4 37 ± 10 4.085 ± 20 4.083 ± 12 4.209 ± 11 4.208 = 25 4.4 52 ± 9 4.451 ± 15 4.526 ± 15 4.522 ± 12 4.581 ± 9 4.582 ± 15 4.717 ± 9 1.718 ± 15 4.866 = 9 4.85 ± 3U 4.968 ± 10 4.976 ± 15 (5.026 ± 16) 5.1 54 ± 12 (5.17 ± 30) 5.315 ± 15 5.301 ± 11 5.407 ± 10 5.42 ± 30 5. 440 ± 11 5.517 ± 15 (5.52 ± 30) (5.680 = 10) 5.697 = 15 5.792 ± 15 5.777 ± 11 (5. 824 ± 13) 5. 84 ± 30 5.91 ± 30 5.893 ± 10 5.994 ± 20 5.983 ± 13 6.1&5 ± 25 6. 154 ± 12 6. 273 ± 20 6.268 ± 13 6.34 ± 30 6.34 8 ± 13 6.40 ± 30 6.39 5 ± 11 6.56 ± 30 6.5 40 ± 12 (6.593 ± 15) (6.628 ± 15) 6.63 ± 30 (6. 711 ± 13) 6.743 ± 13 6.763 ± 20 6.834 ± 11 (6.84 ± 30) 6.862 ± 12 6.896 25 6.99 30 7.0·1 8 20 7.036 ± 11 7. 181 20 7.1 61 ± 11 7.1 99± 13 7.310 ± 11 7.522 20 30 7.60 7.66 30 (7.726±15) 7. 738 20 Average AjzcnbergSelovc and Wiza 1966 O:> N 1-'- 0 Assumed QG 3.677 ± 17 Q 0 X . 33 a 8 lll 5,479 ± 17 E 45 (natural) = 9,156 ± 4 {Endt and van der Leun , 1962). 7.341:!: 18 1.815 ± 18 8 5.464 ± 17 3.692 ± 17 a 3,826 ± 18 5.330 ± 18 3.828 =18 5.328 ± 18 X E in 33sa Q X E in 33sa 0 20 {natural) Q 10 (natural) Units: MeV ± keV 348 (3He, a.)3 38 TABLE V1I 5.472:!: 12 7.341 ± 18 1.815:!: 18 3,827 :!: 13 X E in 338 a 3.6 85 ± 12 5.329 ± 13 Q Average 7.353 ± 6 (7.3 35:!: 6) 7.330 ± 6 5,479 ± 6 3,834:!: 5 X E in 338 Endt & Paris {195 8) CJ:) (]) 1-' mils ug/cm XGS90 TTGT ± degrees Me/sec mils THOUT FIN XN90 1-1g/cm YGSTGT TllACK ± 40. a • 001 o. ob o. ob . 04 . 0015 - . 0000 .0010 ± 31. 438 ± - . 0089 • 0089 Slit half \vidth . The error calculated equals one half of the maximum geometrically allowed error. The e rror in se tting the target angle is i ~'llorcd. a b • 010 • 050 30. 15. a 15. a QGS " 5. 539 ± . 016 20. 109 ± ± ± ± . 0000 o. 282. 0. • 005 ± • 00005 ± . 00005 38. 635 ± 0. 0. - . 0023 EX = 1. 254 ± • 023 . 001 40. a • 0018 . 0074 . 0008 • 0016 . 0047 . 0006 . 0012 -. 0142 - . 0074 . 0002 -.0016 -. 0009 .0025 • 0046 -. 0006 . 0009 • 0007 . 01 42 • 0011 - . 0003 . 000 5 - . 0011 .0000 -. 0001 . 0004 -. 0002 - . 0145 - . 0012 - - 0001 • 0016 - . 0025 QN = -. 452 ± • 017 EX = 5. 991 ± • 022 . 001 0 . 0039 -0025 . 0046 . 0009 . 0019 • 0015 . 04 0 b 0. b • 0004 . 0004 • 0015 - . 0145 - . 0012 -. 0026 . 06 . 06 8. 0 • 001 40. a . 0113819 ±. 00000 12 0. • 0023 -. 0001 ± ± ± ± ± ± ± 21. 272 ± 10. 10. 0. 0. 0. 78.4 0. 21. 272 ± • 0199048 ± . 0000042 Input Error Error Error introduced introduced introduced in QN in QGS in EX (MeV) (MeV) (MeV) Level (25), 20° (natural) in Figure 11 . 0009 . 0040 • 002 5 . 00 39 • 0046 -. 0008 . 0001 . 0009 • 01 45 • 0012 • 0000 . 0000 . 0000 - . 0000 - . 0145 -. 0012 • 0046 . 0008 . 0017 - . 0145 - . 0012 . 0015 .0004 • 0004 • 0015 -. 0026 .0025 . 0019 • 0009 • 0015 .0004 . 0004 Q.N = 4. 285 ± • 018 . 010 37.2 57± Me/sec F3N Results: QGS = 5. 539 ± . 01 6 15. a . 050 ± 0. 20. 109 ± mils degr ees 30. YNTGT ± ± 282. 0. • 005 15. a ± • 00005 38. 635 ± 0. • 011 38 19 ± • 00000 12 ± • 00005 0. 0. 21.272 ± 10.0 ± ± . 06 . 06 8. 0 -. 014 5 40. a - . 0026 -. 0012 • 00 1 TH3 2 Me/sec mils F3GS EK3N EK3GS MeV / (Mc/sec) 10.0 ± degrees TlUN K30 0. AUHE4 ± 0. CDSHE4 ± 78. 4 ± 0. 21. 272 ± • 0199048 ± . 00000 42 0~ 2 2 Input CDSHE3 2 Me/sec MeV/(Mc/scc) Units FIGS K1 Arguments Error Error Error introduced introduced introdu ced In QGS in QN in EX (MeV) (MeV) (MeV) Level (1) , 20° (natural) in Figure 11 Described in Appendix A Input and Results for Typical Calculations with the Q- value and Excitation Progr am TABLE V1ll ~~ Ol 1-'- 10° natural 5. 531 ± 18 Angle Target Q- value 32 3 31 S( He, a) S 5. 53 9 ± 16 natural 20° 5. 53 7 ± 17 natural 45° Units: MeV= keV QGS for TABLE IX 5. 5 28 ± 16 enriched 20° 5. 52 4 = 16 enriched 45° J-l O'J C)l 166 TABLE X 32 3 31 . Optical Parameters for S( He, a.) S 3 He Parameters v w r Set I 181.0 16. 12 Set II 30 Set III 33 4 a r0' at . 854 • 85 1. 81 1. 60 . 592 32 1. 07 1. 60 . 85 9. 5 1. 66 . 62 1. 67 • 81 a r0' a' 0 He Parameters v w r Set I 40.0 10.0 1. 75 . 520 1. 75 . 520 Set II 30 12 2.00 .5 2.00 .5 Set III 95 15.0 1. 57 • 60 1. 57 . 60 0 0 5. 440 5. 517 7. 036 19 20 37 s(p, d) s Kozub (19~)~ Gla shauscr and Ric· key (1 967 ), d 32 s(p, ct) 31s s(p, cl) 31 s e 32 31 32 Ka va losk! et al.( 19G3 ), 1/ 2+ (5/2+) s( !le,a) 31s 32 s(~He , a) 31 s 32 3 Fou and Zurmuhlc (1966), 5. 407 18 0 Present expe rim en t on 5. 301 17 b 5. 154 16 (1) 2, (3) a 4. 968 (5. 026) 4. 866 13 15 4. 717 14 4. 581 4. 522 11 4. 452 9 10 12 4. 209 8 3 (3/2+) (5/ 2+) (2) (5/ 2)+ (2) 2 3. 437 3. 347 1/ 2+ 1/ 2+ l' 4. 083 3. 286 4 5 0 a 7 3. 075 3 0 t-value 6 2. 234 2 1. 246 0 X 318 E In Level Number In 318 2 2 2 2 2 0 t-value b (5/ 2)+ (5/2) + (5/ 2t (5/2t (3/ 2)+ 1/ 2+ l' 1 2 2 0 t - va!ue c J~ TABLE XI 31 t -values and Spins for s n from Angular Distribution Measurements d 2 t -valuc 5/ 2+ 3/ 2+ 1/ 2+ l' 2 2 .t-value (5/ 2t (3/2t J -J ClJ 1-l Jn 3/ 2+ 5/ 2+ 1/2+ 5/2+, (3/2t (7/ 2+, 3/ 2) 3/ 2(+) Level S(1) 31 318(2) 318(3) 31S(4) 31S(5) 31S{6) 2.1 9 1. 20 0.36 31S(6) -· 318(2) 318(6) .. 31S(3) 31S(5)- 31S(3) 31S(G) _ 31S(l) 1.11 0.27 31S(5)- 31S(2) 13.73 2.10 13.73 31S(5)- 31S(1) 3.44 3.35 31S(5)- 31S{O) 31S(G)- 31S(O) 1.05 0.21 2.04 13.73 31S(4)- 31S(O) 31S(1) - 31S(1) 31S{4) - 31S(3) 3.29 ll. 73 31S(3)- 31S{2) 31S(4) - 31S{2) 1.83 0.84 31S{3)- 31S(1) 3.08 14.41 0.99 31S(2)- 31S(1) 31S(3)- 31S{O) 2.23 14.41 1.25 13.73 \MeV) H(cm) y 318(2) - 31S(O) 31S{1) - 31S(O) Transit ion E .9010 .9000 .8999 ,9082 . 9075 ,8976 Q2 .6967 .6 938 .6 936 •7170 . 7149 ,6870 Q4 For Correlation .4414 .4367 .4364 .4733 .4698 .42 57 Q6 TAIILE XII ,1974 . 19 20 , 1916 .2328 .2288 ,1792 Q8 s E2/M1 E2/M1 M3 / E2 1.291 ± . 585 for J ; (3/2) undete rmined undeterm ined .577 ± .220 -.775 ± .616 for J ; (3/2) -.467 ± .521 or -2.204 ± 2.920 for J;(7/ 2) undetermined .213:.107 or 1. 882 ± .521 for J ; 5/2 E2/M1 -.053 ± .036 or -2.411± .243 -.349 o .015 or 5.272:.393 X. 31 E2/M1 M3/E2 E2/ Ml Multi polarity Mixture Correlation and Branching Ratio Meas urements in 3<:"f. 8~{- a4 . 5311 ± .0044 - .6772± .0067 . 1480 : .0267 a2 6';- 6~ .$ 2c:;. 54+ 3 -4 46+ 3 -4 5 :5 21 "(. ? 78';; 5 :5 15'} 25~~~ - 1.1 05 ± .018 .4022: .550 a6 -1.9735± 1.273 - .4197± 1.9938 +3 75_17'!(- -.8352 =.2088 -.2444 ± .4067 :5 12\i 5 :5 13\} 2: 85/} s ~ 97% 100\"f Branching Ratio f---4 C)) (f) b Harris and Breitenbecker (1966 ) Ha rris and Seagondollar (1963) Broude et al.(l958) a b c -0.41::0.03 or 7.1 ± l.Oa 3. 44 .... 0 3. 35 .... 1. 25 b 0. 13 ± o. 02 3. 41 .... 1. 27 3. 51 .... 0 3. 29 .... 1. 25 2. 23 .... 0 a c 1. 25 .... 0 Transition -0. 44 ± 0. 02 0. 028 ± 0. 018 or -5. 23 ::: 0. 06 -0. 28 ± 0. 02 x 3. 29 .... 1. 27 2. 23 .... 0 1. 27 .... 0 Transition 3lp Mixing Ratios TABLE XIII X =0. 521 for J = 5/2 =2. 920 for J = (7/ 2) o. 577 =0. 220 -0. 775 ± 0. 616 for J = (3/ 2) 0. 467 ± 0. 521 or 2. 204 1. 291 ± 0. 585 for J = (3/ 2) 0. 213 ± 0. 107 or 1. 882 0. 053 :!:: 0. 036 or 2. 411 :: 0. 243 -0. 349 ± • 015 or 5. 272 :: 0. 393 318 O'J tO ...... 0 5) The homogeneity of the target material and the backing foil spectrometer 14) The width of the slit in front of the counter in the focal plane of the 13) The variation of the spectrometer current this angular range (6 8 = 0. 64 ° ) 12) The angular acceptance of the spectrometer 68 and the variation of da/dO over 11) Aberrations in the spectrometer keV 12.4 keV <1 5. 7 keV < 1. 5 keV 0 0 9) Energy dependence of the stopping power in the target 10) Energy dependence of the stopping power in the s upporting foil 6. 5 keV 8) The energy straggle in the supporting gold foil < 13.0 keV 0 4) The energy dependence of the reaction cross section 7) The energy straggle in the target material 4. 3 keV 3) The vertical dimension of the beam spot, = 0. 762 mm ::; 15. 0 keV 0 2) The variation of the beam analyzer current 6) The target thickness 0 1) Variation of the beam intensity across the beam analyzer slits Contributions to the Resolution in Figure 55. All FWHM TABLE XIV 0 ....:) I-' h 7 6 0 2. 687 ± 19 2. 817 ± 19 2. 681 = 19 2. 815 ± 19 2.68 1 ±19 2.354 ± 19 1. 965 = 20 =20 2. 976 = 20 2. 843 ± 19 2. 683 = 19 2. 351 . 811 ±20 . 810 = 19 45° 45° 150° . 809 2. 854 ± 19 2.977± 19 2. 85 1 = 19 2. 693 = 19 2.986 ± 19 =19 2. 687 =19 2. 345 4. 120 = 27 2. 850 = 26 4. 133±19 2. 850± 19 2. 693 ± 19 4. 114±19 2. 846 = 18 2. 688 ± 18 4. 111 :1 8 2. 845 = 17 2. 698 = 17 9" 4. 119 = 10 2. 980 = 9 2. 818 ' 2. 686 = s" 2. 351 = 9 3. 986 4. 127 4. 127 ± 12 2. 97~ '· 2. 855 2. 847 2. 315 o 15 3.986, 12 2. 856 = 12 2. 848 = 12 2. 53 ± 6U 2. 11 = GO 0 . 813 ± Arc rage 1. 99G ± enriched • BOG = 4 110° enriched • 81 0 = 9 enriched l. 978 ± 11 Single Detector =19 l. 975 =19 2. 318 =19 45° enriched 4 Detector Array 0 natural c1 33 0 45° enriched Fnnn the· compilati~J'il Uy Endl ancl van dc r Lcun (19G2) . 32 33 Fr um a study nf tile rcact bn s(p, y) ci by Pro>Scr and Gord~n (1967). A\·c ragt• :)f l G drtecbr array results only. 2. 981 ± 20 2. 980 ± 20 2. 357 = 20 2. 354 " 20 1. 98 1 ~2 0 . 811 ± 20 . 810 = 20 0 20° enriched 0 45q natural ' 2 0° natural 0 10° natural 0 Level Numbt·r 16 Detector Ar ray Units: MeV =kc V Exci tation Energies of Levels in TAOLE XV f---' --...l f---' Q-value Angle Target -3. 217± 14 - 3. 212 ::: 14 20° natural 10° natural - 3.214::: 14 natural 45° QGS for -3.217± 14 enriched 20° 45° enriched -3.221± 14 32 3 33 S( He, d) Cl TABLE XVI 45° -3.214 ::: 14 natural 45° -3, 221 ± 14 enriched - 3.217:::5 Average -:y l'V 1-' -4.135 ± 15 -4.531 ± 15 -4. 120 ± 15 -4. 520 ± 15 -4.771 ± 15 -4.801 ± 15 -4. 873 :!: 15 -4. 516 ± 14 -4.774 ± 15 -4.799 =15 -4. 877 ± 15 -4.552 ± 14 -6. 685 ± 38 X 5. 752 = 5. 678 ± 9 5. 651 :!: 8 5. 406 ± 8 5. 005 ± 10 4. 178 ± 7 4. 056 ± 7 E Presenta From the compilation hy Emit and van dor Lcun (1 962). 31 35 From a study of S(p, y) Cl by Hazewimlus _0 ~L (1963). - 6. 688 :!: 18 7. 561± 18 - 6. 683 ± 27 7.559:27 -4. 876 ± 7 -4.802::8 QGS = . 8761 ± . 0030 MeV was assumed (Maples£!~- ,19GG). - 6. 688 ± 18 -4. 800 ± 14 -4. 775 ± 7 -4.530±7 b -4. 873 :!: 15 -4. 550 ± 15 -4. 780 ± 14 -4. 129 ± 9 -3. 302 ± G -3. 180 ± 6 _Q Average a 4 Detector Array -6. 680:!: 37 Single Detector - 4. 880:!: 14 -4.808 ± 14 -4. 778 ± 14 -3.310 ± 15 -3. 304 ~ 15 -4. 131 ± 15 -3.300 ± 14 -3. 176 ± 14 Q 45° enriched -3. 182 ± 14 -3. 296 ± 14 Q 20° enriched -3.301 ± 14 - 3. 180 ± 14 Q 45° natural - 3. 178 ± 15 Q 20° natural Units: MeV± keY - 3. 182 ± 14 Q 10° natural 16 Detector Array TABLE XVII 34 3 35 s( He, d) Cl X 7. 545 7. 559 7. 597 7. 545 7. 597 7. 597 4.174;,5 4. 113 :!: 5 4. 058 ± 5 3. 163 ± 5 3. 006 ± 5 2. 695 ± 5 2. 645 ~ 5 1. 762 ± 3 1. 220 ± 3 0 E b -::I ""' ...... 5. 22 ± 40 X 5. 03 ± 50 E c 174 TABLE A."VIII 3 He Parameters v w r Set I 181.0 16. 12 Set II 30 Set III 33 a r 0 ""a, ' 1. 07 . 854 1. 8 1 . 592 32 1. 60 • 85 1. 60 . 85 9. 5 1. 66 .62 1. 67 • 81 a r a' . 650 1. 558 0 r Deuteron Parameters Set IV v W' r 57. 8 203.2 1. 563 0 r 0 . 374 175 TABLE XDC -e-. p-values for 33 Cl ,nd Number Excitation (MeV) a b c <.1 0 0 (2) 2 2 3/2+ 1 . 810 0 0 1/2+ 2 1. 978 2 3/2+,5/2+ 3 ·2.351 4 2.686 (2) (3/2+ ' 5/2+) 5/2+ 5 2.848 1 3/2- 6 7 2.980 8 3.986 9 4.119 3/2- 1 a Present experiment. b Endt and van der Leun (1962) from c 33 s(d, n) c1. 32 33 Mubarakmandand lV.tacefield (1967) from s(d, n) cl. d Known values of Jn or the values of Jn implied by these -e- -values. 32 p 176 TABLE XX Energy Losses for a Typical Peak in Figure 61 33 (. 810 MeV level in c1 at eLab = 40°) Beam energy, protons 12.011 MeV Energy loss of protons in nickel entrance foil Energy loss of protons in 1. 1 em of 36 Ar at 14 em 0 of Hg pressure and 340 K • 007 Resulting incident energy 11. 993 Energy loss of alphas in 1. 1 em of 36 Ar at 14 em 0 of Hg pressure and 340 K Energy loss of alphas in 10 • 011 4 Xnickel foil Energy of alphas entering the spectrometer .130 • 402 5. 964 177 TABLE XXI Comparison of Yields 32 3 33 s( He, d) Cl 32S(d, p)33 8 n a (relative) Excitation Energy in 3 3cl (MeV) Intensif,Y at 45 b (relative) 0 4.0 0 4.0 1 0.839 1.1 • 810 1.6 2 1. 965 (0. 4) 1. 978 0.05 3 2.314 0.8 2.351 •2 4 2.869 1.2 2.686 4.2 5 2.936 9. 1 2.848 3.8 6 2. 971 weak 7 3.222 8. 1 2.980 0.06 Number Excitation Energy in 33g (MeV) 0 (2J+1)e 2 a Quoted by Endt and van der Leun (1962). b Taken from the spectra shown in Figure 55. 178 Figure 1 Initial Experimental Information for 31 31 P and 31 s A summary of the experimental information on 31 p and s that was available at the start of the present investigation is shown. This summary is essentially the same as thaf given by Endt and van der Leun (1962). page 1.) (See 17J 7.768 7.886 7934 1/2+ .312+ 7.286 3oSi+ P 6 43 6.55 . (6.25) - ~- - - - - - - - - - (§.. Q~ - - - - - - - - - 6.4 6.08 5.9 30p+p 5.48 325+ 3He+a 5.012 · 4 784 4 (1/2 3/2+) 4.63.)~4.590 = ~4257 4.188 . 5/2+ 3.505 3.414 3.29_2 3.133 3/2+ ;_z_+ 3/2+ 2.232 512+ 1.265 3/2+ 1/2+ j5/2) 4.5 3.3 2.3 1.1 1/2+ 180 Figure 2 Models for A = 31 Two models which were available at the start of the present investigation are shown. Both the shell model calculation by Glaudemans et al.(1964) and the Nilsson model calculation by Broude et al.(1958) predicted a lowlying 1/2+ level and a 7/2+ level, neither of which had been 31 identified. Both of these levels were located in s in the present experiment. (See page 1.) 18 1 A =31 MeV 5 7/2+ 7/2+ 3/2+ 1/2+ 5/2+ 3/2+ 1/2+ 3/2+ 5/2+ 4 3 !------~ 5/2+ 2 1---------i 3/2+ 1 - - - - - - - - - 1 3/2+ .___ _ _ _ ___..,/2+ GLAUDEMANS ET AL (1964) 1/2+ BROUDE ET AL (1958) 0 182 Figure 3 Initial Experimental Information for 33 s and 33 c1 A summary of the experimental information on and 33 33 c1 that was available at the start of the present investigation is shown. This summary is essentially the same as that given by Endt and van der Leun (1962). page 2.) (See s .841 1.965 33 5 0 2 3/2+ I 2) '2 3 j;2 3 I! 3) I12+ 7/2-) 2 .970 2.937. 2.869 2.313 3/2- 3.224 3.939 3.834 In .806 2.1 2.5 2 .86 2.85 4.13 r - - 3.99 33CI 312+ 1/2+ 512+ 3/ 2- 3/2- 2 0 32 5 + P 0 .587 0.580 1.754 J p. y 2.29 1.900 Po co ....... w 184 Figure 4 Model for A = 33 The result of a shell model calculation by Glaude mans ~ al. (1964) which was available at the beginning of this investigation is shown. (See page 2. ) 1G5 A= 33 MeV 1 - - - - - - ---1 7/2 + 5 I 12+ 1=============1 3/2+ 5/2+ 4 3/2+ 3 1--------1 7 /2+ 2 t - - - - - - - - 1 5/2+ t---------tl/2+ L-..--------' 3/2+ GLAUDEMANS ET AL { 1964) 0 186 Figure 5 (a) Thin Target Spectrum of the 31 s Ground State Group A spectrum of alpha particles from the bombardment 3 of a thin ZnS target with 8. 5 MeV He++ particles is shown. The spectrum was taken to check for the presence of other 31 groups near the S (G. S.) group. None were observed. (b) Thick Target Spectrum of the 31 s Ground State Group A spectrum of alpha particles from the bombardment 3 of a thick ZnS target with 8. 5 MeV He ++ particles is shown. The contribution to the step width from or are shown. , o 9, and or s,sp c,sp The midpoint shown was used to calculate the ground state Q- value. (See page 4. ) ! I S (g.s.) I I I j J JOO 160 0 0 :::::> z 29500 401- 80 ..... 120 (f) -........ I() 0 29600 29700 ~ 80 20 40 I FREQUENCY ( Kc/sec) 29800 29600 0 0 :::::> z ~ 60 ........ (\J I \ ~ ~\ I 29700 ~\ H 8r c,sp 8r s, sp 189 ~ ];-- r,.::__ - _ !:J:._ \ ~ \' "' I H \~MIDPOINT ,, \\ _-r1~ ~ (b) 120 I 140 :::1.. 31 I :::1.. / I 0 {o) I 0 2001- 24J 280 29800 I co -.:J ...... 188 Figure 6 Electronics for Single Detector The electronics used with the single detector in the focal plane of the magnetic spectrometer are shown. The RID L 400- channel analyzer was used as a monitor, and the single channel analyzer window was set so that only the particles of interest were counted by the scaler. (See pages 6, 10, 17, and 83.) 129 l l SILICON SURFACE BARRIER DETECTOR ! PREAMP: TENNELEC MODEL IOOA POWER SUPPLY: TENNELEC ~----.-----~ MODEL 901RM PREAMPLIFIER AND BIAS SUPPLY I DOUBLE DELAY LINE AMPLIFIER RIDL 400CHANNEL ANALYZER RIDL MODEL 30-23 SINGLE CHANNEL RIDL ANALYZER MODEL 33-IOB ! SCALER RIDL _ _ ___,~MODEL 49-28 190 Figure 7 (a) Calibration Spectrum for the Magnetic Spectrometer with the Single Detector A spectrum of the 8785 keV (Wapstra, 1964) alpha 212 particle group from a standard Po source (described by Groce, 1963) obtained with a single detector in the focal plane of the magnetic spectrometer is shown. The peak frequency of 27689 ± 1 Kc/sec was used to calculate the calibration constant for the spectrometer, k sa. . (See page 10. ) (b) Calibration Spectrum for the Beam Analyzing Magnet 4 A spectrum of a beam of He++ particles from the tandem accelerator passing through a 0. 203 mm diameter hole in 0. 127 mm thick sheet of tantalum placed at the target position is shown. The spectrum was obtained with a single detector in the focal plane. The spectrometer was placed at 0°, and the beam analyzing magnet NMR magnetometer frequency was 20935 Kc/sec. The peak frequency of 27672 ± 1 Kc/sec was used to calculate the calibration constant for the beam analyzing magnet k . a (See page 10.) L) 0 :::> 27660 I I • I I • 27700 i~ IC3~ I I FREQUENCY ( Kc/sec) I I I • 1000 r- ~ 2000 z ........ {\J ~ ~ 3000 I- w (/) 40001- {a) I l) ::> 0 z 1- (/) ......... - l{) (/) u w 277 40 I I I -1 I 0 I I 0 I I I 27672 ( 0\ • I 0 \ FREQUENCY ( Kc /sec ) 2766 4 LL '-VVVI I ovvv 1 ~ I • L{b~ 10000 I- 12000 0 \ 27680 1 f-l CD f-l 192 Figure 8 3 A spectrum of 10 MeV He++ particles scattered from a target of CdS on a gold foil is shown. The spectrum was measured with the s pe ctromet e r and the 16 detector array. A similar spectrum was taken with the target rotated 180°. The shifts in the midpoints of the high energy sides of the peaks from gold and cadmium were used to calculate the target thickness. (See page 17.) 0 ::::> 0 24000 500 z 1000 1- (j) 1500 BLAB = 150° INCIDENT E3 He 24500 • j FREQUENCY ( Kc/sec) I \ !\ Cd =10.0 I I ~ 25000 +24865± 2 I • I f.:. , • Au 2000 r----r---.----.----.----.---.----.----.----r---,--~ C.0 w f-l 194 Figure 9 Calibration Spectrum for the Mag11etic Spectrometer with the 16 Detector Array A spectrum of the 8785 keV (Wapstra, 1964) alpha 212 particle group from a standard Po source (described by Groce, 1963) obtained with detector 8 in the 16 detector array and the 1. 84 mm slits is shown. The peak frequency of 27703 ± 1 Kc/ sec was used to calculate the calibration constant for the spectrometer k sa • (See page 17. ) 195 5000 <f) w 4000 f- ::J z :2: 0J 3000 ............ <f) I- z :::> 0 • 2000 L) 1000 27660 27700 FREQUENCY ( Kc/sec) 27740 196 Figure 10 Yield Factors Spectrum A region of a spectrum at 150° of the elastic 3 scattering of 12. 0 MeV He++ particles from a thick tantalum target is shown. The open circles shown the region as scanned by detector 8 of the 16 detectors, and the straight line is an approximation to this spectrum. The solid circles shown the region as observed with the array. The yield factors are shown in Table II, column a. (See page 18. ) 197 I I I I I ~ lot \~ .___ ~ ~\~ lot !OJ ~ ~ ·~ i- - 0 0 00 1'- o<-> lei 0~ - tO' r-u 1-d,:ll \ -~ , t-o-1 1111 >- \ 0 z w :::J PI k>{ oo )q\~ r- PI - ow ¢0::: I'-LL toi let 101 \ r ~ ,~ r-- 101 - J-o-1 0 0 (\J 1'- \ I I I I I 0 0· 0 0 0 0 0 0 0 0 0 0 00 1'- 0 0 ' <D l() 0131A 0 ¢ 0 0 0 1'0 198 Figure 11 . 32 3 31 16 Detector Array Spectra from the Reaction S( He, a.) S (This figure is in the rear pocket. ) a) An alpha particle spectrum obtained at eLab = 10° from the bombardment of natural sulfur with 12.0 MeV 3He++ particles is shown. Each point represents 150 ~C of incident charge. The lower scale is the N:MR magnetometer frequency for the magnetic spectrometer, and the upper scale is the corresponding alpha particle energy. The scales are shifted so that corre- sponding levels fall on a vertical line. The levels are numbered as in Table VI. b) An alpha particle spectrum obtained at eLab = 20° from the bombardment of natural sulfur is shown. Each point above FREQUENCY= 33600 represents 150 ~C of incident charge, and the scale on the right is to be used. Each point below FREQUENCY = 33600 represents 300 ~C of incident charge, and the scale on the left is to be used. c) An alpha particle spectrum obtained at e Lab = 20° from the bombardment of sulfur enriched to 98. 1% 32s (natural sulfur 32 contains 95. O% s) is shown. The scales are similar to those in b). d) An alpha particle spectrum obtained at e Lab = 45° from the bombardment of natural sulfur is shown. Each point represents 300 ~C of incident charge. e) An alpha particle spectrum obtained at eLab = 45° from the bombardment of sulfur enriched to 98. 1% 32s is shown. scales are similar to those in d). (See page · 20.) The 199 Figure 12 Comparison of the Predictions of Sets I, IT, and ITI Typical examples of the angular distributions predicted by DWBA calculations with the optical model parameters in Sets I, IT, and ITI are shown. Set I was used for all of the levels in the present experiment. page 27.) (See ~ b.- 0 ~ ;:-_ 0.8 ·---_o ~ 0 __, q 0.6 -o '-... b 0.4· -o ·..... / . 0.2 ·;/. . . \.._/ 0 10 20 30 BcM 40 50 60 201 Figure 13 Angular Distribution for 31 s(G. S.) The angular distribution of the alpha particles 32 3 31 from the reaction s( He, a.) s (G. S.) is shown. The 31 curves are DV/BA predictions. Level s (G. S.) must have tn = 0 because J rr = 1/2+ (Endt and van der Leun, 1962). (See page 27.) 202 1.6 ! 1 32 1.4 - E3 S( 3 He,a } 31 S( G.S.) He =12.0 1.2 ( /) !- z :::::> ... . ·.,., ........' . ' ...· ., ·. ......'· .. .,.,_.!....:-~,.,. . ·.. .< \. 1.0 ...... >- .~ ..· 0:: <£ 0:: I- 0. 8 \ ·... / \ ./~ I= 3 , · ..\ - \ _,..· , -2 -··-y· . -z; -... /=1 . \ •.. "'0 ......... 0 ro 0::: <{ ~ 0.6 - 0.4 \ ·. \ \ . \ . \ \ l \ -t'~ o . ' \ b "'0 \ { =4 \ \ \ \ ~-.. \ \ ' '·....... _ ' '' ... ..... . .. .. ' ·.' / ~- ...... ;. 0.2 . .,.., ........... ......... ' 0 L-----~----~------~----~----~------ 0 10 20 30 BCM 40 50 60 203 Figure 14 Angular Distribution for 31 s (3. 08) The angular distribution of the alpha particles 32 3 from the reaction s( He, a.) 31s (3. 08) is shown. The 31 curve is a DWBA prediction. Level s (3. 08) is assigned ,e_ :::: 0. n (See page 28.) 204 I. 6 r-----.----,---____,.---~--.,----g 32 1.4 E3 S( He 3 He,a ) 31 S( 3. 0 8 ) = 12 .0 - I. 2 ( j) t- z :J 1. 0 I >- 0:: <! 0:: I- m 0. 8 0:: <( ......., ~ 0. 6 '"0 .......... b "'0 I I i-v- ! \=0 0 .4 0.2 50 60 205 Figure 15 Angular Distribution for 31 s (3. 29) The angular distribution of the alpha particles from 32 3 31 the reaction s( He, cx.) cl (3. 29) is shown. The curves are 31 DWBA predictions. Level s (3. 29) is assigned .e, = 2 and n on the basis of J -dependence, J = (5/2) . (See page 28.) 20G 1.6 . ----~------~-----~-----r----~------, 32 1.4 s( 3 He,a ) 31 S(3.29) E 3 He=l2.0 1.2 0. 4 0.2 0 ' ' ...._ __ 0 ------~----~'----~'------~----~----~ 0 10 20 30 40 50 60 BcM 207 Figure 16 Angular Distribution for 31 s (3. 44) The angular distribution of the alpha particles from 32 3 31 the reaction s( He, a) s (3. 44) is shown. The curves are 31 DWBA predictions. Level s (3. 44) is assigned t = (2) n and on the basis of J-dependence, J = (3/2). (See page 29.) 2U8 1.6 32 1. 4 I E3 s{ He 3 He,a ) 1 31 S(3 .44} = 12.0 - 1.2 ( .{) 1- z- :J ..,.... 6 . ), 1.0 .I. / Y' >- I a:: \ I <( I 0::: \ I [--- 0. 8 co \ \ 0::: <l: \ \ ~ ~ 0.6 -o \ \ \ ......... b ~= I '"0 0.4 \ \ \ \ \ _/ 0.2 / ' ' ........o - - TI 0 0 0 10 20 30 8CM 40 50 60 209 Figure 17 Angular Distribution for 31 s (4. 08) The angular distribution of the alpha particles from 32 3 the reaction s( He, a.) 31 s (4. 08) is shown. At forward 31 11 angles the S (4. 08) group was obscured by the C (G. S.) 31 group. The curves are DWBA predictions. Level s (4. 08) is assigned t n (See page 29.) = (2) and on the basis of J-dependence, J = (5/2). 21v I. 6 ,.---~----r------r-----r----,------, 32 1.4 - (/) E3 s( He 3 He,a } 31 5{4.08) = 12.0 11 1.2 1- C(g .s. ) ~ z ::::) >- 1. 0 o:.: <( 0:: 1- co \ 0.8 \ 0::: - 0.6 <( /'~I I \ I ~ -o \ I .......... b \ \ I "'0 0 .4 Q. I / \ \ \ 0.2 - 0 '- / ~----------~----~----~-----~--~ 0 10 20 30 BcM 40 50 60 211 Figure 18 Angular Distribution for 31 s (4. 45) The angular distribution of the alpha particles from 32 3 the reaction s( He, a.) 31 s (4. 45) is shown. The angular , 31 11 range wnere the S (4. 08) group was obscured by the C (G. S.) group is indicated. The curves are DWBA predictions. 31 Level s (4. 45) is assigned -t = 3. (See page 29.) n 212 32 S( 3 He, a ) 31 S( 4.45} E 3 He = 12.0 zn 1.2 11 C(g.s.) 1- 1- ~ z :::> >- 1.0 0::: <( 0::: l- eo 0.8 0::: '=3 <! q 0.6 \ I '"0 ........ b '"0 0.4 - I 0.2 o~----~----~'----~----~~----~--~ 0 10 20 30 BcM 40 50 60 213 Figure 19 Angular Distribution for 31 s (4. 52) The angular distribution of the alpha particles from 3 31 3 the reaction ~s( He, a) s (4. 52) is shown. The angular 31 range where the s (4. 52) group was obscured by the 11c (G. S.) group is indicated. The curves are DWBA predictions. 31 Level s (4. 52) is assigned t = 2. (See page 29.) n I. 6 ,..----.---..,----....-----,-----,-----, 32 1.4 ..-- E3 s(3 He,a ) 31 s (4.52) He =12.0 1.2 <.f) 1- - z ::J 1.0 >- 0:::: <( 0:::: ..__ m 0.8 0:::: <( .._,., I c::; 0.6 11 I -o ......... 1- I b -o 0.4 I C(g.s.) -1 /I 0.2 10 20 40 50 60 215 Figure 20 Angular Distribution for 31 s (4. 58) The angular distribution of the alpha particles from 31 32 3 the reaction s( He, a,) s (4. 58) is shown. The angular 31 range where the s (4. 58) group was obscured by the 11c (G. S.) group is indicated. The curves are DVvBA predictions. 31 No assignment is made for level s (4. 58). (See page 29.) 216 1 .6----~----~----~-----~----.----. 32 1.4 E3 S( He 3 He,a) 31 S(4.58) = 12.0 - 1.2 1'1 c./) 1- C(g.s.) 1.. -1 z :::J >- 1.0 0::: <t (1::' IOJ 0.8 0::: - <t ~ 0.6 ......... b "'0 0.4 0.2 . . . . . . . . ... . ... . .. . 10 20 40 50 60 217 Figure 21 Angular Distribution for 31 s (4. 72) The angular distribution of the alpha particles from 32 3 31 the reaction s( He, a) s (4. 72) is shown. The angular 31 range where the s (4. 72) group was obscured by the 11 c (G. S.) group is indicated. The curves are DWBA predictions. 31 Level s (4. 72) is assigned -e,n = 2, (3), and on the basis of Jdependence, J = (5/2). (See page 29.) · 218 I. 6 n----r----.,..----.---.....----.-----, 32 1.4- E3 s ( 3 He,a ) 31 S(4.72) He = 12.0 - 1.2( /) 1- z ::J 1.0 >- 0:: <( 0:: 1- 0.8 0.2 0 ~----~----~----~----~------~--~ 0 10 20 40 50 60 219 Figure 22 Angular Distribution for 31 s (4. 87) The angular distribution of the alpha particles from 32 3 31 the reactioH s( He, a.) s (4. 87) is shown. The curves are 31 DWBA predictions. Level s (4. 87) is assigned -f- = (1). n (See page 29. ) 220 I. 6 . -- - . - - - - . - - - - - r - - - r - - - r - - - - - - , 32 1.4 E3 S ( 3 He , a ) He 31 S ( 4 . 87 ) = 12.0 I. 2 (j) l- z =:) 1.0 \ >- 0::: \ <1: 0::: l- \ 0.8 \ \ co 0::: <1: ..._.. c; 0.6 \ \ \ ""0 '-.. b ""0 0.4 I \ l=o \ \ 0.2 \ \ 0 \ 0 10 - 0 20 30 8CM 40 50 60 221 Figure 23 Angular Distribution for 31 s (4. 97) The angular distribution of the alpha particles from 32 3 the reaction s( He, a.) 31 s (4. 97) is shown. The curves are 31 DWBA predictions. Level s (4. 97) is assigned t = 1. n (See page 30.) 222 1.6 -----.---,-----r---.,.---.,--~ s( 3 He,a) 31 S(4.97) E.- = 12.0 32 1. 4 -=>He 1.2 if) I- z :::> l'J/'" 1.0 >- I 0:: <( 0:: I- co I 0.8 . / I 0:: - 0.6 <( ~ '"0 ~ \ \\ -~~ 2 .t _, \ - 'b \ \ \ \ "0 0.4 - \ 0.2 o~----~----~----~----~----~------ o 10 20 40 50 60 223 Figure 24 Angular Distribution for 31 s (5. 15) The angular distribution of the alpha particles from 32 3 the reaction s( He, a) 31s (5. 15) is shown. The curve is a 31 DWBA prediction. Level s (5. 15) is assigned t = 0. n (See page 30. ) I. 6 ------,------,-----;-----r-----r-----, 32 1.4 E3 s( 3 He,a ) 31 s (5 .15) He = 12.0 I. 2 (j) 1- - z ::) 1.0 >a: <! 0:: 1- 0.8 0') 0:: <! c:; 0.6 -o .......... b ""0 0. 4 0.2 o~-----L--~~~----~----~--= o--~----~ 0 10 20 30 Bc M 40 50 60 225 Figure 25 Angular Distribution for 31 s (5. 30) The angular distribution of the alpha particles from 32 3 the reaction s( He, a) 31 s (5. 30) is shown. The lack of 31 structure suggests that level s (5. 30) is not populated by a pickup reaction, and no assignment is made. (See page 30. ) 226 1.6 I I I 32 I I 5( 3 He, oz) 31 5(5.30) 1.4 I - E3 He - =1 2. 0 .......-- 1.2 1- - (f) -:- c ::> 1.0 - - ~ ~- I 0 ).:: 0 .8 i - ·_o I ~ 0 ~0 . 6 u "-... b 0 .4 u :-- T I I I - I I - i- - 0 . 2 r- - 0 I I I I I 10 20 30 40 50 BcM 60 227 Figure 26 Angular Distribution for 31 s (5. 52) The angular distribution of the alpha particles from 32 3 the reaction s( He, a) 31 s (5. 52) is shown. The curves are 31 DVvBA predictions. No assignment is made for l evel s (5. 52). (See page 30. ) 228 1.6 ~---r----...----.,.---,---.,----, 32 1.4 I I. 2 3 S( He, a ) 31 S(5.52) E 3 He=l2.0 <f) 1- z => 1.0 >- cc <! cc 1- m n::: 0.8 <t ~ "'0 0.6 ........ b "0 0.4 0.2 10 20 40 50 60 229 Figure 27 Excitation Functions for 32 3 s( He, a.) 31 s The excitation functions measured at eLAB = 10° 32 3 31 for the reaction s( He, a.) s to the first six excited states 31 of s are shown. The arrows indicate the beam energies selected for the correlation and branching ratio measurements. (See page 37.) 230 I EXCITATION I I FU N CTIONS I FOR 2000 1- - (f) 1- z :::> 0 (..) 1 I I I 8 9 10 E3 II He (MeV) 12 13 231 Figure 28 Schematic Diagram of the Correlation Setup A schematic diagram of the setup used for the 32 3 measurement of the correlations in the reaction s( He, 31 ay) s is shown. The alpha particles were detected in the magnetic spectrometer at 0° with a silicon surface barrier detector. The beam was stopped in a tantalum cup. The gamma rays were detected in 12. 70 em (diameter) x 10. 16 em (length) Nai(Tl) crystal which could be moved from· 90° 0 to 150 . (See page 37.) " I _,• \ Tar<JCf Chamber Slits / -- ~ "'-135° lsoa Target / ~ \120° A Magnet Spectrometer ~7 Beam Catch er ~ ?:-.:> t ·.? 233 Figure 29 Electronics for the Correlation and Branching Ratio Measurements A diagram of the electronics for the correlation and branching ratio measurements is shown. The lower level discriminator gate is a modification of the RIDL 400- channel analyzer which reduces the dead time for high count rates. The two diodes prevented cross-talk between the two coincidence units (RIDL 32-3). (See page 38.) ~ SILICO N ·s . s. ~ ~/Jl.-~--,, I. fsTABIUZER I39RIDL o;o RIDL 4 AMP. 30-23 I I ~ VALOUR 443 81 IDELAYJ $I TE NNELEC I RIDL PREA MP. IOOA HiV·J40 - 98 V I PREAMP. ! ... RIDL... .:>0-2.:> DETECTOR ~RI RIDL 33-108 DL 33 - lOB {,) ~ I> DEL AY S, STRETCHERS, RIDL 32-3 CO IN. DELAY S , STRETCHERS, RIDL 32 - 3 CO IN. L_~Tv1 -vi '"'ll--...11 RE ALS 1 11 ROUTE TO FIRST 200 RANDOMS v LO WER LEVEL DISC. GATE 'iJ ROUTE TO SECOND 200 RIDL 400 - CHANNEL ANALYZER INPUT 235 Figure 30 Gamma-Ray Spectrum from the Decay of The gamma-ray spectrum at 8 31 S (1. 25) = 1200 from the decay of the level at 1. 25 MeV excitation ener~y in 31 s is shown. The gamma-ray S.C. A. was set so that pulses were stored only above channel 34. The randoms spectrum multiplied by the number of reals rat 10 number of randoms has already been subtracted. (See page 40.) o 236 1.25 MeV By= 120° 600 <f) I- s 400 0 u 200 0 LEVEL 237 Figure 31 Angular Correlation of 31 s (1. 25) The angular correlation of the photopeak of the 1. 25 MeV gamma rays detected in coincidence with the alpha 31 particles at 0° corresponding to s (1. 25) is shown. The number of counts has been normalized to the number of alpha particles detected. The err or bars represent the statistical unc ertainties. For one of the two solutions the mixing parameter i s X ::: -. 349 ± • 0 15, and the lines are for X == - . 349, -. 015 ::: 0. 364, -. 349, and -. 349 + • 015 ::: -. 334. The lines for the other solution which are not shown are very s imilar . (See pages 41 and 48. ) 233 Ey=l.25 -X= -.364 . /1- 4000 ~ :lx=-.334 . (f) 1- z :::> 0 0 X=-.34 -~,./ ~1~ 1/1 . I ,/?-~ . 1.25---.-- 3/2+ [7" r X ?7 0 _---~~.-_ I 12+ 3000 ~~~--~~--~~--~~--~~ 0 0.2 0.4 cos 0.6 2 e 0.8 1.0 239 Figure 32 Gamma-Ray Spectrum from the Decay of 31 s (2. 23) The gamma-ray spe ctrum at e = 135° from the decay 31 of the level at 2. 23 MeV excitation ener1y in s is shown. The gamma-rayS. C. A. was set so that pulses were stored only above cha1mel 27. The randoms spectrum multiplied by the . number of reals ratio b f d has already been subtracted. The num er o ran oms gamma-ray energy calibration was established with gamma- ray sources. (See page 41.) 6 00 r--- - - r -- -- r- - - - - , r - - - --.--- --,-----, 2.23 MeV LEVEL By = 135° 400 2.23 <f) 1- z 1.2 5 (._) 0 ::::> 0 200 2 .23 241 Figure 33 Angular Correlation of 31 s (2. 23) The angular correlation of the photo peak of the 2. 23 MeV gamma rays detected in coincidence with the 31 alpha particles at 0° corresponding to s (2. 23) is shown. The number of counts has been normalized to the number of alpha particles detected. statistical uncertainties. (See pages 42 and 49. ) The error bars repres ent the The fit shown is for X = • 053. 242 0 I 1'0 !{) 0 I . . C\.J +C\.J 1.{) .......... .......... X" H CD " 0 -xl ,_ l N <.0 • oct> 0 f() C\.J . . (\J (f) 0 ~ 0 0 1'0 . C\J C\.J C\J II 0 >-.... · w , ~,~ 0 0 0 1.{) 0 0 0 ¢ 0 0 0 0 0 0 r0 C\J S.lNno~ 0 0 0 0 243 Figure 34 Gamma-Ray Spectrum from the Decay of 31 S (3. 08) The sum of the gamma-ray spectra obtained at 0 0 0 = 90 , 120 , 135 , and 150 0 from the decay of the l evel 31 a{ 3. 08 MeV excitation energy in s is shown. The randoms t u· . d b Y th e rat·10 number number of reals , spec ra mu IP1w of randoms nave already been subtracted. The gamma-ray energy calibration 8 was established with gamma-ray sources. (See page 42.) 240 I 3.0 8 . MeV I I 3.08 L EVEL ] 200 !--1/2 + 3.08 160 - - '-- 1/2+ 0 (f) 1- 10 </ tI j_r 3 120 0 L) 0 80 - 0 0 0 c 0 - · 0 0 0 0 0 c I - \ 0 0 \ 40 - 0 0 10 I 20 30 CHANNEL NUMBER I 40 \ 0 'o 50 245 Figure 35 Angular Correlation of 31 s (3. 08) The angular correlation of the photopeak of the 3. 08 MeV gamma rays detected in coincidence with the alpha 31 particles at 0° corresponding to s (3. 08) is shown. The number of counts has been normalized to the number of alpha particle s detected. uncertainties. 49.) The error bars represent statistical The theoretical fit is shown. (See pages 42 and ~--~---------.---------~------~ 0 . ·- ro. 0 --- 0<..0 co . 0 N 0 (\J +(\J ............ ............ + r<) II >-... w <f) - 0. c;:j" 0 . (\J 0 0 LO f"() CD Jl o:> 0 0 . r<) 0 0 f"() Sj_NnOJ lo 0 LO (\J 0 0 (\J 0 L) 247 Figure 36 Gamma-Ray Spectrum from the Decay of The gamma-ray spectrum at 8 == 90 31 S (3. 29) 0 from the decay 31 of the level at 3. 29 MeV excitation ener~y in s is shown. T' d t It· . d b th t· number of reals ne ran oms spec rum mu 1p11e y e ra 10 number of randoms has already been subtracted. The gamma-ray energy calibration was established with gamma- ray sources. (See page 42. ) L) 10 :::> 20 0 ·z 1- _(f) 0 40 '-:) 'J 1- 0 o o 0 0 0 2.0 4 00 I I v 0 oo v o '-"'-"' ,; V •Vo V v CHANN EL NUM BER .!...l....__;;......._ _ _ ~~--....:..~....L...., ~ - . I) ':',.,..,--r::'- 180 ~G \o..:.J a v ' -... .....1 Jw V ___ _ . O T I 112+ •25JS 2 23 I ~ 12 -·~ -~,-- 3.29 -r~ 5/ 2+ _ I 0 ° 2 23 0 0 0 0 0 0 0 0 0 0 o • <? dJ (')_r. o ooooo r..._") {? o Oo .r)'-, G Cr G ur-) o J 0 c:-;CJY'-"' C'C:"--I' C".:'--q_,..,.._v.:)"~f'J v,0 "'--' 60 80 100 120 140 160 j-:Jo 0 0 0 0 0 1.25 ey =90° 3.29 MeV LEV EL I 1.06 oo0 ,o C\ o 30 ·- 40 ~~ t-V c-::> 249 Figure 37 Angular Correlation of 31 s (3. 29) The angular correlation of the photopeak of the 2. 04 MeV gamma rays detected in coincidence with the alpha 31 particles at 0° corresponding to s (3. 29) is shown. The number of counts has been normalized to the number of alpha particles detected. The error bars represent the statistical uncertainties. The fits shown are for J = 5/2, X = . 213, and J = 3/2, X = 1. 291. (See pages 43 and 50.) 250 0 0J 0J ........... ........... 1.{) r<> . . ro II J 0 (.0 OCD + ~ 0J 0 r0 ........... . C\.1 + <J) 0J ........... (\J ~ 0 II >-... X w . 0J (J) L() . 0J 0J . f() 0 0 0 0 0 0 ro 0 0 0 (.0 ~ 0J Sj_NnOJ 0 . 0 251 F i gure 38 Gamma-Ray Spectrum from the Decay of 31 S (3. 35) = 90°, The sum of the gamma- ray spectra obtained at 8 0 120°, 135 , and 150 y 0 from the decay of the level at 3. 35 MeV 31 excitation energy in s is shown. The randoms spectra m ulti. d b th . number of reals 1 d b b 1 p! 1e y e ratiO num b er o f ran doms J.ave a rea y een su tracted. The gamma- ray energy calibration was established with gamma- ray sources. (See page 43 . ) l.) 10 5 20 0 ~ 0 20 ~-· 0 1.2 5 60 ~ \ () 80 100 o 120 o\ \ fY 0 ;b f.)o I ~~ - o 2.10 o ooo Toe:> c! oo oo o 0¢ \ I :> 0 o o ool~o oo c:J g CH ANNEL NU MBER 40 J o -c 0 /o \ ooo o/ ~ 0 {\ 00 0 <.:)~, 0 o 1 oo\ J o o 0 1/2+ 7/2 + 0 (7/2, 3/ 2 ) l- I 3 . 3 5 f\.~ e V LEV EL I 1.2 5 3.35 I (f) 30 1- 40 i:'.:l !:-.:> Ul 253 Figure 39 Angular Correlation of 31 s (3. 35) The angular correlation of the photopeak of the 2. 10 MeV gamma rays detected in coincidence with the 31 alpha particle at 0° corresponding to s (3. 35) is shown. The number of counts has been normalized to the number of alpha particles detected. statistical uncertainties. The error bars represent the The fits shown are for J = 7/2, X = -. 467, and J = 3/2, X = -. 775. (See pages 43 and 52.) 254 0. +N N (\J .......... .......... r- f'() .......... 1'0 J + N .......... II J ro. 0 0 X . Q) tO l() 1.{) 1'0 1'0 N . 0 0 0 C\l (/) 0 0 (\J N II 0 >... w ~;--~0:-----0J__ __c:~~ ~----~ 0 "''" ('!") ~ S_LNnOJ 0 0 . u .cy- . 255 Figure 40 Gamma- Ray Spectrum from the Decay of 31 S (3 . 44) The sum of the gamma- ray spectra obtained at , = 90 0 , 1200 , 1350 , and 1500 from tne decay of the level 31 a~ 3. 44 MeV excitation energy in s is shown. The randoms 8 . . . number of reals spectra multiplied by the ratio num ber of rand oms have already been subtracted. The gamma- ray energy cal ibration was established with gamma- ray sources. (See page 44.) 0 • 20 40 • 20 • • A 2.23 + 2.19 ....--~ 0 1.25 2.23 3.44 I I 40 60 80 100 CHANNEL NUMBER • 3/2 ~ I I 3.44 I I 1I /. 120 1/2+ 3/2+ I I 1 5/2+ I .~,. .... .... . . . ··~ . . .. . . "..... ~...-..'.~. . . ' . I. ••.. • ) .\ .:~ ·}. ·\. . [1 .. . '1 • 80 ::::> 0<...) 60 2 (/) ~ • 100 3.44 MeV LEVEL 1.25 + 1.21 120 140 ~ CJ1 0) 257 Figure 41 Angular Correlation of 31 s (3. 44) The angular correlation of the photopeak of the 3. 44 MeV gamma rays detected in coincidence with the alpha 31 particl es at 0° corresponding to s (3. 44) is shown. The number of counts has been normalized to the number of alpha particles detected. uncertainties. The e rror bars represent the statistical The fits is for X = 0. 577. (See pages 41 and 53.) 2 58 I 2 4 0-F- 1 Ey =3.44 200 160 (}) 1- z ~ 0 u 120 80 3.44 - - , 3 / 2 X 40 0 0 ----'~'------ I I 2 + 0.2 0.4 cos 2 0 .6 e 0.8 1.0 259 Figure 42 Notation for the Calculation of Qk The notation for the calculation of the attenuation factors Qk is shown. (See page 45.) ""'\ ...~ '" 261 Figure 43 2 Q Versus Arctan X for Plots of the minimum of Q 2 31 S (1. 25) with respect to I(l/ 2) versus arctan X for various values of J for the transition 31 31 S (1. 25) -+ S (G. S. ) are shown. For these plots, a = 0 in Formula 4, Section III. B. The 0. 1 percent confidence limit is shown, and all points on the curves which lie below this limit are assumed to be possible solutions. Only J = 3/2 gives a fit. (See page 47.) 262 200 50 10 5 2 .5 .2 - 80 -60 - 40 - 20 0 20 ARCTAN X 40 60 80 263 Figure 44 Q 2 Versus Arctan X for 31 Plots of the minimum of Q 2 S (2. 23) with respect to ! (1/2) versus arctan X for various values of J for the transition 31 31 , S (2. 23) _, S (G. S.) are snown. For these plots, a = 0 in Formula 4, Section III. B. The 0. 1 percent confidence limit is shown, and all points on the curves which lie below this limit are assumed to be possible solutions. J = 5/2 gives a fit. (See page 48.) Only 1000 500 200 L-/-:..----~~t..__----~ =7 I 2 ----~~ 02 100 I 50 5 2.23--:-- J v 2 0 -80 ---'~"--- I 2+ I -60 -40 -20 0 20 ARCTAN X 40 60 80 265 Figure 45 2 31 Q Versus Arctan X for S (3. 08) 2 Plots of the minimum of Q with respect to I(l/2) versus arctan X for various values of J for the transition 31 31 ' S (3. 08 .... S (G. S.) are snown. For these plots, a = 0 in Formula 4, Section III. B. The 0. 1 percent confidence limit is shown, and all points on the curves which lie below this limit are assumed to be possible solutions. Both J = 1/ 2 and 3/2 gives fits, but only J == 1/2 is allowed because .t (See page 49.) n = 0. 23G 200~~--~----~--~----~--~----~--~----~~. I00 d -::.---:;::::~: : : : :;: ~==-.... 50 220 Q ~ ' IOt~._O_.I_o_~----~~~~ 5 2 - 80 -60 -40 - 20 0 20 ARCTAN X 40 60 80 267 Figure 46 2 Q Versus Arctan X for 31 S (3. 29) 2 Plots of the minimum of Q with respect to I(l/2) versus arctan X for various values of J for the transition 31S (3. 29) ... 31 S (1. . 25) are shown. For these plots, cr = 0 in Formula 4, Section III. B. The 0. 1 percent confidence limit is shown, and all points on the curves which lie below this limit are assumed to be possible solutions. and 3/2 give fits, but J = 5/2 is favored. Both J = 5/2 (See page 50.) 2se .5 J 3 . 29 v /\ .2 1.25 -80 -60 '~ 3/2+ -40 - 20 0 20 ARCTAN X 40 60 80 269 F igure 47 Q 2 Versus Arctan X for Plots of the minimum of Q 2 31 s (3. 35) with respect to I (l/ 2) versus arctan X for various values of J for the transition 31 31 " S (3. 3 5) -• S (1. 25) are shown. For these plots, cr = 0 in Formula 4, Section ill. B. The 0. 1 percent confidence limits are shown, and all points on the curves which lie below this lim.it are assumed to be possible solutions. In the order of preference, fit s were obtained for J = 7/2, 3/ 2, 9/2, and 5/2. There is only a 1 percent probability that J d = 9/2 is a fit and only a 0. 3 percent probability that J d = 5/2 is a fit. (See page 52.) 27U 50 5 ___ J=712---~ 2 3.35,-J .5 X 0 _ .2 -80 -60 -40 -20 0 20 A RCTAN X 40 __.!.__ 3/2 + 60 80 271 FigLtre 48 2 31 Q Versus Arctan X for S (3. 44) Plots of the minirrmm of Q 2 with respect to I(l/2) versus arctan X for various values of J for the transition 31 s (3. 44) _, 31s (G. s.) are shown. For these plots, 0:.:: 0 in Formula 4, Section IE. B. The 0. 1 percent confidence limit is shown, and all points on the curves which lie below this limit are assumed to be possible solutions. gives a fit. (See page 53. ) Only J :.:: 3/2 272 J 5001' I 200 [J=7/2 ==~ ~· ====~~==~~==========~==~ J = 5/2 100J = 1/2 50 - 5 J 3.44 X 2 .s I - 80 0 v 1/2+ l - 60 - 40 - 20 I 0 ARCTAN 20 X 40 60 80 273 Figure 49 Sche matic Diagram of Setup for Branching Ratio Measurements A schematic diagram of the setup used for the branching 31 ratio measurements in s is shown. The front face of the 10. 16 em x 10. 16 em Nai(Tl) crystal was 3. 556 em from the center of the beam spot. (See page 54. ) 2 74 P.M. No I (T/) ~ STEEL ~ALUMINUM H I em TANTALUM BEAM 7 / TO MAGNETIC SPECTROMETER 275 Figure 50 (a) Gamma- ray Decay Spectrum of the 2. 23 MeV Level in 31 s The gamma-ray decay spectrum taken with the aluminum c up (Figure 49) of the level at 2. 23 MeV excitation 31 energy in s is shown. The positions of the 0. 99 and 1. 25 MeV gamma rays which would be emitted in a cascade throu gh the 1. 2 5 MeV level are indicated by arrows. (b) 1. 25 MeV Gamma- ray Line Shape A line shape for a 1. 25 MeV gamma ray obtaine d by 31 observing the decay of s (1. 25) with the setup in Figure 49 is shown. (c) 2. 31 MeV Gamma-ray Line Shape A line shape for a 2. 31 MeV gamma ray obtained by 14 observing the decay of N (2. 31) after formation by the reaction 12 3 14 c( He, p) N is shown. Again the setup in Figure 49 was used. This line shape was used as an approximation to the line shape of a 2. 23 MeV gamma ray. (See page 54.) 276 I r I I 1 ... 0 ~ 800 - T. ~ ~.~ 00 0 .o,.o 400 - • 0 - ~· • - • • •• : •• • :)_c.,. ~10:0.. ~ ·~':.:Vo .~· ~· • Gr, •. • 8 y -- 90° ..··· .. 1.25 .98 I DECAY OF 2.23 MeV LEV EL .. 1200 ,_ I - ~· 1600 r - I I 2 . 23 0 •• - . o• 0 (~~.,o·,. . . ~..;?,.-~/,\-... ..,~! 1. ,.. ... ..... J.. w.. A, "<! .•.-~·-~ "' !-------l-----!~---+--:---+-~--+---t--~=:.J..:L;~-..~-~-~~,~---l I ! 1.25 MeV GAMMA RAY . 600 f - - 0 (f) I- z ::J 400 ,_ 0 0 - .. 0 0 • 200 - 0 - . "· ~---+-----:~---+--~ -~~~ [.~--~~ ·~----4!-----+-----~ f ---4----~ 1600- 0 •• • 2.31 MeV GAM MA RAY - 0 1200 • 800 . "t ..,..~g Q,· ---.f~ f- 0 - .• • ·~ 0 • - .,. o.. . <I~":'~f:'~ OQ.,.::.:J .... 0 ~ ()» ~·.....~"'"v~••o.• 400 }- ~ t 0 I I 0 40 .., I I ~...,.ci)-J""' ........- ..L,•..~-·---""'----~-::~ 60 80 CHANNEL NUMBER 100 120 277 Figure 51 Gamma-ray Decay Spectrum of the 3. 35 MeV Level in 31 s The gamma- ray decay spectrum taken with the aluminum cup (Figure 49) of the level at 3. 35 MeV excitation 31 energy in s is shown. (See page 60. ) 278 0 0 (\j 0 , 0 1 0::: ~ OJ w i 0~ 00::) z __j w oz wz -:- <! -1- I (\j (._) ' 0 i l() 0J N 0 • 0 C\.J 279 Figure 52 31 S . 31 Energy Level Diagrams for P and shown. . 31 31 The energy level diagrams for P and S are 31 The infor mation on P published since the compi- lation by Endt and van der Leun (1962) comes mainly from 30 31 30 31 studies of the reactions Si(p, y) P and si(d, n) P. All 31 of the information on s was determined in the present experiment except the .t - values for t he levels at 1. 25, 2. 23, n and 7. 04 (s ee Section TI. C. 6). (See page 61.) 23\., ?IL?.+i/2·'793 789 ' • . 7.77 ' - '·- . '", /')'• 1= • 2-D------- ---- ]j o ~_22_Q::7,16 ~7 , 15 J.2 --~'-:89 6,83-6.74= J\lL=b..b.9.=6..,">9=~ :14""".~~6-~.o..= (}35 6 2 7 l f>.OR4 6 .15 ~fi.77 5 .53 .2.__2 5 5.12 4.78 4.43 5.9a 5 _89 ..5.az===3oP+p ~§.68_ _ _ 5 .66 .ct. tJ-: - 5.: --;. 1 ,5 • r 11/2+) 5.0 1 3/2 4 .63 4.5~ 5/~~...J.I.Gl ::.n ::112+ 7/2 - 4.26 4.19 3L2+ 512+ ._2 .2 1'/:.!.~~----------'5~/_,.2~+1---- 5.15 '-· ~ 5 03 · 5. __ 52 30 Zl. 45 ~ 0___ i /2 "':_ 0 4.97 - 1 (5J2+Jfi)l ~7 1----=-::::--Ll-'-,,__,_. 7_.2=-- 4. 58 4.52 ___ 2 •( 3) 2 3 4 .2 1 4.08 512+) (2) 2. 2 3 5/2+ 2 281 Figure 53 Decay Schemes for 31 P and 31 S The gamma-ray decay schemes for the low- lying 31 31 P and s are shown. The decay schemes for levels in 31 P is taken from references cited in the text. The decay 31 scheme for s was measured in the present experiment. (See pages 56 and 61.) 31p 5/2+ 1'/2+ L l 16 0 ' 64 20 1-l I 3/2+ - 7J2"t 512+1/2+ 3/2+ j_ 77 23 I J _l 1.27 2 .23 3.51 --3.41 ;i,29 3 .1 3 0 1.25 2.23 3.08 v 3.4Ll ,),,);:) 3:29, 75 25 f- 3 1s l 46 ' '--v-' 54 I 1/ 2 + 3/2 + 5/2 l/2t .3L~ ( 7/2,3/ ~5/~'::'...:..=L ::."d c~ i.'V 283 Figure 54 Models for A = 31 The predictions of several models for A = 31 are compared with the experimental results. discussed in the text. (See page 63.) The models are ... " w )( > 0 2 ~ 6 NUCLEON I 3 NUCLEONS + I NUCLEON + VIBRATING CORE SHELL MOD EL I NUCLEON + 1/2 + 31s EXPERIMENTAL 112+ 3 12+ ,.......---v''' -3/2+ 1/2+ 312+ ----- 512+ (B ISHOP ETAL)(KAMAVATARAM) (CHI B OAVIDSON)(G L AUDEMANS (TH ANKAPPAN ) . ET AL) + ASYMMETRIC ROTAT ING CORE 112+ 312+ SYMMETRI C ROTAT ING CORE . 112 + 312+ _,.. ' 5/2+/ -- SYMMETR IC ROTAT ING CORE _ _. . :;11:. . ::2:. .,+-+/ 312+/ I I ' 3 /2 "1J 5/2 +..... I 3/2+ 512+ 112+ I 31p 112+ 3/2+/ I 5/2+ I I 7 s CO RE STATES (CRAWLEY) 32 o+ 2+ 3(-) co ..:;:.. N 285 Figure 55 . 16 Detector Array Spectra from the Reaction 32 3 S( He, d) 33 Cl (This figure is in the rear pocket. ) a) A deuteron spectrum obtained at e Lab = 10° from the bom3 bardment of natural sulfur with 12. 0 MeV He++ particle is Each point represents 150 ~C of incident charge. shown. The lower scale is the NMR magnetometer frequ e ncy for the magnetic spectrometer, and the upper scale is the corresponding deuteron energy. The levels are number ed as h1 Table XV. b) A deuteron spectrum obtained at e Lab = 20° from the bombardment of natural sulfur is shown. Each point above FREQUENCY = 33600 represents 150 ~C of incident charge, and the scale on the right is to be used. Each point below FREQUENCY= 33600 represents 300 ~C of incident charge , and the scale on the left is to be used. c) A deuteron spectrum obtained at eLab = 20° from the bombardment of sulfur enriched to 98. 1% 32s (natural sulfur contains 95 . O% 32 s) is shown. The scales are similar to those in b). d) A deuteron spectrum obtained at e Lab = 45° from the bombardment of natural sulfur is shown. Each point represents 300 ~C of incident charge. e) A deuteron spectrum obtained at eLab = 45° from the bombardment of sulfur enriched to 98. 1% 32s is shown. are similar to those in d). (See page 71.) The scales 286 Figure 56 Single Detector Spectra from the Reaction 32 33 3 s( He, d) cl Deuteron spectra obtained at eL . = 20° in (a) and at ao 8 _ b = 45° in (b) from the bombardment of natural sulfur with La 3 12. 0 MeV He ++ particles is shown. The lower scale is the NMR mag11etometer frequency for the magnetic spectrometer and the upper scale is the corresponding deuteron energy. The levels are numbered as in Table XV. The gaps in the spectra correspond to regions of severe elastic scattering from the gold foil. (See page 75.) <)' ,.-, '-• ·. . { 4 .5 6.0 (5)+(6) 5.0 DEUTERON ENERGY(MeV) (9) 800 (a) 600 400 200 (/) f-- z r J .. ...........~...../'\ .. 0 28000 29000 4.0 1/20 N(2.367) · 27000 :::::> 0 13 35 X ·· 30000 4.5 1200 5.0 (5)+(6) xl/ 10 (b) 13 (9) 26000 N (2.367) • 27000 FREQUENCY ( Kc /sec) 288 Figure 57 Angular Distribution for 33 c1 (G. S.) The angular distribution of the deuterons from the 32 3 reaction s( He, d) 33 cr (G. S.) is shown. This distribution was obtained as a by- product of the angular distribution of 32 3 the alpha particles from the reaction s( He , a.) 31 s (G. S.) shown in Figure 13. The curve is aDvV:SA prediction. Level 33 cr (G. S.) must have -t = 2 because for this level i 7 = 3/2+. p (See page 80. ) ') ("\(1 E..J V \J 1.6 ·~ . ------1------~----~-----~------~----~ I 32 1.4 1- 3 S( He,cl) E-. -=-He 33 Ci(G.S.) = 12 .0 1.2 l rJ) 1- 3 1.0 ~ I >cc < 0:::: l- 0.8 q 0.6 0 -o 'b '"'0 o.: ;:___ -----.!...-----!..---!----l. . .-----l .!.-1 0 10 2 0 50 6 0 290 Figure 58 Angular Distribution for 33 c1 (2. 35) T he angular distr ibution of the deuterons from the 33 32 3 reaction s( He, d) cr (2. 35) is shown. This dist ribution was obtained as a by- product of the angular distribut ion of 31 · partlC 1es rrom " t'·ne reac t-1011 32s( 3 -J - a 1pna he, a. ) s• "'h 1 e t 11e 33 curves are DVIBA predictions. Level c1 (2. 35) is assigned J_ · t p = (2). (See page 80.) . 32 s(3 He,d) 33 CI (2.3 5) E-, ,:)He =12 . 0 -t 1.2 I (./) 1- 3 I. 0 1!::-::=.:-::.~.=-· ·.. - >- - . _)~y - ........~~ _1 ........ '' 0::: <( 0::: 1- 0.8 co a: <r ~ '" .2_\ ) -{ =2 0.6 =3 '\ -o ........... <_I·= I b -o '\ " ·.. ·. 0 · X . ... ... .. . . . 0 .4 - () ' '' ·.. ·.. .. '' () 0.2 "-.... .. 0~----~'------~----~'------~----~----~ 0 10 20 3 0 BCM 40 50 60 292 Figure 59 Angular Distribution for 33 c1 (2. 69) The angular distribution of the deuterons from the 32 3 reaction s( He, d) 33 cr (2. 69) is shmvn. This distribution was obtained as a by- product of the angular distributions of 32 3 the alpha particle from the reaction s( He, cx) 31 s. The curves are DWBA predictions. The predictions for -t. p agrees best with the experimental distribution, but no assignment is made. (See page 81.) =3 1.6 1.4 (.[) 1.2 1- z ~ >- 1.0 f l i__ co 0.8 <! ~ '"0 0 .6 ........ b - 0 ...... <::[ 0::: 7 ·l- 0::: 0::: 1- E ,:) He = 12.0 ~I ' o ..., 0 ........ 0 ...... ...... 0 0 '' "' ' ' -{ = 2 r ' '\ I '"0 0 ! :3 ' ' '\. 0.4· - ........ - 0.2 !0 20 30 BcM 40 50 60 294 Figure 60 36 Gas Cell for the Reaction Ar(p, a) 33 cl The gas cell used in the magnetic spectrometer for 36 33 the study of the reaction Ar(p, a) cl is shown. Foil A was 0 0 5000 A thick, and foil C was 10000 A thick. were not used . (See page 82.) Foil B and D 205 !ZIZZ2ZZ2ZZz:;22::;2:::;:;2:::;:;Z::L7~ZZ7ZZ7ZZZ:ZZ4~ ~~~ : ~Z 7 Z Z ZZZ Z Z 7 7 77777! I I : _j w w f- I I U) W 0::: ~r >< 0::: W W I o_ <( ~:~ 0 0 I I (f) (f) I I I <[ I I I I I u 0 I 0 E f'.~ 0 LO 0 I 0 0 L0 0 0 r0 - _J- - . (\j LL _j 0 LL 296 Figure 61 . 36 33 16 Detector Array Spectra from the Reaction Ar(p, a.) Cl The alpha particle spectra o btained at eLab = 20° in 36 (a), 40° in (b), and 60° in (c) from the bombardment of Ar with 12. 0 MeV protons is shown. of incident charge. Each point presents 180 j...tC The lower scale is the NMR magnetometer frequency for the magnetic spectrometer and the upper scale is the corresponding alpha particle ene rgy. numbered as in Table XV. (See page 85.) The levels are (c) 150 200 0 0 50 19000 50 I 400L zf- 100 (f) (b) ::> (a) ' 600 1- 800 I • t 20000 A (3) 20000 5:o ' 36Ar(p, a)33C I ALPHA ENERGY (MeV) ' 6.0 n (I) el =2o· A (2) (2) 2 1000 5.0 • a..'ll:a.c •••••••• 5.0 22000 '(I) el =6o· 6.0 L- e -4o· 23000 A A 13N (g.s.l (I) 6.0 24000 \~...~~t'f~:~P~~1!~ \J 2 1000 22000 23000 24000 "' (2 ) .• .••••• •• ••• r ' 7.0 25000 ~X (0) 1/3 25000 !\ l II X 1/ 10 (0) (0) 7.0 !.'-' CD -~ 298 Figure 62 . 33 33 Energy Level Diagrams for S and Cl shown. . 33 33 The energy level diagrams for Sand Clare 33 The information on s was taken from the compi- lation of Endt and van der Leun (1962) as well as from more r ecent work by Becker et al.(l966), O'Dell et al.(l966), and 33 Moss (1967). (See Appendix G.) The information for c1 was taken from Endt and van der L eun (1962) and the present 33 work. The levels at 2. 686 and 2. 980 MeV in c1 were locate d in the present work. (See page 86. ) 299 4.425 4.377 4.2 12 _4.149 4.09 81/2 3/2) 4 . 052_3.939 3.834 3/2- 3.224 2.970 2.937 2.869 7/2:, ( 4) I ( 3) 3/2+ 1.965 512( +) 0.841 1/2+ 3/2+ 3/2- l 3 l 3 2 2 .313 4.119 3 .986 2.980 2.848 2.856 512+ 3 / 2- 2 .bt3b (3) 2.351 (2) 2 ( 2) 0 2 I 1.978 0.810 1/2+ 3/2+ 0 2 300 Figure 63 Models for A= 33 The predictions of several models for A= 33 are compared with the experimental results. discussed in the text. (See page 88. ) The models are K7T=3/2+ L I I I K7T=I/2+ NILSSON MODEL 312+ SHELL MODEL (GLAUDE MANS ET AU 312+ 1/2+ I 1 Ll I I - 712++ 3/2+ - 5/2+~ 312+ - 7/2 + 5/2+ - L.. I I I I 1/2+ 5/2+ I L 1-r I 3/2+ - 5/2 + - 7/2+ 1 I I I I I I II I. I I I I r I ~ SHELL MODEL (ERNE) 312 + 7/2- 3/2- 3.986- 33c' ~- - 3/2+ 1/2+ I I 2 0 (EXPERIMENTAL) .810 1.978 2.980 312- ~ 2.856" 512+: 2.848 (3) 2.686 2.351 (2) 4.119 lp c ........ ~ 302 Figure 64 Notation for the Calculation of ee ff ect 1ve · The notation used in the calculation of the effective laboratory angle of the magnetic spectrometer is shown. The square represents the entrance to spectrometer. page 102.) (See 303 304 .. Figure 65 Array Electronics A block diagram of the 16 detector array electronics is shown. Since all detectors have identical circuitry, only the circuitry for detector 1 is shown in detail. (See page 143.) 16 % cz: .. :;) "' BLOCK DIAGRAM OF PO$. PRE-AMP OUT J'' ATTEN . X I SUMMING AMP. I -J"I:--5 LOW LEVEL OU NEG. ROUTING TRIGGER PAIR .750 MeV THRESHOLD • 16 CHANNEL ARRAY FOR 61 em SPECTROMETER XIO LIN. AMP. AMP. OUT NEG. 16 BINARY ENCODER NO 160 PHA INPUT F AOC ..f1_ I LJ LGO U1 "' 0 .