Excitation Energies and Decay Properties of T= 3/2 States in ¹⁷O, ¹⁷F and ²¹Na

Citation

McDonald, Arthur Bruce (1970) Excitation Energies and Decay Properties of T= 3/2 States in ¹⁷O, ¹⁷F and ²¹Na. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/P0TR-DH36. https://resolver.caltech.edu/CaltechTHESIS:08112015-113730783

Abstract

The two lowest T = 3/2 levels in ²¹ Na have been studied in the ¹⁹ F( ³ He, n), ²⁰ Ne (p,p) and ²⁰ Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷ O and ¹⁷ F to the ground state and first two excited states of ¹⁶ O, by studying the ¹⁵ N( ³ He,n) ¹⁷ F*(p) ¹⁶ O and ¹⁸ O( ³ He, α) ¹⁷ O*(n) ¹⁶ O reactions.

The ¹⁹ F( ³ He,n) ²¹ Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½ ⁺ , Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰ Ne(p,p) and ²⁰ Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E _x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2 ⁺ , Γ ≤ 1.2 keV,
^Γ p _o = 0.1 ± 0.05 keV; E _x = 9.217 ± 0.007 MeV, J ^π = ½ ⁺ ,
Γ = 2.3 ± 0.5 keV, ^Γ p _o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷ F were measured by the ¹⁵ N( ³ He,n) ¹⁷ F*(p) ¹⁶ O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶ O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶ O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷ O, were measured by the ¹⁶ O( ³ He, α) ¹⁷ O*(n) ¹⁶ O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶ O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T _z .

Item Type:

Thesis (Dissertation (Ph.D.))

Subject Keywords:

(Physics)

Degree Grantor:

California Institute of Technology

Division:

Physics, Mathematics and Astronomy

Major Option:

Physics

Awards:

The Nobel Prize in Physics, 2015. Caltech Distinguished Alumni Award, 2018.

Thesis Availability:

Public (worldwide access)

Research Advisor(s):

Barnes, Charles A.

Group:

Nobel Prize, Caltech Distinguished Alumni Award

Thesis Committee:

Unknown, Unknown

Defense Date:

14 July 1969

Additional Information:

The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald "for the discovery of neutrino oscillations, which shows that neutrinos have mass."

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Funding Agency	Grant Number
National Research Council of Canada	UNSPECIFIED
Caltech	UNSPECIFIED

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CaltechTHESIS:08112015-113730783

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https://resolver.caltech.edu/CaltechTHESIS:08112015-113730783

DOI:

10.7907/P0TR-DH36

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https://www.nobelprize.org/prizes/physics/2015/summary/	Organization	Nobel Prize announcement (Physics, 2015)

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EXCITATION ENERGIES AND DECAY PROPERTIES OF T = 3/2 STATES IN 17 0, 17 F AND 21 Na Thesis by Arthur Bruce McDonald In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1970 (Submitted July 14, 1969) ii TO MY WIFE, JANET iii ACKNOWLEDGMENTS It has been a great pleasure to work in the Kellogg Radiation Laboratory and I wish to express my sincere gratitude to all those who create the stimulating and enjoyable atmosphere there. I particularly wish to thank Professor C. A. Barnes for his helpful guidance throughout this work. The majority of these experiments were performed in collaboration with Dr. E. G. Adelberger. I am very grateful to him for education in the laboratory, and for introducing me to his methods of enthusias tic experimentation. The 20 Ne(p,p) experiment was carried out in collaboration with Dr. J. R. Patterson and Dr. H. Winkler and the mass 17 branching ratio measurements with Dr. A. P. Shukla, Dr. D. Ashery and Mr. Hay Boon Mak. I am deeply indebted to them all for their extensive contributions to all phases of the experiments. I Financial assistance from the National Research Council of Canada and the California Institute of Technology is gratefully acknowledged. Finally, I wish to thank my wife for her help and encouragement at all times, and my young son, Bruce, for keeping me entertaine d dur i ng the long task of pr eparing this thesis . iv ABSTRACT The two lowest T = 3/2 levels in the 19 21 Na have been st udied in 3 20 20 . . F( He,n), Ne(p,p) and Ne(p,p') reactions, and their exci- tation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in 16 17 0 and 17 F to the ground state and first two excited s tates of 0, by studying the 15 17 16 18 3 3 N( He, n) F>'< (p) 0 and o( He, u ) 17 o'" (n) 16 0 reactions. . . 'd ent energies Th e 19F(3He,n )21N a reaction was stud.ie d at inci between 4.2 and 5.9 MeV u sing a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > 1/2) and 9 . 22 ± 0.015 MeV (Jn = 1/2+, r < 40 keV). The spins and parities were determined by a comparison o f the measured angular distributions with the results of DWBA calculations. These two levels were also observed as isospin-forbidden resonances in the 20 Ne(p,p) and 20 Ne(p,p') reactions. Excitation energies were measured and spins, parities, and wid th s were determined from a single level dispersion theory analysis. were obtained: The following results v E r 1 8.973 ± 0.007 MeV, J c = 5/2+ or 3/2+, r ::;_ 1.2 keV, x Po = 0.1 ± 0.05 keV; Ex r 2. 3 ± 0.5 keV, r po 9.217 ± 0.007 MeV, J Jl = 1/2+, 1. 1 ± 0 .3 keV. Isospin assignments were made on the basis of excitation energies, spins, parities and widths. Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in 15 17 F were measured by the * 3 17 16 . N( He,n) F (p) 0 reaction to be 0.088 ± 0.016 to the ground state of levels of 16 0 and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV 16 0. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in 17 0, were meas ured by the * 16 0( 3 He, a ) 17O (n) 16 O reaction to be 0.91 ± 0.15 to the ground state of 16 0 and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror d e cays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T • z vi TABLE OF CONTENTS Part I. INTRODUCTION II. T = 3/2 LEVELS IN 21 Na AS SEEN IN THE 19 3 F( He,n) REACTION 4 A. Introduction 4 B. Apparatus 7 1. 2. 3. 4. 7 9 10 C. D. E. III. 1 Beam Pulsing System Neutron Detection Electronics Target Chamber and Targets 11 Experimental Methods 12 1. 2. 15 Detector Efficiency Target Thickness 12 Results 15 1. 2. 3. 4. 15 16 Identification of T = 3/2 Levels Angular Distributions Level Widths Q-Values Conclusions T = 3/2 LEVELS IN REACTION 21 18 20 24 Na AS SEEN IN THE 20 Ne(p,p) 25 A. Introduction 25 B. Experiment 27 1. 2. 27 Apparatus Excitation Functions and Angular Distributions 29 C. Results 30 D. Analysis 31 E. Conclusions 39 vii Title IV. ISOSPIN-FORBIDDEN PARTICLE DECAYS OF THE 17 17 LOWEST T = 3/2 LEVELS OF 0 AND F 44 A. Introduction 44 B. Proton Decay of the Lowest T = 3/2 Level in 1. 2. 3. C. n. 17 F Apparatus Experimental Method Branching Ratios 46 46 50 54 Neutron Decay of the Lowest T = 3/2 Level 17 in 0 55 1. The 15N(3He,p)l70* (n)l60 Reaction 55 2. The 180(3He, a )l7o* (n) 160 Reaction 58 a. b. c. d. 58 61 Apparatus Experimental Details Line Shapes Branching Ratios Conclusions 64 66 69 REFERENCES 76 TABLES 80 FIGURES 88 I. INTRODUCTION This thesis describes an experimental investigation of the properties of some higher isospin levels in light nuclei, in an attempt to gain further information on the magnitude and nature of the charge dependence of nuclear forces. Nucleon-nucleon experiments have shown that nuclear forces are charge dependent to within ~ 5% of the strength of the interaction (see Henley 1966) and the synunetry observable in the energy levels of nuclei with the same mass number is also a strong indication of the approximate charge independence of nuclear forces. If charge dependent interactions are neglected, then all members of an isospin multiplet with total isospin T, and T of T,(T-1), ••• , - (T-1), - T, have equal masses. z values Deviations from this result are an indication of the magnitude of charge dependent interactions, which include, of course, the Coulomb interaction. As the form of the Coulomb interaction is well known, it might be hoped that a comparison of the measured masses of the members of an isospin multiplet with those predicted from calculations including only the Coulomb interaction would provide information about other char g edependent forces present, if any. If charge-dependent effects are treated in first order perturbation theory, and if they are only of a two-body character (as is the Coulomb force), then the masses of the members of a multiplet are given by the so-called quadratic mass equation 2 (Wigner 1958, Wienberg and Treiman 1959, Wilkinson 1964): M(T ) z = a + b Tz + c T z 2 T = 3/2 multiplets, with four members, are the lowest order multiplets where mass measurements of all members overdetermine the parameters of this equation and permit the T tested. z dependence to be Such tests have been recently made in a number of these quartets in the light nuclei (for a summary, see Cerny 1969a). With the exception of the more precisely measured A = 9 multiplet (Barnes et al • . 1967, Nettles et al. 1969), the masses satisfy this equation within experimental errors. For the A= 9 case, Janecke (1969a) has recently shown that the discrepancy can be explained by including the Coulomb interaction to second order, as suggested earlier by Barnes et al. (1967). As all charge dependent interactions of a two-body character will have a similar dependence on T , the identif ication of a z . specifically nuclear, charge-dependent, two-body force would depend on a comparison of the constants of the mass equation with those derived from the Coulomb perturbation alone. A number of studies of ..systematic mass variation·s have recently been reported (Hardy et al. 1969a, Jlmecke 1968, 1969), but· a precise calculation of Coulomb effects is difficult, as pointed out by Wilkinson (1966). Sections II and III of this thesis describe the use of 3 ( He,n) and (p,p) reactions to locate and accurately determine the mass of T = 3/2 levels in 21 Na(T z = +1/2). The lower lying T = 3/2 levels in the A = 4n + 1 nuclei are of particular interest as they 3 are bound to isospin-conserving particle decays and their widths and decay properties give an indication of the magnitude and extent of the isospin impurities in their wave functions. mind, the With this in 20 Ne(p,p) reaction was studied experimentally, with high resolution, and the data were analyzed using single level dispersion theory to determine total widths and partial decay widths for the two lowest T = 3/2 levels in 21 Na. Section IV describes a detailed examination of the isospinforbidden particle decays of the lowest T = 3/2 levels in 17 F. 17 0 and A comparison of the decay properties of these mirror levels can be a sensitive probe of the nature of the isospin impurities responsible for the decays. These impurities are proportional to the off-diagonal matrix elements of charge-dependent forces, which affect nuclear masses only in second-order. It is hoped that know- ledge of such impurities, coupled with precise measurements of the masses of the members of isospin multiplets, may eventually provide further information on the character of the charge dependence of nuclear forces. 4 II. T = 3/2 LEVELS IN 21 A. Na AB SEEN IN THE 19 3 F( He,n) REACTION Introduction At the time that this study was undertaken (McDonald and Adelberger 1968) very little was known about the excitation energies of the T = 3/2 levels of 21 Na. A state, believed to be the lowest T = 3/2 level, had been observed at an excitation energy of 8.90 ± 0.04 MeV as a delayed-proton-emitter following the ~+ decay of 2 ~g (McPherson and Hardy 1965; Hardy and Bell 1965). The ground state of the T z = -3/2 nucleus, 21 F, had been as- signed spin-parity 5/2+ from the log ft value for its ~ and Wien, 1963). Twenty-four levels of 21 decay (Kienle F had been observed in the 19 F(t,p) react ion and angular distributions had been obtained for most of these transitions (Horvat 1964). The most intense transition observed was to the first excited state at 0.277 MeV and its angular distribution was fitted well by plane wave Born approximation calculations assuming L = O. . 1/2+. parity This implies that the level has spin and The transition to the ground state was weaker and was fitted adequately with L = 2. Other observed transitions were also relatively weak with maximum differential cross sections a factor of 5 to 50 smaller than those for the first excited state. More recently, in a detailed study of the A = 21 isobaric quartet, Butler et al. (1968), studied the lowest T = 3/2 level in 21 Na with the 23Na(p,t) reaction and assigned an excitation energy of 8.92 ± 0.03 MeV. Levels at higher excitation energy were also 5 observed but not identified as to isospin. lowest three T = 3/2 levels of 21 Ne in the They also observed the 22 Ne(d,t) reaction and the ground state and first four excited states of 24 3 6 Mg( He, He) reaction. The T = 3/2 levels of 21 2 Ne have also been studied recently by Hensley (1968, 1969a) using the 19 \tg in the 22 3 Ne( He, a ) and 3 F( He,p) reactions. The approximate energies of the low-lying T = 3/2 levels of 21 Na may be predicted from the known excited states of its ground state mass. 21 F and If it is assumed that there are no appreciable Thomas-Ehrmann shifts, then the mass of the members of an isobaric multiplet are expected to be identical, except for energy differenc es due to the Coulomb interaction, and the neutron-hydrogen mass diffe rence. Thus, the masses of the members of an isobaric multiplet may be ex pressed (approximately) as: M(T ) z = Z M__ + (A-Z) Mn -B + Z(Z-l)KAl/ 3 -""H where B is the binding energy due to the nucle ar fo r ce , assumed to be constant within a given multiplet, and the Coulomb cons t an t K i ti ass umed to be the same for all levels of a given nucleus . constant K is evaluat~d from the 21 Ne- 21 If the Na gr ound· stat e mas s dif f er- ence, excita ti on ene r g ies of 8.80 and 9 .08 MeV ar e predic t ed for the lowes t two T = 3 /2 l evels i n 21 Na. 3 The ( He,n) reaction h as been obser v ed to pref erent ially populate low-ly ing T = 3/2 l evels in light nucle i (Die t rich 1964 and Adelber ger 1967), because the simple configurations of t hese l e ve ls are easily reached by one - s tep diproton stri pping . 6 The extreme single particle Nilsson model may be used to make some qualitative predictions about the configurations of the lowest T = 3/2 levels of protons outside an 16 21 Na. For the two neutrons and three 0 closed shell, we may assume that two neutrons and one proton are in Nilsson orbit 6 (n = 1/2+) and two protons are in Nilsson orbit 7 (n = 3/2+)o The lowest two T = 3/2 levels, with J n = 5/2+ and 1/2+, could then be members of a K = 1/2 rotational band based on this configuration (Bhatt 1962, Horvat 1964). ground state of 19 The F has been interpreted as a member of a K = 1/2 rotational band based on a configuration with two neutrons and one proton in Nilsson orbit 6 outside an 16 0 core (Paul 1957, Bhatt 1962)0 We would therefore expect to preferentially populate the lowest two T = 3/2 levels in 21 . 19 3 Na in the F( He,n) reaction because their configurations are easily reached by one-step diproton stripping, whereas the neighboring T = 1/2 levels at such a high excitation energy have complicated configurations which have a small overlap with the 19 F(Oo0) surrounded by two correlated protonso In analogy to 19 F(t,p) reaction, we would expect the angular distribution of the levels at 8.80 and 9.08 MeV to exhibit L = 2 and L = 0 double stripping patterns, respectively. T = 3/2 levels in 21 Na at energies above 12070 MeV are unbound to isospin-conserving particle decays to and may therefore have appreciable widths. other T = 3/2 levels in 21 20 Ne(l0.27, T = 1) + p, Although at least eight Na may be expected to lie below this threshold, they are all expected to be weakly populated in the 7 3 ( He,n) reaction since only two of these states have peak intensities as great as 1/5 of that of the first excited state in the 19 F(t,p) reaction. B. 1. Apparatus Beam Pulsing System The experiments were performed using the pulsed-beam-timeof-flight spectrometer associated with the ONR-CIT tandem accelerator to obtain time-of-flight spectra of the neutrons produced in the 3 ( He,n) reaction. The beam pulsing system and neutron spectrometer have been described in considerable detail elsewhere (Dietrich 1964, 1965, and Adelberger 1967); only a brief description will be given here, together with a discussion of some additional characteristics of the apparatus which were discovered during the process of this and other more recent experiments. Figure 1 is a block diagram of the system. The beam from the tandem accelerator is pulsed by sweeping it vertically across a pair of slits to produce bursts of approximately two nanoseconds duration at intervals of 280 nanoseconds . In order to increase the current in the pulses, the ions are velocity-modulated before entering the tandem so that they arrive at the chopping slits in bunches. If the amplitude and phase of the bunching voltage are properly adjusted, these bunches will arrive just as the beam is sweeping past the opening in the slits and the current in the transmitted beam pulse will be enhanced. As the phase of the bunches, relative to the 8 sweeping voltage, is very sensitive to fluctuations in the energy of the ions from the ion source, it is necessary to control this phase by means of a feedback system. This circuit (Adelberger 1967a) balances the beam collected on the upper and lower chopping slits. I A typical operating value for the beam-burst length is 2.5 ns for 10 MeV 3 He-I+ ions with a time-averaged beam current of 200 nano- amperes on target. In his discussion of limits on the time resolution of the system, Adelberger (1967) suggested that the restriction of time resolution to 1.8 ns for 3 -!+ He at 10 MeV was due to nonisochronous paths through the 90° analyzing magnet. To test this hypothesis, the time resolution was investigated using an 8 . 5 MeV 4 He-I+ beam which would have a predicted minimum beam burst duration of 2.2 nsec, assuming the max imum possible difference in path lengths through the magnet (1.75") as Adelberger had for the 3 He-I+ beam. The time resolu- tion was determined by observing the width of the peak produced by prompt gamma rays from a quartz target; this includes both the beam burst duration an d the e l ectronic c i r c u i t resolution, the latter of which has been determine d to be 1 nanosecond f ull width at half max imum (FWHM) by using coi ncident-gannna-ray sources (Adelbe r ger 1967) . For the usual r.f. voltage on the deflec ting plates (-5kV), wi th t h e chopping slits set at ± 0 . 150", the observed FWHM was 2 n sec. In- creasing the chopping voltage by a factor o f 2 reduced the FWHM to 1.6 ns. Reducing the chopping slit spacing to ± 0.030" f urther reduced the FWHM to 1.25 nsec . If we assume that the total . t i. me AtB)2)1/2 wh e r e 6 tE and 6 tB are t h e e 1 ectronic FWHM = ((6 tE ) 2 + (~ 9 resolution (1 nsec) and beam burst width respectively, one obtains 6tB = .75 nsec. This is not a very precise determination, due to uncertainties in 6tE' but certainly 6tB ~ 1 nsec. A time resolution of this order has also been observed with 7 MeV proton beams by similar reductions in chopping slits. Of course, such small slit spacings result in a reduction in the time-averaged beam current by a factor of 10 to 15 so that beam currents on target are less than 10 nanoamperes. However, it is clear that there is no lower limit on the beam pulse width of the system, at least down to ~ 1 nsec, other than that set by the practical requirement of sufficient beam current. 2. Neutron Detection Neutrons were detected by the observation of proton-recoil scintillations in a 2" thick by 5" diameter piece of "Pilot B" plastic scintillator, mounted on a 5" diameter phototube (XP1040). The detector is mounted inside a large neutron collimator and shield, ancl is surrounded by a lead cylinder 1.625" thick, to reduce background from gannna rays. The target is viewed by the scintillator through a 5" diameter cylindrical hole in a 22" diameter cylinder of lithium carbonate and paraffin. This "cannon" extends for 0.84 meters in front of the detector to serve as a neutron collimator, as well as surrounding the detector to reduce the background of scattered neutrons from directions other than that of the target . A 1/2" thick lead disc in front of the neutron detector 10 attenuates low energy gannna rays by a factor of about 8.5, while attenuating neutrons in the range 1-20 MeV by an approximately constant factor of 1.5 . The collimator and detector are mounted on a cart which moves on an I berun so that the detector can be reproducibly positioned at distances from 1 to 3.6 meters from the target, over the angular range from 0 0 0 to 150 • 3. Electronics In this experiment, neutron flight times were determined from the time interval between pulses from the neutron scintillation counter and a timing pulse produced by the r.f . deflection voltage, as discussed below. Figure 2 is a block diagrrun of the electronic apparatus. A negative, fast timing signal, derived from the anode of the XP1040 photomultiplier, is clipped by a 1.22 m long shorted cable, inverted by a pulse transformer and inspected by the START input discriminator of the ORTEC Model 437 time-to-runplitude converter (TAC)o The discriminator triggers at - 250 millivolts, near the zero-crossing point of the signal. The photomultiplier was operated at a voltage of +2250 volts which was chosen as a compromise between large signal output and low noise. The length of the clipping cable was selected empirically to give the best time resolution for a peak produced by prompt gamma rays having a large range of energies. An r .f . signal, derived from a two-turn loop mounted neur the berun-deflecting plates, was passed through a variable delay 1.1.nc, 11 amplified, and inspected by a fast discriminator whose output went to the STOP input of the TAC. The variable delay line was used to change the phase of the STOP pulses, relative to the time of arrival of beam pulses at the target, so that the region of interest of the time spectrum fell within the range of the TAC. A digital spectrum stabilizer monitored the position of the prompt gamma ray peak and continuously adjusted the zero level of the multi-channel analyzer to compensate for residual time drifts of the STOP pulses. A linear signal, derived from dynode 11 of the photomultiplier and referred to later as the slow channe~was inspected by a discriminator whose output gated the multichannel analyzer. This discriminator level was set to eliminate phototube noise and small scintillator pulses which would have poor time resolution" Its effect on neutron detection efficiency is described in Section II, C. 4. Target Chamber and Targets Targets were prepared by evaporating 100 to 300 µg/cm reagent grade CaF 2 onto 0.015" thick tantalum backings " neutron group from the 12 2 of Since a 3 C( He,n ) reaction occurred at a flight 0 time close to that of the lowest T = 3/2 level of 21 Na, the target was surrounded by a copper sleeve, cooled by a liquid nitrogen bath to reduce carbon buildup. Carbon targets were used for calibration runs; these were 30 ± 6µg/cm 2 thick natural car bon foils purchased from Yissum Re search Developme nt Company, J e rus alem, I srae l. 12 The target chamber consisted of a l" outside diameter glass "tee", centered over the pivot point of the I-beam which positioned the neutron detector cart. The targets were maintained at +300 volts potential, to reduce secondary electron emission, and the glass tube before the target was encircled by a wire suppression ring at -300 volts. The beam charge was collected and integrated by a BNI model 1000 current integrator, which was used to turn off the multichannel analyzer after a predetermined total charge. C. Experimental Methods 1. Detector Efficiency The measured neutron detection efficiency is displayed in Figure 3. The sharp reduction in efficiency at low energies is pro- duced by the slow channel discriminator described in Section II, B. This discriminator level was set at the midpoint of the high energy edge of the Compton electron spectrum produced by y rays from a source, with an 18 db attenuator insert~d 137 cs at the input to the slow I channel amplifier. After setting the discriminator level, the attenuator was removed; the resultant discriminator level corresponded approximately to an energy of 60 keV for electron-induced scintillator pulses and 450 keV for proton recoils produced by incident neutrons. For neutron energies between 1.95 and 10.75 MeV the detection 3 efficiency was measured using the d(d,n) He reaction at 7.6 MeV incident energy. The gas target cell described by Adelberger (1967) was used so that the number density of target nuclei could be 13 determined with precision. The absolute d + d neutron cross sections were interpolated from the table of Brolley and Fowler (1960). At energies below 2.6 MeV, the relative detection efficiency was determined by using the ZrT target. 3 t(p,n) He reaction at 3.6 MeV, with a Relative cross sections were taken from Goldberg et al. (1961), and the relative efficiency was matched onto the absolute efficiencies determined from the d(d,n) reaction in the region where the neutron energies overlapped. All neutron peaks were observed to have a "tail" on the low neutron energy side, as shown in Figure 4, a neutron peak from the 13 c(a,n ) reaction. 0 This tail is presumed to be caused by neutrons scattered from the inside walls of the neutron collimator and from (n,n'y) reactions in the collimator and shield. It is observed to be dependent on neutron energy and flight path. The size of this tail relative to the ma.in peak was studied by observing a 6.8 MeV neutron peak, from the 13 c(a,n0 ) reaction, at various detector distances. The main peak was approximated by a synnnetric triangle defined by the peak height and the slope of the high energy side, as shown in Figure 4. the "tail". as r- 2 The remaining counts were assumed to make up The main peak defined in this manner was found to vary (r =detector-target distance), as expected for the detector solid angle. The tail, however, was found to vary approximately as 5 r- 3 • , so that the ratio of tail to main peak was not constant. At a distance of 2 meters, where the detector efficiency measurements were made, the tail was 15 percent as large as the main 14 peak, and at the closest distance employed, 1.1 meters, it was 25 percent. Since it is difficult to separate the tail from the main peak in more complicated spectra with varying background levels, the detector efficiency was calculated with the tail included, and all peaks for which the absolute intensity was needed were integrated in a similar manner. For distances greater than 1.5 meters, the error due to the fact that the tail does not satisfy the inverse square law is less than 10 percent. For measurements at shorter distances than this, the neutron angular distribution may be significant in determining line shapes so that more care should be exercised in determining effective detector efficiency for individual cases. The solid curve shown in Figure 3 has been computed from an expression, quoted by Dietrich (1964), in which multiple scattering, scattering from carbon in the scintillator, and scattering and absorption in the collimator and shield are neglected. discriminator cutoff at 450 keV lation. A slow channel proton energy was used in the calcu- The measured efficiency does not fall as steeply with energy as the computed curve; so for interpolation above 1 MeV, the efficiency has been approximated by the two dashed straight lines . In all data presented, the detection efficiency has been taken from the dashed lines, with an assumed relative error of ± 5 percent. An overall error of ± 10 percent has been assumed for the absolute efficiency. 15 2. Target Thickness The energy loss of 3 He particles in the CaF targets at 2 the energies of interest, was determined from a comparison of the energies of 3 0 He particles, elastically scattered at 90 ; from the target backing and from a clean piece of tantaluin. The 24" radius magnetic spectrometer and 16 counter array were used to examine the spectrum of elastically scattered a typical run. 3 He; Figure 5 shows the results of Part (a) shows a plot of the number of 3 He particles detected versus NMR frequency, for a clean piece of tantalum inclined at a 45° angle to the beam. 3 Part (b) shows a similar plot where the He particles have to traverse the CaF 2 coating on a tantalum backing . The reduction in the maximum energy of the scattered particles, due to the energy loss in the CaF 2 layer; may be determined with sufficient precision, even though the slope of the high energy edges are different due to energy loss straggling in the CaF 2 layer, by taking the differ- ence in the energies of the midpoints of the edges as a measure of the total energy loss in the CaF 2 D. 1. The layer. Results Indentification of T = 3/2 Levels 19 3 21 . 3 F( He,n) Na reaction was studied for various He incident energies between 4.2 and 5.9 MeV, covering excitations in 21 Na up to 11 MeV. A neutron time of flight spectrum at an incident energy of 5.855 MeV and an angle of 0° is displayed in Figure 6. A l6 number of neutron groups may be seen above a large continuum due to reactions with multibody final states. In the region around 9 MeV excitation, where the low-lying T = 3/2 states are expected, three levels were observed: an intense forward-peaked group at a 21 Na excitation energy of 9 .22 MeV, a weaker group at 8 .41 MeV, and a group at 8.99 MeV which is partially obscured by neutrons f rom the 12 3 c( He,n ) reaction. 0 Since the 8.99 and 9.22 MeV levels have angular distributions and energy spacings similar to those observed in the 19 F(t,p) reaction (Horvat 1964), we tentatively identify them as the lowest two T = 3/2 levels in 21 Na and proceed to investigate their properties further, to substantiate this hypothesis. For this purpose angular distributions were taken, and Q-values were measured at all angles to verify that the levels were produced by a target of mass 19. As these levels are bound with respect to isospin-conserving decays, they are expected to be narrower than the experimental resolution; hence only an upper limit for their width could be determined from the data. A number of other weakly populated levels were observed in the excitation energy region between 9.2 and 11 MeV but none of them could be clearly discerned to be analogues of levels in 21 F. 2. Angular Distributions An angular distribution of neutrons corresponding to the 9.22 MeV state is pre&ented in Figure 7, for E 3 He = 5.86 MeV. In 17 addition to the errors shown in the figure there is an overall uncertainty of ± 20 percent in the absolute normalization due to uncertainties in target thickness, detector efficiency and charge integration. The density of target nuclei was determined from the energy loss measurements described in Section II,C and the dE/dx tables of Demirlioglu and Whaling (1962) • It was not possible to obtain a reliable angular distribution for the 8 . 99 MeV level due to the presence of carbon contamination, which built up slowly during the accumulation of the experimental data in spite of the presence of the cold sleeve . However, the angular distribution of neutrons from the combination of the 8.99 MeV state and the 14o{O.O) level was not forward peaked. The 12 3 14 . C( He,n) 0(0.0) reaction was examined at the same incident energy and found to be strongly forward peaked; it may be concluded therefore that the angular distribution for the 8.99 MeV level is peaked away from 0°. Figure 8 shows the neutron time of flight spectrum obtained at an incident energy of 5.855 MeV and a laboratory angle of 60°. Both the 8.99 and 9.22 MeV levels are clearly visible, and from the 12 c( 3 He,n 0 ) angular distribution and the peak observed at o0 , it can be calculated that the 8 . 99 MeV peak could not contain more than 20 percent contribution from the carbon contaminant, at this angle . Direct reaction distorted wave Born approximation (DWBA) calculations were performed using the computer code Julie written by Bassel, Drisko and Satchler (1962). The assumptions made in using this code for two particle transfer reactions have been dealt with in detail by Adelberger (1967). The essential feature is that the 18 two protons in the transferred diproton are assumed to be in a relative ls state with total spin S = 0 and total isospin T = 1. The calculations may then be performed in the same way as for single particle stripping, using the zero range approximation, and assuming that the diproton is transferred as a single particle. The optical model potentials used in the calculations are listed in Table 1. of 3 The 3 He potentials were obtained from an analysis He elastic scattering on 19 F by Matous et al. (1966). The neutron potentials are those used for protons in an analysis of the (t,p) reaction on a series of light nuclei (Glover and Jones 1966) (without the Coulomb potential, of course) and were also used in analysis of 3 ( He,n) reactions to other T = 3/2 and T = 2 levels in light nuclei (Adelberger et al. 1969). , The solid curve in Figure 7 is the result of the calculation for transferred angular moment\llll L = O; the curve is easily distinguished from the L = 1 case, shown as the dashed curve. This establishes the spin and parity of the 9.22 MeV level as 1/2+. Since the neutron group leading to the 8.99 MeV state is not forward-peaked, we conclude that L > 0 for the transition to the state. This is consistent with the L = 2 double stripping expected from our identification of this state as the lowest T = 3/2 level, with spin-parity 5/2+. 3. Level Widths Time-of-flight spectroscopy is not a very sensitive method for the determination of the width of narrow levels, but it is possible to do so if a n\llllber of simplifying approximations are made for 19 various contributions to the experimental resolution. 1. It may be assumed that the shape of the prompt gannna ray peak is a good representation of the beam burst s hape and electronic resolution for neutrons. The electronic resolution was measured to be 1.4 ns FWHM for 60 to 120 keV gamma rays, which produce a scintillation light output similar to that for 1 MeV neutrons , and 1 ns FWHM for 511 keV gannna rays. Since these are both small compared to the typical beam burst width o f 2.5 ns, this difference is not significant. 2. The time broadening function due to detection of neutrons at different points through the scintillator may be approximated by a rectangle of width equal to the flight time of neutrons through the 2" scintillator thickness. 3. The resolution function due to finite target thickness may be approximated by a rectangle of width equal to the difference in flight times of neutrons for the level in question produced by the maximum and minimum incident energies. A computer program was written which folded together the s e three contributions with a theoretical level shape obtained by converting a Breit-Wigner shape into the corresponding function with flight time as the independent variable. The resultant shape was then compared with the observed peak and x2 was calculated for various assumed values of the total width r. This calculation ignores the presence of "tails" on the neutron peaks due to scattering in the neutron collimator. For this reason, another set of calculations was performed folding together 20 the neutron line shape from the 12 3 C( He,n ) reaction on a thin 0 carbon target, the target thickness rectangle and the Breit-Wigner s hape. The derived upper limits on l' were similar for both methods. The total width of the 9.22 MeV level was determined to be less than 40 keV. It was not possible to make such a determination for the 8.99 MeV level, due to the presence of the unresolved contaminant group from the 12 3 c( He,n ) reaction. 0 4. Accurate measurement Q-Values of Q-values is dependent largely on the calibration of the time scale of the time-of-flight spectrum. For approximate measurements, the time scale could be determined from the shift in peak position caused by the insertion of a delay cable whose length was known to be 149.7 ± 0.3 nanoseconds from previous calibrations with reactions having known Q-values. However, better precision is obtained when a direct comparison can be made between the neutron peak in question and a neutron peak with the same flight time from another reaction with an accurately known Q-value . The spectrometer is then used only as a device for comparing flight times, and errors due to uncertainties in the detector distance and angle, nonlinearities in the time scale and uncertainties in time calibration are either greatly reduced or totally eliminated. The remaining uncertainty arises from the calibration of the incident beam energy, target thickness, and the precision with which a peak can be located in the time spectrum. 21 The 12 3 14 . C( He,n) 0(0.0) reaction was used as a calibration for the determination of the Q-values of the 8.99 and 9 . 22 MeV levels. The incident energy had to be changed by less than 10 per- cent in each case to produce neutrons of the same energy leading to o(O.O) and to the 21 Na state. 14 A computer program developed originally by Dietrich (1964) and extended b y Adelberger (1967) data. was used for the analysis of the At the beginning of each running day the linearity of the TAC plus multichannel analyzer was determined by accumulating a time spectrum with START signals produced by a radioactive source near the detector and STOP signals from the 3.531 MHZ o s cillator. As the source events occur randomly in time, this spectrum should be completely flat if the channels correspond to equal time intervals; the deviations from linearity are used by the computer to correct the time scale . The zero of the time scale is determined from the we lldefined position of the peak produced by prompt g amma rays from the target which may be seen near channel 190 in Fig ures 6 and 8. The computer program uses the calibration information to determine th e neutron energy for each channe l, and also calculates the equivalent excitation energy in the residual nucleus . A recent useful addition to the program produces a point plot of the data similar to Fig ures 6 and 8, complete with excitation energy scale to fac i litate peak identification. The program also calculate s the errors in Q-value resulting from the uncertainties in incident e n e rgy, counte r d is tanc e and angle, and pea k location f or both the re ac tion under s tudy and the calibration reaction. 22 The statistical uncertainty in the incident beam energy was taken to be one-third of the theoretical maximum allowed by the 0 finite slit spacings of the 90 beam analyzing magnet (Pearson 1963), OE -= E where s 1 and s 2 are the full widths of the object and image apertures and R (= 34") is the radius of the analyzing magnet . For sl = s2 = 0.10011 we obtain The main contribution to the error in the Q-value determinatiori for the 9.22 MeV level results from the uncertainty in the shape of the background underlying the T = 3/2 peak. For this reason, it was necessary to work at incident energies about 3 MeV above the threshold for production of the level in order to enhance its population cross section relative to the background . As the accuracy of the time-of-flight spectrometer is reduced when the neutron energy increases, it was necessary to accept larger errors in Q than have been previously achieved with this apparatus (Adelberger et al. 1969) . Three separate measurements were made of the Q-value leading to the 9.22 MeV state, with a standard deviation of only 6.7 keV o However, the systematic error arising from uncertaintie s in the shape of the background under the peak can contribute a maximum error of ± 13 keV. We therefore adopt a Q-value of -1.662 ± 0.015 Me V, which corresponds to an excitation energy of 9.221 ± 0 . 015 MeV for the 23 second T = 3/2 state of 21 Na. The 21 Na ground state mass was taken from a recent measurement by Bloch et al. (1967). The presence of the contaminant peak from the 12 3 C( He,n ) 0 reaction produced a large uncertainty in the location of the centroid of the 8.99 MeV peak. The best value which could be obtained was 8.99 ± 0.05 keV for the excitation energy of the lowest T = 3/2 level . 21N a. in To establish that the 9.221 MeV level was in fact produced by reactions on a mass 19 target, Q-values were computed from the series of runs maki ng up the angular distribution, assuming various target masses from 12 to 28. 2 The X value for a fit to a constant Q-value is shown as a function of target mass in Figure 9 and it may be seen that the best fit is obtained for a mass 19 target . This demonstrates that the 9.221 MeV level belongs to the nucleus 21 Na. It was not possible to determine the target mass for the group leading to the 8.99-MeV state since it could not be obs erved over a sufficiently wide range of angles. However, it could not . . h ave more t h ese r eactions h ave b een pro d uce .d f rom 16 0 or 40c a since negative Q-values. It is unlike ly that the group is produced by a target with Z much greater than 10, in any c a se, be caus e the Coulomb barrie r would strongly inhibit the reaction . Since the n eutron group cannot be ascribed to any like ly contaminants i n the t ar get, and appears with equal intensities in spectra taken with several dif f erent CaF 2 targets, we conclude that it also is produc ed by an and corres ponds to a l ev e l in 21 Na . 19 F target 24 E. Conclusions The lowest two T = 3/2 levels of 21 Na have been identified at excitation energies of 8.99 ± 0 . 05 MeV and 9.221 ± 0.015 MeV. The identifi cations are based on a comparison of intensities , angular distributions, and separation energies with the levels of served in the 19 F(t,p) reaction. assumed to be the analog of the 21 F ob- The 8.99 MeV level has L > 0 and is 21 F ground state. The 9.221 MeV level is populated by an L = 0 transition implying J J( = 1/2+ and has a width less than 40 keV. The information which has been obtained for these levels is not as accurate as has been obtained in the past for similar lowlying T = 3/2 levels in light nuclei . The 50 keV error in the exci- tation energy of the lowest T = 3/2 level does not allow a very sensitive test of the quadratic mass law. As a result, another experiment was undertaken to look for these same levels in 21 Na as isospin-forbidden resonances in the 20 Ne(p,p) reaction, an experiment which should produc e more accurate numbers for excitation energies and total widths, and which could provide further information regarding the partial decay widths for the levels. 25 III. T = 3/2 LEVELS IN 21 A. Na AS SEEN IN THE 20 Ne(p,p) REACTION Introduction The lowest T = 3/2 levels in 21 Na are bound with respect to isospin-conserving particle decays, as may be seen in Figure 10, which is an isobar diagram for mass 21. These levels can only decay by y emission, or by p and a emission as a result of isospin impurities in the T = 3/2 states or in the energetically-allowed final states of 20 17 Ne or F. For this reason, the T = 3/2 states are expected to be narrower than neighboring T = 1/2 levels, and should be observable as compound nuclear resonances in the elastic and in20 Ne provided that I' /r is not po negligible, and r is not too much smaller than the experimentally elastic scattering of protons from achievable energy resolution. This method of studying these levels is capable of higher precision in the determination of excitation energies and widths than the 19 3 F( He,n) reaction. The method, however, can be tedious and unfruitful if the positions of the T = 3/2 levels have not been previously determined with sufficient accuracy to restrict the region of excitation energy which must be surveyed in small energy steps, and with high resolution. A number of T = 3/2 and T = 2 levels in light nuclei have already been observed as resonances in isospin forbidden reactions. For example, T = 3/2 levels in 13 N have been observed by Tennner and 26 and Van Bree (1966) and Levine and Parker (1967) in the reactions 12 C(p,p) and (p,p') and by Dietrich et al. (1968), in the 12 C(p,y) 13 . 13 N reaction; T = 3/2 levels in C have been observed by Miller and Kavanagh (1966) and Snover et al. (1968), in the 9 13 17 Be(a ,y) C reaction; T = 3/2 levels in F have been studied by Hardie et al. (1963), Patterson et al. (1967), and Tenuner et al . (1967), in the 16 o(p,p) and (p,p') reactions; a T = 2 level in has been seen in the reaction 19 F(p,p) by Bloch et al. (1967a), and by Kuan et al. (1967), who also observed it in the a T = 2 level in 20 Ne 19 F(p,y) reaction; 24 Mg has been studied by Reiss et al. ( 196 7), in the reactions 23 Na(p,y) 24Mg* and 23 Na(p,p ). 0 The observed widths for these levels are all les s than 8 keV, and are generally of the order of 2 keV, although the lowest T = 3/2 level of 1.2 keV. 17 F has been shown to have a total width less than Isospin assignments for these resonances were made on the basis of their narrow widths and from correspondences with the excitation energies and spins and parities of their analogue levels as measured in isospin allowed reactions. This section reports a search for resonances corresponding to the lowest T = 3/2 levels in 21 Na, in the 20 Ne(p,p) and (p,p') reactions, over an excitation energy range f rom 8 . 87 to 9.42 MeV in 21Na. This range includes the regions where T = 3/2 leve l s were observed in the 19 3 F( He,n) reaction as reporte d in Section II. As these scattering anomalies are expected to be very narrow, a differentially-pumped gas target of natural neon was used, so that the energy resolution would be limited only by the berun 27 energy spread. Two cross section anomalies were observed which were much narrower than others nearby and occurred near the expected positions of the T = 3/2 states. Section III, D. describes the analysis of the data which indicates that the spins and the parities of these states are consistent with those expected for the T = 3/2 levels. These anomalies are theref.o re assumed to correspond to the two lowest T = 3/2 levels in 21 Na and their excitation energies were determined to be 8.973 ± 0.007 MeV and 9 .217 ± 0.007 MeV. B. Experiment 1• Apparatus The differentially-pumped gas target system is shown in Figure 11. It was designed and originally used for the observation . 17F in . t h e 160( p,p ) and ( p,p I) reactions . by o f T = 3/2 1 eve 1 s in Patterson, Winkler and Zaidins (1967). The target was mounted inside a 60 cm.-diameter scattering chamber and aligned optically with the beam axis. Three silicon particle-detectors, one fixed at 90° and the others movable from 35° 2 to 162°, viewed the gas through 0.5 mg/cm thick mylar foil windows. The solid angles of the detectors were defined by two sets of rec0 tangular slits which allowed an average angular spread of ± 4 • At all angles investigated, the counters viewed only the target gas and the mylar foil windows on both sides of the target so that scattering from the walls of the target cell was reduced. The beam left the target 28 2 cell through a 2 mg/cm Havar foil at the end of a 10 cm long extension tube and was collected in a Faraday cup. The entrance canals were 3.5 and 3.2 mm in diameter and the second canal was threaded to minimize scattering. With natural neon target gas, a pressure of 3 Torr was maintained for a gas flow rate of about 3 liters (STP) per hour. The pressure in the section of the vacuum system immediately above the 1200 liter/sec diffusion ptnnp was about 6 X 10 -4 Torr. The maximum target thickness, which occurred at the 162° counter position, was 700 eV, and the Doppler effect at 30°c contributes an FWHM~ additional energy spread of 300 eV The energy loss before entering the observable region of the gas target was estimated to be less than 500 keV. Slit openings of 1.2 mm were used at the object and image of the 90° analyzing magnet with resultant beam energy spreads as low as 2 keV FWHM. The corona stabilizer gain was set to minimize the voltage fluctuations of the accelerator terminal, as displayed by the calibrated signal from a capacitive pick-up plate. To obtain better energy resolution for the observation of the scattering anomaly corresponding to the lowest T = 3/2 level, whose observed width was 2.1 keV, a variable compensation voltage was applied to the insulated target chamber. An energy error signal was take n from the image s lits of the 90° analyzing magnet and used to control a ± 2 keV variable power supply connected to the target chamber . The gain of this compensation system was adjusted to correspond to the voltage fluctuations of the accelerator terminal as observed by the pick-up plate. With this energy-compensation system the observed width of the lowest 29 T = 3/2 level was reduced to 1.5 keV. Energy spectra from the three detectors were routed to three quadrants of an RIDL 400 channel analyzer. A computer pro- gram was used to sum the counts in the regions of interest of the spectra and to plot them as a function of incident energy. 2. Excitation Functions and Angular Distributions The energy range from 6.76 to 7.33 MeV (lab) was surveyed in steps of 2 keV with detectors at 90°, 142° and 162° (lab). The scattering yields were recorded simultaneously at the three angles, in order to improve the chance of detecting a narrow resonance. Subsequently, the energy range was surveyed with detectors at 90°, 0 54 , and 107 0 (lab), using 2 keV steps in the region of the observed narrow resonances and 5 keV steps in the intervening regions. Final- ly, the two T = 3/2 resonances were examined at a total of 8 angles with energy steps of 1 keV. Figure 12 shows a typical pulse height spectrum obtained at 35° (lab). Clearly resolved groups corresponding to the ground and ex cited states of 20 Ne up to E = 4.97 MeV are seen, i n addit i on to x several groups resulting from the 10 percent natural abundance of 22Ne. The rise in the spectra at low energies is due to neutron and ganuna-ray background. produced by 22 Except at 162°, the elastic scattering peak Ne could not be s epara ted fr om that due to 20 Ne; all excitation functions of the elastically scattered protons thus inelude a small contribution f rom 22 Ne. However, all the anomalies 30 reported in this work were present in both the elastic and inelastic scattering, which confirms that they are produced by reactions on 20Ne. Angular distributions were also measured at four energies near the narrow resonances (6.862, 6.882, 7.109, and 7.145 MeV), in 10 0 steps from 40 0 0 to 150 (lab). The absolute cross section was determined by comparison with the elastic scattering from xenon gas introduced into the target chamber. At the proton energy used, the scattering of protons by xenon follows the Rutherford scattering law to at least 70°. The absolute error, which depends on the statistical accuracy of the number of counts recorded, and on the comparison of target pressures and charge integrations, is less than 20 percent. C. Results The elastic scattering yields at five angles, covering a range of excitation energies in 21 Na from 8.87 to 9.42 MeV, are presented in Figures 13 to 17. Only two of the anomalies observed in this range have widths less than 13 keV and they occur near the expected positions of the T = 3/2 levels as observed in the 19F( 3 He,n) reaction, which are indicated by horizontal bars in the figures. These two anomalies occur at incident proton energies of 6 . 872 ± 0.005 and 7.128 ± 0.005 MeV and have observed widths of 2.1 and 3.8 keV respectively. energies in 21 These incident energies correspond to excitation Na of 8.973 ± 0.007 and 9.217 ± 0.007 MeV when combined with the recent value of 2.432 ± 0.005 MeV for the proton binding energy in 21 Na due to Bloch et al. (1967). 31 These anomalies are most easily observable in the elastic 0 scattering at 163 , where the non-resonant' background is a minimum, and do not show up as strongly in the yields of protons to the 1.63 (p ), 4.25 (p ) and 4.97 (p ) MeV levels of 2 3 1 seen in Figures 18, 19 and 20. in the p 1 and p 3 1 channel. The 8.97-MeV level shows small effects channels, whereas the 9.22-MeV level does not appear to resonate in the p p 20 Ne, as may be 2 or p 3 channels although it does show up in the The proton yields in the pl and p 2 c hannels at 163° are presented in Figure 21 for the entire energy range. A total of six levels with widths greater than 13 keV were observed in the elastic or inelastic yields in the energy range covered. These are all assumed to be T = 1/2 levels and their exci- tation energies are presented in Table 2, together with their observed widths, determined from the data for the reaction channel and angle which best exhibited a Breit-Wigner resonance shape. D. Analysis In order to determine the spins and parities, and partial widths of the T = 3/2 levels, calculations were performed using a single-level approximation, in an attempt to fit the elastic scattering data. The cross sections f or elastic scattering of protons from a spin zero target may be written (Feshbach 1960) as: do(e) dn cm = (3-1) 32 where l oo 2i (ID -(.!) ) 0 A= f (e) + .k ~ e p, [(£+l)(U 0 +-l) + £ (U.e --l)] P0 ( cos G), 2 l. £=0 c ,,, ,,, 1 2ik B f c 00 ~ £=1 exp [- = .e ~ tan -1 i~ ln sin2 (e/2)], (~/n), n=l where 8 is the center-of-mass scattering angle, ~ = z1 z2 e 2 / h v where v is the relative velocity in the center-of-mass system, k is + the wave number, and the Up, - represent the elements of the collision matrix for collisions with total angular momentum J = P, ± 1/2. For the cas e in question, where there are reaction channels open, the collision matrix may be expressed in terms of c omp lex phase + s hifts 5p, -: + up, - =e 2io .e ± or up, -+ real. The A P, coefficients take i nto account the absorption of f lux f rom the entrance channel. On the assumption that the observed narrow anomalies are produced by a s ing le level, it is possible to express the col lision matrix for the resonant partial wave in terms o f a non-resonant b ackground and a resonant term ( see Lane and Thomas 1958) : 33 ir ± E-E where Po 0 + ir/2 J 5£± are the non-resonant background phase shifts, E 0 is the resonant energy, r is the total width of the resonance and r the partial width for decay to the ground state of 20 Ne. is po In terms of R matrix theory, this parametrization amounts to the assumption that the penetrability and shift functions are constant over the width of the resonance, which is a good approximation for the narrow levels in question. In the following discussion all energies and widths are in the center-of-mass system unless otherwise stated. The method of analysis used was as follows: 1. Non-resonant background phase shifts 5£± were chosen to fit the observed angular distributions near the resonances. 2. Resonance shapes were calculated with typical background phase shifts for all values of J n corresponding to £ < 4 for e = ss 0 , cm 93° , 143°, 163°. 3. .T hese shapes were compared with the observed resonances and appropriate values of J 4. n were selected. Values of E , r and r were determined by careful comparison of po calculated and observed resonance shapes at all angles, taking o into account the effects of energy resolution. The measured angular distributions near the T = 3/2 level s are presented in Figure 22. In order to restrict the number of free parameters available to fit the data, the initial phase shifts were + restricted to be real (A£ - = 1), dependent only on e (5£ and phase shifts for £?:. 4 were excluded. + = 5p, -), 34 A computer program in Citran language was written for the IBM 360-50 computer to calculate off-resonance angular distributions for various values of the phase shifts. As the remote console facility permitted direct access to the computer, the phases could be conveniently varied until acceptable fits were obtained for the angular distributions. The angular distributions which were calcu- lated from the final values of 5£ listed in Table 3,A are presented as solid lines in Figure 22. To calculate resonance shapes a computer program due to Goosman (1967) was used which evaluates equation 3-1 for £ dependent phase shifts and appropriate values of E , 0 r, r p , and averages the 0 result with a gaussian resolution function with FWHM = R to approximate the experimental resolution. Resonance shapes calculated for phase shifts near the final accepted values are presented in Figure 23 for all £ :5, 4. 0 The 0 anomaly shapes at the smaller angles (55 / 93 ) are not as significantly affected by changes in the background phase shifts (5£) as are the shapes at 143° and 163°. term (fc) in ~ The reason is that the Coulomb scattering contributes the major portion of the background scattering at angles less than about 90°, whereas at the larger angles the background is predominantly due to the nuclear scattering terms, containing the 5£' and is very sensitive to them. However, a compari- son of the 55° and 93° shapes in Figure 23 with the observed anomalies presented in Figures 13 and 14 is sufficient to establish the spinparity of the 9.22 MeV level as 1/2+ and to strongly suggest that the 8.97 MeV level has spin-parity 3/2+ or 5/2+. The calculated 1/2+ 35 shapes are the only ones to have a strong rise at 55 dip at 93° as observed for the 9.22 MeV level. 0 and strong The 8.97 MeV level has a small rising anomaly at 55° and a dip at 93°, similar to the 3/2+ and 5/2+ shapes, but an investigation of anomaly sizes is necessary before the 1/2+ shapes can be ruled out. Detailed elastic scattering excitation functions at 8 angles for the two T = 3/2 resonances are presented in Figures 24 and 25. The experimental energy resolution R for this data was determined from a comparison of the anomalies for the 8.97 MeV level at 143° and 163° with those obtained when the target compensation voltage was used, which are presented in Figure 26. The minimum possible R, resulting from energy loss and Doppler effect in the target is about 0.7 keV. The solid lines in Figure 26 show the fit to the data obtained with R = 0.7 keV, r = 1.2 keV, and r p = 0.15 keV. 0 This sets an upper limit of 1.2 keV for r so that the observed width of 2.1 keV for the data presented in Figure 24 is predominantly due to the experimental resolution. Values of R in the range 2.0 ± 0.1 keV provide acceptable fits to this data for all r < 1.2 keV and a value of R = 2 keV was used in the analysis for both of the T = 3/2 levels. The solid lines in Figure 24 are the shapes calculated for the 8.97-MeV level with J n = 5/2+, r = 0.5 keV and r using the background phases tabulated in Table 3A. = 0.1 keV, Po The quality of the fits at all angles establishes the £ value of the resonance to be 2, 36 although it is not possible to distinguish between J n 3/2+ and 5/2+ • Curves for J n = 1/2+ exhibited anomalies which were the wrong shape a t 123° and 143° and did not have the correct relative s izes at other angles, thus eliminating this possible choice of spin-parity. To test the sensitivity of the s hapes to the parameters r and r , calculations were performed for r = 0.1 keV, J n = 5/2+ p po with various values of r between 0.1 and 1.2 keV. I t was found that the sizes of the anomalies were not strongly dependent on r except for the two extremes of this region. For anomalies which are Breit-Wigner shaped, such as those at 143° and 163°, the height of the anomaly is roughly proportional to r /r (for r /r << 1) and its width i s proportional to r . Therepo Po fore, its area, which is the quantity determining the anomaly size after averaging with resolution R >> r, is approx imately proportional The validity of the two approximations (r /r << 1 and R >> r) po breaks down near the ends of the investigated range of r, but the calculations give a reasonable fit to the data for 0.3 keV < r < 0.9 ke V with r = 0.1 keV. and R = 2 keV. po for r = r po R = 1.9 keV. 0.05 keV, R Acceptable fits we re also obtained 2.1 keV and for r = 1.2 keV, r po = 0.15 kev, On this basis, r was determined to be 0.1 ± 0.05 keV. po The results obtained for the 9.22 MeV l evel with r = 2.3 keV, = 1.1 keV and R 2 keV, using the real, £ -dependent phase shifts po listed in Table 3A, are presented in Figure 25. The calculations match r the data reasonably well for all angles e ~ 123° but are too large at 143 0 and do not reproduce the anomaly shapes at 153 0 0 and 163 • 37 As no other J < 7/2 produced the correct anomaly shapes at as many angles, and as the discrepancy occurred at the largest angles where the results were most sensitive to background phase shifts, it was concluded that the background phase shifts were the source of the error. Attempts were made to find other phase shifts which would fit the observed angular distribution and produce the correct 0 anomaly shapes for e > 123 • Although a number of other sets of real, £-dependent phase shifts were found which produced similar 0 angular distributions and different anomaly shapes for e > 123 , none of them reproduced the experimentally observed anomalies. At this point the restrictions on the background phase shifts were removed, and a fit to the background angular distribution was attempted with complex, J-dependent phase shifts for£ S 2. This analysis was performed by Dr. M. J. Levine at Brookhaven National Laboratory using a nonlinear least squares fitting routine written by Birnbaum (1965) and utilized by Levine (1968). The angular distri+ bution which was calculated from the resultant values of 5 - listed £ in Table 3, B is presented as a dashed line in Figure 22. Goosman's computer program was modified to accept Jdependent phase shifts, and used to calculate anomaly shapes with the new background phase shifts and the same values of r and R. po These shapes are presented as dashed curves in Figure 25, and may be 0 seen to be very similar to the solid curves at angles e < 123 , but they represent the data better at the larger angles than the solid curves do. 38 As the values of r and r Po necessary to fit the data at most angles are the same for both sets of background ph ase shifts, rand r appear to be well determined. The values are: Po r = 2 .3 ± 0 .5 keV and r 1.1 ± 0 .3 keV. The errors have been po estimated from the variation of anomaly sizes observed for changes in these parameters. The difference in the character of the non-resonant phase shifts necessary to describe the background at the positions of the two T = 3/2 levels is somewhat disturbing. However, although the background does not change significantly over the widths of these narrow resonances, it does change considerably between them, due to the presence of the T = 1/2 resonances (see Figures 13 to 17). In any case, the possibility always exists that other sets of background phase shifts would also fit the angular distributions. reason, the accuracy of the r For this parameter rests primarily on the fits po obtained in the region e ~ 123°, where the anomaly shapes are least sensitive to the choice of background phase shifts. No analysis was attempted for the inelastic scattering data. The 8. 97-MeV level exhibits small anomalies in the p p 3 0 , pl' and channels, whereas the 9.22 MeV level shows anomalies only in the p 0 and p 1 levels in channel. Transitions from the 9.22 MeV leve l to higher 20 17 17 Ne and to a + F(O.O) or a + F(0 . SO) are inhibited by the Coulomb barrier, as may be seen from Table 4, which lists the penetrabilities calculated f rom P.e = 2 p 2 , where F p, and Ge are F.e + G.e the regular and irregular Coulomb f unctions and p = kr. Thus, it i s 39 likely that r makes up most of the remainder of the width of the pl 9.22 MeV level, so r ~ 1.2 keV. P1 For the 8.97-MeV level, the ratio r /r can be calcuP1 po lated from the energy spectrum of delayed protons following the p+ decay of 21Mg, presented by Hardy and Bell (1965). The calcu- lation is complicated by the presence of contaminant groups due to delayed protons following the p+ decay of 17 Ne, but a value r /r = 2.5 ± 0.6 can be obtained after subtracting the contriP1 po butions from the contaminant. Combining this number, and the present , we obtain r = 0.25 ± 0.15 keV. po P1 The T = 1/2 levels in the observed energy range overlapped results for r to such an extent that a single level approximation was not considered to be justified and no analysis was attempted for them. E• Conclusions In surrnnary, the lowest two T = 3/2 levels in observed in the 21 Na were 20 Ne(p,p) and (p,p') reactions at excitation energies of 8.973 ± 0.007 MeV and 9.217 ± 0.007 MeV. From an analysis of the elastic scattering data the following parameters were extracted: for the 8.973 MeV state, J r po = 1( + (or 3/2+ ), r < 1.2 keV, = 5/2 0.1 ± 0.05 keV and for the 9.217 MeV state, J n = 1/2+, r = 2. 3 ± 0.5 keV, r Po 1.1 ± 0.3 keV. These results agree with, and are more accurate than, those obtained from the 19 F( 3He,n) reaction presented in Section II. comparing the two reactions, one can readily see the selectivity By \ 40 3 with which the ( He,n) reaction populates the T = 3/2 levels in the presence of a large number of T = 1/2 levels. The results obtained for the excitation energy of the lowest T = 3/2 level do not agree with the measurement McPherson by et al. (1965), of 8.90 ± 0.04 MeV nor with the results of Butler et al. (1968), 8.92 ± 0.03 MeV. This latter result has been recently revised to 8.97 ± 0.03 MeV (Brunnader et al • . 1969) and is now in good agreement with the present results. These levels have recently been seen as resonances in the 20 Ne(p,y) reaction by Bearse et al. (1969) . ratios The observed branching are in agreement with the assumption, that these levels are members of a K = 1/2 rotational band (Nilsson orbit number 6) with J n = 5/2+ and 1/2+, as discussed in Section II. The 21 Na(T = 3/2) mass may be combined with the observed masses of the other members of the 3/2 multiplet to test the validity of the quadratic mass law. The most accurately determined values of these mass excesses are presented in Table 5 for the two lowest T = 3 /2 levels. The 21 F ground state mass ex ces s comes from Mattauch et al. (1965), and the ex cited state mass is the average of the results of Hinds et al. (1962), and Horvat (1964). The 21 Ne mas s excesses are the results of Hensley (1969a) which are significantly more accurate than other determinations for 21Ne. The 2 ~a masses are from the present work, combined with the mass of 20Ne obtained from Mattauch et al. (1965). The mass of 2 \ig is a recent result from Cerny (1969) which was obtained in a remeasurement of the result obtained by Butler et al. (1968), using the 24 Mg( 3He, 6He) 41 reaction. 21 Butler et al. (1968), observed both the ground state of Mg, with a mass excess of 10.62 ± 0.12 MeV and a first excited state at 0.22 ± 0.030 MeV, but the count rate from this ver y difficult experiment was so low that the statistical precis ion of the dat a was low. In the remeasurement, only one peak was observed, which is assumed to correspond to the ground state of 21Mg (Hardy 196 9c). If the quadratic mass equation is fitted b y least squares to the masses in Table S a chi-square value of 6 X 10- 3 is obtained, which corresponds to a 94 percent statistical probability. tively, if a cubic term dT to be -1.66 ± 20.S keV. 3 z Alterna- is add e d to the equation, d is determined Deviations from the quadratic mas s equation due to higher order perturbations are expected to be s uch that l ~I <;_Z a where Z is the average nuclear charge of the multiplet, and a is the fine structur e constant. For thi s case, - cZu. = 19 ± 2.3 keV, which i s about the same size as the error ind. Another way to comp are the masses in the T = 3/2 quartet is to use the mass e x cesses of 21 F, 21 equation to predict the mas s excess of Ne and 21 21 Na and the quadratic Mg; one obtains the equation: M( 21 21 21 Mg) = 3 [M( Na) - M( Ne)) which predicts M( + M( 21 Mg)= 10.940 ± 0.029 MeV. 21 F) Although the experi- mental result, 10.95 ± 0.1 2 MeV, is extremely close to this prediction, the error is as yet too large to provide a quadratic mass equation. signi f icant test of the 42 The 21 Na (T = 3/2) masses from the present work have been used in a systematic investigation of displacement ene~gies throughout the (ld 512 J shell (Hardy 1969a). Formulae, calculated by in- · eluding the Coulomb interaction to first order, for two limiting coupling schemes (Hecht 1967 and 1968), are expressed in terms of five parameters which are determined by a fit to the experimental data. The resultant fits, with 17 and 19 degrees of freedom, are reasonably good, as were other such fits in the (lp) and (lf) shells based on the same formulae (Janecke 1968 and 1969). The two-body Coulomb matrix elements, determined from the semi-empirical parameters, were in reasonable agreement with values calculated using harmonic oscillator wave functions. However, the simplifying assumptions underlying the theoretical equations did not permit the extraction of further information about other possible charge dependent interactions. The narrow widths observed for the 21 Na (T = 3/2) levels suggest that the wave functions for these levels do not contain large isospin impurities. The striking differences observed in the isospin impurities of mir.r or T = 3/2 levels in A = 13 and 17, to be discussed in Section IV, suggest that an expe~imental study of the widths and decay properties of the corresponding T = 3/2 levels of 21 Ne would be very interesting. forbidden resonances in the 17 A search for these levels as isospin- 0 +a reaction might be difficult, since they would be expected to occur at incident alpha particle energies of about 2 MeV, which are below the Coulomb barrier. It appears that the reactions most likely to yield information about the decay 43 properties of these levels would be 22 Ne( 3He,a) 21 Ne* (n) ZONe and 21Ne( 3He,a) 21Ne* (a) 17 o, using experimental methods similar to those described in Section IV. 44 IV. ISOSPIN-FORBIDDEN PARTICLE DECAYS OF THE LOWEST T = 3/2 LEVELS OF A. 17 0 AND 17 F Introduction Recent measurements in this lab by Adelberger, Cocke, Davids, and the author (Adelberger et al. 1969a) have revealed quite striking differences in the isospin-forbidden particle decay properties of the lowest T = 3/2 levels in 13 c and 13N. The results of these studies are reproduced in Table 6 together with recent theoretical calculations by Arima and Yoshida (1969) which include isospin mixing due to the Coulomb interaction. The magnitude of the effects in the mass-13 case and the apparent inadequacy of the theoretical explanation on the basis of Coulomb mixing alone, stimulated a similar study of the isospin. 17 17 forbidden decays of the T = 3/2 levels in 0 and F to gain further information about the character of isospin impurities in higherisospin levels. The T = 3/2 levels of the mass 17 multiplet have been extensively studied in isospin-allowed reactions such as (t,p), 3 3 3 ( He,p), ( He, a ) and ( He,n). . d in . the ob serve Twenty-one levels in 17N have been 15 ( . (Hart et a 1 • N t,p ) reaction • state has been assigned J T( = 1/2 1965) and the ground (Silbert and Hopkins 1964). Hensley (1969a) has reported the lowest T = 3/2 level in 17 0 at an excitation energy of 11.075 ± 0.004 MeV and six other T = 3/2 levels seen in the 15 3 18 3 N( He,p) and o( He, a ) reactions. Detraz and Dulnn 45 (1969) have also observed these levels and an additional one at 18 15.101 MeV excitation, in the 3 0( He,a) reaction. Adelberger and Barnes (1966) have observed the lowest T = 3/2 level in 17 F at an excitation energy of 11.195 ± 0.007 MeV and two other T = 3/2 levels, in the 15 17 3 N( He,n) F reaction. These T = 3/2 levels in 17 16 isospin-forbidden resonances in the et al. 1967 and Temmer et al. F have also been reported as . O(p,p) reaction (Patterson 1967) and the lowest level has been found to have a width less than 1.2 keV. lowest T = 3/2 levels in 17 these reactions to be 1/2-. Bell 1965; Braid et al. the branching 0 and 17 17 The spin and parity of the F have been determined in all Ne has also been studied (Hardy and 1965; Esterlund et al. 1967) and recently ratios for isospin-forbidden proton decays of the lowest T = 3/2 level in 17 F have been determined from the delayed- proton energy spectrum following the superallowed beta decay of 17 Ne (Hardy et al. 1969b). Since the total widths of the lowest T = 3/2 levels in and 17 17 0 F have not been accurately determined, it was necessary to measure the branching ratios for decay to the ground state and to excited states of 16 0, so that ratios of reduced widths for the T = 3/2 two levels could be compared. In addition, the comparison of such ratios of reduced widths imposes restrictions on the form of isospin impurities in the T = 3/2 levels involved, as has already been pointed out in the A= 13 case (Adelberger et al. will be discussed in Section IV, D. 1969a) and 46 With these motivations, experiments were undertaken to determine the branching ratios for the proton decay of the lowest T = 3/2 level in 17 F(ll.195 MeV) to the ground state and the 6.05 and 6.13 MeV levels of 16 0 and for the neutron decay of the analogous . 17 16 T = 3/2 level in 0(11.075) to the same levels of o. These transitions are indicated on an isobar diagram in Figure 27. B. Pro t on Decay o f th e Lowes t T - 3/2 Level 4n ~ 1. 17 F Apparatus In order to measure the branching ratios (B.R.'s) for proton decay of the lowest T = 3/2 level in lated with the 15 17 F, the level was popu- 16 3 17 N( He,n) F*(p) o reaction, and the decay protons were detected in coincidence with the neutrons. The neutron detector used was the same one described in Section II and slow channel energy discrimination was set as described there; hence the detector efficiency was as shown in Figure 3. Protons were detected by a 1000µ, silicon surface barrier detector mounted in a cylindrical brass scattering chamber of wall thickness 1/8", together with the 15 N gas cell. The gas cell was designed so that the proton and neutron detectors both observed the total volume of interaction between the beam and target gas, as shown in Figure 28. The wall thickness of the stainless steel gas cell was 3/32" and the back of it was 0.02" tantalum to reduce the background counting rate. The beam entered 47 the cell through a 10,000 Rcircular nickel foil which was offset from the axis of the gas cell, so that the proton detector could observe the total volume of interaction, as shown in Figure 28. The 10,000 ~Ni foils were mounted on 0.02 11 tantalum frames with epoxy resin, and the frames were then attached to the gas cell. Foils which were "sandwiched 11 in this manner were found to be more reliable under bombardment and could withstand higher gas pressures than those which were simply glued to the front of the gas cell. The beam passed through two collimators which restricted its diameter to 1/8'' to reduce uncertainty in the solid angle subtended by the proton detector. The solid angle was defined by a rectangular opening whose dimensions were measured with a traveling microscope. The distance from the detector to the center of the gas cell was carefully measured with a ruler, and was estimated to be 0.81 ± 0.02" from a series of independent measurements. was (1.71 ± 0.2) X 10 -3 The resultant solid angle I steradians, where the error includes the effect of the finite size of the beam spot. Aluminum foil, 2.25 mil thic~, was placed before the proton detector to stop elastically scattered The population 15 3 He particles. of the lowest T = 3/2 leve l in 17 F by the 3 N( He,n) reaction was determined by observing a neutron time-of- flight spectrum, using a pulsed beam as described in Section II. The apparatus used to measure neutron-proton coincidence is illustrated in Figure 29. Timing signals from the neutron detector were fed to the START side of an Ortec Model 437 time-to-amplitude converter (TAC). STOP pulses were derived from the silicon detector 48 by means of an Ortec Model 260 time pickoff circuit. The output of the TAC was fed to the Y axis of a 64 X 64 Nuclear Data multichannel analyzer, and the linear output of the silicon detector was amplified and fed to the X axis. In the following discussion, the Y axis will be referred to as the neutron axis and the X axis as the proton axis. A linear signal, derived from dynode 11 of the photomultiplier was inspected by a discriminator. The discriminator l eve l was set to eliminate phototube noise and small scintillator pulses which would have poor time resolution. Coincidences between the output of this discriminator and pulses from the TAC which fell in the 64 channels o f interest on the neutron axis were u sed to gate the multicnannel analyzer. In thi s manner, two dimensional spectra of neutron flight time versus proton energy were accumulated, as illustrated in Figure 30. In this figure neutron flight time increases from bottom to top , and proton energy from left to right. Gamma rays , which are also de t ected by the scintillator, h ave the shortest flight times, and produce a curve at the bottom of the figure. The deviation of this curve from a straight line is a n indication of the variation of triggering time with pulse h eight from the proton detec tor, and its width is a meas ure of the overall time resolution. The midpoint of this curve is assumed to correspond to 3.3 n s /m, wh ich then allows the zero point of the time scale to be determined without further corrections for the time-slewing of the proton d etector . The time sc ale can then be cali - brated from the separation of the neutron peak corresponding to the 49 lowest T = 3/2 state in singles spectrum. 17 F from the gannna ray peak, in the pulsed-beam The proton energy s cale can be calibrated from the . 17 proton and deuteron peaks corresponding to known energy levels in O and 16 o, after making the appropriate correction for energy loss in the aluminum foil. The other curves which can be seen in the spectrum are the loci of allowed proton energies versus neutron flight times for the two cases wh ere 16 0 . 1 f . . . . is e t in its ground state, or in one o f its first excited states at 6.05 and 6.13 MeV which are not resolved. These loci will be referred to as kinematic lines. The decay of levels in 17 17 16 0 or F to these states in 0 should be indicated b y enhancements in the number of counts on the kinematic line, at the proton energy or neutron flight time appropriate 3 3 to the population of the level in the primary ( He,p) or ( He,n) reaction. To display the data and exhibit these enhancements more clearly, a number of channels in the proton (neutron) direction, centered on the kinematic line, are sunnned at each neutron (proton) channel and the results are displayed as a one dimensional spectrum of counts versus neutron (proton) channel number. A computer pro- gram was developed to process the data and provide such projections of kinematic lines on either the neutron or proton axis. The background due to chance coincidences is uni f orm along the neutron flight time axis, but reflects the variation of count rate with particle energy on the other axis. The region of the spectrum between the gamma ray peak and the ground state k i nematic 50 line should contain only chance coincident events and the average number of chance counts in each proton channel is determined from this region. The appropriate chance coincidence background is then subtracted from the entire spectrum by the computer. The positions of the kinematic lines are determined from the time scale and proton energy calibrations, incident energy, Q-values, particle masses, detector angles and neutron counter distance, and the calculated positions of the kinematic lines are indicated on the print-out of the spectrum for comparison with the observed lines. In order to obtain the relative normalization of the coincidence spectra and the pulsed-beam singles spectra, the proton energy spectrum was simultaneously recorded in an RIDL 200 channel analyzer. The number of counts accumulated in an isolated peak produced by the 15 3 N( He,d ) 0 16 . 0(0.0) reaction could be accurately determined for both runs, and served as a measure of the number of beam-target interactions, independent of beam fluctuations and gas pressure changes. A single channel analyzer was also set to cover this peak and its output was counted by a short dead-time scalar in order to provide a check on the loss of counts due to the larger dead-time of the multichannel analyzer. 2. Experimental Method Since the lowest T : 3/2 level in 17 F has spin 1/2, its decay angular distributions are isotropic in the center of mass coordinate frame, and a measurement at one angle suffices to determine its branching ratio. 51 The main problem in the determination of the branching ratio is the identification of those enhancements on the kinematic lines of the coincidence spectrwn, which can be unambiguously attributed to the decay of the 17 F level. There are two other ways in which genuine coincidence counts can be produced on the kinematic line: 1. From the reaction 15 3 16 N( He,np) o, which does not proceed through a definite intermediate state, and may be assumed to have a smoothly varying cross section with neutron or proton energy. 2. From the reaction 15 N( 3He,p) 17 0 * (n) 16 0 if . there happens to be a state populated in 17 0 within the appropriate energy range. For this reason, it is necessary to have the greatest possible population of the 17 F (T = ~/2) level, together with good time resolution, and if possible, to choose the incident energy and the detector angles so that there are no 17 O energy levels which could produce enhancements at the same place on the kinematic line. A computer program was written which calcula ted and plotted kinematic lines as a function of neutron flight time and proton energy, as well as marking the positions cf the known energy levels of 17 F 170 . . 1 1ne. . and on t h e k 1nemat1c The useabl e rang e of incident energies was chosen from previous investigations of the population of the T = 3/2 level by the 15 3 N( He,n) reaction (Adelberger et al. 1969). The neutron detector angle was chosen to be o 0 since the angular distribution for the ( 3 He,n) reaction is strongly forward peaked, and the detector was placed 1.5 meters from the target as a 52 compromise between good time resolution and reasonable solid angle. Incident energies and proton detector angles were chosen so that the decay of the lowest T = 3/2 level of state of 16 17 F to the ground 0 produced an enhancement on the kinematic line which lay between enhancements due to levels in and could be resolved from them. 17 0 at 4.55 and 5.08 MeV The projection on the neutron axis of the kinematic line for this case is shown in Part (b) of Figure 31 and the enchancement resulting from the decay of the 17 F(T = 3/2) level is indicated by an arrow. Part (a) of the figure illustrates the spectrum obtained from a pulsed-beam, single15 3 counting measurement of the ( He,n) reaction on N, at the same incident energy, detector angle, and time scale, and the enhance- ment in Figure 31 (b) can be seen to appear at the same flight time as the peak due to the T = 3/2 level. Three other coincidence and singles spectra were taken 0 0 at an incident energy of 8.25 MeV and angles of 90 , 110 , and 120°. The 17 F enhancement was observed at the correct neutron energy in all runs and was found to be isotropic within the errors. For decays of the MeV levels of 16 17 F(T = 3/2) level to the 6.05 and 6.13 0, the density of interfering high, so that it is impossible to resolve the from them. 17 17 0 levels is quite F (T = 3/2) decays However, it is found that the levels are so dense as to produce a rather uniform background upon which the ment appears. 17 F enhance- This is illustrated in Figure 32 which shows the. projection on the neutron axis of the kinematic line corresponding to the 6.05 and 6.13 MeV levels of 16 O. Parts a, b, and c corre spond 53 3H . . 1y. . e inci. d ent energies o f 9 • 18 , 9 • 03 an d 8 • 93 Me V, respective to 17 Enhancements due to the neutron decay of levels in 0 are expected to occur at a constant neutron flight time, determined by the energy available for the 17 0 decay, and the 17 0 center of mass energy, which is not strongly dependent on the beam energy. hand, enhancements due to the proton decay of the 17 On the other F (T = 3/2) . h t time . . appropriate to t h e 15N (3 He,n ) 1 eve 1 · occur at a neutron fl ig 17 F(ll.195) reaction, and have different flight times at the three different incident energies. Two peaks may be observed in the spectra, one of which remains fixed at a position corresponding to a level in 17 0 at 11.6 MeV. The other has a centroid which occurs at the expected position of the 17 F (T = 3/2) level as determined from pulsed-beam, single-counting spectra at the three energies and is assumed to be an enhancement due to the proton decay of the 17 F(T = 3/2) level. The number of counts in the peaks was determined for runs (b) and (c) and a linear background was subtracted, as shown in the figure. The branching ratios could then be calculated as: B.R. (cfo ) where N x C.M.F. x 4 n x N (SING.) p mon N X l1 X N (COINC.) n p mon N = number of counts in enhancement on kinematic line, p N n - number of neutrons in T = 3/2 pe ak in singles spectrum, C .M .F. - anLAB/dn CM , n - solid angle subtended by the proton detector p (steradians), 54 Nmon ( COINC·) = number of counts in the d 0 peak in the coincidence run, Nmon ( SING• ) = number of counts in the d 0 peak in the singles run. 3. Branching Ratios The ground state branching ratio was determined from five separate coincidence spectra and associated singles spectra. The results are listed in Table 7A. The errors in each run are the square root of the sum of the squares of contributions from the following sourc es: 1. Statistical errors in the number of counts within the peak region including the error due to subtra ction of the chance coincidence background. 2. The error due to uncertainty in the background under the enhancement on the kinematic line. 3. The error in the solid angle subtended by the proton detector , including the effect of the finite size of the beam spot. 4. Errors due to incorrect counting of the number of c ounts in the d 0 monitor peak. The number of counts conta ined withi n the monitor peak in the RIDL analyz er was found to correspond with the number counted in the sc a ler, onc e a correction was ma de for ·t he dead time of the analyzer. in However, at the count r a tes used the proton counter for the coincidence runs (as high as 3 20 X 10 sec -1 ) a sma ll amount of pileup wa s observed to occur. 55 By observing the number of counts obtained in the d p~~ ak 0 for a fixed total charge at various rates, it was estimated that about 5 <fo of the counts in the d 0 peak were lost through pile-up. It was assumed that this effect would affect the T = 3/2 enhancement in the same way, and the number of counts in the d 0 peak, above the flat background due to the pile-up, was taken as a measure of the total number of monitor counts for both the singles and coincidence runs. The error arising from this source is certainly less than 5 %and can theref ore be neglected in comparison with errors such as 1 and 2. The branching ratio to the combined 6.05 and 6.13 MeV 16 states of 0 was determined from the two coincidence runs (b) and (c) of Figure 31, and corresponding single-counting runs. The results and errors are listed in Table 7B. C. Neutron Decay of the Lowest T = 3/2 Level in 1. The 15 17 0 * 3 17 16 . N( He,p) 0 (n) 0 Reaction An attempt was made to measure the neutron decays of the * 17 15 3 17 16 0(11.075; T = 3/2) leve l from the N( He,p) 0 (n) O reaction by methods similar to those described in Section IV,B. detector was positioned at 15 The proton o0 where the yield is a maximum in the 3 N{ He,p) reaction, which populat es the level {He nsley 1969a). The gas cell which was used was a 1/2" diameter stainless steel cylinder with 1/16" wall thickness. The beam entered through 0 a 10,000 A nickel foil and the protons left the cell through a 2 mil 56 Cu foil, which was su ffic i en tly thick to prevent the beam from · reaching the detector. The resultant resolution in the proton detector was 250 keV full width at half maximum for the proton peak 17 corresponding to the 0(11.075) level. The population of this level was difficult to determine from the silicon detector spectrum because of the poor resolution and the presence of peaks from other particles, such as deuterons. Therefore, the 24" magnetic spectro- meter was used to determine the population of the level, relative to the peak from the reaction. 15 17 0(11.075) 3 16 N( He ,d) 0(7 . 12 MeV) This latter peak was the most prominent feature in the silicon detector spectrum and could be compared with the d which had been monitored. the e nergy of the d 0 peak A direct comparison was impossible as peak was above the range of the magnetic spectro- o meter. The effect of the brass target chamber on neutron detection efficiency was d e t e rmined by accumulating a spectrwn from the 16 3 18 O( He,n) Ne reaction using the pulsed b eam at 10 MeV and a thin- walled gas target . This spectrum was compar ed with one accumulated f or the same integrated charge, w i th a 1/8" sheet of brass between the target and the neutron detector to simulate the effec t of the target chamber wall s . The spectrum contained five neutron group s with energies ranging from 1 to 7 MeV. Th e r educt ion in count s in eac h peak was 8 ± 1 % due to the introduction o f the bra ss absorber and it was assumed that the brass tar ge t chamber wall reduced the overall neutron detection efficiency by this amount. 57 To measure the branching ratios for the neutron decay, a series of neutron-proton coincidence spectra were taken at various incident energies and neutron angles. Figure 30 shows a typical two-dimensional coincidence spectrwn. An enhancement on the ground state kinematic line can be observed at the expected position of the 17 O(T = 3/2) level. Figure 33 shows projections on the neutron axis for the kinematic line corresponding to the 6.05 and 6.13 MeV states of 16 0. Enhancements due to the neutron decay of levels in 17 0 are expected to occur at nearly the same neutron flight time, for each of the three incident energies illustrated. No such constant peak is observed with a centroid corresponding to the correct neutron flight time for the decay of the the 6.05 or 6.13 MeV state of 16 17 0(11.075; T 0. However, a peak was observed which corresponds to the decay of a level in the 6.13 MeV level of 16 16 3/2) level to either 17 O at 11.02 MeV to 0, or of a 10.94 MeV level decaying to 0(6.05). No such levels were previously reported in the 15 3 N( He,p) 17 0 reaction, nor were any other levels observed within 250 keV of the T = 3/2 level (Hensley 1969b). Because of this dis- crepancy, Hensley and Nettles undertook a re-examination of this . reg ion o f t h e proton spectrum f rom t h e 15 N c3He,p) reaction, . wit h better resolution than was us e d in the original investigation (Hensley 1969a). 0 The use of 5 1 000 A nickel foils on the 15 N gas 0 cell, (rather than 10,000 A) as well as lower gas pressure, and a reduction of the entrance slits on the 24" magnetic spectrometer, 58 provided sufficient resolution to observe an as shown in Figure 34(a). 15 0 level at 11.023 MeV, The presence of this level made it im17 possible to determine the B.R.'s of the accurately from the 17 3 N( He,p) 0(11.075; T = 3/2 level) 17 * 16 0 (n) 0 reaction, by the methods described previously, since the 11.023 and 11.075 MeV levels could not be resolved in the degraded spectrum of the proton detector. Using data similar to those displayed in Figure 33, it was possible to set upper limits for the 17 B.R. for decay of the o(ll.075;T = 3/2) level to the 6.05 and 6.13 MeV levels of 16 0 of lD,t and 15·J,, respectively. The decay of the combination of the 11.07 5 and 11.023 MeV levels of 17 0 to the ground state of 16 0 was quite well determined from coincidence spectra similar to those shown in Figure 35. From a knowledge of the relative populations of these two levels in the 15 N ( 3He,p ) reaction . . was possi. bl e to set a 1 ower 1 imit on the B.R. it of 17 0(11.075) to 16 0(0.0) + n of 48%· These numbers are so inaccurate that it was decided to try again to measure the neutron decays, using the which does not populate the populate the 17 o(ll.023;T 3 17 0( He,a) 0 reaction 1/2) level, but does O(ll.075;T = 3/2) level. 2. a. 17 18 The 18 3 0( He,a) 17 * 0 (n) 16 0 Reaction Apparatus The 18 3 17 . . 0( He,a) 0 reaction is very selective in pop- ulating the ll.075;T = 3/2 level in 17 0 as may be seen in Figure 34(b) , which is a plot of a particle count rate versus NMR frequency 59 obtained with the CIT-ONR 24" magnetic spectrometer. The target 0 used was a 1000 A Ni foil which had been oxidized by heating in an 18 0 2 atmosphere. Hensley (1969a) determined that the width of this level is less than 20 keV, and has seen no evidence for population of the 11.023 MeV level by this reaction, even in high-resolution spectra. This feature makes the 18 3 16 17 o( He,a) o* (n) 0 reaction a suitable choice for studying the neutron decays of the lowest T = 3/2 level in without interference from T = 1/2 levels. The differential cross section of the populating the 17 18 3 0( He,a) reaction o(ll.075;T = 3/2) level is peaked at about 10°, and is lower by at least a factor of 5 at all angles greater than 40°. Unfortunately, the yield of 3 He particles scattered from the target is so large at angles less than 40° that it is not practicable to use the approach and methods described in Section IV,B due to excessive count rates in the silicon detector. The 24" spectra- meter magnet with a 140 mic r on thick silicon detector in the focal plane was therefore used to detect the a particles without interference from the elastically scattered 3 He . The n e utron detector used the same scintillator and photomultiplier as described in Section II,B. It was mount e d in a cylindrical lead s hield, 2 inches thick, with 1/ 2 in c h o f l e ad cove ring the front surface of the scintilla tor. The d e t ec tor was mounted on a stand so that it pointed directly at the 90 . the magnetic spectrome t e r tar ge t chamber. 0 port of The "blank off" c a p on the port was 1/8" thick aluminum and the dis t anc e f r om t h e target 60 to the mid - point of the s cint illator was measured to be 0.52 meters. 1 0.005 With this geometry, neutrons traveling in a straight line from the target to the detector passed only through the 1/8" thick aluminum cap and the 1/2" piece of lead immediately in front of the detector. A block diagram of the electronic apparatus is shown in Figure 36. A timing signal was derived from the a detector by means of an ORTEC Model 260 time pickoff and fed to the START input of an ORTEC Model 437 time-to-amplitude converter (TAC). A fast signal from the anode of the XP1040 photomultiplier was inverted, clipped and fed to an ORTEC Model 417, fast, zero-crossing discriminator. The output of this discriminator went to the STOP input of the TAC. A linear signal derived from the 11th dynode of the XP1040 photomultiplier was amplified and inspected b y a discriminator. The discriminator threshold was set so that it accepted all pulses which exceeded 1/10 the size of the mid-point of the Compton edge for 662 keV gamma rays from a 137 u s e d i.n the p r eviou s " "'<p2r iments j Cs source rather than 1/8, a s was this inc reas ed t .1e d '». -:.ct ion e fficiency for 0 .8 MeV neu trons , corresponding to the d ecays of 17 . 16 O(T = 3/2) to the 6.05 and 6 . 1 3 MeV levels o f 0. The detection efficiency for 6.8 MeV neutrons , corresponding to decays to the ground state of 16 ~was di sc rimin dtor t hreshold . found to be unaffec t ed by the c h ange in The efficiency fo r dete ct ion vf 0 .8 MeV neutrons, with the threshold set at 1/10, was determined in the ' 1 cannon mount", by comparison with the known value for 6 .8 MeV neutrons, using the values for the 0° cross sections o f the 61 3 t(p,n) He reaction at the two energies, presented by Seagrave (1.960). The energy signal from the silicon detector was amplified and fed to a single-channel analyzer (SCA) which was c e ntered on the alpha-particle peak in the charged particle spectrum. The output of this SCA was counted by a scalar which measured the total number of a-particles detected. The outputs of the two SCA's were fed to an ORTEC Model 409 slow coincidence unit and its output was used to gate the RIDL multichannel analyzer, which was analyzing the spectrum from the TAC. In this manner, a time of flight spectrum was obtained for all detected neutrons which were in coincidence with a -particles counted in the magnetic spectrometer. b. Experimental Details The difference in path length between particles which transverse the magnet on paths with the maximum and minimum accepted radii of curvature is 0.6 meters. For a 12 MeV incident energy, the alpha particles corresponding to the 11.075 MeV level in 17 0 have a reciprocal velocity of 40 nanoseconds (ns) per meter, so that the maximum spread in transit times through the magnet is 24 ns. It was therefore necessary to reduce the "~" entrance slits of the magnet, restricting the accepted paths through the magnet, to irnprove the time resolution. A pulsed beam was used and a time spectrum was observed fr om the TAC, which was started by pulses from the alpha-counter time pickoff, and stopped by signals derive d from the b e am-pulsing 62 system in the usual manner. The full width at half maximum (FWHM) of the observed peak was found to decrease nearly linearly with the angular opening of the magnetic spectrometer and a FWHM of 3 ns was obtained for 0 slit settings of± 4.5(6.0 = 2°). The time resolution was found to be insensitive to the angular aperture in the B-direction and so the B-slits were opened to their maximum values The magnet was set at 10°, which was found to be the maximum yield point on the a-particle angular distribution. The neutron detector was then at 80° from the beam axis, and on the opposite side from the magnet. With the entrance slit settings as described 0 .18 17 above, and a 2000 A Ni o target the 0(11.075) peak was three 2 times as broad as that shown in Figure 34b. servable level nearby was due to the 12 The only other ob- 3 11 C( He,a) C(O.O) reaction, from carbon contamination in the target, and this level is bound to neutron decay so that it will not contribute to the neutron spectrum. For this reason poorer a-particle energy resolution was quite acceptable, and a 1/2"-slit was used in the focal plane in order to obtain larger counting rates. A coincidence run of twelve hours duration was taken with the magnet set on the 17 O(T = 3/2) peak and a five-hour run was taken for the background on each side of the peak. A flat background due to chance coincidence events was observable in all the spectra and could be determined from the average number of counts in the region of the spectrum corresponding 63 to flight times faster than gamma rays (3.3 ns/m). This average random-coincidence background was subtracted from all spectra. The two real-coincidence background spectra were added, and normalized to the same integrated charge as the spectrum taken on the peak. 17 O(T = 3/2) This summed and normalized background spectrum was then sub- tracted from the spectrum obtained on the peak, and the result is shown in Figure 37. The time scale was determined by the use of the 150 ns calibrated cable described in Section II,D,4, but a problem arose in the determination of the zero point of the time scale. Hensley and Nettles (1969) have studied the energy spectrum of gamma rays in coincidence with alpha particles populating the 17 O(T = 3/2) level, and they see very few events which can be attributed to gamma rays de-exciting this level. Therefore, the usual method of determination of the zero point of the time scale, from a peak produced by gamma rays from reactions in the target, is not useful here. From the information already obtained in the 17 * 0 (n) 16 0 reaction, it was expected that the would decay predominantly to the ratio greater than 48 %· 16 17 15 3 N( He,p) 0(11.075) level o(O.O) level, with a branching Only one peak in the spectrum corresponds to a branching ratio this large, and, if it is assumed to be the peak from 17 0(11.075) ~ 16 o(O.O) + n, the resulting time-zero is consistent in the following ways: 1. The zero of time is near the position calculated from a knowledge of the lengths of cables from the detectors to the TAC, 64 the flight time for alpha-particles through the magnet and the approximately-known delay t i me in the photomultiplie r. 2. A peak is observed at flight times slightly larger than those expected for prompt gamma rays from the target, but consistent with gamma rays produced by inelastic neutron scattering in the walls of the target chamber. 3. The major peak has a line shape consistent with that expected for neutrons of about 6 MeV energy, as will be discussed below. 4. The only other observed peak in the spectrum, which may be seen above the tail of the major peak, is found to occur near the expected flight time of neutrons from the decay of the T = 3/2 level to the 6.05 and 6.13 MeV levels of 16 0. For these reasons, the above interpretation of the observed neutron spectrum appears to be unambiguous, and the two peaks marked by arrows in Figure 37 were used to determine the branching ratios for neutron decay of the c. 17 O(T = 3/2) state. Line Shapes The magnitude of the "tail" on the peak corresponding to decays of the 17 o(T = 3/2) level to the ground state of 16 0 (ground state peak) makes it necessary to determine the true line shape for neutrons of this energy rather carefully, in order to determine the branching ratios. As the "tail" is undoubtedly due to neutrons scattered into the detector by surrounding material, the line shape may be dependent 65 on the angular distribution of neutrons from the reaction used to study it. 17 Since the O(T = 3/2) decay angular distribution is isotropic (except for small center-of-mass corrections), a reaction was sought which produced neutrons of approximately the correct energy, did not produce other neutron groups with energies within 6 MeV of the primary group, and had an angular distribution which was as close as possible to isotropic. The 13 C(CX,n) 16 . 0(0.0) reaction satisfies all of these requirements at an incident energy of 4.70 MeV, corresponding to a compound-nucleus resonance with an excitation energy of 9.95 MeV in 17 0. The angular distribution for this energy, has been studied by Morris (1967) and was found to be reasonably isotropic over the angular range from 20° to 160°. This angular region comprises about 65% of the total neutron cross section at this energy. The solid curve in Figure 37 is the neutron line shape obtained from the data at the peak. 13 c(o:,n) 16 o(O.O) reaction, normalized to fit the It appears to fit the data reasonably well over a wide range of flight times and it may thus be used to remove the contribution from the tail of the region of the peak due to the 16 16 0 ground state peak in the 0 6.05 and 6.13 MeV levels. A similar determination of the line shape for the peak corresponding to decays to 16 . 3 0 (6.05) and (6.13) was made using the t(p,n) He reaction at 1.7 MeV incident energy, which also exhibits a nearly isotropic angular distribution; the observed shape is presented as the darker dashed curve in Figure 37. The efficiency of the neutron detector has been well 66 determined by measurements made with the detector mounted inside the "cannon" mount described earlier. Peaks obtained with this geometry however, show small amounts of "tail" compared to that shown for the ground state peak in Figure 37. Therefore, in order to determine the effective efficiency of the neutron detector in the geometry of the 16 coincidence runs, spectra were obtained from the 3 o( He,a) 13 13 o*(n) 16 o C(a ,n) and t(p,n) reactions in this geometry and in the cannon mount. the spectra obtained for the 17 Figure 38 shows c(a,n) reaction in the two geometries, and the arrows indicate the region which was sununed in the two spectra to measure the relative detector efficiency. d. Branching Ratios From the measured data and efficiencies, the branching ratios were calculated from the following expression: x 4:rr nnxn·•rel xn' 1abs where N n = number of counts in the region of the peak in the coincidence spectra which was used in the determination of the relative detector efficiency. 71 = ratio of neutron detector efficiency in the magnetic-spectrore 1 meter geometry to that obtained in the cannon mount. 71 b . a s = absolute detector efficiency measured in the cannon mount geometry. 67 nn =neutron detector solid angle, in steradians. N a = total number of a-particles detected during the run with the magnetic-spectrometer set on the peak, minus the number obtained in the normalized background runs. From this expression, the branching ratio for decay to the ground state of 16 0 was determined to be 91 ± 15%. The major source of error was the uncertainty in the determination of the detector efficiency in the magnet geometry, estimated to be ± 15%; the absolute neutron-detector efficiency in the cannon mount geometry is known only to ± 10%, and there were additional uncertainties involved in the comparison with the magnet geometry arising from beam current integration and target uniformity. For the determination of the branching ratio to the first two excited states of 16 0, there was an additional unce rtainty caused by the lack of an accurate knowledge of the background underneath the peak. The 13 c(a ,n) line shape passed through the error bars on the data points, in the neutron energy region 1.2 MeV < E points. n < 4 MeV, but was generally lower than the actual data This line was therefore assumed to be a lower limit on the background level. An upper limit was estimated from a parallel line which passed through the majority of the error bars but fell generally above the data points in the region 1.2 MeV < E as shown by the lighter dashed curve in Figure 37. n < 4 MeV, This uncertainty is unavoidable since the ground-state calibration line-shape was obtained for neutrons 1 MeV lower in energy than those from the 68 17 o(T = 3/2) state, and the angular distributions wer e not identical in the two cases. The r e sulting branching ratio f or decay of the state to the unr e solved 6.05 a nd 6.13 MeV l e vel s of 16 17 o(T = 3/2) 0 was 5 The error was calculated as the square root of the sum 2rf,. :t- o f the squares of errors resulting from the counting statistics and the uncertainties in detector efficiency and background subtraction discussed above. It is interesting to compare these results with those obtain ed from the 15 3 N( He,p) cribed in Section IV,C,l. 17 o*(n) 16 o reaction, which was des- Now that further knowledge of the branching ratio of the 11.075 MeV (T = 3/2) level in 16 17 0 to 0(6.05 + 6.13) has been obtained, it is possible to d e t e rmine the branching ratio of the 11.023 MeV level to the s e lev els, f rom the data illustrated in Figure 33. Taking possible e rrors into account, a lower limit of 25% is obtained for decay of the 11.023 level of 17 0 to the 6.05 and 6.13 MeV levels of 16 O. The remainder of the decay of the 11.023 Me V leve l may proceed by neutron decay to the ground state of 16 O, or by alpha particle decay to the ground state or first e x cited state of The determination of the branching ratio of the 11.075 MeV to the ground state of 16 17 13 c. 0 l e vel 0 is thus uncertain due to the contribution of a possible 75% branching ratio from the less-strongly-populated 11.023 MeV level. The resultant limits on the branching ratio for the 11.075 MeV level to the ground state of 16 0 are 69 54 < BR( %) < 100, consistent with the more precise determination 18 91 ± 15%, obtained in the study of the D. * 3 17 16 0( He, u ) 0 (n) O reaction. Conclusions The results for the neutron and proton branching ratios of the lowest T = 3/2 levels in These results for Table 8. 17 17 0 and 17 F are summarized in F are in good agreement with recent measurements by Hardy et al. (1969b), who measured 12 ± 4~ for the decay to the ground state of 16 0, 26 ± 8% for the decay to the 6.05 MeV level and set an upper limit of 10% for the decay to the 6.13 MeV level. The branching ratios for 17 F and 17 0 are considerably different, but the energies available for decay are also quite different as may be seen from Figure 27. To make a meaningful compari - son, it is necessary to remove the effects due to differences in phase space and barrier penetration. calculated as These penetrabilities were P.e = p/F.e 2 + G.e 2 where F.e and G.e are the regular and irregular Coulomb functions , respectively. The penetrabilities for the neutron case were obtained by assuming a v ery small charge (O.OOle) for the neutron, which effectively removes the Coulomb e f fects. The ground state and 6.05 MeV state of and the 6.13 l e v e l is 3 16 0 have J n = 0+ so penetrabilities we re calculated with .e = 1 and 2, respectively, for the transitions from the 1/2 , T = 3/2 levels. A radius of 4.4 fm was used in the calculations. Reduced widths, e2 , were calculated by dividing the branch- ing ratios by the pentrabilitie s. For the decay s to the two un- 2 resolved excited s tates, the e •s were calcula ted by as suming that 70 the decay went entirely to one or the other of the sta : es . The ratios of these reduced widths to that for the ground state decays , are tabulated in Table 8, and may be seen to be quite different for the two mirror T = 3/2 levels, independent of the as s umption of 16 0 fina l state. The difference in the ratio of reduc e d wi dtt s observed here is, in fact, larger than that observed in tP..e ma ss 13 case (see Table 6). It is interesting to note that in the mass 17 case the larger ratio is observed for the neutron rich member whereas the opposite is true for mass 13. Arima and Yoshida (1969) have calculated decay widths for the mass 13 case and the results are lis ted in Table 6. They calculated transition matrix elements for a Hamiltonian containing a charge independent nuclear potential and a Coulomb potential. The wave functions for the T = 3/2 levels were obtained by calculating isospin impurities in first order perturb ation approximation, using the charge independent wave functions of Cohen and Kurath (1965) as a basis. The final state wave function was determined in a similar fashion but included the scattering particle wave function dis torted by an optical potential. As may be seen from the table, they did obtain correct orders of magnitude for the widths and found differences for the partial wid ths of the two mirror T = 3/2 levels, although detail ed agreement is not good . As the c alculation is based on the mixing of T = 1/2 levels whose positions have been predicted theoretically, it is likely that the results could be improved if experimental information becomes available on the excitation energies of these levels. 71 It is interesting that differences in the ratios of reduced widths can be produced solely by charge independent nuclear forces and the Coulomb interaction, but it remains to be seen whether the extent of the observed differences can be explained on this basis alone. It is hoped that a similar calculation will be performed for the mass 17 case. A considerable amount of information can be obtained regarding the form of the isospin violating interaction causing these effects by considering the formula. for the ratio of the reduced widths, in first order perturbation approximation. The wave functions for the initial mass 17, (T = 3/2) and final ( 16 o + nucleon) states may be written as the sum of a dominant T = 3/2 part and a T = 1/2 isospin impurity, in the following manner: Ii) = la; T = 3/2, T z ) + ~ ~ . (T ) 1 i If) ={Jc; T = o,o) + z Ib.; T = 1/2, T ) 1 z ~ 5 .ld.; T = 1, o>} IT= 1/2, Tz ) j J J where the sums run over all the states of the same spin and parity which could be admixed. a, b., c, and d. characterize all the other 1 J properties of the levels and the~1 (or 5.) can be written explicitly J as ~.(T 1 where Ea' Eb z) are the energies of the states a, bi and ~C is the isospin-nonconserving Hamiltonian operator which is being treated 72 as the perturbation. For the Coulomb interaction, or any two-body charge dependent interaction, ~C may be written as a sum of spherical tensor operators of rank< 2. Using the Wigner-Eckart theorem, we can write < b., T ]_ = (3/2 O T < b.ll ]_ T 1/2, T z ± l/2 J ~cl a, T = 3/2, T z 0 J 1/2 T z ) < b.]_ 1 2 = ± 1/2 > \I Toll a > + (3/2 1 T z 0 I 1/2 T 2 ) x l\a> + (3/2 2 T z 0 I 1/2 T z ) < b.]_ II T2 II a> Therefore, 13.]_ (T z = ± 1/2) and there are two ways in which the T = 1/2 admixture in the T = 3/2 levels can be different for T 1. = ± 1/2: The proximity of admixed T = 1/2 levels may be different so that (Ea-Eb)-l is different for T 2. z 2 = ± 1/2. The reduced matrix elements of T 1 and T size so that 2 may be of comparable ~-]_ is affected by the sign of the T 2 term. We can write the ratio of reduced widths to the two final states C( 16 o(O.O)) and C 1 ( 16 o(6.05 or 6.13)) as 73 2 For T z = I < fli> I < f'li > 12 ± 1/2 < f l i > =~ pi (Tz) < c; T = 1/ 2 1 bi; T = 1/2 > 1 2 + (2/3 ) / I: j c/: < d . ; T +terms of order po , 3/ 2 > 3/2 1 a; T J J to be neglected . So, e2 c I: p. (T ) - -= ec ' 2 i l. z I: p . (T ) i l. z < c lbi > + (2/3) 1/2 I: o. J j < c' lbi > + (2/3) 'i< < d . la> J I: D . --;: I J j < d. J I la> From this express i on it may be seen that isospin i mpur ities must be significant in the T 3/ 2 l e ve l s to produce a difference in the ratio of r e duced wi dths. p(T ) is the only T z z dependent quantity, so the o b served effect require s that it is not neglig i ble. The ca l culations by Arima a n d Yoshida (1969 ) indicated that the matrix elements of the isos pin impurities in the initial and f inal s t ates were of the same orde r of ma gnitud e . In this case, the observed differences could be produced by the admix ture of just one T = 1/2 level into the T = 3/2 level s and ~(T z ) may be dependent on the position o f the T = 1/2 l evel relative to the T = 3/2 l evel in the two nuc lei. In fact, in the mas s 13 cas e , the s hell model calcu- lations by Cohe n and Ku rath (1965 ) , whic h we re us e d by Arima and Yo sh i da (1969), predic t a T = 1/2, i = 3/2- s tate ve ry n e ar the 1 74 T = 3/2, J~= 3/2 level. As a result, Arima and Yoshida (1969) observed a strong admixture of this level. mass 17, (Margolis 1966) In calculations for no 1/2-, T = 1/2 levels are predicted which are particularly close to the lowest T = 3/2 level. In a recent paper considering the effects of second order perturbations due to the Coulomb interaction, Janecke (1969) has calculated the magnitudes of the off-diagonal isov~ctor and isotensor matrix elements necessary to explain the deviations of the masses of the members of the mass 9 multiplet from the values expected from first order perturbations. Assuming that the only level which is ·mixed into the T = 3/2 levels is a T = 1/2 level at lower excitation, he calculated an isovector matrix element about 35 times the size of the isotensor term. In the present formulation, this would suggest that ~(-1/2) ~ ~(+1/2) and large differences would not be predicted for the ratios of branching ratios for particle decays ' of the T z = ± 1/2 members of the mass 9 multiplet. Although experimental uncertainties are larger for higher mass multiplets, Janecke discussed a trend observable in the second order perturbations which suggests that the perturbations result. I mostly from one or several states with T = 1/2 at lower excitation energies than the T = 3/2 levels. He suggests a possible explanation of such a trend based on the strong admixture of so-called "anti.:analogue" states, with similar space structure and T = 1/2, which would be expected at lower excitation energies. As the Coulomb interaction has only a weak spatial dependence, the similar space structure of these levels could lead to large matrix elements connecting with the 75 T 3/2 levels. Two particle transfer reactions have been found to populate T = 3/2 levels strongly due to their simple structure and such reactions would also be expected to populate these anti-analogue levels. 3 It is interesting to re-examine spectra from ( He,n) reactions (see Adelberger et al. (1969), to look for such levels. 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M. and R. G. Thomas 1958, Revs. Modern Phys. 30, 257. Lauritsen, T. and F. Ajzenberg-Selove 1966 , Nuc. Phys. 78, 1. Levine, M. J., and P.D. Parker 1967, Proc . Int . Conf. on Nuclear Structure, Tokyo, Japan, ed. by J. Sanada, Physical Society of Japan, p. 703. Levine, M. J. 1968, Ph.D. Thesis, Yale University (unpublished). Margolis, B. and N. DeTakasy 1966, Can . J. Phys. 44, 1431. Matous, G. M., G. H. Herling and E . A. Woliki 1966, Phys . Rev. 152, 908. Mattauch, J. H. E., W. Thie le and A. H. Wapstra 1965, Nuc. Phys . 67' 1. McDonald, A. B. and E. G. Ade lberger 1968, Phys. Letters 26B, 380. McPherson, R. and J. c. Hardy 1965, Can. J. Phys . 43, 1. Miller, R. G. and ·R. W. Kavanagh 1966, Bull. Am. Phys. Soc • .!l,315. 79 Morris, J.M. 1967, Ph.D. Thesis, Australian National University, Canberra (unpublished). c. Hensley and T. A. Tombrello 1969, Proc. Nettles, P. H., D. Second Conf. on Nuclear Isospin, Asilomar, Calif., (to be published). Patterson, J. R., H. Winkler and C. S. Zaidins 1967, Phys. Rev. 163, 1051. Paul, E. B. 1957, Phil. Mag. £, 311. Pearson, J. D. 1963, Ph.D. Thesis, California Institute of Technology (unpublished). Reiss, F., W. J. O'Connell, D. W. Heikkinen, H. M. Kuan, S. S. Hanna 1967, Phys. Rev. Letters 19, 367. Seagrave, J. D. 1960, Nuclear Forces and the Few Nucleon Problem, ed. by T. c. Griffith and E. A. Power, Pergammon Press, New York, p. 583. Silbert, M. G. and J. C. Hopkins 1964, Phys. Rev. 134, Bl6. Snover, K. A., E. G. Adelberger and F. Reiss 1968, Bull. Am. Phys. Soc • .!l, 1662. Temmer, G. M. and R. Van Bree 1966,Proc. of the Int. Conf. on Nuclear Physics, Gatlinberg, Academic Press, New York, p. 880. Temmer, G. M. B. Teitelman, R. Van Bree and H. Ogata 1967, Proc. of the Int. Conf. on Nuclear Structure, Tokyo, Japan, ed. by J. Sanada, Physical Society of Japan, p. 299. Weinberg, S. and S. B. Treiman 1959, Phys. Rev. 116,465. Wigner, E. P., 1958,Ptoc. of the . R~A. Welch Found. Conf. on Chem. Res. I. The Structure of The Nucleus, Houston, Texas, p. 67. Wilkinson, D. H. 1964, Phys. Rev. Letters ld, 571. Wilkinson, D. H. 1966, Isobaric Spin in Nuclear Physics, ed. by J. D. Fox and D. Robson, Academic Press, New York, p. 30. 80 TABLE 1 Saxon - Woods Parameters used in DWBA Calculations (see page 17). -u V(r) r - r Xu a iW u Al/ 3 r - r ~= u u w (MeV) (MeV) r u (fm) a 113 A w w r w (fm) J I I a a u (fm) (fm) 0.829 0.592 0.51 0.30 w I 21 Na+ n 201.55 25.90 1.05 54.4 20.0 I 1.2 l 1.811 ! 81 TABLE 2 T = 1/2 Levels in 21 Na Observed in the Excitation Energy Range from 8.87 to 9 . 42 MeV. Ep (MeV) (lab) ( ± 0.010) E (MeV) x (See pa ge 31) f'total(keV) ( ± 0.011) 6.825 8 .928 24 ± 7 6 .913 9.012 34 ± 9 6 .972 9.068 30 ± 8 7 .077 9 .168 13 ± 4 7.024 9. 289 29 ± 7 7.284 9.365 30 ± 7 82 TABLE 3 A. Values of Real, £ -dependent Background Phase Shifts Used to Calculate Solid Lines in Figure 22. E lab p 50 51 52 6 .872 -28° ·20 00 (See Page 34 .) 53 I I 60 I 7.128 -100 -116° -40 -16.5° I B. Values of Complex, J-dependent Background Phase Shifts Used to Calculate Dashed Line Ep lab l in Figure 22. (S ee Page 37.) 50 5 1- 5 + 1 02 (' + '2 57.3° 165 .3° 39.2°+i58.0° -15 .2°+il4 .3° -18.2°+il6.3° I 7 .128 83 TABLE 4 Penetrabilities for the Decay of 21 Na (9.217) 8 (see Page 38.) j, p b p + 20Ne (0.0) (O+) 0 2.07 (1.63)(2+) 2 0.625 "(4.25)(4+) 4 0.00043 (4.97)(2-) 1 0.147 (5 .6'3) (3-) 3 0.00011 (5 .80)(1-) 1 0.013 (0.0) (5/2+) 2 0.074 (0 .50) (1/2+) 0 0.053 Final State a + 17F a b - Calculated for R = l.3(A Pp,= p/Fp, 2 + Gp, 2 113 1 p, + A2 l/ 3 ) 84 TABLE 5 Mass Excess (keV) of T = 3/2 Quartets in Mass 21a -46 ± 7 3126 ± 6 6788 ± 7 233 ± 9 3409 ± 6 7033 ± 7 a b - For references, see Page 40. 3[M( 21 Na) - M( 21 Ne)) + M( 21 F). 10950 ±120 10940 ± 29 11105 ± 29 85 TABLE 6 Decay Properties of the Lowest . T = 3/2 States in Mass 13 (see Pages 44, 70) 13 N(15 .07) ... 12c + p 12 13 c(15 .11) ... 12c + n c(O.O)) 0.202 ± 0.020 0.065 ± 0.014 c(4.43)) 0.121 ± 0.015 0.250 ± 0.036 e (0.0)/B2 (4.43) 1.18 ± 0.11 0 . 17 ± 0.03 r (keV) 1.17 ± 0.21 6 .2 ± 1.1 or r (keV) (EXPER) 0.24 ± 0.05 0.40 ± 0.11 (keV)(THEOR)a 0.21 0.13 (keV)(EXPER) 0.14 ± 0.03 1.55 (keV)(THEOR)a 0.46 0 . 39 BR( BR( 12 2 r r po po n or r r. or r r or r ,pl P1 a. n 0 0 nl nl Arima and Yoshida (1969). ± 0.35 86 TABLE 7 Branching Ratios for the Proton Decay of the Lowest T = 3/2 Level in 15 A. 17 17 F From the 17 16 3 N( He,n) F*(p) o Reaction (See Page 54.) F(ll.195) ~ 16 o(O.O) + p ep BR(<fo) 8.44 135° 10.2 ± 2 .8 8.25 90° 11.3 ± 5 .o 8.25 110° 8.0 ± 3.2 8.25 120° 7.0 ± 3 .o 8.8 ± 1.6 E3 ~ Weighted Ave: B. 17 F(ll.195) ~ 16 0(6.05 + 6.13) + p E3 · He en BR{ 1~2 8.93 145° 25.0 ± 6 .8 9.03 145° 20 .3 ± 5.3 Weighted Ave: 22 . 1 ± 4.2 87 TABLE 8 Decay Properties of Lowest T = 3/2 Levels in Mass 17 (See Page 69) 17 16 17 F(ll .195) 0(11.075) o(O .0)) 0.088 ±0.016 0.91 ±0.15 o(6.05 + 6.13)) 0.22 ± 0.04 0.05 ±0.02 2 2 8 (0.0)/8 (6.05) 0.16 ±0.05 3.4 2 2 8 (0.0)/8 (6.13) 0.066 ± .019 BR( BR( 16 ± 1.4 0.32 ±0.14 FIGURE 1 Schematic diagram of the beam pulsing system for the Model FN tandem accelerator, discussed on Page 7. The JN is a Van de Graaf accelerator used to produce 0.5 MeV beams of 3 4 He+I- or He++ ions, which are velocity modulated in Buncher No. 1, neutralized in the adder canal, and then drift to the center terminal of the tandem accelerator where they are again converted to positive ions and accelerated. of negative ion beams. room. Buncher No. 2 is used for velocity modulation The items enclosed within the dashed line are located in the control CX> CX> BEAM PULSING SYSTEM FOR CIT/ONR TANDEM SLITS TO -z__\. REGULATE ~'\ JN TANDEM JN CX> "O r--------- -1 ELECTRONIC PHASE SHIFTER 1 I I I I I I I IBUNCHER AMPLITUDE CONTROLS MANUAL PHASE SHIFTER MANI.JAL PHASE SHIFTER I MASTER OSCILLATOR I 3.51 MHz IL ___________________ _ CHOPPING SLITS 90 FIGURE 2 Block diagram of the electronic apparatus used to measure neutron flight times (see Page lO)o The connnercially available instruments symbolized by the blocks are: 1. Time-to-pulse height converter - Ortec Model 4370 2. Amplifier - discriminator - Ortec Models 410 and 420. 3. Fast amp No. 1 - Hewlett-Packard Model 460 BR . 4. Fast amp No. 2 - Nanosecond Systems Model 281. S. Fast discriminator - Nanosecond Systems Model 205 FG. 6. Multichannel Analyzer - RIDL 400 Channel. 91 SLOW -- __ PICKUP _/ XP1040 --.... VARIABLE DELAY ___,....._, ~COIL ..... ~ ,, FAST FAST AMP #I INVERTER AND SHORTED CABLE FAST AMP #2 FAST DISCRIMINATOR y-vr, , STOP START,, Tl ME - TO - PULSE HEIGHT CONVERTER ,, AMPLIFIER ~----------- DISCRIMINATOR ../\r , r IN GATE.... .... MULTl-CHANNEL ANALYZER FIGURE 3 / Detection efficiency of the neutron detector, determined from the d(d,n) and t(p,n) reactions, discussed on Page 12. In addition to the errors indicated, there is an overall error of ± 10% in the absolute efficiency. The solid curve is computed from an expression quoted by Dietrich (1964), neglecting multiple scattering, scattering from carbon, and scattering and absorption in the shield and collimator . The reduction in efficiency at low neutron energy is due to the slow-channel discriminator, which is assumed in the calculation to be set at a threshold of 450 keV proton energy. approximations to the data, used for interpolation. The dashed lines are In all results presented, the detection efficiency has been taken from the dashed lines, with an assumed relative error of ± 5 ~ . -0 ...., 93 I I I I e! I I I ...:.. 0 I 0 I ~ . I I -.. -.. -:c: ,,,-:c: I ...,... .....I c:: c:: "'O Q. - o> • Cl) Q) {\J • <J :E ->- (!) er ow .z <D w I z I 0 I 0::: I l- I o ::> I ·w Vz ~ g I I e ~/'OI I H>-1 '~ ~---- q _o '-..&.........&.--.i..........L.---.L-..&........L.--..i....--.1..-__.i....____,,,________________ om a:>,._ ·oao <D o 10 o ,,,. 0 {\J 0 AON3101.:J.:13 ~0.103.l30 0 94 FIGURE 4 Experimental line shape produced by the energy. 13 c(a ,n) 16 observed for 6.8 MeV neutrons o(Oo0) reaction at 4.7 MeV incident 0 The neutron detector was at 0 , at a distance of 1.1 meters from the target. For the discussion on Page 13, the triangle indicated by the solid lines was used to approximate the "main peak" and the remaining counts were assumed to make up the "tail" due to the collimator and shielding o 95 I I 13 c(a,n) 160(0.0) .... 6K - - Ill z z ~ :c u 'z...."' 4K :::> 0 u 2K """"" - - • • • •• o.___.·~·~·~·-·-·__ •..._t•_•__________ •___•....,.--..... ---20 30 40 CHANNEL 50 96 FIGURE 5 A comparison of the energies of 5.6 MeV 3 He particles, elastically scattered at 90° from a clean piece of tantalum and from the tantalum backing of a CaF the energy loss of a. 2 target, used to detennine 3 He particles in the CaF 2 layer. A plot of the number of 3 (See Page 15.) He particles detected in the 24 11 radius magnetic spectrometer as a function of NMR frequency, for scattering from a clean piece of tantalum inclined at 45° to the beam . b. A similar plot for traverse the CaF 2 3 He particles which have to coating on a tantalum backing. The energy loss in the CaF 2 layer i s determined from the difference in the energies of the midpoi nts (indicated by arrows) of the edges. 97 a 4K 2K "' 0 TANTALUM ~ z 17.7 18.0 17.8 ::> 0 4K b u • 2K CaF2 + TANTALUM ••• 0------------------------------------·--· 17.4 17.2 NMR 17.3 FREQUENCY (MHz) FIGURE 6 Neutron time-of-flight spectrum from the 0 incident energy for el.AB= o • rays. 19 21 3 F( He,n) Na reaction at 5.855 MeV The intense peak near channel 190 is caused by prompt garrana Neutron flight time increases from right to left and the time scale is approximately one nanosecond per channel. The peak labeled on carbon contamination in the target. 14 o(O.O) is produced by the 12 c( 3He,n) reaction For further discussion see Page 15. '° CX> 19 1200 1 3 21 F( He,n) Na E3 = 5.855 MeV FLIGHT PATH = 3.30 M ~~r-~~r-~---,,_~~~~~r-~~r-~~.--~~;~~===He T=3/2 t r BL =00 t 900 x 1112 _J w z z '() <{ '() :t: (.) 600 'r- CJ) z:'.:) 0 (.) 300 EXCITATION IN 11.0 00 20 10.5 40 21 • • "11,-.\~ Na (MeV) 10.0 9.0 60 80 8.0 6.0 100 CHANNEL 3.0 o.o 120 140 "r I~ • 160 180 200 100 FIGURE 7 Angular distribution of neutrons from the 19 3 21 . F( He,n) Na (9.221) reaction at 5 . 86 MeV incident energy. Error bars indicate statistical errors and uncertainties in background subtraction. There is an additional uncertainty of ± 20~ in the absolute cross section due to uncertainties in target thickness, detector effic iency and charge integration. The smooth curves are DWBA calculations using the optical model potentials listed in Table 1, with only the normalization treated as a free parameter. cussion, see Page 16. For furthe r dis- 101 19 1.0 /"' - F ( 3 He, n) 21 ---........ E3 '\ \ / \ Na (9.221) L=O L= I He =5.86 MeV \ \ \ \ \ \ .8 - \ \ "- (/) ~ \ \ \ E \ \ \ \ \ \ .4 \ I 1 \ \ \ \ \ .2 \ '\ '\ 0 20 40 '\ ....._ __ ..,,,....- .- 60 BcM DEGREES 80 --- -100 .......... FIGURE 8 Neutron time spectrum from the for e.::.AB = 60°. 19 21 3 F( He,n) Na reaction at 5.855 MeV incident energy, The peaks labeled T = 3/2 correspond to excitation energies of 8.99 and 9.22 MeV 0 tv . 21N a. The peak corresponding to the 8.99 MeV level contains less than 20~ contribution from in the 12 c( 3He,n) 14o(O.O) reaction. For further discussion, see Page 17. 19 F( 3 He,n) 21 Na =5.855 MeV E3 FLIGHT PATH = 3.30M He aoo--~....,.-~~r-~-,-~~r-~-,-~~.---~--..~~.---~--,~---, T=3/2 I T:3/2 r BL =60° ~ ~ 600 _J xl/25 • w z z ..... 0 <l: w I u ....... CJ) 1- z ::J 0 u 200 ..,,_..,..-:-... • ' EXCITATION IN 10.5 00 20 40 10.0 21 Na ( MeV) 9.0 60 ••• • 8.0 7 .0 80 • .. .. -.. .._,,. I I ,~.... 9'.- 5.0 3.0 0.0 100 CHANNEL 120 140 160 180 200 104 FIGURE 9 Demonstration that the peak ascribed to a 90221 MeV level in 21 Na was in fact produced by the 19 3 F( He,n) reaction. Q-values were computed from the series of runs making up the angular distribution of Figure 7, assuming various target masses. 2 The x value for a fit to a constant Q-value is plotted as a function of assumed target mass. Page 23. For further discussion, see 105 200 19 3 21 F( He,n) Na(9.2 21) 160 Q Ill 120 11111: cc ::> .,,0 . - 80 I :::c u 40 OL.......112~-'-~1~6~-----==~-----~24~-----:2~8~ TARGET FIGURE 10 A= 21 isobar diagram. 21 Information for 21 F levels comes from Horvat (1964); for Ne from Hensley (1969a) and Ajzenberg-Selove and Lauritsen (1959); for present work and Endt and Van der Leun (1967); for 21 21 Mg from Cerny (1969) . comparison of multiplets, energy scales have been shifted relative to 21 Na from the To facilitate Na, to take into account the neutron-hydrogen mass difference and the Coulomb energy, the latter calculated from E c = 0.60 Z(Z-l)/A 1/ 3 (MeV), as suggested by Lauritsen and Ajzenberg-Selove (1966). Since the lowest T = 1 level in lowest T = 3/2 level in T = 3/2 levels in (See Page 25 ,) 21 17 20 Ne occurs at an excitation energy of 10.27 MeV, and the F occurs at an excitation energy of 11.20 MeV, the lowest two Na are bound with respect to isospin conserving particle decays. 0 °' 2.07 1.75 1.10 n '>a ,~ 512 + 21 - - - - - - I'· zy 1 1 F I ' I86 r 14 'I + 2 12- 1/ 2- 3 112-. 3/ 2 - · ··*·'' .,~ t" I ______ [9.12] 21Mg 7 6 .76 20Ne+n MANY T: 1/2 170+a _. MANY T: 1/2 LEVELS LEVELS 2.43 20Ne+ 0.35 l / 2•, 5 /2• [0.02] l / 2• 21Ne 0.3 0. ·21Na 6. 11 F+a 0 "" 108 FIGURE 11 Differentially-pumped gas target system, which was mounted inside a 60 cm. diameter scattering chamber. Cross hatched sections are aluminum; the entrance canals are brass. Note the lucite base used to insulate the target for application of the compensation voltage. The beam was collected in a Farraday cup about 20 cm. from the Havar exit foil. description, see Page 27. For further 109 COUNTER BEAM HAVAR CANAL 3.5 mm IOOmm LONG cp, CANAL 3.2 mm cp, 27mm LONG, TAPPED 1 FOIL 5cm COMPENSATION ----0 VOLTAGE BEAM LUCITE Ta COLLIMATOR 2.5mm cp TO FIRST PUMP l<Si!L-------· FIGURE 12 Energy spectrum of elastically scattered particles from the neon gas target, obtained at E p = 7.11 MeV with a 1.5 mm thick silicon counter at 35° (lab). The excitation . " 1 states in . 20Ne and 22Ne are given . . MeV• The elastic scattering peak energies of t he f ina in contains a contribution from the 10% natural abundance of low energies is due to neutron and gamma-ray background. 22 Ne. The rise in the spectrl.llll at For further discussion, see Page 29. 0 100,000c I I • 20 Ne(0) I I Ne+p :J Ep =7.11 MeV 20Ne (1.63) 35° _J w z a.. 22Ne(l.28) 22 \ z <{ :c (.) ffi I 10,000 \ ~,000 Ne(4.47) 22 0 Ne(4.97l Ne(3.35l j '. I \ ' en 1- z => (.) 100 I • 20Ne(4. 25) _. _. _. r· I i .,. l • : ., . . . '• . I• ~ "Af • • J • ~ I . ; ., .,~~•,.. ~ ~ ..~~ ... •• • . \. lr t 22 '•/\ 0 i : • Ne(p,a) ~ ~ \ ~ 11 • ., 50 • -~ ~ .. l~· 100 150 CHANNEL NUMBER - 200 FIGURE 13 Excitation function for 20 Ne(p,p) elastic scattering at ecM= 55°. The horizontal bars show the expected positions of the T = 3/2 levels as determined in Section II. errors are less than the size of the points. absolute normalization. There is an uncertainty of ± 20% in the See Page 30 for further discussion. Statistical ,...., 11 3 .. 0 .. ~ a) .. .. .. ~ " u r<) ~ " .. 0 l{) l{) 0 .. r<) __ a) > CV z 0 -& Q) N ~ __.. - >-o (.? N 0::: . w ()) z M 14 M N 0. Cl> z 0 . ... ... z 00 .. I-~a) .. u x w .. .. .... .... ..,. "' .. 0 0 0 co 0 l{) .. .. .. .. . .. 0 N ~ I l ,,,,, "" ~ ~ 0 ~><..? 0::: .... w w z 01-- oz .. . .. . .. ~w 0 u z 0 ()) 0 .... ..."'~ 0 co <.D l{) I'- t:jS/8V'J NI '1V'J81S -> - Q) ... , a) ~ .. . .. .. .. .... .... ......... ,. .. N w 0 0 FIGURE 14 Excitation function for 20 Ne(p,p) elastic scattering at eCM = 93°. The horizontal bars show the expected positions of the T = 3/2 levels as determined in Section II. J:o,. Statistical errors are less than the size of the points. in the absolute normalization. There is an uncertainty of ± 2°';b See Page 30 for further discussion. EXCITATION ENERGY (MeV) 9.00 120 9.10 9.20 9.30 9.40 20 Ne( p, Po) 20 Ne 93° C.M. 0::: <J) "m ...... ...... ~ )'-...! z60 <! ~ <..9 \ ..... <J) (./1 ~ .. _.J .,.,,.,. , .... I' ; I .r·v-· % ../~. l .. t r.. I • .,;., :& z u ·•1 1 I I I I '..• •.. , J 6.80 ' 6.90 I I I t--+-t I I / \l 0 • 7.00 7.10 INCIDENT ENERGY (MeV) 7.20 7.30 FIGURE 15 Excitation function for 20 Ne(p,p) elastic scattering at eCM = 109°. The horizontal bars show the expected positions of the T = 3/2 levels as determined in Section II. errors are less than the size of the points. absolute normalization. Statistical There · is an uneertainty 0f ± 20~ in the See Page 30 for further discussion. °' 117 0 I .....r'" .. .. . .. .. .. ~ ..... .. .. .. ~ <...) -~ 0 ~ ..... (j) .. .. ...... .. Cl> z 0 C\J 2 .....__.. - 0. 0. Q) 0 0 - C\.J !'-'. . , .......I "". . 0 >-o <...? C\.J 0:: . w (j) z w z .. C\J .. " .. .. z 00 ,__ r--: :<! (j) ~ .... .. .. . .... 0 x w 0 0 Oi r--: ..." 0 (j) 0 0 - r0 - N .. Q) 2 0 ............ - r--: >- <...? 0:: .. .. w z w or.. .. -oz !'-'. w .. " (j) Cl) ") - z 0 - O'? <.D 0 - Cl) <.D I 0 C\.J 0 <.D t:IS I 8V'J NI \1V'J91S 0 u ( 0 -> 0 FIGURE 16 Excitation function for 20 Ne(p,p) elastic scattering at eCM = 143°. The horizontal bars show the expected positions of the T = 3/2 levels as determined in Section II. Statistical errors are less than the size of the points. in the absolute normalizationo There is an uncertainty of ± 20~ See Page 30 for further discussion. CXI 119 .... 0 ¢ \.. .. ...... (j) ~ c.j 0 r<) 0 ¢ (j) z r<) - > 0 <I) N !'-= 0 -z <l) C\J ~ ....._ 0 a. a. >-o 0:: . w (J) z w (.9 N <l) I f ~ Q) ~ 0 .... .... "'~ 0 ....._ !'-= ~ " .... .. C\J -> 0:: w w z z 00 01- 1-- ~<Yi u x .. .... 0z t--= w .. .. .. w 0 ............ u .. .. .... "" .. z 0 0 (j) 0 (J) <.6 0 0 ro <.D O'? ro 0 LD I{) N ~S /8~ NI 'Q'~81S 0 FIGURE 17 Excitation function for 20 Ne(p,p) elastic scattering at e GM = 163°. The horizontal bars show the expected positions of the T = 3/2 levels as determined in Section II. errors are less than the size of the points. absolute normalization. There is an uncertainty of ± 20~ in the See Page 30 for further discussion. I-.> Statistical 0 EXCITATION ENERGY (MeV) 60 8.90 9.00 9.10 9.20 9.30 9.40 20 Ne ( p, p ) 20 Ne 163° C.M. 1. 0 J JI J a::: (f) I ........... CD ~ J ..... ..... I tv J z 30 I I <! I • • J ~ I" <.9 I • • • (f) I I J . .. I I ~v 0 6.80 6.90 JI JI J J 'Ii I JI JI JI I I JI JI J I I I I I I I •11'. I ~ I JI JI ."-.) 7.00 7.10 INCIDENT ENERGY (MeV) 7.20 7.30 ••• FIGURE 18 Excitation functions for the 20 20 Ne(p,p ) Ne (1.63) reaction over the regions of 1 incident energy covering the resonances corresponding to the lowest two T = 3/2 levels in 21 Na (see Page 31). The resonances were observed at 6.872 ± 0.005 MeV and 7.128 ± 0.005 MeV incident energy in the elastic scattering data. absolute normalization. There is an uncertainty of ± 20% in the "-> . "-> 20Ne (p, p ) 20Ne ( 1.63) 1 21 25~ 201- ~l ~ 45t i 40 55° • • • • ••• I I I • • 90° •• • I Na ( 8. 973) •• •• • • •• I •••• J J • ·j ::? u ~.g 45 ~ ~ • • • • • •• • • 401•• 143° • • •• 163° 40135130 •• • ••• • • • •• 6.864 6.872 •• 2or 21 55° • •• • •• • Na(9.217) ..-· • 16 40 93° 35 30 l • ••••••••• • •• • •••• I 2 20 • 143° ••• •• • ••• • ••• •• •• 16 35 45 24F ••• 25 163° • •• 20 15 10 • •••• • • 7.120 6.880 INCIDENT ENERGY (MeV) ••• • 7.128 •• • • 7.136 I'-.) (.,.) FIGURE 19 Excitation function for the 20 20 Ne(p,p2 ) Ne (4.25) reaction over the regions of incident energy covering the resonances corresponding to the lowest two T = 3/2 levels in 21 Na (see Page 31). The resonances were observed at 6.872 ± 0.005 MeV and 7.128 ± 0 . 005 MeV incident energy in the elastic scattering data. The data include a contribution from the background due to neutrons and ganuna rays in the energy spectra from the silicon detector (see Figure 12). t-..) ~ 20 Ne (p, p } 20 Ne (4.25} 2 21 20~ - 10' ] I+ No (8.973) 550 • • • • ••••• •. • •• I 93° >0::: • • • • • 93° 60 • •• • •• •• • • • <l 0::: 7 I I • 20 _J 0 w >- 6 10 r 0 ••• • • •• I I I I • • • • • •• • • • I ~ 40 -I 35 6.872 • •••• so, • I .••...... • ••j 4t 10 ~ 6.864 I 60 • • • • • • ••••• • • • • 20~ 163° • • •• •••• • • •• • • •• • I 143° 143° I • ••• 50 <l 0::: 0... • No (9.217) 8 ::::> 8 CD 0::: 55° 1or ( /) r ·z r 21 6.880 163° t ....... • • • • I 7.120 INCIDENT ENERGY (MeV) I I 7.128 • • • •• I • j 7.136 "" Ut FIGURE 20 1-..) Excitation function for the 20 20 Ne(p,p ) Ne (4.97) reaction over the regions of 3 incident energy covering the resonances corresponding to the lowest two T = 3/2 levels in 21 Na (see Page 31). The resonances were observed at 6.872 ± 0.005 MeV and 7.128 ± 0.005 MeV incident energy in the elastic scattering data. The data include a contribution from the background due to neutrons and gamma rays in the energy spectra from the silicon detector (see Figure 12) • °' 20Ne(p,p ) 20 Ne(4.97) 3 21 201151- - 10· z 30 550 • • • • •• 1 •••• I Na(8.973) • • •• 20 >- 0::: <I 0::: 25 93° • • •• ••• • ••• • • CD 0::: 85 •••••• 80 I - 100 0 _J w >- 80 z 0 I0 60 143° • • •• • 80 I I I I I • • •• ••• • 100~ 1430 • • • 80 • •• ••• •• •••• ••••• • 60 120~ 1630 IOOr • • • •• • •• •• • • 75 <I 0.. .....• • • • • •• 93° -I- 20 0::: Na (9.217) 10 I- :::> I 55° 15~ CJ) 21 • • • • 6.864 • •• • •••• 6.872 -1 1aor 163° • ..·1140~ 100 6.880 • ••• • • • • • I 1 7.120 INCIDENT ENERGY (MeV) • • ••••• • 7.128 • 7.136 IV ""-I 128 FIGURE 21 . 20 . 20 Excitation functions for (A) the Ne(p,p ) Ne(l.63) 1 20 20 . 0 reaction and (B) the Ne(p,p ) Ne(4.25) reaction at 163 (C.M.) 2 (see Page 31). The data in Part (B) include a contribution from the background due to neutrons and gamma rays in the energy spectra from the silicon detector (see Figure 12). The absolute normalization is accurate to ± 25~. I I 129 INELASTIC SCATTERING 80 20Ne(p, p ) 20 Ne* ( 1.63 MeV) 1 ffi 20 (a) ........... (() 163° ~ z 6.80 <{ 6.90 7.00 7.10 7.20 7.30 ~ <.9 Cf) 6 163° 4 2 ( b) 20 0 6 .80 6.90 7.00 Ne(p,p 2 ) 20 Ne* (4.25 MeV) 7.10 7.20 INCIDENT ENERGY IN MeV 7.30 FIGURE 22 Angular distributions measured on either side of the two T = 3/2 anomalies. The statistical errors in the data are less than the size of the points; the absolute error is ± 20%. The arrows indicate the angles at which the elastic scattering data presented in Figures 13 to 17 were taken. real, The solid curves are calculated from the £ -dependent background phase shifts listed in Table 3, A. The dashed curve is calculated from the complex, J-dependent phase shifts listed in Table 3, B. discussion, see Page 33. For further w 0 - 1000 20Ne (p, Po) 20N e -I ,._ NEAR FI RST T = 3/2 STATE CJ) ..0 • E ............ z 0 r- ! ! ! l l I NEAR SECOND T = 3/2 STATE CJ) ..0 -~ E 0 w w Cf) I i ! l \; ~~- ! ! CJ) CJ) CJ) x Cf) Cf) 0:: 0 20Ne (p, Po) 20Ne -,._ -r- 100 100 0 0 - 1000 \ 10 0 x \ LL 0::: 0 u..: -0LL • Ep = 6.862 MeV LL 0 ~ " EP = 6.882 MeV ~ (j - 0 40 60 80 100 120 140 160 C. M. ANGLE (DEG.) 10 • Ep =7.10 9 MeV x Ep =7.145 MeV I I I I I I 40 60 80 100 120 140 160 I I C. M. ANGLE .(DEG.) I ..... w ..... 132 FIGURE 23 20 Single level resonance shapes for the reaction at E p 0 = 7.1 MeV and 55 , all the values of J :n: formed with £ < 4 . backg round phase s hi fts used were: 0 - 8.6 ' " 03 0 93 , 143 -1 . 4° and 6 4 0 0 = - 0.2°. 0 Ne(p,p ) 0 and 163 0 20 Ne (C .M. ) for The real, £ -dependent = - 63°' 0 1 = - 30° ' The individual shapes have been normalized to have the value 100 at the resonance energy. For fur ther discussion, see Page 34 . 133 55·~::y v ~::\/ 93·~~ ~ ~::v 143•f \) v :o_J\_ _A_ f: _)\__ Jl 120 120 100 163° 100 80 80 60 60 RESONANCE SHAPES FOR 20Ne (p,p) AT Ep a 7 MeV FIGURE 24 Excitation functions for the to the 8.973, T = 3/2 level of 21 Na. 20 20 Ne(p,p ) Ne reaction over the resonance corresponding 0 Statistical errors in the data are less than the size (,..) of the points; there is an uncertainty in the absolute normalization of ± 20%. The solid curves are calculated from the expressions discussed on Page 31, with J n = 5/2+, E lab= 6.872 0 r = 0.5 keV, r = 0.1 keV, R = 2.0 keV, using the non-resonant background phase shifts Po listed in Table 3, A. For further discussion, see Page 35. .i:... 21 Na (8. 973) RESONANCE IN 20 Ne (p, p) -~ IOOf- 55° • • • •• •• • • • •• 95f- - 901---- --1 45 I 123° 40, 351 I al I .. • E - ~ • 67° 45 I I I ·~ 25 L 143° 55 ti 50 ~ - 30 I I I .• • ••••• v. .. • 20 ••• -4 • 15~ I u ~ I '\.....! I I I~ 20 ~ b 35 -0 I 153° • • • • 15 ~ 1···· • I IOr 301- 25~ 40t 93° - .. Y '\... ... I 5 15 • • • ••e - 351- 1090 301 I 6.864 AW ......., I I 6.872 ~ ••• I I j 6 .880 I 163° 10 5 0 6.864 INCIDENT ENERGY (MeV) 6.872 6.880 w Ln FIGURE 25 Excitation functions for the to the 9.217 MeV, T = 3/2 level of 21 20 20 Ne(p,p ) Ne reaction over the resonance corresponding Na. 0 Statistical errors in the data are less than the size of the points; there is an uncertainty in the absolute normalization of ± 20%. The curves are calculated from the expressions discussed on page 31, with J n = 1/2+, E lab= 7.128, r = 2.3 keV, 0 r = 1.1 keV, R = 2 keV. The solid curves are calculated using the real, £ -dependent background po phase shifts listed in Table 3, A and the dashed curves are calculated using the complex, J-dependent background phase shifts listed in Table 3, B. For further discussion, see Page 36. w °' 21 Na (9.217) RESONANCE IN 20 Ne (p, p) 123° 60 •). 55° 40 --...-......- .1 7 -" \ 30 t= \ "//\~. ....__.,_T __ _ '- 20 10 151- 20 ----- • · - ..... 143° 10 - ~ ~ .0 E - 30 5 20 :::? q c::=- O l--....l-~__J~~-'-~~J..._~-'-~---1 67° (.) 153° 15 I"' ~ 10 b "060 ~ 45 _._ O l--.L...~__L~~....l-~--1.~~--'-~-; 93° 163° 20 30 I 60 40 .... ____.... 1 • •", 10 ---- -• • 109° 20 7.120 7. 128 7.136 I ""\ \. . I ', /I • • ' -- - - 10 .-.~. ° 7.120 INCIDENT ENERGY (MeV) I • 7.128 • • •• • • 7.136 w 'I 138 FIGURE 26 . 20 20 Excitation functions for the Ne(p,p ) Ne reaction at 0 163° and 143° (C.M.) over the resonance corresponding to the 8.973 MeV, T = 3/2 level of system described on page 28. 21 Na, using the energy-compensation Statistical errors in the data are less than the size of the points; there is an overall uncertainty of ± 20Cfa in the absolute normalization. The solid curves are calculated from the expressions presented on Page 31, with n + lab=6.872, r = 1.2 keV, r = 5/2,E = 0.15 keV, R= 0.7 keV, o Po using the background phase shifts tabulated in Table 3, A. For J further discussion, see Page 35. 139 21 Na (8.973) RESONANCE WITH COMPENSATION VOLTAGE f = 1.2 keV 163° R = .7 keV 16 12 - 8 '- < -E • • ..0 143° • 22 1.5 keV • •• 18 --::.--.:-- 14--~~--~~--'~~~-'"-~~--t..~~ 6.864 6.868 6.872 6.876 INCIDENT ENERGY (MeV) 6.880 140 FIGURE 27 Mass 17 isobar diagram, illustrating some available modes for particle decay of the lowest T = 3/2 levels of and 17 F. For further discussion, see Pages 46 and 69. 17 0 141 6 .92 2+ 12.469 3;i_ ~-=l_g 12. 540 3/i ~12- 11.075 3 112 T= 12 --- 11 . 195 112- 6.13 6 .05 [4.143] o+ 5.94 112- 5 . 38 3/i 3.058 1/2- 0.871 112+ 7.12 1- 6 .92 6 .1 3 3- 6 .05 o+ [0.601] o+ 2+ o+ t6o + n ...... ............ 3.10 112- 0 .500 112+ 512• 170 (512} t7F 160 + p FIGURE 28 The gas target cell used for the Section IV. 15 3 17 16 N( He,n) F*(p) o experiment described in The 10,000 R Ni foil was mounted off center so that the proton and neutron detectors both viewed the total volume of interaction between the beam and target gas. For further description see Page 46. ~ IV 143 ~ "' ..."' "' "' .., "' ~ 0 N 0 z 41( 0 II 041( = oO ~ 0 Zt- 0 Ill.. 0 ~~ 0.., u"' ::.: u - ou _... z ~"' -C "' ... i 41( c Q) . ~ ~ ,., ::c ~ ~ ...z u 144 FIGURE 29 Block diagram of the electronic circuitry used in the . d escri"b e d in . s ection . IV. stud yo f t h e 15N (3 He,np )160 reaction, The coIIIlllercially availab le instruments symbolized by the boxes are: 1. Time pick-off - Ortec Model 290. 2. Time-to-pulse-height converter - Ortec Model 437. 3. ddl amplifier - Ortec Model 410. 4. Single channel analyzer - Ortec Model 420. 5. Discriminator - Ortec Model 420. 6. Charge sensitive preamp - Ortec Model 109A. 7. Multichannel analyzer - Nuclear Data 64 X 64. 8. Slow coincidence - Ortec Model 409. This circuitry is discussed on Page 47. DDL AMPLIFIER I~ CHARGE 14-- SENSITIVE PREAMP .... TI ME PICKOFF ' ... - - p n '--- --~ DELAY SINGL E CHANNEL ANALYZER STOP SLOW DDL AMPLIFIER - FAST I TI ME- TO-P ULSE- HEIGHT CONVERTOR . - - START ' ~ :... ISCALER ~ x 64 x 64 MULTI-CHANNEL ANALYZER t GATE - DISCRIMINATOR y •I SCALER ' DISCRIMINATOR , SLOW COINCIDENCE ... ' SCALER VI FIGURE 30 ~ °' Two dimensional spectrum of neutron flight time versus proton energy, from the 15 3 16 N( He, np) o reaction. from left to right . Neutron flight time increases from bottom to top, and proton energy For further discussion of this figure, see Page 48. 15N( 3He,np) 16 an = 70° 8p :QO o E3He =9.58 MeV o~~~--.--~~~~~~..--~~--.--~~--r~~~..--~ 0 0 0 0 0 0 10 17 0 0(5 38) 0 00 0 0 0 0 0 00 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _J w z z 0 I 0 0 0 0 0 0 0 0 <r 30 u 0 0 0 ~ "" 0 w 0 0 0 0 000 0 0000 ~ 0 " ••• 0 0 oo o •• • o f-- 40 17 o o ~ oo ~~ 0(1 1075;T=3/2) 0 0 o e• OO Q o 0 0 •• 0 0 0 COUNTS oo e oooeo 0 -31 31 - 90 91-211 212- 4 50 >4 50 ~ 00000 0 00 0 0 0 000~ 0 0 0 50 60 00 • SYMBOL • 0 • •000000000000 0 0000 ooo•••OOOO• • OO • •••• • ••• •• ••• • ••O • •o • •oeooooooooooooo ••• • •OOOeeooooooo oO • • • ••000 00• • 0 10 20 30 40 PROTON CHANNEL 50 60 148 FIGURE 31 Neutron time-of-flight spectrum from the 15 3 17 N( He,n) F reaction at an incident energy of 8.44 MeV. The peak n ear A. channel 10 corresponds to the 17 F(ll.195; T = 3/2) level . The peak near channel 76 is due to prompt gamma-rays. B. Projection of the kinematic line from the 15 3 16 N( He,np) 0(0 . 0) reaction on the neutron axis, with the same time scale as Part A. A peak which is assumed to b e due to the decay of the 17 F(ll.195; T 3/2) level to 16 o(O.O) + p, is observable near channel 10. For further discussion of these spectra, see Page 52. 149 A 15N(3He, n) 17F E 3 He = 8.44 MeV 3000 Bn = 0° 2000 x 1/10 17F(ll.195; T=3/2) + 40 50 60 80 B 200 170 15N (3He, np) 160(0.0) (5.2) E 3 He = 8.44 MeV ~ Bn =0° 8p =135° 100 SUM ALONG GROUND STATE KINEMATIC LINE, PROJECTED ON NEUTRON AXIS 10 20 30 TIME CHANNEL 150 FIGURE 32 Projections on the neutron axis of the kinematic line from the 15 3 16 . N( He,np) 0 (6.05 + 6.13) reaction at (A) 9ol8 MeV, 0 (B) 9.• 03 MeV and ( C) 8. 93 MeV incident energy for e = o n ' e = 145°. For a discussion of the peaks and background levels p indicated by the solid lines, see Page 52 . 151 15N ('He, np) 160 (6.05 + 6. 13) 8p = 145° A E 5 He =9 .18 MeV SUM ALONG KINEMATIC LINE, PROJECTED ON NEUTRON AXIS 120 80 40 17F(ll.195; T=3/2) E5 He = 8.93 MeV r-' F(ll.l95; T=3/2) c 7 120 80 I 40 0 65 B E 5 He = 9 .03 MeV 60 55 50 45 NEUTRON FLIGHT TIME (NS/M) 152 FIGURE 33 Projections on the neutron axis of the kinematic line from the 15 3 N( He,np) 16 . 0 (6.05 + 6.13) reaction at (A) 9 .68 MeV, (B) 9.58 MeV and (C) 9.48 MeV incident energy for 0 n = 30° . e = o0 p The solid lines are merely to guide the eye. ' The arrows indicate the expected positions of enhancements due to the neutron decay of levels in 16 0(6.13) and see Page 57. 16 0(6.05). 17 0 at 11.023 and 11,075 MeV to For further discussion of these spectra, 153 SUM ALONG KINEMATIC LINE PROJECTED ON NEUTRON AXIS 17 r - 17 0(11.023; T=l/2ll t r 160( l ) 6 3 0(11.075; T=3/2if n + . 400 t L10(11.075; T=3/2~ 16 n + 1 200 L 10(1J.023; T= l/2~ 0(6.05) ....J w z z B <l: :r: ~ Cf) 200 E 3 He =9.58 MeV 1- z :::::> 0 u 100 c 200 E 3 He =9.48 MeV JOO 90 80 70 60 NEUTRON FLIGHT TIME (NS/M) 50 154 FIGURE 34 A. Spectrum of protons detected in the 24" radius magneticspectrometer from the energy of 9.6 MeV. 15 3 17 N( He,p) 0 reaction at an incident The horizontal scale is NMR frequency, which is proportional to particle momentum . B. Spectrum of a -particles from the 12 MeV incident energy. the 12 18 3 o( He, a ) The peak labeled 17 11 o reaction at c(O.O) is due to 3 c( He, a ) reaction on carbon contaminants in the target. For further discussion of these spectra, see Page 58. 155 2000 170 (11.075; T=3/2) ~ A t5N (~He, p) t7o E 3 He = 9 .6 MeV Bp =5° .+ 1000 Cf) 11 0 (11.023; r = 112) 0 ....__2~3-.1-0~0--~2~3~ .9~0~0---2~4~.1~0~0--~24~.~30~0,,........~2~4~ .5~0~0~--_. ~ z :::) 110 ( 11.075; T= 3/2)9 0 u B ieo(3He, a) 110 E 3 He = 12 MeV 2000 Ba =10° "c (O.O) ~ 1000 OL_~~~!!!!~---L~~:_~ll!!!J~~~~ 33.600 34.0 00 34.400 FREQUENCY (MHz) 34.800 156 FIGURE 35 A. Energy spectrum of protons and deuterons from the 15 3 17 15 3 16 . N( He,p) O and N( He,d) O reactions at 9.58 MeV incident energy. ponding to the 17 Clearly visible are the peaks corres0(11.075; T = 3/2) level and the d which was monitored during all 0 peak 16 15 3 N( He,np) o coincidence runs. B. Projection on the proton axis of the kinematic line due to the 15 3 16 . N( He,np) 0(0.0) reaction at an incident energy of 9.58 MeV, fore p = 0°, en = 70°. The peak near channel 12 is assumed to correspond to decays of the level to the ground state of 16 17 0(11.075) O. For further discussion of these spectra, see Page 58. 157 24K 170 ( 11.075) (T= 3/2) 16K ' A d4 15N(3He, p) 170 E 3 He = 9.58 MeV x 1/5 8 p = 0° 170 (5.94)(5.38) 170 ( 5 _94)( 5 .3S) 600 E.3 He = 9 .58 MeV Bp =0, 80 =70° 170(11.075 ~ T= 3/2) 1 SUM ALONG KINEMATIC LINE PROJECTED ON PROTON AXIS 200 ~ ~ ro PROTON ENERGY CHANNEL oo 100 15 8 FIGURE 36 Block diagram of the electronic circuitry used in the . d escri. b e d in . Section . stud y o f t h e 18 0 (3 He, ct ) 170 * (n ) 16 0 reaction, IV, C. The corrunercially available instruments symbolized by the boxes are: 1. Time pickoff - Ortec Model 290. 2. Preamplifier -Tennelec Model TC 130. 3. Amplifier - Ortec Model 410. 4. Single channel analyzer - Ortec Model 420. 5. Zero-crossing discriminator Ortec Model 417. 6. Time-to-amplitude converter Ortec Model 437. 7. Coincidence - Ortec Model 409. 8. Multichannel analyzer - RIDL 400 Channel. This circuitry is discussed on Page 60. SLOW ~040 n FAST .... ZERO-CROSSING DISCRIMINATOR ~ 3 He " - - STOP - a START ,.. TIME PICKOFF ~ L. v , - PREAMPLIFIER ...... (JI -0 AMPLIFIER TIME TO AMPLITUDE CONVERTER AMPLIFIER SINGLE CHANNEL ANALYZER MUL Tl - CHANNEL ANALYZER SINGLE CHANNEL ANALYZER GATE COINCIDENCE SCALER FIGURE 37 Time-of-flight spectrum of neutrons in coincidence with ~ -particles detected from the 18 17 3 o( He, a ) o(ll.075, T = 3/2) reaction. A uniform chance coincidence background and normalized real-coincidence background spectra have been subtracted. 5.6 MeV neutrons, obtained from the 13 The solid curve is a line shape for c(~,n) 16 o(O.O) reaction at an incident energy of 4.70 MeV; the darker dashed curve is a line shape for 0.86 MeV neutrons, obtained from the t(p,n) reaction at 1.7 MeV. The lighter dashed curve indicates the maximum background assumed in the calculation of the branching ratio for the decay of the discussion of this spectrum, see Page 63. 17 o(T = 3/2) level to 16 0 (6.05 + 6.13). For further °'0 IOOO.--~~~--.-~~~-.--~-.~~-.~--.-~--.----.-,-rrr.-r-~~-, ( 6 0(0) 180 (3He, a) 170 ( 11.075) L160 + n E3He= 12MeV (f) w 100 u z w ..... 0 °' u z 0 u c I 10 LINE SHAPES ~ En= 5.6 MeV ---- En = 0.86 MeV l 0.5 0.75 1.0 1.5 2.0 NEUTRON ENERGY (MeV) 4.0 6.0 10.0 162 FIGURE 38 Line shapes for 5.6 MeV neutrons determined from the 13 3 16 . 0 C( He,n) O (O.O) reaction at 80 for 4.7 MeV incident energy with the neutron detector in the magnet geometry (solid curve) and inside the cannon mount (dashed curve). The arrows indicate the region sunnned to determine the relative detection efficiency for the two geometries. see Page 58. For a discussion of the magnet geometry, For a description of the cannon mount, see Page 9 . For further discussion of this figure, see Page 66. 163 •--MAGNET (x1/s) o ___ "CANNON• 2000 1000 ...... z 500 z c 0 :z: ~ 200 0 .... "' o/ z ::> 0 u I 100 I I \ ·i I 0 /oo 01 50 cy 0 0 0 20 • 10 / /o o/ • lo J'o •• b \· 0 10 20 30 CHANNEL 40