A Study of T = 1, T = 3/2, and T = 2 States in Some Light Nuclei Using (He³,n) Reactions Citation Adelberger, Eric George (1967) A Study of T = 1, T = 3/2, and T = 2 States in Some Light Nuclei Using (He³,n) Reactions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/D6GW-RW22. https://resolver.caltech.edu/CaltechTHESIS:11022015-134907826 Abstract The (He 3 , n) reactions on B 11 , N 15 , O 16 , and O 18 targets have been studied using a pulsed-beam time-of-flight spectrometer. Special emphasis was placed upon the determination of the excitation energies and properties of states with T = 1 (in Ne 18 ), T = 3/2 (in N 13 and F 17 ) and T = 2 (in Ne 20 ). The identification of the T = 3/2 and T = 2 levels is based on the structure of these states as revealed by intensities and shapes of angular distributions. The reactions are interpreted in terms of double stripping theory. Angular distributions have been compared with plane and distorted wave stripping theories. Results for the four reactions are summarized below: 1) O 16 (He 3 , n). The reaction has been studied at incident energies up to 13.5 MeV and two previously unreported levels in Ne 18 were observed at E x = 4.55 ± .015 MeV (Γ = 70 ± 30 keV) and E x = 5.14 ± .018 MeV (Γ = 100 ± 40 keV). 2) B 11 (He 3 , n). The reaction has been studied at incident energies up to 13.5 MeV. Three T = 3/2 levels in N 13 have been identified at E x = 15.068 ± .008 MeV (Γ ˂ 15 keV), E x = 18.44 ± .04, and E x 18.98 ± .02 MeV (Γ = 40 ± 20 keV). 3) N 15 (He 3 , n). The reaction has been studied at incident energies up to 11.88 MeV. T = 3/2 levels in F 17 have been identified at E x = 11.195 ± .007 MeV (Γ ˂ 20 keV), E x = 12.540 ± .010 MeV (Γ ˂ 25 keV), and E x = 13.095 ± .009 MeV (Γ ˂ 25 keV). 4) O 18 (He 3 , n). The reaction has been studied at incident energies up to 9.0 MeV. The excitation energy of the lowest T = 2 level in Ne 20 has been found to be 16.730 ± .006 MeV (Γ ˂ 20 keV). Angular distributions of the transitions leading to the above higher isospin states are well described by double stripping theory. Analog correspondences are established by comparing the present results with recent studies (t, p) and (He 3 , p) reactions on the same targets. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Barnes, Charles A. Thesis Committee: Barnes, Charles A. (chair) Frautschi, Steven C. Neugebauer, Gerry Tombrello, Thomas A. Defense Date: 15 March 1967 Funders: Funding Agency Grant Number NSF UNSPECIFIED Caltech UNSPECIFIED Record Number: CaltechTHESIS:11022015-134907826 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11022015-134907826 DOI: 10.7907/D6GW-RW22 Related URLs: URL URL Type Description https://resolver.caltech.edu/CaltechAUTHORS:20150908-150520567 Related Item Article in CaltechAUTHORS Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9267 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 03 Nov 2015 17:20 Last Modified: 11 Mar 2024 20:28 Thesis Files Preview PDF - Final Version See Usage Policy. 36MB Repository Staff Only: item control page

A STUDY OF T = 1, T = 3/2, AND T = 2 STATES IN SOME LIGHT 3 NUCLEI USING (He , n) REACTIONS Thesis by Eric George Adelberger In Partial Fulfillment of the Requirements For the Degree of . Doctor of Philosophy California Institute of Technology Pasadena, California 1967 (Submitted March 15, 1967) / ii ACKNOWLEDGMENTS It is a distinct pleasure to acknowledge the stimulating and thoroughly enjoyable atmosphere provided by the staff of the Kellogg Radiation Laboratory. Especially pleasurable and helpful · were numerous conversations with Professor C. A. Barnes, who suggested much of this work, and with Professor T. A. Tombrello. Dr. N. B. de Takacsy has been exceedingly generous with his time and his theoretical insights. I am deeply indebted to Dr. F. S. Dietrich III who introduced me to the techniques of time-offlight spectroscopy. Financial assistance from the National Science Foundation and the California Iristitute of Technology is gratefully acknowledged. It has been a pleasure to work with Mr. A. B. McDonald in the later stages of these experiments, and to have had the able assistance of Mr. R. W. Moore in data reduction. Finally, I wish to thank my wife for choosing to spend weekends with me in the incomparable high mountains of California, rather than prosaically typing up this thesis. iii ABSTRACT 3 11 15 The (He , n) ·reactions on B , N , 0 16 , and 0 18 targets have been studied using a pulsed-beam time-of-flight spectrometer. Special emphasis was placed upon the determination of the excitation 18 energies and properties of states with T = 1 (in Ne ), T = 3/2 (in 20 13 17 and F ) and T = 2 (in Ne ). The identification of the T = 3/ 2 N and T = 2 levels is based on the structure of these states as revealed by intensities and shapes of angular distributions. The reactions are interpreted in terms of double stripping theory. Angular distributions have been compared with plane and distorted wave stripping theories. Results for the four reactions are summarized below: 16 1) 0 3 (He , n). The reaction has been studied at incident energies up to 13. 5 MeV and two previously unreported levels in Ne 18 were observed at Ex= 4. 55 + • 015 MeV (r = 70 ± 30 keV) and Ex = .5. 14 +. 018 MeV (r = 100 ± 40 keV). 3 (He , n). The reaction has been studied at incident 13 energies up to 13. 5 MeV. Three T = 3/2 levels in N have been 2) B 11 identified at Ex= 15. 068 ± • 008 MeV (r < 15 keV), Ex= 18. 44 ± • 04, and Ex= 18. 98 + • 02 MeV (r = 40 ± 20 keV). 3) N 15 3 (He , n). The reaction has been studied at incident 17 energies U.P to 11. 88 MeV. T = 3/ 2 levels in F have been identified at Ex= 11. 195 ± • 007 MeV (r< 20 keV), Ex = 12. 540 + • 010 MeV (r < 25 keV); and Ex= 13. 059 + • 00.9 MeV (.r < 25 keV). 4) 0 18 3 (He , n). The reaction has been studied at incident energies up to 9. 0 MeV. The excitation energy of the lowest T = 2 20 level in Ne has been found to be 16. 730 ± • 006 MeV (r < 20 keV). iv Angular distributions of the transitions leading to the above higher isospin states are well described by double stripping theory. Analog correspondences are established by comparing the present results 3 with recent studies of (t, p) and (He , p) reactions on the same targets. v TABLE OF CONTENTS PART PAGE L INTRODUCTION 1 II. APPARATUS 7 A. Beam Pulsing System 7 B. Neutron Detector and Shielding 12 c. Counting Electronics D. IIL 14 Target Chambers and Integration 16 EXPERIMENTAL METHOD 18 A. Calibration of the Time Scale and the Measuring of Q- Values IV. B. Determination of Detector Efficiency 21 c. Determination of Level Widths 16 18 3 A STUDY OF THE o (He ,n)Ne REACTION 22 25 Introduction 25 B. Experiment 27 c. Excitation Energies 28 D. Widths 30 A. v. 18 E. Angular Distributions 31 F. Conclusions 38 OBSERVATION OF T = 3/ 2 STATES IN N 11 13 3 USING THE REACTION B (He , n)N A. Introduction 13 39 ,-,\ f 39 B. Experiment 42 c. Excitation Energies 44 vi PART PAGE D. Widths 46 E. Angular Distributions 48 F. Conclusions 50 OBSERVATION OF T = 3/2 LEVELS IN Fl 7 IN 3 15 THE REACTION N (He ,n) 53 . A. Introduction 53 B. Experiment 55 VL c. Excitation Energies 57 D. Widths 59 E. VIL vm. Angular Distributions and DWBA Fits 60 F. Conclusions 62 OBSERVATION OF THE LOWEST T = 2 STATE IN Ne 2 0 IN THE REACTION o 18 (He 3 ,n) 64 A. Introduction · 64 B. Experiment 66 C. Excitation Energy of the Lowest T = 2 State 20 D. Width of the Lowest T = 2 Level in Ne 68 E. Angular Distributions · 70 CONCLUSION 72 70 APPENDICES 74 REFERENCES 83 TABLES 87 FIGURES 102 1 L INTRODUCTION This thesis describes an investigation of the (He 3 , n) 18 16 11 15 reactions on targets of B , N , 0 , and 0 , with special emphasis on the determination of the excitation energies and 18 13 17 · properties of states with T = 1 (in Ne ), T = 3/2 (in N and F ) 20 and T = 2 (in Ne ). The neutrons were detected and studied by means of a pulsed-beam time-of-flight spectrometer which is . described in Part II of the thesis. Because of current interest in the electromagnetic splitting of isobaric multiplets an effort was made to obtain as precise values as possible for the excitation energies of the T = 3/2 and T = 2 levels. The identification of the . levels with T = 3/ 2 in the T z = 1/2 nuclei and T = 2 in the T z = 0 nuclei is, of necessity, somewhat . indirect. The widths of these states cannot be measured with the present technique since they are expected to be much less than the experimental resolution. They lie at high excitation energy where the level density is so great that one cannot identify them on the basis of excitation energy alone, since many states may lie within the range of excitations where the higher isospin state is expect ed. The identifications therefore were made on the basis of the structure of these states, as shown by angular distributions and intensities, using the selection rules imposed by a simple, one-step, stripping mechanism. These can be summarized as, 2 . tJ.A = 2 /J.1T = (-1) --+ L (1) _. !J.J = L ' where L is the orbital angular momentum of the transferred protonpair which can usually be inferred from the shape of the neutron angular distribution. The first two selection rules, on A and T, are of course quite rigorous, depending only upon the properties of the nucleon. The last two are approximate, depending on the s-wave 3 purity of the :He wave function, which is quite good, and upon the validity of the assumed model of a one- step stripping process. The latter assumption is somewhat questionable since simple stripping must compete with other reaction mechanisms (such as stripping with core ex citation, the so-called heavy-particle stripping, and compound nuclear formation). This simple model, however, will be shown to be rather successful in describing the reactions reported in this thesis. It should be noted that for (He 3 , n) stripping, unlike deuteron stripping, there is no ambiguity in the selection rule for J. --+ The bi. T = 1 selection rule is, of course, one of the main reasons why this reaction is so attractive as a device for studying states of higher isobaric spin. Although the (p, n) reaction has the same selection rule, it is not expected to be as effective in identifying the low-lying T = 3/2 levels in the light nuclei with 3 A = 4n + 1. (A similar argument applies to the T = 2 levels.) To see this, we shall assume that the extreme single particle shell model describes the lowest lying T = 3/2 levels, which are bound in the (4n + 1) nuclei with respect to the strong interactions. Then 17 the lowest T = 3/2 level in F , for example, should have a two16 particle, one-hole configuration based on an 0 core. The "quasi17 elastic" (p, n) reaction on 0 should mainly populate single-particle 17 states, especially the ground state of F , which is the "mirror" of 17 the 0 ground state. In other words, it changes T but not T. z 15 3 N (He , n) on the other hand, will strongly populate two-particle, one-hole states and should be much more effective than 0 17 (p, n) in identifying the lowest T = 3 / 2 levels in F 17 • The influence of the structural properties of the higher isospin levels upon the intensities observed in a one- step stripping 9 3 process is well illustrated by the reaction Be (He , n)c 11 (T = 3/2). This transition is, of course, allowed by the isospin selection rules . . 11 However, the spin and parity of the lowest T = 3/2 lev.e l in c are expected to be 1/2+ (Talmi and Unna 1960) which cannot be reached by a one- step stripping process except via ls hole impurities in the 9 Be ground state, or by placing a proton in the 2s shell. The (He 3 , n) transition in this case should be very weak. We have examined this reaction and were unable to see the transition to the lowest T = 3/2 level. In order to take full advantage of the selection rules (1) it is necessary to determine the transferred angular momentum L. In order to extract this quantum number, one needs a detailed theory of the stripping process. The simplest form of such a theory uses the Plane Wave Born Approximation (PWBA). Although it has been claimed that the PWBA is never a good approximation (see for 4 example Satchler 1964) it has the virtue of yielding analytic solutions. A widely used approximate form of this theory for double stripping (Newns 1960) yields the expression (2) . where m k=k _ _!k He3 y = • 255 f mF n ' -1 m and mF are the masses of the target and residual nuclei, and r 0 1 is a cutoff which should be on the order of the nuclear radius. This approximation has met with some success in describing the shape of angular distributions, particularly in the extensive study of (t, p) reactions by Middleton and Pullen (1964a, 1964b). However, absolute cross sections predicted by the theory are quite unreliable. Further- more, Middleton and Pullen have pointed out that for negative Q-value transitions the plane wave theory is very sensitive to the choice of r , 0 since k is not necessarily small at forward angles. It is often possible to get equally good fits with several L-values by making small changes in r 0 • Therefore, they regard L-value assignments for negative Q-value transitions as tentative. This defect in the theory is of serious concern in the present study since the transitions 5 of interest have Q-values between -3. 2 and -8 MeV. Similar difficulties with the plane wave theory were encountered in this work and are discussed in Part m. Recently it has become practical to make a more sophisticated approximation, in which the first Born Approximation matrix element is taken between elastic scattering, rather than plane waves. This distorted wave Born Approximation (DWBA) in which the scattering waves are generated by the optical model has been treated extensively; a detailed discussion is given by Bassel, Drisko, and Satchler (1962). Although DWBA calculations cannot be carried out analytically without making unsatisfactory approximations, a vast body of deuteron stripping data has been successfully fitted by DWBA calculations in many cases where difficulties were encountered with the PWBA. Recently a few two-nucleon DWBA stripping calculations have been ·published which appear to be quite successful (see for example Glover and Jones 1966b). We have also attempted to fit our data using the DWBA, with results which are, in general, quite acceptable. The success of the calculations has made it possible to extract some unambiguous L-values (which was not possible with the plane wave theory) and supports the assumption that a one-step stripping process 3 dominates the (He , n) transitions to the observed low-lying states with T = 1, T = 3/2, and T = 2. Since DWBA two-nucleon stripping calculations have not been extensively treated in the literature, a brief discussion of this topic is presented in Appendix B. The logical outline of the work presented here is as follows: 1) Since the identification of higher isospin levels rests upon the double- stripping model, we first tested the model in a case where the structure of the low-lying states of the residual nucleus is fairly 6 well known, the reaction 0 16 3 18 (He , n)Ne • This reaction was studied in some detail and it was found that the DWBA theory provided an acceptable description of the transitions to the low18 lying levels of Ne • This work is discussed in Part IV. 2) Having thus achieved some confidence in the double-stripping model; in Parts V, VI, and VII we describe a search for higher11 3 13 isospin states in the reactions B (He ,n)N (T = 3/2), . N 15 (He 3 ,n)F 17 (T = 3/2) and o 18 (He 3 ,n)Ne 20(T = 2). These reactions were expected to populate the low-lying higher- isospin levels strongly and this expectation has been well confirmed in the present work, and in an earlier study of the reaction 9 Li7 (He3 , n)B (T = 3/2) by Dietrich (1964, 1965). 7. II. APPARATUS The experiments reported here were all performed using the pulsed-beam time-of-flight spectrometer facility at the ONRCIT tandem accelerator. This system has been described previously (Dietrich 1964). However, since 1964 several important . changes have been made which significantly improve the performance of the system. We shall therefore describe the spectrometer with particular emphasis upon those features which have been modified since 1964. A. Beam Pulsing System A schematic drawing of the beam pulsing system is presented in Figure 1. The continuous beam from the tandem accelerator is chopped into pulses with a duration of approximately one nanosecond by applying a radio frequency (RF) voltage to a pair of deflection plates located at the high energy "tee" of the tandem. The beam is swept vertically (in order to avoid interfering with the energy regulation of the tandem) at 3. 531 MHz across a pair of chopping slits located near the image focus of the 90-degree analyzing magnet, immediately behind the slits used to regulate the accelerator. Placing the chopping slits at the image rather than between the object of the 90-degree analyzer and magnet itself as was done prior to 1964 offers several advantages. Since the chopping slits are after the image slits, a larger beam current is available for regulating the tandem, which makes it easier to obtain regulation before the beam has been tuned for maximum current. Also since .the beam spot at the new slit location has a smaller 8 diameter (being close to the image focus) and is a greater distance from the deflector, a smaller angular deflection is needed to obtain a given burst duration. In order to increase the time-averaged pulse beam current, the ions are velocity modulated (bunched) before entering the tandem so that the current immediately before the chopping slits passes through sharp maxima. If the phase and amplitude of the bunching voltage are properly adjusted the current maxima will occur just as the beam is sweeping past the slit opening and the beam current pulses will be greatly enhanced (Dietrich 1964). Two separate bunchers are required--one for negative-ion (hydrogen isotope) injection and one for neutral (helium isotope) injection. This is necessary since the helium ions have already been neutralized before passing through the negative-ion buncher. (see Figure 1). In order for the bunching to be effective the fluctuations in the mean flight time T F of ions from buncher to deflector must be smaller than the beam burst duration c, or else the current maxima will be out of phase with the deflector. This requirement of phase stability imposes a severe restriction on the energy spread 6. E/E of the ion source, 6.E E (3) For example, in the case of neutral injection, helium ions are injected at 650 keV and must travel about 13 meters before being accelerated and passing through the deflector. If one desires 1. 5 nanosecond bursts, the injection energy must therefore be regulated to better than 500 eV to gain full advantage from the buncher. 9 Prior to 1965 the small electrostatic generator which serves as a helium ion injector was regulated only by the generating voltmeter; the energy stability was so poor that constant manual control of the injection energy was necessary 3 to achieve time-averaged He ++ currents as high as 30 nanoamperes, even with bursts as long as 5 nanoseconds. Following a suggestion of C. A. Barnes an improved energy regulator for the helium injector was installed in early 1965. It derives its energy regulation signal from the un-neutralized fraction of the injected beam which is momentum analyzed by deflection in the 20° magnet supplied with the accelerator. The improved injector still required constant manual fine control of the injection energy, but allowed one to obtain time-averaged He3++ currents up to 100 nA with approximately 2 nanosecond beam bursts.· This method of beam stabilization could probably have been much improved by deflecting the charged beam through a larger angle and by improving the optical properties of the deflection magnet, both of which would have required the acquisition of a new magnet. However, accurate regulation of the injection energy is not the only way to achieve phase stability. As an alternative, one can accept relatively poor regulation of the injection energy and electronically adjust the phase of the bunching waveform to compensate for variations in the injection energy. In the summer of 1966 a phase stabilizer working on this principle was developed. Details of the stabilizer principles and circuitry are ·found in Appendix A. With the phase stabilizer in operation time-averaged He 3++ currents up to 200 nA with 1. 5 nanosecond bursts are achieved with no manual control of the energy regulation. In addition, the beam 10 current is very steady, which greatly simplifies tuning procedures on the tandem accelerator. It is interesting to consider some of the factors which limit the ·shortness of the beam bursts as observed at the target. These are: 1) the minimum attainable burst duration at a point immediately after the chopping slits, 2) the spreading of the bursts due to variations in the lengths of orbits between the chopping slits and target 1 3) the spreading of beam bursts due to space charge effects, and 4) the spreading of the bursts due to fluctuations in beam energy. Such fluctuations come from the · energy modulation introduced by the buncher and chopper as well as imperfect regulation of the tandem. Let us consider these in inverse order. The distance from chopping slits to the target is approximately 20 meters. Over this 3 distance a 10 keV variation in the energy of a 10 MeV He beam will produce a flight time difference of only O. 4 . nanoseconds. The energy spread introduced by the buncher should be less than 10 keV since the most heavily modulated ions do not arrive at the deflector in phase t o pass through the slits. A direct calculation of space charge effects is quite difficult. However, Flerov (1957) has bunched a 200 keV ion beam to give O. 5 nanosecond bursts and peak currents of 5 mA. Since peak currents 11 on the Caltech tandem after bw1ching are at best only ,...., 30 µA, it is not expected that space charge effects are a significant factor in determining the beam burst duration. Next we estimate the possible variations in path length of orbits between the chopping slits and the target. Since there are two quadrupole magnets along the 20 meter path between chopping slits and target we will consider that the beam passes through a point focus 3 times. The maximum variation in flight paths is given by the difference between the lengths of the "straight" orbit and the orbit limited by the magnet apertures, taken to be 2. 5 cm in radius. In this case the variation in path length is only • 25 mm. This corresponds to a time spread of 10 picoseconds which is negligible. One might think that the duration of the beam bursts immediately after the chopping slits could be made shorter than 1 nanosecond, at the expense of beam current, merely by making the deflection voltage sufficiently large. This is not true for the deflection geometry used in these experiments. This can be seen as follows. Those ions which pass through the chopping slits (i.e., which have the correct vertical deflection) must all have passed through the deflection plates within a time interval which can be made very short by increasing the deflection amplitude. However, if the orbits between deflector and choppi~g slits are not isochronous, the beam bursts at the chopping slits cannot be shorter than the variation in transit time. In the geometry used here the orbits are definitely not isochronous because of the range in orbits allowed by the 90-degree analyzing magnet. We can estimate the magnitude of this effect as follows: We assume that inhomogeneities in beam 12 energy and slit spacings are negligibly small. We then assume that the beam at the foci of the magnet has the full angular spread allowed by the horizontal aperture of the mag11et, taken to be 1. 25" (Pearson 1963), so that the difference in path length of orbits which just graze the inner and outer edges of the vacuum box is 1. 75". (Variations in path length due to the 6.r/r allowed by the entrance and exit slits . are negligible in comparison with this difference.) For 10 MeV 3 He ++ ions, this corresponds to a minimum burst length of 1. 75 nanosecond. These calculations are supported by experience with the pulsed- beam apparatus. As the deflection voltage is increased to a certain value the time resolution of the system is improved and the time- averaged current goes down. If the voltage is increased to yet higher values the time- averaged current continues to drop-but the time resolution never gets better than about 1. 8 nanosecond. B. Neutron Detector and Shielding A neutron detector for time-of-flight applications must have the following properties: 1) it must have a large enough area to subtend a reasonable solid angle at the flight paths contemplated (in this case 1. 0-3. 5 m). 2) it must detect the neutrons by as efficient a process as possible so that the detector thickness introduces only \ a small uncertainty in the flight path. 3) it must have a fast time response. 13 These requirements are conventionally met with a protonrecoil scintillation counter which takes advantage of the large p-n scattering cross section and the fast response of a plastic scintillator. All the work described in this thesis was done using a 2" thick by 5" diameter piece of "Pilot B" plastic scintillator monnted on a fast 5"-diameter phototube of type 58AVP or XP1040. The rise time of this combination is approximately 3 nanoseconds. In order to reduce the background, principally gamma rays and neutrons, the detector is buried in a massive collimator and shield. Room-scattered neutrons are attenuated by a 6. 5"-thick cylinder of lithium carbonate and paraffin while the gamma rays are attenuated by a lead cylinder 1. 625" thick. Since a major source of the gamma background is from annihilation radiation produced by 3 the positron decaying products of He -induced reactions, a 1/ 2"-thick lead disc is · placed in front of the neutron detector. This attenuates 511 keV gamma rays by a factor of 8. 5. The total neutron cross section for lead in the range 1. 0-20. 0 MeV is quite flat and neutrons in this energy region are attenuated only by a factor of about 1. 5. The collimation of neutrons with energies between O. 5 and 30 MeV is not as simple as for charged particles, however, and the shield is a mixed blessing as can be seen from Figure 2 7 which shows a . 11 B (p, n) spectrum. Note that, although the gamma peak is very clean, the neutron peak has a pronounced tail on the side corresponding to longer flight times. This tail is not present when the detector is used without the shield, and seems to arise from two sources: 1) neutrons which scatter off the inner walls of the collimator and thus have longer flight times, and 2) (n, y) reactions in the shielding material. 14 The main difficulty caused by the tail are ambiguities in determining the detector efficiency, and a distortion of spectrum shapes in complicated spectra-especially in those cases with a pronow1ced continuum. The detector, shielding, and fast electronics are all mounted on a cart which is constrained to move along a steel !beam. The I- beam is pivoted about a spot directly below the target, allowing the detector to be easily and reproducibly placed at laboratory angles between 0 degTees and 150 degrees, and flight distances from 1. 0 to 3. 6 meters. C. Counting Electronics The electronic circuitry directly associated with the measurement of flight times is described and shown in a block diagram in Figure 3. In pulsed- beam experiments the flight time is determined by the time interval between two signals--one derived from the detector and the other from either the beam current pulse at the target or the RF waveform used in the beam pulsing apparatus. In the present work,. the ST ART pulse for the time-to-pulse-height converter (TPHC) is taken from the neutron detector and the STOP pulse from the RF waveform. Two signals are obtained from the photomultiplier tube, a fast bipolar timing signal from the anode, and a slow, chargemeasuring signal taken from dynode 11. The anode signal is clipped at the tube base by a shorted cable 37 cm long, producing a fast signal which is roughly proportional to the time de rivative of the current pulse at the anode and crosses through zero with a large positive slope. The START pulse for the TPHC is generated 15 by a discriminator which "picks off" the zero crossing point of the fast signal. Ideally the zero-crossing discriminator (ZCD) should produce a pulse with a constant shape whose delay relative to the zero crossing time should be independent of the amplitude of the start pulse, that is, it should exhibit no "time-slewing". The majority of the data for these experiments was taken using a Tektronix Type 661 Sampling Oscilloscope as a ZCD--with the ST ART pulse obtained from the Delayed Pulse output of the oscilloscope. The oscilloscope has a slewing of 1-1. 5 ns/20db, and provides a convenient monitor of the apparatus. . In addition, a ZCD was developed based on a design of Brafman (1965). It has superior slewing properties but has a more limited dynamic range. The slow signal from the photomultiplier is used to gate the multichannel analyzer. It is amplified and fed into a lower level discriminator which rejects almost all phototube noise and those pulses due to events producing insufficient light to give good time resolution. Thus the discriminator bias partially determines the detector sensitivity, especially for low energy neutrons. The STOP pulse for the TPHC is derived from the RF signal induced in a two-turn loop located near the plates of the beam deflector. The signal is amplified and squared before being fed to a discriminator which therefore "picks off" the time at which the RF signal went through zero. The performance of the detector and counting circuitry was tested as shown in Figure ·4. A Na 22 source was used as a source of coincident 511 keV gamma rays and was viewed by two scintillation counters both using XP1040 tubes. The phototube, scintillator, and fast electronics in one channel were those used in the time- of-flight work. The other channel used similar apparatus. The resolving 16 time of the apparatus was 1. 5 nanoseconds FWHM, which yields approximately 1. 0 nanoseconds per counter and associated . electronics, since the time converter and slow amplifier contributes little to the observed time spread. With the improved resolution ma.de possible by the phase stabilizer it was found that phase drifts in the STOP pulses were . a ma.j or source of line width broadening. This contribution to the · resolution was greatly reduced in the summer of 1966 by using a digital spectrum stabilizer operating on the prompt gamma peak to adjust the zero level of the analyzer to compensate for the STOP pulse drift. It was also found that a 1% change in the amplitude of the chopping voltage caused a shift of O. 1 nanosecond in all pea.ks. In order to reduce this source of phase drift, an automatic gain control was added to the main chopper amplifier. D. Target Chambers and Integration Since both solid and gaseous targets were employed in the course of this work two different target chambers were used. The chamber used for solid targets was made of glass and was of conventional construction. The gas target is shown in Figure 5. The nickel entrance foils used were nominally 5000 angstroms thick. The gas cell is constructed of stainless steel and lined with tantalum to reduce the empty target background. In all cases the targets were held at +300 V to prevent loss of electrons caused by secondary emission from the target, and the 17 beam passed through a suppressor electrode at -300 V before reaching the target. Integrated beam charge was collected on an Eldorado Model CI-110 Current Integrator which was used to gate the multichannel analyzer. 18 III. EXPERIMENTAL METHOD .. . A. Calibration of the Time Scale and the Measuring of Q- Values · We first discuss some general features of the time spectra obtained in this work and then discuss the techniques by which they are converted into equivalent spectra with neutron energy as the · independent variable. All spectra were taken using 200 charu1el subgroups of the RIDL analyzer with the time scale chosen to be approximately 1 ns/ channel. However, due to extreme nonlinearity in the multichannel analyzer the lowest 20 channels are unuseable so that in effect the longest measureable flight time is about 180 nanoseconds. Since the time-to-pulse-height converter measures the interval between a START pulse triggered by a neutron arriving in the detector and the next STOP pulse, short flight times correspond to large pulses from the time converter. Thus, · neutron energy increases with increasing channel number. Since the STOP pulses are not, in general, coincident with the arrival of beam bursts at the target, but are delayed by a constant but arbitrary interval, one cannot measure flight times directly. Instead, one always measures the difference in flight time between neutrons and the prompt gamma ray group which is present in all our spectra. The time scale calibration and calculation of relativistic Q-values were performed with the aid of a 7094 program developed by Dietrich (1964). At the beginning of every running day a linearity spectrum (see Figure 6) was taken with a Cs 137 source producing the START pulses, and the STOP pulses generated as usual from the RF . waveform. Since these time intervals are random, the linearity 19 spectrum would be flat if the time-to-pulse-height converter, amplifier, and analyzer were indeed linear. The linearity spectrum is first "smoothed" by averaging the counts in a given channel with those on either side of it, and then a time interval proportional to the counts in the smoothed spectrum is assigned to each channel. The proportionality constant can then be evaluated . if the time difference between any two channels is known. Two methods for producing peaks separated by a known time interval were used. The most convenient is to use a calibrated delay cable inserted between the STOP pulse discriminator and the time converter to shift the time spectrum a known amount. The cable (approximately 100' of RG 8/U) was calibrated by two independent means - by using neutrons of known energy and by using an RF oscillator. The calibration using neutrons was made by producing neutrons of about 1 MeV from the B 11 (p, n) and Li7 (p, n) reactions, for which the Q-values are well known. The flight paths and energies were adjusted so that the flight time difference between neutrons and gammas was nearly equal to the delay time of the cable. The mean of seven separate determination gives a delay time of 149. 5 ± O. 2 nanoseconds. The calibration using an oscillator was made by shorting one end of the cable and driving the other end with an oscillator. The driving frequency was adjusted to produce a node in the standing wave pattern at the oscillator end of the cable, and this frequency was measured using the Hewlett Packard Frequency Meter which is used in the NMR apparatus. Ten nodes were found corresponding to the fundamental and the first nine harmonics. The ten frequencies f n were fitted with an empirical formula 20 n - • 00621 ) /fn L = ( "2 (4) and give a mean delay time of 150. 5 ± O. 1 nanoseconds. Combining these results yields 150. 0 ± O. 5 nanoseconds .for the cable length, which provides an accurate enough time calibration for all but the most precise work. When the maximum precision was desired from the time- offlight spectrometer, as in the accurate determination of Q-values, a different means of calibrating the time scale was employed. A calibration reaction with a well known Q-value was used to produce neutrons having essentially the same energy as the neutron group from the level under study. Then the spectrometer was used only as a device for comparing flight times, and errors due to nonlinearities in the time scale, uncertainties in the flight path, etc., cancelled out. In addition, some other important sources of error are partially cancelled by the procedure, for example, possible errors in the calibration constant of the 90° analyzipg magnet. With this calibration technique, errors in the resulting Q-value are usually dominated by uncertainties in the incident beam energies. Therefore, the calibration reaction was chosen so that the effects of any systematic errors in the beam energies were minimized. In order to minimize the effects of differential hysteresis in the beam analyzing magnet, the following procedure was used in setting the magnet current during Q-value determinations. The magnet current was first increased to approximately 40 A. , then reduced to zero, before carefully setting the current so as not to "overshoot" the resonance on the NMR magnetometer. 21 B. Determination of Detector Efficiency The pulse height spectrum produced by monoenergetic neutrons incident upon a proton- recoil scintillator extends from zero up to a maximum value determined by the neutron energy. Thus the detection efficiency is a function of the bias used in the slow channel. In order to keep the efficiency reproducible from day to day the bias was always set by the following technique. The lowerlevel discriminator was adjusted to reject those pulses having a height less than a point half way down the high energy side of the 137 Compton edge of 662 keV Cs gamma radiation. The gain of the slow amplifier preceding the discriminator was then increased by a factor of eight, effectively lowering the threshold by the same factor. The gain of the photomultiplier was always set so that all events which exceeded the bias in the slow channel also triggered the time-to-pulse-height. converter. The relative detection efficiency was measured with neutrons from the T(p,n) reaction, produced in a zirconiumtritide target. The efficiency was determined using the same detector and shielding geometry employed for all the work described here to eliminate the need for corrections due to scattering and absorption in the collimator and shield. The results of this determination are displayed in Figure 7. Here we have used the T(p, n) cross sections of Wilson et al. (1961) and Goldberg et al. (1961). The curve in Figure 7 is an expression derived by Dietrich (1964) in which multiple scattering, scattering from carbon, and scattering and absorption in the collimator and 22 shield are all neglected, and the (n, p) cross section is approximated by a simple analytical expression. Agreement is better than 5%, and for all purposes in data reduction the relative efficiency was taken to be the value given by Dietrich's expression with an error of± 5%. An absolute determination of the detection efficiency was . made for 6. 23 MeV neutrons using the D(D, n) reaction and a gas target. With the assumption that the effective temperature of the gas along the beam path did not differ appreciably from the temperature of the walls of the cell, and using the cross sections of Goldberg and LeBlanc (1960), the detection efficiency was measured to be .o. 323 + • 033 at 6. 23 MeV. Dietrich's expression predicts O. 282. All absolute cross sections were computed using Dietrich's expression with an uncertainty of ± 10% in the absolute normalization. C. Determination of Level Widths The determination of level widths using time-of-flight spectroscopy is difficult since the energy resolution of the apparatus depends upon many factors, some of which are very difficult to determine accurately. Among the factors which contribute to the resolution are beam energy resolution, beam burst length, electronic resolution, the total neutron flight time, the flight time of neutrons through the scintillator, and target thickness; the resolution function depends in a complicated way upon neutron energy and the energy of the incident beam. It is sometimes possible to measure the resolution of a given experimental configuration directly. This can be done if there exists a reaction which allows one to produce neutrons with the energy 23 of interest leading to a very sharp state, without changing the beam energy or target thickness appreciably. Then the resolution is simply given by the observed width of the sharp group. Unfortunately this is usually not possible when studying highly excited levels 3 populated by (He , n) reactions, since there are almost no known sharp states with high thresholds available for comparison. It is possible, however, to calculate the resolution function by making some reasonable approximations. These are: 1) The electronic resolution for neutrons is independent of neutron energy and identical to the electronic resolution for gammas. This assumption is not strictly valid because the electronic time resolution for events which produce little scintillation light is broadened by statistical fluctuations, and neutrons of interest usually produce smaller pulses than the gammas. However, variations in the electronic time resolution will not be very important since the total resolution for gamma rays has been measured to be 1 nanosecond, and we are dealing· with an overall resolution of 3- 5 nanoseconds for low energy neutrons. 2) The time resolution function due to the finite scintillator thickness can be approximated by a rectangle. 3) The beam energy spread is due entirely to energy losses in the target, and that the time resolution function due to this effect can likewise be approximated by a rectangle. The shape of the -prompt gamma peak present in all our time spectra is due to the effects of the beam burst duration plus the electronic resolution (which according to assumption 1) is the same for neutrons and gammas). The resolution function for neutrons is 24 then obtained by folding in the effect of the finite scintillator thickness and energy losses in the target. This is easily done by numerical methods. Of course, this technique does not reproduce the "tail'' due to the collimator. The procedure has been checked by computing the widths of neutron groups corresponding to bound levels in the residual nucleus, and comparing these with the observed widths. This technique predicts the widths to within O. 2 channels. For a sample fit see Figure 2. It is interesting to note that the predicted width of bound groups is always slightly less than the observed width, which is reasonable since assumptions 1) and 3) both cause us to slightly underestimate some contributions to the width. Once the resolution function is known, level widths can be determined in a straightforward manner by folding the time . resolution into the natural level shape, and varying the level width to give the best fit. The natural level shape is obtained by converting a Breit-Wigner shape into the corresponding function which has flight time as the independent variable. 25 IV. A STUDY OF THE o 16 (He 3 , n)Ne 18 REACTION A. Introduction The low lying T = 0 and T = 1 levels in the mass 18 nuclei have received considerable theoretical attention since they may be described with some success as two interacting nucleons outside a . doubly closed 0 16 core. Experimental work has been directed 18 18 almost exclusively toward 0 and F , since at tandem energies 16 18 3 Ne can be reached only via the 0 (He , n) reaction. A good summary of experimental and theoretical work on the low lying 18 states of 0 is given by Litherland et al. (1961) and Ollerhead 16 3 et al. (1965). Previous work on the (He , n) reaction by Towle o and Macefield (1961) using the counter ratio method had located levels in Ne 18 at 1. 88, 3. 36, and 3. 61 MeV excitation. Gale et al. (1961) and Krick and Legge (1966) have measured the angular distributions of neutrons corresponding to the ground and first excited states and interpreted the results in terms of Newns' plane wave theory (1960). Our interest in the o 16 3 18 reaction was originally (He , n)Ne directed toward testing double- stripping theories and this reaction provides an excellent test case. It was possible to obtain accurate experimental data since spectra are characterized by prominent sharp peaks and a weak continuum. This contrasts with the usual 3 situation with (He , n) reactions where the continuum dominates, and uncertainties in the background subtraction are a major source of error. The theoretical interpretation was also expected to be quite "clean". Because of the 6. 05 MeV gap between the ground and first excited states in 0 16 , core excitations should play a relatively . 26 unimportant role, and the double-stripping selection rules allow 16 only a single L-value for each transition since the 0 ground state has J:;: O. In addition wave functions for the T ::;; 1, A::: 18 levels, expressed as two coupled nucleons surrounding an inert core, are available, which allows one to compute spectroscopic factors. If we consider the. extra-core nucleons in Ne 18 to be restricted to the d 5; 2 and s subshells, we expect 6 states. 112 From the (d / )2 configuration we get the sequence o+, 2+, 4+, 5 2 d ; ) a 2+ and a 3+ state. It has from (s )2 o+, and from (s 112 5 2 112 been suggested (Ollerhead et al. 1965) that the lowest 5 states in 18 0 (see isobar diagram ;Figure 18) are due mainly to these o+, 2+, and 4+ configurations and that the 3+ occurs at 5. 37 MeV. 18 The spin of the 6th excited state in 0 at 4. 45 MeV has recently and unexpectedly been definitely established as 1 (Ollerhead et al. 1965) and there are strong indications that its parity is negative (Zeidman and Braid 1965). Such a state of course cannot be fitted 16 into the simple model of an inert 0 core surrounded by two sd shell nucleons, and it cannot be populated by double stripping except via impurities (for example 2 particle-2 hole or 4 particle-4 hole) in 16 the 0 ground state or by promoting a nucleon into the f shell. 712 18 In light of the extensive work on 0 and the simple model of the mass 18 nuclei, it was deemed interesting to examine the 18 mirror correspondences in Ne , and to use the reaction as a test of double-stripping theory. 27 . . B. Experiment The 0 16 3 (He , n) reaction was investigated at 8 different bombarding energies between 9. 0 and 13. 5 MeV. Angular distributions were taken at 9. 0, 9. 5, 10. 5, 11. 0 and 12. 5 MeV. Three different targets were employed. The majority of the data was taken using a target formed by oxidizing a carefully cleaned blank of tungsten to a deep blue color in an induction furnace. Domingo (1963) reports that such targets have a chemical composition of and are ~ 10 KeV thick for 2. 6 MeV protons. This target 6 was very stable and showed little tendency to pick up carbon. wo 2 • However, it had the disadvantage that the oxide layer was not well defined and therefore contributed some uncertainty to measurements of excitation energies and widths. 0 The gas cell (shown in Figure 5) with a 5000 A nickel entrance foil was used to obtain absolute cross sections, and permitted the thickness of the tungsten oxide target to be computed by comparison of yields from the wo2. 6 and gas targets. For Q·-value measurements attempts were made to use a target prepared by evaporating BaO onto tantalum, but it picked up carbon so rapidly that useful results were difficult to obtain. At all energies studied, the continuum is very weak and time spectra are dominated by sharp groups corresponding to previously ·observed states in Ne 18 at 0. O, 1. 88, 3. 36, and 3. 61 MeV excitation energy. These groups are readily resolved in the 9. 0 MeV spectrum shown in Figure 8. In addition spectra taken at 12. 5 and 13. 5 MeV (Figures 9 and 10) show intense groups 18 corresponding to previously unobserved levels in Ne at excitation energies of 4. 55 and 5. 14 MeV. No other narrow groups were seen 18 at excitations in Ne up to 7. 6 MeV. · 28 We demonstrate that the 4. 55 and 5. 14 MeV groups do 18 indeed correspond to levels in Ne in Figure 11. Here we have plotted the measured Q-value of the transitions to these levels assuming targets with 14 ::;, A ~ 18. We have made measurements at laboratory angles up to 150°. The points for the correct target mass should lie on a horizontal line. It is seen that in both cases . the best fit to a single Q-value is obtained for an A = 16 target, and targets with A= 14, or A= 18 are definitely excluded. 15 N can definitely be excluded as responsible for either the 4. 55 or 5. 14 MeV state since it has been studied (see Section VI of this thesis) and no sign is seen of the continuum or the intense · neutron group leading to the 3.10 MeV state in F 17 • This state would produce neutrons of a higher energy than any groups from o 16 (He3 , n) and would be clearly visible. . The relative intensities of the Ne 18 groups are the same for targets of tungsten oxide and natural oxygen gas. Since natural 17 oxygen contains only o. 37% 0 , the observed intensity of the 4. 55 MeV group in Figure 9 would require a zero degree differential 17 cross section of 370 mb/sr if it arises from 0 • We conclude therefore that the 4. 55 and 5. 14 MeV states are definitely in Ne 18 • C. Excitation Energies Q-values for the o 16 (He 3 , n) reaction leading to the previously unobserved levels at 4. 55 and 5. 14 were made using both the wo and BaO targets. The time scale in these measure2• 6 . 11 ments was calibrated using the ground state group from the B (p, n) reaction. 29 The energy loss of protons in the B 11 target was foW1d indirectly by using the magnetic spectrometer to determine the energy loss, in the boron layer, of He 3 ions elastically scattered from the tantalum target backing. This energy loss was then scaled for protons using the tables of Demirli.oglu and Whaling (1962). The energy loss in the BaO target was determined in a similar manner; however, the intense elastic scattering from the barium com pli.cated the determination. 3 The energy loss of He ions in the tungsten oxide target was estimated in two ways: 16 (He 3 , n) yield from the oxide target was 16 compared with the yield from 0 in a gas cell, to give the number 2 16 of 0 atoms/cm in the oXide target. The target was then assumed 1) The o to consist of a layer of wo 2 • 6 followed by pure W. The energy loss in the wo • layer was computed using the tables of Demi.rli.oglu and 2 6 Whaling. This method estimated the target as being 44. 6 keV thick . 3 . to 9. 9 MeV He ions. The 10 keV energy loss given by Domingo for 2. 6 MeV protons in the wo 2 • targets was scaled to He 3 ions using the tables 6 of Demirli.oglu and Whaling. With this method the target thickness 3 is estimated as 35. 4 keV for 9. 9 MeV He ions. The discrepancy 2) between the determinations is small enough that it contributes negligibly to the uncertainty in the incident energy. A sample calculation of the Ne 18 Q-values taken from runs using the tungsten oxide target is summarized in Table L A sample calculation of errors in the derived excitation energies is summarized in Table II. From the rW1S with the BaO target we obtain Ex= 4. 55 ± • 018 and Ex= 5. 13 + • 02 MeV; for the tungsten oxide 30 measurements we find E x = 4. 545 -+ • 016 and E x = 5.15+ - .02 MeV. A major contribution to the quoted errors arises from uncertainty in the beam energies. This error is systematic (we cannot be sure 3 that proton and He orbits through the analyzing magnet do not differ slightly) and we therefore combine our results to give E x = 4. 55 -+·. 015 and E x = 5.14 -+ .018 MeV. The uncertainty in incident . energy ± oE was taken to be one half of the theoretical maximum beam spread + oEm allowed by the slits (see Pearson 1963) oE 1 oEm 1 8 1 + 8 2 = -2( ). E=2 -E R (5) where E is the beam energy. 2 s 1 and 2 s 2 are the full widths of the object and image slits and R is the radius of the 90° magnet, taken to be 34". The only other significant source of error lies in the location 18 of the centers of the peaks corresponding to the levels in Ne • This error is dominated by counting statistics. A spectrum from which one of the Q-value measurements of the 4. 55 MeV state was taken is presented in Figure 12. D. Widths The levels at 4. 55 and 5. 14 MeV are unbound to particle 16 17 decays into F + p, and 0 + p + p(the 5. 14 MeV state can also 14 decay via 0 +a), and hence have measurable widths. Widths for · these levels were obtained from runs using both the barium oxide and tungsten oxide targets. The resolution function was calculated as described in Section illC of this thesis. The level widths were 31 found by folding the time resolution into that function which corresponds to a Breit-Wigner curve in an energy spectrum. The level width was adjusted to give the best fit by a chi-square test, with the experimental and calculated points normalized to the same area. With this procedure we obtain widths of 70 + 30 keV for the 4. 55 MeV state, and 100 ± 40 keV for the 5. 14 MeV state. The · errors are largely statistical and should be interpreted as standard deviations. E. Angular ·Distributions Angular distributions taken at 9. 0, 10. 5, and 12. 5 MeV incident energy are presented in Figures 13, 14, and 15 respectively. Sample spectra from which these distributions were derived a re shown in Figures 8 and 9. The choice of background is indicat ed by the straight lines. In the 9. 0 and 10. 5 MeV spectra, the groups corresponding to the O. 0, 1. 88, 3. 36, and 3. 61 MeV levels are clearly resolved, and the new levels are not visible. At 12. 5 MeV, the 3. 36 and 3. 61 MeV levels are not resolved, but the 4. 55 and 5. 14 groups are quite intense. The 10. 5 MeV distribution was taken with a gas target and hence cross sections at this energy are absolute. Cross sections were computed by the relation dcr j - do CM 2 q 1 -2 - - x 3. 839 x 10 mb/sr d"cM Qri n p doL d = Y -- - where Y = NTOT - NBACK is the experimental yield with background subtracted. (6) 32 Q = total charge collected Tl = detector efficiency - taken as the value predicted by Dietrich's expression d = flight path in meters qe = charge of bombarding ion n = atoms/molecule in the target gas p = pressure in crri Hg of the target gas The numerical constant is evaluated for a gas cell 1. 54 cm long containing gas at a temperature of 293°K. The error bars include contributions from counting statistics, uncertainty in choice of the mean background, and a 5% uncertainty in beam current integration and relative detector efficiency. The relative errors e were computed by the relation, 2 € where =± NTOT NTOT + (oNBACK) [ (NTOT - NBACK) 2 + (. 05) 2] 1/2 ' (7) is the total number of counts under a peak, · NBACK is the number of background counts under the peak, and oNBACKis the uncertainty in the mean background under the peak. In addition to the errors denoted by the flags there is an estimated uncertainty of ± 10% in the absolute normalization.· 33 When this work was begw1, we expected that the (He 3, n) results would be similar to those found at Et = 10 MeV in the 18 16 by Middleton and Pullen (1964b). mirror reaction o (t, p)o This data is shown in Figure 16, the smooth curves are planewave fits (Newns 1960). All levels can be fitted with a radius of 5. 5f except for the 4. 45 MeV state which is very weak and does . not seem to be reached by stripping, and the 5. 33 MeV stat~ which requires 5. Of. We have also analyzed our data at 9. 0 and 12. 5 MeV incident energy using the plane-wave theory. See Figures 13 and 15. The data can be fitted equally well with several sets of L-values by making small changes in the cutoff radius. The sensitivity of the shape of the plane-wave distributions to the choice of cutoff radius appears to be most pronounced in negative-Q transactions, an effect that has pre viously been observed by Middleton and Pullen. L-values for the levels at 4. 55 and 5. 14 MeV were obtained by assuming that the spins and parities of the ground and first excit ed 18 states of Ne could be inferred from the systematics of even - even nuclei and the known values in the mirror nucleus. This fixed the L value for these transitions as 0 and 2 respectively and required cutoff radii between 4. 0 and 4. 75f. A search for L = O, 1, 2, or 3 fits was then performed using cutoff radii between 3. 75 and 5. 25f, leading to tentative assignments of 1- for the 4. 55 MeV state and o+ or 2+ for the level at 5. 14 MeV. The 2+ assignment is favored since it requires a radius closer to that used in fitting the other levels. There are several troublesome points in the plane-wave analysis: 34 1) It is impossible to get a good fit to the ground and first- excited states using the same radius in both cases. This is true at both 9. 0 and 12. 5 MeV incident energy. 2) The cutoff radius necessary to fit :an experimental distribution with a given L-value is energy dependent. For the L = 0 ground state transition Gale et al. (1961) use 4. 3f at 5. 6 · MeV. We need 4. 5f at 9. 0 MeV and 4. Of at 12. 5 MeV. 3) The radii required by our data (4. 0 - 4. 75f) are much 16 smaller than the 5. 5f value used in the mirror reaction o (t, p). However, our cutoff is consistent with the 4. Of value we find for the B 11 (He 3 , n) reaction (see Figure 28). In the B 11 (t, p) reaction, however, Middleton and Pullen use a radius of 5. Of. Thus, it 3 appears that (He , n) transitions require systematically smaller radii than found for the (t, p) reactions on the same targets. Distorted wave calculations were undertaken to see if the . DWBA would remove the ambiguities found with the plane-wave theory. Results for the data at 10. 5 and 12. 5 MeV are presented in Figures 14 and 17. · The potentials used, taken without modification · 16 (except for Coulomb effects) from an analysis of the 0 (t, p) by Glover and Jones (1966b), are listed in Table XIV. parameters are the normalizations. The only free The fits are quite good, especially for the L = 0 transition, and are unambiguous as to Lvalue. It is not possible to greatly alter the shape of distributions by changes in the potentials and, except near threshold, different L-values have distinct shapes. In these and other respects the DWBA is clearly superior to the plane-wave theory. 35 An interesting and unexplained feature of this reaction is the variation in the shape of the angular distribution of the 1. 88 I MeV state. The zero-d~gree minimum is comparatively shallow at 9. 0 and 12. 5 MeV (Figures 13 and 15), and quite deep at 10. 5 . MeV (Figure 14) and 9. 5 and 11. 5 MeV (not shown). The dip appears to be deepest at incident energies around 10 MeV, as can be seen in the zero-degree spectrum taken at 9. 9 MeV (Figure 12). With the 10. 5 and 12. 5 MeV angular distributions and DWBA fits it is possible to assign spins and parities to some of 18 the levels in Ne , and to find mirror correspondences between 18 18 O and Ne . An isobar diagram of the mass-18 nuclei which summarizes this is presented in Figure 18. The ground and first excited states are well fitted by L = 0 and L = 2, and hence can definitely be assigned spin parities of o+ and 2+ respectively. The 18 analogs in 0 are obvious. The 3. 61 MeV level is fitted by L = 2, and not by L = 0, 1, 3, or 4. It probably is the analog of the 3. 92 18 MeV state in 0 • The angular distribution of the 3. 36 MeV "state" cannot be fitted with L = 0, 1, 2, 3, or 4. It is therefore likely that this "level" is an unresolved doublet corresponding to the 4+ and o+ 18 states in 0 at 3. 55 and 3. 63 MeV. In Figure 14 we have fitted the 3. 36 MeV level with a mixture of L = 0 and L = 4, and it seems satisfactory. The 4. 55 and 5. 14 MeV states are unbound to diproton decay and cannot be handled by our DWBA code, forcing us to rely upon the plane-wave results. We obtain fits for the 5. 14 MeV state for both L = 0 and L = 2. may be a The state has a significant (100 ± 40 keV)width and resolved doublet consisting, perhaps, of analogs of the 5. 25 18 MeV o+ and 5. 33 MeV o+ states in 0 • Such an assignment is favored by the relative intensities in the o 16 (He 3 , n) and o 16 (t, p) reactions. 36 18 When we try to fit the 4. 55 MeV state into the 0 level 16 3 sequence we find some striking difficulties. The o (He , n) transition to this level is quite strong, and is fitted in plane-wave theory by L = 1, and not by L = 0, 2, or 3. The plane wave L = 1 assignment must be tentative, but the level is intense and well fitted by L = 1, indicating that the reaction is most likely proceeding . by one-step stripping. We shall consider three levels in 0 18 as possible analogs of the 4. 55 MeV state: 1) the 0 18 4. 45 Me V 1 state. This state is an obvious choice since it would require the smallest level shift (+30 keV 18 18 between F and Ne ) of the three candidates, and its known spin 18 and parity is consistent with the strong L = 1 transition to the Ne 18 4. 55 MeV state. However, the 0 4. 45 MeV state is very weakly 16 populated in the o (t, p) reaction, as would be expected for L = 1 16 stripping from a doubly closed 0 core. If these states are analogs, the departure from mirror symmetry is quite remarkable. The ratio of peak cross sections of the "1-" level to the ground state is seven 16 3 16 times greater in o (He ,n) than in o (t, p). See Figures 15 and 16. This apparent violation of isospin conservation does not necessarily imply that the 4. 45 and 4. 55 MeV levels are not isobaric analogs, 18 since a similar difficulty is found for the lowest 2+ states in 0 and 18 Ne which are clearly analogs. The ratio of peak cross sections of the lowest 2+ state to the ground state is 2. 5 times greater in o 16 (He 3 ,n) {Figure 15) than in o 16 (t, p) (Figure 16). 2) the 0 18 5. 09 MeV state. If this state were the analog of the 4. 55 MeV state it would require a larger level shift (-570 keV 16 between F 18 and Ne 18). The angular distributions in the o (He 3 , n) and 0 16 (t, p) ·reactions to the states have different shapes, and the 37 peak cross section of the transition (in each case normalized to the 16 3 ground state) is three times larger in the 0 (He , n) reaction. 3) the 0 18 5. 25 MeV o+ state. If this state were the analog of the 4. 55 MeV level it would require a large (-710 keV 18 18 between F and Ne ) level shift, but the peak cross sections of the transition (normalized, in each case, to the ground state) are 16 16 3 . about equal in the o (He , n) and o (t, p) reactions. The L = 1 plane wave assignment favors alternative 1). If this assignment is correct, mirror symmetry is apparently broken. This apparent violation of isospin conservation may occur in either 18 18 16 the 0 target or in the residual nuclei 0 and Ne • The strong 16 3 16 L = 1 transition in o (He ,n) suggests that 0 has a substantial p-shell hole impurities. This is consistent with the wave functions 16 of Brown and Green (1966) who find that the 0 ground state is O. 874 Op-Oh, O. 469 2p-2h, and O. 130 4p-4h. The difference in o 16(t, p) and o 16 (He 3 , n) transitions to the 4. 5 MeV states appears to imply either that 1) the impurities in the 0 16 wave function violate isospin conservation, being more important in the proton shell, or 2) that the wave functions for the presumed analog states 18 18 in Ne and 0 are different. It is quite unexpected that the Coulomb interaction in such light nuclei should cause so blatant a departure from mirror symmetry. The solution to this intriguing puzzle must await further study, and perhaps a DWBA theory for unbound states. 38 F. Conclusions 3 (He ,n) reaction at incident energies up to 13. 5 MeV, corresponding to excitation in Ne 18 up We have investigated the 6 16 to 7. 6 MeV. In addition to previously reporte d levels at O. 0, 1. 88, 3. 36, and 3. 61 MeV excitation the reaction populates l e vels at 4. 55 ± • 015 and 5. 14 ± . 018 MeV. Angular distributions to all levels show characteristic stripping patterns. Some difficulties were experienced in analyzing our data with plane-wave stripping theory (Newns 1960), rendering the L values obtained somewhat uncertain. For the O. 0, 1. 88, 4. 55, and 5. 14 MeV levels we find L = 0, L = 2, L = 1, and L = 0 or 2 respectively. On the other hand, calculations using the distorted wave Born approximation reproduce shapes and intensities quite faithfully. The DWBA calculations give L = 0, L = 2, and L = 2 for the O. O, 1. 88, and 3. 61 MeV states respectively. The 3. 36 MeV state can be fitted with a mixture of L = 0 and L = 4. Higher levels are unbound to diproton decay and cannot be handled with conventional DWBA theory. A striking departure from mirror symmetry may have been 16 observed in the transition to the 4. 5 MeV state in the o (t, p) and o 16 (He 3 , n) reactions. The Ne 18 state is populated strongly in o 16 (He 3 , n) with L = 1, the 0 18 state has been found to have J = 1-, 16 but is very weak in 0 (t, p). · This discrepancy merits further investigation. 39 . · V. OBSERVATION OFT= 3/2 STATES IN N13 USING THE REACTION B 11 (He 3 , n)N 13 A. Introduction In the T z = 1/2 light nuclei with A = 4n + 1 . (n > 1), the lowest T = 3/2 levels are bound with respect to isospin-conserving particle decays. Thus, they are expected to be quite narrow, in spite of their high excitations. The first such levels to be seen were in 7 3 mass 9. Lynch, Griffiths, and Lauritsen (1965), studied Li (He , 9 7 3 p)Be (T = 3/2) and Dietrich (1964, 1965) used Li (He ,n) to study 9 B (T = 3/2). Continuing this program, we have searched for 13 11 3 T = 3/2 states in N using the reaction B (He , n). 11 13 Prior to this work and the related study of B (He 3 , p)c by Hensley and Barnes (1965), very little was known about the A = 13, T = 3/2 isobaric multiplet. · As usual, the T = -3/2 z member of the quartet had received the most attention. Middleton 11 and Pullen (1964a) used B (t, p) to see the ground and first nine 13 excited states of B , and assigned seven L-values using plane-wave double-stripping theory. No T = 3/2 states were known in either 13 13 C or N • 0 13 was seen via its delayed proton activity (Barton et al., 1963 and McPherson et al., 1965), but the mass was not directly determined. One may estimate the mass of the lowest T = 3/2 level in 13 13 N since the B ground state mass is known. We neglect ThomasEhrmann shifts and assume that except for Coulomb effects and the · neutron-proton mass difference, the masses of the different members of an isobaric multiplet are identical. Then we may write the mass of a member of an isobaric multiplet as 40 M(T ) = Z(M + M ) + (A - Z)M - B + Z(Z - l)KA-l/3 z p e . n (8) where B is the binding energy of the strong forces and is taken to be constant within a given multiplet, K is the Coulomb constant, which is assumed to be the same within an isobaric multiplet and for all levels of a given nucleus. We have, of course, neglected the .electron binding energies. If we evaluate K from the C 13 - N13 . 13 ground state mass difference, we can then use the B mass to predict an excitation of 15. 17 MeV for the lowest T = 3/2 levels 13 13 13 in N and C • The lowest T = 3/ 2 particle decay in N proceeds 12 via C (T = 1) + p. Thus T = 3/2 levels with excitations less than 17. 05 MeV are bound with respect to isospin-conserving strong decays. The first four excited states in B 13 have excitations between 3. 483 and 3. 712 MeV. Therefore, by analogy we expect 4 T = 3/2 13 states in N at excitations between 18. 65 and 18. 88. MeV. These states would be unbound to strong decays and therefore expected to have appreciable widths. It is interesting to note that equation (8) predicts that analogous levels in mirror nuclei should have equal excitation energies. This result depends upon the assumption that the Coulomb constant K is the same for all levels in a given nucleus. If we make the reasonable assumption that the nuclear radius is greater for the T = 3/2 states than for the T = 1/ 2 states we find that equation (8) predicts that the T = 3/2 states in a T z = -1/2 nucleus (in the convention where T for the proton is +1/2) have higher excitations than the z analogous states in the nucleus with T = +1/2. This is exactly what z is observed in the A = 13 nuclei. The argument, · however, ignores level shifts, which in some cases (mass 9 would seem to be a good example) are not negligible. 41 We may make some qualitative predictions about the 13 configuration of the lowest T = 3/2 level in N using the extreme single particle shell model. If Coulomb mixing with T = 1/2 states is small, the simple shell model should be as valid an approximation for the lowest T = 3/2 levels as· for the lowest 12 T = 1/2 levels. Then, based on C , the dominant configuration . -1 2 of the lowest T = 3/2 state should be (p312 ) (p 1; 2)T = l, J = o· This is supported by the known J 11 of B1'3 which is 3/2-. This configuration, which can be coupled to either T = 1/2 or T = 3/2, 11 is readily reached by L = O, one-step double-stripping, on B 1 which is predominantly (p f • In fact in the approximation of 312 a pure (p 312) -1 structure for B11 , (p 312)-1 (P1; 2)2T = l, J = 0 is the only configuration reached by L = 0 stripping unless two nucleons are promoted across a major shell closure. Thus in this simpleminded picture we expect our spectra to be dominated by L = 0 transitions to low lying 3/2- states with T = 1/2 and T = 3/2. This two- particle stripping strength should be concentrated upon the lowest T = 3/2 level, and upon the lowest T = 1/2 level with spinparity 3/2-, which occurs at 3. 51 MeV, because of the large energy gap between them and other 3/2- states. The next T = 1/2, J 11 = 3/2- state occurs at 9. 47 MeV (Lauritsen and Ajzenberg-Selove 1962) while the next T = 3/2, J 11 = 3/2- state is expected at 24. 8 MeV (Boyarkina 1964). We, therefore, expect to preferentially populate the lowest 13 T = 3/2 state in N because its configuration is easily reached by one- step diproton stripping, whereas the neighboring T = 1/2 levels 11 have complicated configurations which have a small overlap with B (o. 0) surround by two correlated protons. With these simple arguments it is not possible to make predictions about the higher T = 3/2 states. 42 B. Experiment The B 11 3 (He , n) reaction was studied at incident energies between 7. 0 and 13. 5 MeV, corresponding to excitation energies in N13 up to 20. 4 MeV. Targets prepared by evaporating met allic boron enriched to 98. 6% in B 11 onto tantalum backings were kindly supplied by D. C. Hensley. These targets contained a significant . oxygen contamination, which produced sharp neutron groups with 13 energies close to those expected from T :;; 3/2 states in N • In an effort to reduce the oxygen content, later targets received a 0 thin (estimated to be 100 A thick) coating of gold before air was admitted to the belljar. With this procedure it was possible to reduce the oxygen content significantly. Time spectra taken at incident energies of 7. 0, 9. 0, 12. 5, and 13. 5 MeV are presented in Figures 19, 20, 21 and 22. They are characterized at excitations above 1. 94 MeV by an intense continuum due to the many possible multi- body breakups. The most prominent structures superimposed upon the continuum are 13 sharp peaks at 3. 51 and 15. 07 MeV excitation energy in N • This is especially noticeable in the 9 MeV spectrum (Figure 20) and nicely confirms the simple arguments above based on double stripping. At a beam energy of 13. 5 MeV some additional structure at higher excitations is apparent. This can readily be seen in the spectrum of Figure 22, where, in addition to the. peak at 15. 07 MeV, an intense peak at 18. 98 MeV excitation and a weaker one at 18. 44 Me V are evident. The 18. 98 Me V group can be distinguished in 12. 5 MeV spectra (see Figure 21), but the 18. 44 MeV group is not sufficiently prominent to stand out above the background. These two sharp groups lie in the excitation region expected for higher 43 T = 3/2 states in N 13 • We tentatively (and perhaps brashly) suggest a T = 3/2 assignment. We next demonstrate that the previously unobserved 13 groups corresponding to levels in N at 15. 07, 18. 44 and 18. 98 MeV are indeed in mass 13. In Figure 23 we have plotted the Q-~alues for the (He 3 , n) transition to the 15. 07 MeV state obtained 0 0 from runs at laboratory angles between 0 and 135 under the · assumption that the target mass was 10, 11, or 12. The points for the correct mass should lie on a horizontal line. The 15. 07 MeV level is conclusively demonstrated to be in mass 13. Unfortunately, it was not feasible to make Q-value measurements for the 18. 44 and 18. 98 MeV states over such a wide range of angles, and at neutron energies where the precision of the spectrometer was as great as for the 15. 07 MeV level. The problem was especially severe for the 18.44 MeV state which is nearly obscured by the intense continuum and nearby structure. . . Due to the small angular range covered (O 0 ~ 0 eL < 30 ) and difficulties in locating the peak, the measured kinematic shift was consistent with 10 $. Atarget ~ 44. We were not able to extend the angular range because the 18. 44 and 18. 98 MeV states are not sufficiently intense to be easily identified at back angles. It was checked that neither the 18. 44 or 18. 98 MeV state could have been produced from the contaminants known to be present on the target. In Figures 24 and 25 spectra from the B 11 target are compared with those observed when natural carbon and 11 oxide targets were substituted for the B target without changing beam energy or detector geometry. It can be seen that the 18. 44 and 18. 98 MeV states could not be produced by these contaminants. 11 Since the target was prepared from B with a nominal purity of 44 98. 6% it is most unlikely that these states could be produced from B lO or any other contaminant. The kinematic shift of neutrons corresponding to the 18. 98 MeV state was measured with sufficient precision to restrict the target to A::= 11. This is displayed in Figure 26 where the goodness of fit of the experimental Q-va.lues to a. constant is shown , for various assumed target masses. C. Excitation Energies Q-value measurements of the B 11 3 (He , n) reaction lea.ding to the sharp 15. 07 MeV state were made at 7 MeV. For a typical spectrum see Figure 19. To obtain the greatest accuracy the spectrometer was used as a comparison device. After a (He 3 , n) 3 run the beam was changed from He to protons as rapidly as possible (generally less than one hour elapsed between runs) and the B 11 (p, n) c 11 (o. 0) reaction was run with the same target and detector geometry. For a sample spectrum see Figure 27. The incident proton energy was adjusted to give neutrons of the same flight time from both reactions. The only significant errors in Q are due to uncertainties in the incident beam energy, Q-value of the calibration reaction, and location of the neutron and gamma peaks. The dominant uncertainty is in the effective beam energy. This arises from possible errors in the frequency constant of. the analyzing magnet, the range of energies allowed by the finite regulating slits, and uncertainties in the mean energy loss in the target. The error due to the frequency constant is small since it is partially cancelled by the calibration reaction•. The target thiclmess was determined by using the magnetic spectrometer to measure the energy loss in the boron layer of He 3 particles 45 elastically scattered from the tantalum backing. This was done before and after the series of runs which established the Q-value. The mean beam energy loss was taken to be one half the total energy loss. This is strictly valid only if (1) the yield is independent of energy and (2) contaminants in the target (most notably oxygen) have the same distribution in the target as the 3 11 B • Since the total energy loss of 7 Me V He particles in the target was only 47 keV it is unlikely that assumption (1) is not justified. We estimate an uncertainty in beam energy due to 2) of 5 keV. The most important source of error is caused by the uncertainty in the incident beam energy allowed by the finite object and image slit spacings. These uncertainties were taken to be 1/2 of the theoretical maximum value (given by formula (5) and yielded an uncertainty in Q of 8 - 12 keV, depending upon the settings. Uncertainties in the beam energy of the calibration spectrum contributed from 4. 6 to 6. 6 keV uncertainty to the individual determinations. A Q-value determination was also performed 19 19 using the F (p,n)Ne (o. 0) reaction to calibrate the time scale. A sample calculation for the Q-value obtained from the spectra displayed in Figures 19 and 27 is summarized in Table DI. The calculation of the errors in this determination is summarized in Table IV. Six separate determinations of the Q-value were made. The results are displayed in Table V. Four of these were independent in the sense that they were made on separate days, with independent tuning of the machine. The runs, however, are not independent in the statistical sense because of the possibility of systematic errors due to differing orbits of protons and He 3 ions through the 90° 46 analyzing magnet. It is very difficult to estimate the size of such possible errors. We have arbitrarily quoted a error + 8 keV, rather than + 3 ke V which is the standard deviation of the mean. It is interesting to note that the spread of the individual determinations is consistent with a beam energy uncertainty of 1/3 the theoretical maximum, rather than the value of 1/2 the .maximum that we used. The excitation energy of the 18. 98 MeV state was found by 11 11 using B (p, n)c (o. 0) as a calibration reaction, and also from several runs using a standard delay cable to calibrate the time . scale as discussed in Section IIIA. The Q-value calculation using the calibration reaction technique is summarized in Table VI and the errors in Table VII. The result is E x = 18. 985 ± • 026 MeV. From the data of Figure 26 taken at an incident energy of 12. 529 MeV we obtain E~ = 18. 993 ±. 028 MeV and from data taken at 13. 522 MeV, where the precision is poorer, we find 18. 952 ± • 039. For the reasons stated above these determinations are not statistically independent; we combine them to give Ex= 18. 98 + • 02 MeV. The excitation of the 18. 44 MeV state was taken from runs at 13. 522 MeV using the 18. 98 MeV group to calibrate the time scale. The result is. E x = 18. 44 ± • 04 MeV. D. Widths Widths for the 15. 07 and 18. 98 MeV levels were determined by computing the resolution functions as described in Part me of this thesis. No attempt was made to find the width of the 18.44 MeV state since it was populated quite weakly and was not clearly resolved from nearby structure. 47 Upper limits on the width of the 15. 07 MeV state were obtained from the same spectra used in measuring the excitation energy of this level. Therefore the method of computing resolution . functions could be checked by comparing the computed line shape with the shape of the neutron group (corresponding to a level with negligible intrinsic width) in the calibration spectrum. It was foW1d that the computed resolution function gave an intrinsic width 13 11 . of 15 keV for both the N (15. 07) group and the e ground state group in the calibration spectrum. A fit of the resolution function 11 to the e group is presented in Figure 2. An explanation for the underestimate of the observed width of the resolution fW1ction is given in Part me of this thesis. We conclude from our data that the width of the 15. 07 MeV state is less than 15 keV. This state, however, has subsequently been seen in 12 the elastic scattering of protons by e (Bredin, et al., 1966) and the width found to be less than 5 keV. The width of the 18. 98 MeV state was obtained from 4 spectra taken at 12. 5 MeV incident energy (see Figure 21 for a sample spectrum). Widths of 40 ± 20, 40 ± 20, 53 ± 25, and 33 ± 20 keV are derived from these spectra. Since the three runs are not truly independent, but are sensitive to the computed resolution function, we combine these values to give a width of 40 ± 20 keV. The 18. 98 and 18. 44 MeV states have subsequently been seen in the scattering of protons by C 12 (Kuan and Hanna 1966) and the widths found to be less than 20 ke V. Our data do not appear to be consistent with such 11 a small width. It is possible that in B (He3 , n) we are actually seeing an unresolved doublet, of which only one component is seen in proton scattering. 48 E. Angular Distributions An angular distribution of neutrons leading to the 15. 07 MeV state was taken at 9. 0 MeV incident energy. The extraction of peak areas from the spectra was subject to large uncertainties in the background subtraction. The difficulty is shown in Figure 20. Even with as good resolution as was conveniently attainable, the proper background was not obvious. At back angles the errors were mainly statistical (Figure 28). We have presented the data (Figure 29) as follows: At forward angles w~ have indicated limits of error established by the. estimated maximum and minimum possible backgrounds. At back angles the errors are statistical. In addition the points at 0, 15, 20, and 30 degrees have been corrected for contri18 butions from the Ne (1. 88) group. The correction was made using 16 the magnetic spectrometer to compare the yields from the o (d, p) 11 reaction in the B target with a tungsten oxide target. Forward angle points were taken with both targets, and the normalization . obtained with the (d, p) reaction was used to make the proper subtraction. The curves in Figure 29 are obtained from Newns' plane-wave theory for L = 0, since the level is expected to be 3/ 2-. 11 In a study of the B (t, p) reaction (Middleton and Pullen 1964a) the forward peaked angular distributions were well fitted by the plane-wave theory using a cutoff radius of 5f. Our data cannot be fitted with 5f, but is well described using 4f, in good agreement with the results of Hensley and Barnes (1965), ··and consistent with the L = 0 transition in our s.t udy of 0 16 (He 3 , n). DWBA calculations employing the potentials (except for 12 differences in the Coulomb barriers) used in an analysis of c (t, p) (Glover and Jones 1966b) gave fair fits with L = O, L = 1, and L = 2, 49 making it impassible to distinguish L-values. We make two observations concerning the DWBA calculations. 1) There is evidence that optical well depth increases markedly as the incident energy is lowered (Matous, Herling, and Walicki 1967). The incoming potentials were derived for 12 MeV tritons and may work rather poorly for 9 MeV He 31 s. 2) We have found that when the neutron energy is low (1-3 MeV) the DWBA angular distributions are frequently forward peaked and quite similar for L = 0, L = 1, and L = 2. The need for experimental resolution prevented us from obtaining an angular distribution at higher energies, where the distributions of different L~ues have characteristically different shapes. In Figure 30 we present an angular distribution of neutrons corresponding to the unresolved 3. 51 and 3. 56 MeV states in N 13 • The smooth curve is an L = 0 fit using the plane-wave theory. We find that the forward peak is well fitted with a cut- off radius of 4. 0 f. 11 3 This confirms our expectation that the B (He , n) reaction should primarily populate 3/ 2- levels at 3. 51 and 15. 07 MeV. It is also of interest because the Q-value to the 3. 51 MeV level is +6. 67 MeV, suggesting that the small radii needed in our L = 0 fits are not due to a Q-value effect of the kind discussed by Middleton and Pullen (1964b). A partial angular distribution of neutrons corresponding to the 18. 98 MeV state was taken at a beam energy of 12. 5 MeV. Results are displayed in Figure 31. 50 F. Conclusions 11 The (He 3 , n) reaction on B strongly populates narrow 13 levels in N at 3. 51 and 15. 068 MeV excitation energy. We 11 suggest that these states consist predominantly of a B (o. O) core surrounded by two protons in the c~nfiguration (p 1; 2>.i. = 1 J=O · The 3. 51 MeV state has the total isospin coupled to 1/2, and we 13 identify the upper state as the lowest T = 3/2 level in N • Angular distributions to both levels are strongly forward peaked. In addition to the lower T = 3/2 level at 15. 068 MeV, other levels in N13 are observed at excitations of 18. 44 and 18. 98 MeV, the transition to the 18. 98 MeV state being more intense. 13 Our T = 3/2 assignment for the state in N at 15. 07 MeV is based primarily upon the intensity of the reaction and the prox. imity of the excitation energy to that expected for the lowest T = 3/2 state. In addition we have found that the width of this state is less than 15 ke V, and the angular distribution of neutrons is fitted by L = 0, implying spin and parity 3/2-, which are expected for the lowest T = 3/2 level. This state has been seen subsequently to the present work (Bredin et al., 1966) as a narrow (r < 5 keV) anomaly in the 12 elastic scattering of protons by c , confirming our T = 3/2 assignment. Our assignment of T = 3/2 to the levels at 18. 44 and 18. 98 MeV is likewise based upon the excitation energies, intensities and widths, although the evidence that these states have T ;;; 3/2 is less compelling than for the 15. 068 MeV state. The strength of the transitions to these states, especially to the 18. 44 MeV level, is 51 less than to the lowest T = 3/2 level and complete angular distributions could not be obtained. In Figure 3 2 we present a mass 13 isobar diagram, showing 13 the results of this work, a related study of C by Hensley and 13 Barnes (1965, 1966), and a recent determination of the 0 mass by Cerny et al., (1966) (who also fow1d the masses of the lowest 13 13 T = 3/2 levels in c and N with less precision than the present . 3 3 work). The correspondence between the (He , n) and (He , p) results is quite good. This is expected, since for isospin-changing transitions both reactions obey the same double- stripping selection rules. 13 We identify the 15. 07 MeV state in N and the 15. 11 MeV . 13 : 13 13 state m C as the analogs of the grow1d state of B and 0 . It 13 is tempting to identify the N "state" at 18. 44 MeVas the unresolved 13 analogs of the 3. 68 and 3. 71 MeV states in B , and the 18. 98 MeV 13 13 state in N as the analog of the 4. 13 MeV state in B • The tentative identification of the 18. 44 MeV state is supported by evidence from proton scattering that the 18. 4 MeV state may be complex, and by the work of Hensley and Barnes who see a partially resolved doublet at approximately 18. 68 MeV. This may explain the slight dependence of the measured excitation energy upon neutron angle. This identification as well as the tentative assignment of the 18. 98 MeV 13 state as the analog of the 4.13 MeV state in B is suggested also by a comparison of relative intensities in the B 11 (He3 , n) and B 11 (t, p) reactions. Some of the interest in locating the T = 3/2 levels of the · 4n + 1 nuclei lies in the opportunity they provide to check the quadratic mass law for members of an isobaric multiplet (Wilkinson 1964), since there are 4 members of a T = 3/2 multiplet and only 52 three parameters ii1 the mass law. With the known masses of B 13 , c 13 (T = 3/2), N13 (T = 3/ 2) we predict an 0 13 mass excess of 13 23. 11 ± . 04 MeV. The mass excess of 0 measured by Cerny et al., . is 23. 11 ± • 07 MeV. We conclude that at this level of precision there are no deviations from charge independence other than a first order term which transforms like the Coulomb force w1der isospin rotations. However, a recent precise check of the mass law in the A= 9 system (Barnes et al., 1966) indicates that small deviations from the quadratic mass law are present, and that such deviations should be expected as higher order quantum electro"'.' dynamic effects. 53 VL OBSERVATION OF T = 3/2 LEVELS IN F 15 (He 3 , n) 17 IN THE REACTION N A. Introduction Prior to this work, and the concurrent study of 0 17 by Hensley and Barnes (1966) experimental information on the A= 17 · T = 3/ 2 isobaric quartet was rather sparse. The delayed neutron 17 emitter N had received the most attention. Although 21 l e vels . 17 had been observed in N (Hart, Norbeck, and Carlson 1965), the only spin assignment was 1/ 2- for the ground state (based on beta 17 decay). No T = 3/2 states had been reported in 0 • Two sharp 16 anomalies (r < 5 keV) in the elastic scattering of protons by 0 were seen by Hardie, Dangle, and Oppliger (1964), at excitations 17 in F of 12. 522 and 13. 039 MeV, and were conjectured to be. possible analogs of the first and second or third excited states of 17 . . N • No evidence was seen for the lowest T = 3/ 2 level. Two possible explanations for this were given by Hardie et al: that the level was so narrow it was masked by the 2 keV experimental resolution, in spite of 1% statistics, or else that the unobserved state was very broad due to strong Coulomb mixing with a nearby T = 1/2 level of the same spin and parity. The fourth member of ' 17 the isobaric quartet, the delayed proton emitter Ne has been seen (McPherson et al. , 1964) although its mass has not been determined. It is possible to make some simple predictions about the 17 T = 3/2 excited state spectrum in F • As was pointed out in Section VA, one can estimate the excitation of the lowest T = 3/2 level by expressing the atomic mass of a state belonging to an 54 isobaric multiplet as M(T ) = Z(M + M ) + (A - Z)M - B + Z(Z - l)KA-l/ 3 z e p n (8) where B represents the binding energy due to the strong forces. This expression assumes that the Coulomb constant K is the same for all levels of a given nucleus. If K is evaluated from the F 1 7 17 17 ·0 ground state mass differ~nce the N mass can be used to predict 11. 002 MeV as the excitation of the lowest T = 3/2 level . 17 15 15 . m F . If, on the other hand, one uses the N - 0 ground state mass difference to evaluate K, the predicted excitation is 11. 302 Jv!eV. Thus, we expect the lowest T = 3/2 level at an excitation of 11. 15 + O. 15 MeV. Although the lowest isospin-allowed particle decays of 17 15 T = 3/2 levels in F are to N + 2p (see Figure 42), the lowest · isospin-allowed single-particle decays occur via the T = 1 states of 16 0 ; thus levels with excitations less than 13. 39 MeV are bound with respect to these decays and are expected to be quite narrow, and to have have an appreciable probability for gamma decay. Therefore, in addition to a narrow level at about 11. 15 MeV, one would expect a 17 narrow state in F at about 12 •.52 MeV, and a pair of sharp states at about 13. 03 MeV excitation energy, corresponding to the first, 17 second and third excited states of N • Analogs of higher levels in N17 are unhound with respect to isospin-conserving decays, and are expected to be quite broad. . Although the ground state spin of N 17 has not been determined unambiguously, observations of the beta-decay branching (Silbert and Hopkins 1964) suggest 1/2-. This is consistent with the extreme single- particle shell model which predicts a two-particle - one-hole configuration and thus J 11 = 1/2-. 55 Since the N 15 1 2 grow1d state has most of the p / -hole strength (Warburton, Parker, and Donovan 1965), one-step 15 diproton stripping on N is expected to pick out states with the following configurations, . 1) one-particle even-parity states (d 512 of course, are T = 1/2 and necessitate an odd L. or s ) which, 112 two-particle one-hole. odd-parity states ( (p f 1 112 2 -1 2 -1 .. (d5/2) ' (pl/2) (Sl/2) ' or (pl/2) (Sl/2) (d5/2) ), which can be either T = 3/2 or T = 1/2 and which are reached by even L 2) transitions. It should be noted that even-parity, T = 3/2 levels can only be reached by crossing a major shell-closure and placing a proton in the 1f shell, or via core excitation or higher configurations in the N15 ground state. Extensive calculations by Margolis and de Takacsy (1966) on negative parity states in A= 17 indicate that the two-particle one-hole configurations are reasonably successful in fitting the low-lying odd-parity T = 1/2 levels. They confirm the simple shell model prediction for the configuration of the lowest T = 3/2 level; 2 1 90% of the amplitude is (p ; f (d 5; 2) . They also find that the 1 2 T = 1/2, J = 1/2- level at 3. 10 MeV is also predominantly -1 ( )2 (pl/2) d5/2 . B. Experiment All work on the reaction was performed with the gas target 15 chamber shown in Figure 5 containing N gas with a nominal isotopic purity of 99. 9%. Pressures were chosen to give target thicknesses between 14 and 32 keV for the bombarding ions. The 56 3 calculated straggling of 5 MeV He ions passing through the 5000 A nickel entrance foil is 31 keV FWHM, which is less than the resolution of the spectrometer when operated under normal conditions. The energy loss of protons in the foil was determined 19 by measuring the displacement of the narrow 872 keV F (p, ay) resonance when the foil was placed ahead of a thin calcium fluoride target. Results for one particular foil are shown in Figure 33 . .This proton energy loss was then scaled to He3 with the tables of · Demirlioglu and Whaling (1962). Although neutrons from o 16 (He 3 , n) were detected in some early runs, no significant outgassing occurred once the target had undergone a few hours bombardment, after having been prepared by heating it and maintaining it under vacuum for several days before the run. 3 The reaction has been studied at He energies up to 11. 88 MeV. Zero-degree spectra have been taken at 16 different incident energies between 7. 72 and 11. 88 MeV and angular distributions obtained at 10. 36 and 11. 88 MeV. The time spectra bear a strong qualitative resemblance to 11 3 13 those obtained from the reaction B (He , n)N as can be seen by comparing Figures 21 and 34. In both cases we see: 1) An intense continuum due to the many open multi - particle channels. 2) The ground and first excited states, which in this case must be populated by L :::: 3 and L :::: 1 capture of a di.proton, are only weakly excited. 3) The lowest lying L:::: 0 transition, in this case to the 1/2- level at 3. 10 MeV, is extremely strong. 57 4) That the only sharp structure at high excitations consists of prominent peaks at excitations very close to those expected for the T = 3/2 levels. A spectrum taken at 11. 88 MeV incident energy is presented in Figure 35. Previously unobserved narrow groups appear at 11. 20, 12. 54, and 13. 06 MeV. No other sharp structure is seen at excitations up to 14. 3 MeV. These levels cannot be attributed to any likely contaminants in the target gas, and empty target runs showed no pronounced structure. C. Excitation Energies Excitation energies for the levels at 11. 195, 12. 540, and 13. 059 MeV were measured using the calibration-reaction teclmique, which permits accurate work with a gas target since any errors in the foil thickness (as well as in the calibration constant of the analyzing magnet) nearly cancel in the derived Q-values. Two largely independent measurements of the 11. 195 MeV state were· performed. The measurements were made on different 0 days, using different 5000 A entrance foils, and different calibration 14 reactions. The calibration reactions selected, N (a., n) and 15 N (a, n), are both induced by a particles · since there are no suitable 3 (He , n) reactions with sufficiently well known, negative Q-values. We feel that by using (a, n) instead of (p, n) calibration reactions, we reduce the possibility of systematic errors due to differing orbits through the analyzing magnet. All measurements were made at zero degrees where dE/ de is least, and cross sections are largest. Beam energies were chosen so that in each case neutrons of about 1. 1 MeV were produced from the levels of interest. 58 The N 14 (a., n) calibration reaction has the advantage that the magnetic rigidity of the a.'s is within 10% of the rigidity of the 3 He 's at the energies chosen. However, the energy loss· in the foil is 214 keV for the a 's, and only 163 keV for the He 31 s. On 15 the other hand the choice of N (a., n) as a calibration has the advantage that the energy loss of a. 's was 164 keV, compared wit h 144 keV for the He 31 s. Since these two values are so close, any errors in the foil thickness are reduced by a factor of 20 in the derived Q-values. The measurement using N E x 14 (a., n) as a calibration yielded 15 = 11. 200 ± O. 010 MeV; using N (a., n) to calibrate the time scale we get E x = 11. 190 -+ O. 011 MeV. The main contributions to · the quoted errors are due to uncertainties in the incident beam energy which was taken to be 1/3 of the theoretical. maximum allowed by the 0. 100 inch object and image slit spacings. Combining these results we arrive at a final value of E = 11. 195 ± O. 007 MeV. x The calculations are summarized in Tables Vill and IX. The 15 N (He 3 , n) and N 15 (a., n) spectra used in one determination of the excitation of the 11. 195 MeV level are shown in Figures 36 and 37. The excitations of the 12. 54 and 13. 06 MeV levels wera 15 measured using the N (a., n) reaction at 8. 915 MeV as a calibration, and also using a 150 nanosecond calibrated delay cable to measure the neutron energy. The calculations are summarized in Tables X and XL The errors again are dominated by uncertainties in the incident beam energy. It was checked that the yield of the N 15 (He3 , n) and N 15 (a., n) reactions did not vary greatly with a change of ± 50 keV in incident energy. Our assumption that the mean beam energy loss in the gas is 1/2 of the total energy. loss in the gas is therefore justified. 59 D. Widths An upper limit for the width of the 11. 195 MeV level was obtained by comparing the shape of the neutron group from 3 15 N (He ,n), with that from the particle stable 3. 36 MeV level in 16 N18 , populated by o (He 3 , n). It was necessary to change the beam energy by only 5% in order to produce reactions of the same · energy from both reactions. The gas pressures were chosen so 16 15 that the energy losses in the N and 0 in the target were nearly equal. Then, if the energy straggle and beam burst duration are assumed not to change with a 5% change in beam energy, the shape 17 of the neutron group from F (11. 195) should be given by the shape of the group for Ne 15 (3. 36) folded into the intrinsic level width of 11. 195 MeV state. A Breit-Wigner curve, with flight time as the independent variable, was folded into the shape of the neutrons from 18 Ne (3. 36) and the level width adjusted to give the best fit to the 17 group from F (11. 195). The goodness of fit was determined by a chi- square test, with the calculated and experimental points normalized to the same area, leading to an upper limit of 20 keV · for the width of the 11. 195 MeV state. However, since this level was not seen by Hardie et al., (1963). its width is probably less than a few keV. This technique could not be used to establish significant upper limits for widths of the 12. 540 and 13. 059 MeV levels because the increased beam energy needed to reach these states appreciably 17 reduced the straggle in the foil, causing the F groups to be narrower 18 than the calibration group from Ne (3. 36). An estimated upper limit of 25 keV for the width of the 12. 540 and 13. 059 MeV levels was obtained by assuming that all contributions to the width combine quadratically, and that the straggle in the entrance 60 foil of the gas cell is described by the formula of Evans (1955). Then we assume the observed width of a level r r 2 = r 2 + r t2 + r 2 + r 0 y S g SC 0 be given by 2 + r. 2 (9) l where r y , r S t, r g , and r SC are the widths due to the observed gamma group, the straggle in the foil, the energy loss in the gas, and the flight time through the scintillator respectively, and r.l is the intrinsic level width. Under these assumptions an upper limit for the widths of the 12. 540 and 13. 059 MeV levels is 25 keV. However, if these states are identified with the levels seen by Hardie et al. , (1963) an upper level of 5 keV can be placed on these widths. E. Angular Distributions and DWBA Fits Angular distributions have been taken at io. 36 and 11. 88 MeV corrected beam energy. At the lower energy only the two lowest T = 3/2 levels were recorded, while at 11. 88 MeV, all three levels were strongly populated. 38 through 41. The data are displayed in Figures The error bars include contributions from counting statistics, uncertainty in the choice of background, and a 5% contribution from the detector efficiency and beam current integration. In addition to the errors denoted by the flags there is an estimated over-all uncertainty in the absolute normalization of ± 10%. In Figures 39 through 41 the ang"ular distributions taken at E 3 = 11. 88 MeV are displayed on a logarithmic scale, together He with angular distributions from known L = 0, and L = 2 transitions :iri. the o 16 (He 3 , n) reaction at 10. 5 MeV incident energy. The F 17 61 and Ne 18 distributions are strikingly similar, as one would expect. The smooth curves are DWBA fits using the zero-range optical model code TSALLY. The curves were computed using published potentials (listed in Table XIV) derived from elastic scattering, there are no free parameters except for the. normalization. The 3 He potentials are identical to those of Glover and Jones (1966a) 16 derived from the 12 MeV elastic scattering of tritons on 0 . The neutron potentials are the proton potentials used by Glover and Jones (1966b) in fitting (t, p) data. Our calculations assumed that only a single radial quantum number was necessary to describe the motion of the diproton about the core. For a more complete discussion of the DWBA calculations see Appendix B. 18 The L = 0 transitions to~ 7(11. 195) and Ne (0. 0) are both 17 18 well fitted by the DWBA curves. The F (12·. 540) and Ne (1. 88) angular distributions have nearly the same shape, and in both cases the L = 2 DWBA curves fail to reproduce the dip at o0 , although they do reproduce the data at large angles. This discrepancy, while unfortunate, is not considered serious, in light of the crudeness of the calculation. The strong · similarities with known transitions in 18 Ne , tog~ther with the DWBA calculations, lead to unambiguous 17 17 assignments of L =0 and L = 2 for the F (11. 195) and F (12. 540) transitions respectively. This limits the spin and parity of the 11. 195 MeV state to 1/2-, and of the 12. 540 MeV state to 3/2- and 5/2-. Hensley and Barnes (1966), in studying the analog of this level in o 18 (He 3 ,a.)o 17 , see an L = 1 transition which restricts the spin of the analog of the 12. 544 MeV level to 1/2- or 3/2-, leading to a likely spin assignment of 3/2-. The level at 13. 059 MeV is unbound with respect to diproton decay, and hence cannot be handled by conventional stripping theory. 62 Calculations arbitrarily assuming a 100 keV binding energy did not allow one to distinguish between different L-values. F. Conclusions The N 15 (~e 3 , n) reaction strongly populates three narrow levels at excitation energies of 11. 195 ± 0. 007 MeV (r < 20 keV), 12. 540 ± O. 010 MeV (r < 25 keV), and 13. 059 ± o. 009 MeV (r . < 25 keV). Double-stripping angular distributions lead to .spin-parity assignments of 1/2- for the 11. 195 MeV level, and 3/2- or 5/2for the 12. 540 MeV state. These levels are identified as analogs 17 of the ground, first, and second or third excited states of N . The levels at 12. 540 and 13. 059 MeV can be associated with the previously reported (Hardie et al., 1963) anomalies in the elastic scattering of 16 protons by 0 , leading to an upper limit of 5 keV for width of these states. Since the 11. 195 MeV level was not seen by Hardie et al., its width is probably less than a few keV. The T = 3/ 2 assignment of these three states is based upon the excitation energies, the spins, the narrow widths, and the intensities of the transitions. The 1/2- levels at 3. 10 and 11. 195 MeV are both intensely 15 3 populated in the N (He , n) reaction indicating that these levels look 15 very much like an N core surrounded by two closely correlated protons. These results are consistent with the calculations of Margolis and deTakascy (1966). The angular distributions to the T = 3/2 levels are reasonably well described by DWBA double- stripping theory, confirming that twonucleon stripping is the dominant mechanism in these transitions. An isobar diagram of the T = 3/2 levels in the A = 17 nuclei is presented in Figure 42. It summarizes the present work and 63 17 includes the T = 3/2 levels in 0 found by Hensl~y (Barnes et al., 18 15 3 1966) using the reactions o (He ,cd and N (He 3 , p). The - - 3 3 correspondence between the (He , n) and (He , p) results is quite good, as one would expect, since for isospin changing transitions 18 3 the two reactions obey the same selection rules. The o (He ,a.) reaction populates analogs of the three T = 3/2 states seen in the 15 3 present work as well as two other states not seen in N (He , p) or 3 15 N (He , n). A comparison with Hensley's work suggests that the 17 13. 059 MeV state in F is the analog of the third excited state in N17. Subsequently to the present work, a narrow (r < 1. 8 keV) anomaly has been observed in the inelastic scattering of protons to 16 the 6. 13 and 7. 12 MeV states of 0 (Patterson, Winkler, and Zaidens, 1967) at E = 11. 277 ± • 015 MeV. This corresponds to an excitation ·e nergypin F 17 of 11. 203 ±. 015 MeV. Since the lowest T ::: 3/2 state in F 17 has a configuration which is predominantly two particle - one hole, one would expect that the state should decay 16 primarily to one particle - one hole states in 0 . This may explain 17 why no anomaly corresponding to the lowest T = 3/2 level in F has 16 been seen in the elastic scattering of protons by 0 , and why anomalies are seen in the Inelastic scattering to the lowest negative-parity states . 016 • ill 64 VII. A. OBSERVATION OF THE LOWEST T = 2 STATE rn Ne 18 3 THE REACTION o (He , n) 20 rn Introduction The first experimental observation of states with T = T + 2 z was made by Garvey, Cerny, and Pehl (1964) who used the (p, t) pickup reaction on T = 1 targets to populate levels in the residual nucleus with T = 0, T = 1, and T = 2. Garvey, et al., bombarded 26 46 54 targets of Mg , Ti , and Fe with 39 MeV protons, and identified 24 44 52 the lowest T = 2 states in Mg , Ti , and Fe in the triton spectra. Subsequently, Cerny, Pehl, and Garvey (1964) found the two l owest 16 18 20 22 T = 2 levels in both 0 and Ne , by bombarding 0 and Ne with 44 Me V protons. The identification of the T = 2 levels in the above work rested partly upon angular distributions and the proximity of the observed levels to the expected positions of these states. The most important evidence for the T = 2 character of these states, however, lay in the intensity of the transition. Garvey, et al. , (1964) pointed out that (p, t) pickup should selectively populate the lowest T = 2 levels in the nuclei studied and pick them out of the dense background of T = 0, and T = 1 levels. In the present work we report upon the observation and accurate determination of the excitation energy of the lowest 18 20 20 3 T = 2 state in Ne using the reaction o (He , n)Ne • We thus demonstrate that two nucleon stripping, as well as pickup, can selectively populate low-lying T = 2 states. Before discussing the experiment we make some observations 20 concerning T = 2 structure in Ne , and some characteristics of the o 18 (He 3 , n) reaction. We can employ the relation 65 M(T) = Z(M +M) +(A - Z)M - B z e p n + Z(Z- l)kA-l/. 3 (8) to predict the excitation energy of the lowest T = 2 level in Ne 20 . 20 We use the mass difference between F (o. 0) and its known analog 20 in Ne (at 10. 27 MeV excitation) to evaluate the Coulomb constant K, and then use K to compute the Coulomb energy difference between 20 20 0 and Ne (T = 2). The formula predicts an excitation of 16. 87 20 MeV. The lowest isospin-allowed particle decay of Ne occurs at 20 19 an excitation of 20. 27 MeV via F (T = 3/2) + p. 0 has a 2+ state at 1. 67 MeV excitation and a 4+ state at 3. 57 M~V. Therefore, 20 in Ne we would expect a narrow T = 2, o+ state at 16. 9 MeV, a T = 2, 2+ state at 18. 5 MeV, and possibly a T = 2, 4+ state close to 20. 4 MeV, which may be shifted enough so that it falls below the isospin-allowed particle decay threshold. Other T = 2 states should be above this threshold and are expected to be quite broad. Cerny 20 et al., find T = 2 states in Ne at 16. 8 + O. 1 and 18. 5 MeV excitation energy. The 16. 81MeV state is quite prominent in their published spectrum; to distinguish the 18. 5 MeV level in the published data requires considerably more talent. The simplest theoretical treatment of the sharp isospin quintuplets in the A= 20 nuclei (Loncke and Pradal~ 1966) treats these states as spherical four-particle states composed mainly of , and 2s ) configurations. The dominant com, ld 31 2 11 2 51 2 ponent of the lowest T = 2 level in this framework is (1d~; )T=l the (ld 2 J=O (ld;; 2)T=l . This configuration can readily be reached with (He3, n) p) ;~ripping by 0 18 (which is predominantly (ld;; 2)T=l. The 3 ,or (t, reaction o 18 J=O (t, p) has been studied by Middleton and Pullen (1964b) 66 20 who find an intense transition to the ground state of 0 , leading us 20 to expect that the transition to the analog state in Ne should likewise be intense. On the other hand, the large number of highly excited levels with T = 0 and T ~ 1 which lie in the neighborhood of the lowest 3 T = 2 state should be populated only weakly by the (He , n) reaction, since they most likely have complicated configurations which have a 18 small overlap with o (o. O) plus two closely correlated protons. B. Experiment The reaction o 18 20 3 has been studied at 11 different (He , n)Ne incident energies between 4. 7 and 9. 0 MeV covering excitations in 20 Ne up to 20 MeV. Angular distributions have been taken at = 5. 70 and 7. 33 MeV. Two different targets were employed. He 3 . Initial runs and some of the width determinations were made using a E target of nickel which had been oxidized some years ago by R. E. 18 Brown in an atmosphere containi~g 71. 7%..o . The thickness of this target was not well defined or known, nor was much confidence placed in its present isotopic composition. Spectra taken with this 16 target we re dominated by the 0 "contaminant", which obscured the 20 18 region of excitation in Ne around 16. 4 MeV (due to Ne (o. 0)) and 18 around 18. 3 MeV (due to Ne (1. 88)). To avoid this problem the gas 18 target of Figure 5 containing 0 gas with a nominal isotopic purity of 99. 56% was used for most of this work. Some difficulty was 16 experienced with outgassing of 0 , making it necessa;ry to recharge 18 the cell with fresh 0 gas periodically. The. energy loss of protons 0 in the 5000 A entrance foil was determined by measuring the 19 displacement of the 872 keV F (p,a,y) resonance. The energy loss of 3 He 's was then scaled by using the tables of Demirlioglu and Whaling (1962), as discussed in Section VIC. 67 Zero-degree time spectra taken at incident energies of 5. 2, 5. 7, 6. 5 and 9. 0 MeV are shown in Figures 43, 44, 45 and 46. The spectra are characterized by an intense continuum due to the three16 19 . + a + n and F + p + n, which open at body channels, 0 excitations of 4. 730 and 12. 844 MeV respectively. The continuum becomes much stronger as the beam energy is raised, at 9. 0 MeV it nearly obscures the sharp groups at excitations between 11 and 15. 5 MeV which were so prominent in the 5 MeV spectra (see Figures 43 and 46). At excitation energies in Ne 20 greater than 15. 5 MeV no pronounced structure is seen except for a single prominent group at 16. 73 MeV, which we identify as the T = 2 level observed by Cerny et al., at 16. 8 ± O. 1 MeV. There are indications of possible weak neutron groups corresponding to levels in Ne of about 17. 3 and 17. 6 MeV. 20 at excitation energies The 17. 3 MeV group can be seen in the time spectrum presented in Figure 45. That the neutron group which we claim corresponds to the 20 lowest T = 2 level in Ne is actually produced in the reaction 18 3 20 o (He , n)Ne is shown by the following checks. The measured kinematic shift in neutron energy with laboratory angle is consistent with targets between A = 16 and A = 26 as is shown in Figure 47. These limits could unfortunately not be improved in this way because the strongly forward-peaked angular distribution prevented measurements from being made at 8 L > 30°. Empty target runs s howed no 14 struct ure except for neutron groups corresponding to o (o. 0) and 18 . Ne (0. O); therefore, the target material must be gaseous. It cannot 15 2 22 be C0 2 , N 2 , N2 , o 2 , Ne 0, or Ne since we have investigated the 3 (He , n) reactions on these targets. Since the nominal purity of the gas 20 used is 99. 56%, we conclude the level is indeed in Ne • 68 It should be noted that there is no evidence in our data for the state at 18. 5 MeV reported by Cerny et al. Such a state would appear in the spectrum of Figure 46 at the spot marked A. The "absence" of this state in our spectra is not unexpected, since in the 18 o (t, p)o 20 reaction the maximum differential cross section of the analogous state is only 1/ 6 of the zero-degree cross section of the ground state. C. Excitation Energy of the Lowest T = 2 State The excitation energy of the lowest T = 2 state was found by 16 3 18 comparing Q-values with the o (He , n)Ne (o. 0) transition. This reaction was chosen because it produces neutrons of nearly the same energy as the reaction of interest. This greatly reduces errors due to uncertainties in the 'f oil thickness and calibration constant of the beam analyzing magnet. The chief disadvantage of this reaction as a calibration is the large ( ± 5 .keV) uncertainty in its Q-value. We therefore express our result in a manner which will permit it to be corrected should a better value for the 16 18 3 o (He , n)Ne (o. O) Q-value become available. [In this work, the Q-value has been taken as -3. 196 MeV.] Six separate determinations of.the excitation energy of the lowest T = 2 state were performed, three with the solid target and three with the gas cell. Each target had its disadvantages. With the solid target there were no foil corrections, but the thickness of this target was not well-known. In addition, the distributions of 16 and 0 18 throughout the target were not necessarily the same, 0 which could give rise to an error in the Q-value since the mean beam energy in the target might be different for the two reactions. With a 69 gas target these uncertainties are removed at the expense of an additional error due to the uncertainty in the foil thickness. Two methods were used to calibrate the time scale. 18 20 3 (He , n)Ne was calibrated against" 18 another spectrum containing the Ne (o. 0) group with the beam 1) A spectrum of o energy adjusted to give neutrons of the same energy as from 20 · Ne (T = 2). Systematic errors due to the time-of-flight spectrometer vanish in this case. 16 18 A spectrum in which both 0 and 0 were present 16 18 3 in the target was calibrated on the o (He ,n)Ne (0.0) group. 2) With this method errors in the resulting excitati.on due to uncertainties in the beam energy were reduced by a factor of 8 over Method 1. However, systematic errors in the spectrometer are not entirely cancelled. Such errors are believed to be very small in the present reaction. A spectrum from which one of the Q-value measurements was taken is shown in Figure 43. The mean excitation obtained from the six measurements is 16. 730 ± • 006 MeV. There does not appear to be any significant di.fference between values obtained from the gas and solid targets. The standard deviation of the mean of six determinations is only 2. 3 keV. The quoted error is largely systematic, due to the 16 3 18 uncertainty in the o (He ,n)Ne (0.0) Q-value. The dependence of our excitation upon this Q-value is given by -1. 0 The calculation of excitations and of the errors are summarized in Tables XII and XIlI. (10) 70 D. Width of the Lowest T = 2 Level in Ne 20 An upper limit on the width of the lowest T = 2 level in Ne 20 was obtained from the gas target runs by the same procedure as . 17 20 used for the 11. 195 MeV state m F . The shape of. the Ne (16. 730) group in a spectrum taken at 5. 204 MeV was compared with the 18 Ne (o. O) group in a 4. 798 MeV spectrum. The gas pressures were the same in both runs, and these beam energies produced neutrons of nearly the same flight times in both cases. A Breit- Wigner curve, transformed to have flight time as the independent 18 variable, was then numerically folded into the Ne (o. O) shape. The intrinsic level width, r, of the Breit-Wigner expression was increased from zero until a good fit could no longer be obtained. The goodness of fit was evaluated by a chi- square test with the calculated and experimental points normalized to the same area. The curve of chi-square as a function of r, and the best fit, are presented in Figure 48. This method yields an upper limit of 20 . keV for the width of the 16. 730 MeV state. A similar limit for the width was obtained from the solid target runs with the technique used to find the width of the 15. 068 13 MeV state in N • The nickel oxide target was somewhat arbitrarily assumed to be 10 keV thick for these calculations. E. Angular Distributions Angular distributions were taken at E 3 = 5. 70 and 7. 33 He MeV. Since the neutron group from the T = 2 state rests upon an intense background due to the continuum, and possibly other states with T = 0 and T = 1, the choice of background is necessarily 71 somewhat arbitrary. In Figure 44 we have indicated a background · subtraction typical of those used to obtain the 5. 7 MeV angular distribution. At other angles similar backgrounds were chosen. The range of subjectively acceptible backgrounds for the 7. 33 MeV spectra was not as great as it is in Figure 44. distributions are presented in Figures 49 and 50. The angular The error bars . are due to counting statistics, a 5% uncertainty in beam integration and relative detector efficiency, and a subjective estimate of the uncertainty in the mean position of an assumed linear background. In addition to the errors denoted by the flags there is an estimated uncertainty of ± 10% in the absolute normalization. The smooth · curves are DWBA calculations, with only the normalization adjusted. The computations were performed as described in 3 Appendix B using the potentials presented in Table XV. The He , 18 0 potentials were obtained from studies of the elastic scattering 19 3 of He from F at 8. 0 MeV (Matous, Herling, and Wolicki 1966). These potentials were chosen since the target nucleus and bombarding energy most closely approximate the present case. The exit channel potentials are those used in the (t, p) analysis of Glover and Jones (1966b). It is seen that the theoretical angular distributions are quite sensitive to the L-value, and that the observed angular distribution is clearly L = O~ One should note that in one18 step stripping, L = 1 can only occur via impurities in the 0 wave function (for example two-particle - two-hole) or by placing a proton in the 1f shell. 72 vm. CONCLUSION 3 We have used (He , n) reactions on T = 1/2 and T = 1 targets to identify higher isobaric spin states in several light 3 nuclei. The (He , n) selection rules imposed by a doublestripping reaction mechanism have now been used to find T = 3/2 9 13 17 levels in B (Dietrich, 1964), N and F , and T = 2 levels in Ne 20 24 and Mg (Adelberger and McDonald, 1967). Because of the apparent success of identifications based upon the selection rules, and the reasonable quality of distorted wave fits to the measured angular distributions, it appears that the double- stripping process 3 provides a good description of those (He , n) transitions having large cross sections. It is interesting to speculate on the possibilities for 3 continuing this program of (He , n) reactions to heavier nuclei. Two difficulties arise: 1) The Coulomb barrier increases roughly as A 2/ 3, necessitating higher beam energies to maintain reasonable counting rates. 2) The excitation energy of the higher T states becomes systematically lower with increasing A. (This must be true since · heavy nuclei have a neutron excess). 3 . These two effects are displayed in Figure 51, where the He Coulomb barriers and excitation energ;i.es of higher T states of several nuclei are displayed. We are thus faced with having to use increasingly high beam energies to measure Q-values which are becoming less negative. Since the energy resolution of the time-of-flight spectrometer is greatest for low energy neutrons, the effective resolution will be greatly reduced. 73 A very promising field for further work, however, lies in studying the decays of these highly excited T ;: : ; 3/ 2 and T ;: : ; 2 levels. Particle decay modes can be investigated via elastic and inelastic scattering, and both particle and gamma-ray decays can be studied in coincidence experiments. Such experiments, which reveal important details of nuclear structure, are only beginning to be exploited in this and other laboratories. 74 APPENDIX A. THE PHASE STABILIZER The phase stabilizer compensates for time-dependent variations in the injected beam energy by electronically adjusting the phase of the bunching wave form. It has two components - a phase detector and an electronic phase shifter which is driven by the detector. The phase of the bunches arriving at the deflector is determined simply by measuring the difference in current hitting the two chopping slits. If the buncher is properly phased so that the current maxima occur just as the beam passes between the slits the currents striking the two slits should be equal. Figure 52 shows how the time-averaged difference current, idiff' and the time-averaged beam current, i pu1se d' vary as a function of phase. As long as the fluctuations in injection energy are small enough so that the phase of the bursts is between cp and cp 2 , idiff provides 1 a good measure of the phase of the arriving ions. The range of phase angles over which the device stabilizes is sufficient to obviate the need for an energy regulator on the injector, and allows the beam energy to be changed without manual phase adjustment. The phase changing circuit (Figure 53) is a variation of the impedance bridge with three back-biased silicon diodes used as a variable capacitor. The difference current .is detected by a sensitive differential amplifier similar to the one used to regulate the tandem accelerator. The output of this vacuum tube circuit when fed into the phase changing circuit is sufficient to provide a variation of about 40°. A block diagram of the phase stabilizer appears in Figure 1. 75 It is interesting to note that the phase detection principle has other applications. Since the phase stabilized beam pulsing system was designed to avoid some very stringent requirements on energy regulation, it could just as well be used as a simple way of providing very precise energy regulation. For instance, it would be possible to use a phase detector in conjunction with a buncher and chopper separated by a long flight path to provide a means of · detecting very small time-dependent variations in beam energy. The output of the phase detector could then be used, for example, to control the electrostatic potential of the target to compensate for these variations. 76 APPENDIX B. CALCULATION OF DWBA DOUBLE-STRIPPING CROSS SECTIONS In this section we describe a scheme for computing DWBA double-stripping differential cross sections using the code TSALLY, (Bassel, Drisko, and Satchler 1962). Our treatment can be thought of as an approximation to the general distorted-wave doublestripping theory of Glendenning (1965). The calculations differ from 3 a previous discussion of (He , n) double stripping (Henley and Wu 1964) primarily in that we use the zero range approximation and a more realistic wave function for the residual nucleus. TSALLY computes cross sections derived from a DWBA transition amplitude for the reaction A(a, b)B The <Ii s are elasti'c scattering waves which satisfy [V 2 +k 2 - 2µ 2h (u(r) + V c (r))J 4J(k, r) = 0 (12) where and V (r) is the Coulomb potential of a uniformly charged c sphere of radius r c having total charge z z • 1 2 In our case the optical potential U (r) has the form U(r) u v - i--- ey' + 1 (13) 77 r- r Al/ 3 where u y:::: au r - r A l/ 3 and v y'::::----a v <aAI VI aA) is taken between internal states of a, A, b and B. In stripping theories we make the approximations that a :::: b + x, 3 B :::: A+ x, and V:::: V b'x(rb)· For (He , n) stripping, b is a neutron, and x is a composite object, the diproton. After some simplification the matrix element becomes (bB] VI aA)= \ L c Jcp x )cp xnt (,.) I ( '!" d'i" vb x ~ bx ~ANL x (14) N; n,t where cp~ - is the relative wave function of the protons in He 3 , n.i cpx is the relative wave function of the diproton in the residual nucleus. n and .i are the radial and orbital quantum numbers of the relative motion, is the orbital wave function describing the motion of the neutron and diproton in the He 3 , ~!L is the orbital wave function (with radial and orbital quantum numbers N and L) describing the motion of the diproton about the target in the final nucleus, 78 ,. represents the internal coordinates of the diproton, and C depends upon all the summed quantities. The zero range approximation V bx (r bJ wbx (r b) o:: o (r bJ leads to (bBjVjaA) o:: l C *!L(r~o(rbJ Jcp~(T)cp~t(,-)dT. (15) N,n,t We further simplify this expression by demonstrating that all but one of the terms in the cross section can be neglected. The wave function of the residual nucleus, B, can be expressed as a core, A, surrounded by two nucleons in single particle shell model orbits cpt n cp nl = JB cpJA cpt 1 n2 cpt l Xl/2 Xl/2 2 (16) I s L J x JB where the x 112 are spinors. We are using a notation where the brackets under the wave functions imply angular momentum coupling. 79 This wave function, where the quantum numbers nl' n , 2 ..e. , and ..e. are given by the shell model, can be expanded as a sum 2 1 of wave functions of the type used in obtaining equation (B4), where the core is surrounded by a composite object x (17) L s I I J x The general transformation between the descriptions (16) and (17) involves a six-dimensional integral and is impractical. However, if the single particle orbits cp.e, n are harmonic oscillator wave functions, the transformations are soluble analytically (see for example Balashov and Eltekov 1960). N. deTakacsy (1966) has calculated the overlap integrals Jx cp' ('T")c:p .n.e, ('T")d-r ' x (17) where cp 1 was taken from a realistic proton wave function for He 3 x nt (Henley and Yu 1965) and the cp were taken from the transx formations of Balashov and Eltekov. He finds that the overlap is almost entirely concentrated in the relative· harmonic oscillator state with ·n = 1, t = O. If we neglect all terms except those with 80 n = 1, .e, = 0, the sum reduces to a single term, and the matrix element becomes (19) The bound state function, ~ Ax' is just as important as the elastic scattering waves, <I>, in a DWBA calculation (Austern 1964). It has been pointed out that oscillator wave functions are inadequate for DWBA two-nucleon stripping, since the calculations are sensitive to the tails of the wa:ve functions (Drisko and Rybicki 1966). We have therefore taken the N and L values given by oscillator NL eigenfunctions, and used these quantum numbers to calculate cpAx from a Schrodinger equation 2 ( _ ti_ \J 2 - U (r . ) - V (r . ) - E ) cp NL (r . ) = 0 µAx = 2µ Ax where AX B Ax AX ' (20) mAmx/(mA + mx) / U(r) c AX u0 - - ey + 1 r - R A l/ 3 0 y=----- ao V (r) = is the Coulomb potential of a uniformly charged c sphere of radius R and total charge ZAZ c x EB = is the binding energy of x and A in B. 81 The well depth U 0 is adjusted to give the correct binding eriergy EB. cp .n.....'{ ". can be computed once mA, m , ZAZ , R , R , a , EB, x x c 0 0 and the radial and orbital quantum numbers N and L are specified. L, of course, is just the transferred orbital angular momentum, and hopefully can be inf erred from the shape of the angular distribution. Terms with different L are incoherent in the cross section. In our calculations we have somewhat arbitrarily taken Rc = 1. 25f, R 0 = 1. 25f, a 0 = O. 65f; and assumed that EB was given by the energy required to separate two protons from the final nucleus. Except for the optical potentials, we have specified all the quantities needed by TSALLY to perform the DWBA calculations. 3 Very few studies of the elastic scattering of He by light nuclei have been analyzed to give up-to-date optical model parameters. Most work had been done with potentials which are too shallow by modern standards. We have therefore taken some of our He 3 potentials from a recent and thorough study of 12 MeV triton scattering from several light elements by Glover and Jones (1966a). They see the usual ambiguities, finding four sets of potentials with real parts approximately 50, 100, 150 and 200 MeV deep which fit the scattering equally well. They then (Glover and Jones 1966b) tried to fit (t, p) reactions with their potentials, and found that only the 150 MeV set of potentials described both the scattering and the reaction. We have, without any modification except to the Coulomb barriers, adopted their potentials, in both the incident and outgoing cha1mels. While fits could doubtless be considerably improved by 3 varying the potentials (this was tried for a set of He potentials with a real depth of 50 MeV) we prefer· the approach of using no free 82 parameters except for normalization, since any deficiencies in the theory cannot be covered up by compensating adjustments in the potentials. The potentials used in our work are presented in Tables XN and XV. 83 REFERENCES Adelberger, E. G. and A. B. McDonald 1967, to be submitted to Physics Letters. Austern, N. 1964, Nuclear Spectroscopy with Direct Reactions II. p. 1, edited by F. E. Throw, Argonne National Laboratory Report No. ANL-6878 (unpublished). Balashov, V. V. and V. A. Eltekov 1960, Nuc. Phys. 16, 423. Barnes, C. A., E. G. Adelberger, D. C. Hensley and A. B. McDonald 1966, Proceedings of the International Conference on Nuclear Physics, Gatlinburg, Tenn. 1966, (to be published). Barton, R., R. McPherson, R. E. Bell, W. R. Frisken, W. T. Link and R. B. Moore 1963, Canad. Jour. Phys. 41, 2007. Bassel, R. H., D. H. Drisko and G. R. Satchler 1962, Oak Ridge National Laboratory Report ORNL-3240 (unpublished). Boyarkina, A. N. 1964, Akademia Nauk: SSSR,English translation of the Bulletin of the Academy of Sciences of the USSR Physical Sciences 28, 255. Brafman, H. 1965, Nuc. Inst. and Meth, 34, 239. Broude, C., T. K. Alexander and A. E. Litherland 1963, Bull. of Am. Phys. Soc., Vol. 8, p. 26. Bredin, D. J., O. Hansen, G. M. Temmer and R. Van Bree 1966, Isobaric Spin in Nuclear Physics p. 472, edited by John D. Fox and Donald Robson Academic Press, New York. Brown, G. E. and A. M. Green 1966, Nuc. Phys. 75, 401. 84 Cerny, J., R. H. Pehl and G. T. Garvey 1964, Phys. Lett. 12, 234. Cerny, J., R. H. Pehl, G. Butler, D. G. Fleming, C. Maples and C. Detraz 1966, Phys. Lett. 20, 35. Demirliuglu, D. and W. Whaling 1962, unpublished. de Takacsy, N. B. 1966, private communication. Dietrich, Frank S. 1964, Ph.D. Thesis, California Institute of Technology (unpublished). Dietrich, Frank S. 1965, Nuc. Phys. 69, 49. Domingo, J. J. 1963, Ph.D. Thesis,California Institute of Technology (unpublished). Drisko, R. M. and F. Rybicki 1966, Phys. Rev. Lett. 16, 275. Evans, R. D. 1955, The Atomic Nucleus, p. 662, McGraw-Hill, New York. Flerov, N. N. and E. A. Tamanov 1957, Atomnaya Energ. ~' 44, translated in Soviet J. Atomic Energy~' 776,1957. Gale, N. H., J. B. Garg and K. Ramavataram 1961, Nuc. Phys. 22, 500. Garvey, G. T., J. Cerny and R. H. Pehl 1964, Phys. Rev. Lett. 12, 726. Glendenning, Norman K. 1965, Phys. Rev. 137, Bl02. Glove r, R. N. and A. D. W. Jones 1966a, Nuc. Phys. 81, 268. Glover, R. N. and A. D. W. Jones 1966b, Nuc. Phys. 81, 277. Goldberg, M. D., J. D. Anderson, J. P. Stoe ring and C. Wong 1961, Phys. Rev. 122, 1510. 85 Goldberg, M. D. and J. M. LeBlanc 1960, Phys. Rev. 119, 1992. Hardie, Go, R. L. Dangle and L. D. Oppliger 1963, Phys. Rev. 129, 353. Hart, Vincent P., E. Norbeck and R. R. Carlson 1965, Phys. Rev. 137, Bl7. Henley, E. M. and D. U. L. Wu 1964, Phys. Rev. 133, Bl445. Hensley, D. C. and C. A. Barnes 1965, Bull. Am. Phys. Soc. 10, 1194. Hensley, D. C. and C. A. Barnes 1966, private communication. Krick, Merlyn and G. J. F. Legge 1966, Bull. Am. Phys. Soc . ..!_!, 44. Kuan, H. M. and S. S. Hanna 1966, Bull. Amo Phys. Soc . ..!_!, 904. Lauritsen, T. and F. Ajzenberg-Selove 1962, Nuclear Data Sheets, Sets 5 and 6, 1961 (NRC, NAS, Washington, D. C. 1962). Litherland, A. E., R. Batchelor, A. J. Ferguson and H. E. Gove 1961, Canado Journ. Phys. 39, 276. Loncke, P. and J. Pradal 1966, Phys. Lett. 22, 320. Lynch, B., G. M. Griffiths and T. Lauritsen 1965, Nuc. Phys. 65, 641. Margolis, B. and N. deTakacsy 1966, Canad. Jour. Phys. 44, 1431. Matous, G. M., G. H. Herling and E. A. Wolicki 1966, Phys. Rev. 152, 908. McPherson, R., J. C. Hardy, R. E. Bell 1964, Phys. Lett. _!!, 65. McPherson, R., R. A. Esterlund, A. M. Poskanzer and P. L. Reeder 1965, Phys. Rev. 140, Bl513~ 86 Middleton, R. and D. J. Pullen 1964a, Nuc. Phys. ~' 50. Middleton, R. and D. J. Pullen 1964b, Nuc. Phys. ~' 63. Newns, H. C. 1960, Proc. Phys. Soc. London 76, 489. Ollerhead, R. W., J. s. Lopes, A. R. Poletti, M. F. Thomas and E. K. Warburton 1965, Nuc. Phys. 66, 161. Patterson, J. R., H. C. Winkler and C. S. Zaidens 1967, private communication. Pearson, J. D. 1963, Ph.D. Thesis, California Institute of Technology, unpublished. Satchler, G. R. 1964, Nuclear Spectroscopy with Direct Reactions II. p. 23, edited by F. E. Throw, Argonne National Laboratory Report No. ANL- 6878 (unpublished). Segel, R. E., P. P. Singh, R. G. Allas and S. S. Hanna 1963, Phys. Rev. Lett., Vol. 10, p. 345. Silbert, M. G. and J. C. Hopkins 1964, Phys. Rev. 134, Bl6. Talmi, I. and I. U1ma 1960, Phys. Rev. Lett. ~' 469. Towle, J. H. and B. E. F. Macefield 1961, Proc. Phys. Soc. London 77, 399. Warburton, E. K., P. D. Parker and P. F. Donovan 1965, Phys. Lett. 19, 397. Wilkinson, D. H. 1964, Phys. Rev. Lett. 13, 571. Wilson, W. E., R. L. Walter and D. B. Fossan 1961, Nuc. Phys. 27, 421. Winkle r, H. 1966, private communication. Zeidman, B. and T. H. Braid 1965, Phys. Lett. 16, 139. 87 TABLE I 18 Sample Calculation of Ne Q-Values (see page 29) L Calculation of Incident Energies Corrected Energy (MeV) ion Nominal Energy (MeV) p 3.840 - . 004 +. 004 3.840 4.200 +. 004 4.200 9.900 - . 004 ._ . 020 +. 010 9.890 10.850 - . 019 +. 011 10. 842 ' p He 3 He 3 II. Corrections (MeV) due to target Calib. thicknessa Const. b Calculation of Q-Value of 4. 55 MeV State Using B Calibration E (MeV) 1 X n-y (ch) 11 Q(MeV) 3.840 120.5 ' -2. 7632 9.890 116.3 ? ? = -7. 739 MeV ill. Calculation of Q-Value of 5. 14 MeV State Using B Calibration (ch) Q(MeV) 4.200 101. 1 -2. 7632 10.842 102.4 ? E (MeV) 1 X n-y (p, n) as 11 (p, n) as ? = 8. 339 MeV a. the mean energy loss in the target was taken to be 1/2 oE where oE is the total energy loss. b. taken to be +1 keV/MeV (Winkler 1966). 88 TABLE II (see page 29) I. Errors in Excitation of 4. 55 MeV State of Ne 18 Uncertainty Resulting Error in E (keV) x E a (calib) a E 1 X X ± 5. 8 keV 3. 5 ± 15 keV 13 (calib) ± O. 2 ch 3 (data) ± O. 6 ch 8 1 (data) n-y n-y Total II. Errors in Excitation of 5. 14 MeV State of Ne 18 Uncertainty Resulting Error in E E a (calib) 1 ± 6. 3 keV 5 a (data) ± 16 keV 13 (calib) ± O. 2 ch 4 (data) ± 0. 7 ch 13 E X X 1 n-y n-y Total a. 16. 0 keV x 19. 5 keV taken to be 1/2 of theoretical maximum allowed by slits (see page 30) (keV) 89 TABLE III Sample Calculation of the Excitation Energy of the 15. 068 MeV State in Nl3 (see page 45) I. Calculation of Incident Energies Corrections (MeV) due to .q ion Nominal Energy (MeV) target thickness a calib. const. b Corrected Energy (MeV) p 4.000 - • 004 +. 004 4.000 7.001 - • 024 + . 007 6.984 He II. 3 Calculation of Q-Values Using B 11 (p, n) as Calibration (ch) Q (MeV) 4.000 143. 7 -2.7632 6.984 143.6 ? E (MeV) 1 X n-y corresponds to E ? = -4. 878 x = 15. 061 MeV a. the mean energy loss was assumed to be 1/2 oE where oE is the total energy loss. b. taken to be+ 1 keV/MeV (Winkler, 1966). 90 TABLE IV Sample Calculation of Errors in the Excitation Energy of the 15. 068 MeV State in N 13 (see page 45) Uncertainty Resulting Error in E (keV) x E a (calib) 1 8. 8 keV 7 E a (data) 1 15. 3 keV 12 x n-y (calib) O. 2 ch 2. 4 x n-y (data) 0. 2 ch 2. 4 Total a. ± 14. 5 keV taken to be 1/2 of the theoretical maximum allowed by the slits (see page 30) 91 TABLE V Mean Excitation Energy of 15. 068 MeV State in N 13 (see page 45) Individual Determinations of E x (MeV) 15.075 15.067 15.075 15.069 15.059 15.061 Mean= 15. 068 MeV S. D. of Individual Determinations = • 007 MeV S. D. of Mean = • 0029 MeV 92 TABLE VI Excitation Energy of the 18. 98 MeV State in N 13 (see page 46) I. Calculation of Incident Energies ion Nominal Energy (MeV) target thicknessa calib. const. b Corrected Energy (MeV) p 4.800 - • 002 + . 005 4.803 12.504 - . 010 + • 013 12.507 He II. Corrections (MeV) due to 3 Calculation of Q-Value Using B E (MeV) 1 X n-y (ch) 11 (p, n) as Calibration Q (MeV) 4.803 135. 8 -2.7632 12.507 135.9 ? ? = -8. 802 corresponds to E x = 18. 985 MeV a. the mean energy loss in the target was taken to be 1/2 6 E where 6 E is the total energy loss. b. taken to be +1 keV/MeV (Winkler 1966). 93 TABLE VII Calculation of Errors in the Excitation Energy of the 13 18. 98 MeV State in N (see page 46) Uncertainty Resulting Error in E (keV) E a (calib) 10. 6 keV 8 E a (data) 1 27.5keV 22.6 (calib) 0. 1 ch 2 X n-y (data) O. 5 ch 10 1 X n-y Total a. x ± 26 keV taken to be 1/2 of the theoretical maximum allowed by the slits (see page 30) 94 TABLE vm Excitation Energy of 11. 195 MeV State in Fl 7 (see page 58) I. Calculation of Incident Energies ion He 3 a. He a. II. 3 foil 8.401 gas calib. const. c Corrected Energy (MeV) -0.163a -0.007 +0.008 8.239 7.100 -0.214a -0.008 +0.007 6.885 8.400 -0.144b -0.164 b . -0.008 +0.008 8.256 -0.010 +0.009 8.915 9.080 Calculation of Q-Values A. Using N 14 lCt, n)F 17 (0. 0 as Calibration E (MeV) 1 X (ch) Q (MeV) 6.885 147.6 -4.7349 8.239 145. 8 ? B. Using N 15 n-y (a., n)F E (MeV) 1 c. Corrections (MeV) due to Nominal Energy (MeV) 18 ? = -6. 192 ± 0. 010 MeV (o. O) as Calibration (ch) Q (MeV) 8.915 156.4 -6.4187 8.256 155.6 ? X n-y ? = -6. 182 ± 0. 011 MeV Final Value Q = -6. 187 ± • 007 MeV or E a. foil 4t l b. foil 41'2 c. x = 11. 195 ± . 007 MeV assumed to be +1 keV/ MeV (Winkler 1966). 95 TABLE IX Errors in Excitation Energy of 11. 195 MeV State in F 17 (see page 58) L Using N 14 (a., n)F 17 (O. O) as Calibration Resulting Error in E (keV) x Uncertainty E a (calib) 1 6. 9 keV 6.0 E a (data) 1 8. 2 keV 7. 0 xn-y (calib) xn-y (data) O. 2 ch 2. 4 O. 2 ch 2. 4 Q (calib) O. 7 keV o. 7 Total IL Using N 15 (a., n)F 17 10 (0. 0) as Calibration Resulting Error in E (keV) Uncertainty x E a (calib) 1 8. 9 keV 7. 5 E a (data) 1 8. 3 keV 7. 2 (calib) O. 2 ch 2. 2 (data) O. 2 ch 2. 2 1. 2 keV 1. 2 X X n-y n-y Q (calib) Total 11 a. taken to be 1/3 of theoretical maximum allowed by the slits (see Pearson 1963). 96 TABLE X Excitation Energy of 12. 540 MeV State in Fl7 (see page 58) L Calculation of Incident Energies ion 3 3 He He a. IL Corrections (Me V) due to Nominal Energy (MeV) 10.240 10. 180 9.080 foil a gas -0.127 -0. 127 -0.007 -0.007 -0.164 -0.010 Calculation of Q-Values Using N 15 (a., n)F 18 calib. const.b Corrected Energy (MeV) +.010 +.010 +.009 10.116 10.056 8.915 (o. 0) as Calibration (ch) Q(MeV) 8. 915 156.4 -6.4187 10.056 140.8 ? ? = - 7. 53 2 ± • 013 MeV 10. 116 137. 2 ? ? = - 7. 525 ± • 013 MeV E (MeV) 1 X n-y III. Q-Value Obtained Using 150 ns Delay Cable as Calibration ? = -7. 540 ±. 016 MeV N. Final Q- Value Q = -7. 532 + • 010 corresponds to E x a. foil #2 b. assumed to be +1 keV/MeV (Winkler 1966) = 12. 540 ± • 010 MeV 97 TABLE XI Excitation Energy of 13. 059 MeV State in F 17 (see page 58) L Calculation of Incident Energies ion He He Nominal Energy (MeV) 3 3 a. IT. I1I. Corrections (MeV) due to Corrected Energy calib. const.b (MeV) foil a gas 10.620 -0.121 -0.007 +.011 10.503 10.560 -0.121 -0.007 +.011 10.443 9.080 -0.164 -0.010 +.009 8.915 Calculation of Q-Values Using N 15 (a., n)F 18 (o. 0) as Calibration E (MeV) 1 X n-y (ch). Q(MeV) 8.915 156.4 -6.4187 10.443 155. 1 ? ? = - 8. 0 5 3 ± . 012 MeV 10.503 150.4 ? ? = -8. 047 ± • 012 MeV Q- Value Obtained Using 150 ns Delay Cable as Calibration Q = -8. 056 .± • 016 MeV IV. Final Q-Value Q = -8. 051 ± • 009 MeV corresponds to Ex= 13. 059+ .009 MeV a. foil #2 b. assumed to be +1 keV/MeV (Winkler 1966). 98 TABLE XII Calculation of Excitation Energy of the 16. 730 MeV State in Ne 20 (see page 69) L Sample Calculation of Incident Energies ion He He Corrections (Me V) due to Nominal Energy (MeV) 3 3 foil gasa 5.000 -.190 -.018 +.005 4.797 5.400 -.182 -.017 +.005 5.206 IL Sample Calculation of Q-Value Using o as Calibration E (MeV) 1 Corrected calib. Energy const. b (MeV) X n-y (ch) 16 18 3 (He , n)Ne (o. O) Q(MeV) 4.797 151. l -3.196 5.206 151. 2 ? ? = -3.616± .o DI. Summary of Excitation Energies A. Solid Target 16. 728 ± • 006 16. 731 ± . 012 16. 719 ± • 012 B. Gas Target 16. 730 + • 011 16. 733 ± . 005 16. 733 ± • 011 C. Mean Value = 16. 730 D. Standard Deviation of Individual Runs About Mean = 5 keV. a. taken to be 1/2 of total energy loss b. taken to be +1 keV/MeV (Winkler 1966) 99 TABLE XIIl Sample Calculation of Errors in the Excitation Energy of 16. 730 MeV 20 State in Ne (see page 69) Uncertainty Resulting Error in E (keV) x 7. 5 keV 6.6 (data) 8.1 keV 7. 1 (calib) O. 2 ch 2.6 (data) O. 2 ch 2. 6 5 keV 5 E a (calib) 1 El X X a n-y n-y Q (calib) Total a. 11. 5 keV taken to be 1/2 of theoretical maximum allowed by the slits (see page 100 TABLE XIV Distorted wave potentials taken from an analysis of the ol6(t, p) reaction (Glover and Jones 1966b). For the analytic form of the optical potentials see App·a ndix B. The incoming potentials were derived from the elastic scattering of 12 MeV tritons from 016. These parameters were used without modification to fit angular distributions from the reactions 01'6 (He3, n) and N15(He3,n). See pages 34 and 61. L Incoming Channel u v 146. 8 MeV 18. 9 MeV r u r a v v 1. 25f 1. 40f 1. 40f o. 55f o. 55f r r a u av o. 51f o. 30f II. Outgoing Channel u v r 54. 4 MeV 20. 0 MeV 1. 25f c u 1. 20£ v 1. 20f 101 TABLE X:V Distorted wave potentials used in the analysis of an angular distribution of neutrons from the o18(He3, n) reaction at 7. 33 MeV incident energy. The incoming potentials were derived from the elastic scattering of 8. 0 MeV He3 from F19 (Matous, Herling, and Walicki 1967). The outgoing potentials were taken from an analysis of the (t, p) reaction on several light nuclei (Glover and Jones 1966b). See page 71. L Incoming Channel v r 23. 23 MeV 1. 25f 1. 05f 1. 8lf · O. 829£ · O. 592f r r r u 183. 31 MeV r c r u au v a Il. Outgoing Channel U 54. 4 MeV V 20. 0 MeV c 1. 25£ u 1. 20£ v 1. 20£ a u O. 51f a v O. 30£ v Figure 1 Schematic diagram of the beam-pulsing system for the CIT/ONR tandem accelerator. The items enclosed within the dotted line are located in the control room. The chopping slits are used to define the beam burst duration and are usually set at± • 125". F'o r simplicity the chopping slits are drawn as if they were horizontal. In practice the beam is swept vertically to avoid interfering with the energy regulation ~ 0 ~ of the tandem accelerator. The beam p·1lsing system is discussed on p3.ge 7 and the phase stabilizer on page 74. BEAM PULSING SYSTEM FOR CIT /ONR TANDEM SLITS TO REGULATE ----z___ \. JN /'\ TANDEM JN CHOPPER PHASE .-------1DETECTING r--------- --1 ELECTRONIC PHASE SHIFTER 1 I I I I I I I I IBUNCHER AMPLITUDE CONTROLS MANUAL PHASE SHIFTER M'ANUAL PHASE SHIFTER MASTER OSCILLATOR I 3.51 MHz IL ___________________ _ A M PLIFIE R~ CHOPPING SLITS >-< 0 C;j 104 Figure 2 The experimental line shape for 1 MeV neutrons 11 11 as produced by the B (p, n)c reaction. The smooth curve is a computed resolution function which includes effects due to finite scintillator thickness, energy losses in the target, electronic resolving time, and beam burst duration. The "tail" on the low energy side of the neutron group is due to the collimator and shielding. It, of course, is not reproduced by the computed resolution function. (see pages 23 and 47). 105 RUN 25 4/27 /65 g11 ( p, no) ell COMPUTED RESOLUTION FUNCTION 3K _J w z z <! :r:: ~ 2K en 1- z :::::> 0 (.) • IK • •• 20 • • 30 CHANNEL 40 106 Figure 3 Block diagram of the electronic circuitry directly associated with the measurement of flight times. The commerCially available instruments symbolized by the boxes are: 1) zero crossing discriminator - Tektronix Type 661 Sampling Oscilloscope. 2) time-to-pulse height converter - Ortec Model 263. 3) amplifier - Tennelec Model TC200. 4) amplifier-discriminator - Hamner Model N328. 5) fast amp #1 - Hewlett-Packard Model 460BR. 6) fast amp #2 - Nanosecond Systems Model 281. 7) fast discriminator - Nanosecond Systems Model 205FG. 8) multi-channel analyzer - RIDL 400-channel. The circuitry is discussed on page 14. 107 SLOW - L/ VARIABLE DELAY XP1040 "--~ .r-- FAST Pl CKUP OIL -~ c ..... FAST AMP # I ,.,+ZERO-CROSSING DISCRIMINATOR FAST AMP :fJ: 2 FAST DISCRIMINATOR y--v-- -y--~ START '(J STOP , "\?_ _ _ _ __y__ TIME-TO-PULSE HEIGHT CONVERTER '(7 AMPLIFIER ------------ AMPLIFIER DISCRIMINATOR I ./\r ~1 IN GATE.._ ... MULTl -CHANNEL ANALYZER j 108 Figure 4 Block diagram of y-y coincidence apparatus used to test the performance of the counter and fast electronic 22 circuitry. Na was used as a source of coincident 511 keV gamma rays. The source was viewed by two scintillation counters both using XP1040 tubes. The phototube, scintillator and fast electronics in one channel were those used in the time-of-flight work. The other channel used similar apparatus. The measurement of resolving time is discussed on page 15. 109 y-y COINCIDENCE APPARATUS SLOW XPI040 XPI040 FAST SLOW FAST ZERO- CROSSING DISCRIMINATOR ~ / START AMPLIFIER STOP Tl ME -TO - PULSE HEIGHT CONVERTER DISCRIMINATOR -----i--.:~ SLOW COINCIDENCE AMPLIFIER GATE IN MULTI -CHANNEL ANALYZER AMPLIFIER DISCRI M INATOR 110 Figure 5 The gas target cell and filling system. Beam ions enter from the left and pass through a collimator, 0 suppressor electrode, and 5000 A nickel entrance foil before reaching the gas. The drawing is to scale. The collimator restricts the beam to a diameter of 3/8", and the gas cell is 1. 54 cm long. (see pages 16, 27, 55, and 66). 111 1 --~ SUPPRESSOR ELECTRODE -300V TANTALUM LINING NICKEL FOIL A TANTALUM COLLIMATOR B MANOMETER TO GAS RESERVOIR WJ STAINLESS STEEL ~ TEFLON l!ll GLASS C 0-RING TO ROUGHING PUMP Figure 6 A linearity spectrum used in establishing the time scale. Tha time converter 137 was started by radiation from a Cs source and stopped by RF clock pulses. The time intervals are therefore random and would. produce a flat spectrum if the time scale were truly linear. The data analysis program uses such spectra to correct for any non-linearities in the time scale. (see page 18). Note that the nonlinearity in channels 180 through 199, is well outside the± O. 3% statistics. This nonlinearity is not in the multicha1mel analyzer. ...... ...... ~ ...... v <D ID ...... (\J z ft) 0:: ::::> 0 0 0 0 ID • 113 C\I 0 0 co ...• >•• •• <D ~ ~ ~ C\I 0 v 0 ID 0 CD 0 0 _J w :I: z z < o<..> C\I 0 v 0 0 •• •• •• .f.. 0 ••• • l. I I ·1 •• ~ t.. 13NN'1H::>/SJ.Nno::> 114 Figure 7 Relative efficiency of the neutron detector. The smooth curve is computed by neglecting multiple scattering, scattering from carbon, and scattering and absorption in the shield and collimator. The curve is computed by assuming that the side channel discriminator bias is set at 450 ke V proton energy. (see discussion on page 21). 115 9 8 7 6 _5 Cf) 1- z ::::> >- 4 0::: <( 0::: I- m 0::: <( 3 >-· u z w u LL LL LU DETECTOR EFFICIENCY 2 CURVE REPRESENTS EXPRESSION DERIVED FROM n-p CROSS SECTION 2 3 4 5 NEUTRON ENERGY (MEV) 6 7 Figure 8 Neutron time spectrum from the reaction o 16 3 18 (He , n)Ne at 9. 0 MeV incident energy. The intense peak at the extreme right is caused by prompt gamma rays. The lines under the peaks indicate the mean background subtraction used in obtaining the 18 angular distributions displayed in Figure 13. The two lines under the Ne (1. 88) peak indicate the range of mean backgro·1nds. This contributes to the errors computed in the differential cross sections. The background is due primarily to phototube noise and room radiation (mostly from ~ + decays). See pages 27 and 31 • The time scale is approximately one ns/ ch. · ..... ..... Cj) RUN 20 8/13/65 W0 3 EHe3 = 9.0 MEV 8L = 10° FLIGHT PATH= 2.00m Q =90µC IOOOr-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ne IS (0.0) Ne IS (l.88) _J w z z <r I u 500 ...... ...... -.J ........ CJ) ~ z :::> 0 u Ne IS (3.36) - e fhvP" I_,."~d#. ,•., 014 (0.0) ,. e e 'fl' • 0'---~~-'--~~--'-~~~-L-.-~~-'-~~~'--~~-'--~~--L~~~-L--~~---' 20 40 60 80 100 120 CHANNEL 140 160 180 200 Figure 9 Time spectrum from the o 16 3 18 (He ,n)Ne reaction at 12. 52 MeV incident energy. The intense peak to the extreme right is due to prompt gamma rays; the small peak to the left marked y is due to prompt gamma rays from the out-of-phase beam burst. The lines under the peaks indicate the background subtraction used in obtaining the angular distributions presented in Figure 15. In addition to the time 18 independent background, at excitations in Ne above 3. 92 MeV there is a weak continuum from multibody decays. See pages 27 and 34. The time scale is approximately 1 ns/ ch. ..... ..... 00 7 /4 /65 RUN II W0 3 EHe3 12.5 MEV BL= 15° FLIGHT PATH = l.80m Q = 150µC 2500r-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,.-,.--~---. 1.88 ! 2000 3.61 ~;6 _J w z 1500~ z <( 5.13 l :r: u ' 4.55 Cf) t-I°~ II l ~ z :::> 1000 0 I u y l ! 500 . •• ._,~,:e• + ~~ -'~ - L----L--J- •~~At~ • • .. ....,..,, o.__~~_.__~~~-'--~~--'-~~~-'--~~-'-~~~-'-~~-'-~~~-'-~~--' 20 40 60 80 100 120 CHANNEL 140 160 180 200 ...... ...... co Figure 10 Time spectrum from the o 16 3 18 (He ,n)Ne reaction at 13. 53 MeV incident energy. The peak to the left indicated by y is due to prompt gamma rays from the out-of-phase beam burst. See page 27. The time scale is approximately 1 ns/ch. ,_. ~ 0 RUN 14 + I /11/66 E 8 = 15° = 13.53 Me V FLIGHT PATH = 2 . 9m BOO....-~~~~~~-....~~~~~~~~~~-----,-~~~~~~~-.--~~~-.--~~--. 600 r ~ x 1/5 -' w ........ z ........ z ~ J: (.) 1:-~ 400 ...... (/) 1- z ::> •• 0 (.) ••••. 4'J' • 200 • • • I 6 .0 I 7.0 I 5.0 EXCITATION IN Ne 18 I 4.0 '--~I 2.0 .... ._.••• .. . • • .,'\P~ • #a:• •••~ ··~ • •~·. 0.0 ••• (MeV) QL--~~--1~~~--1~~~~~~~-l..~~~~~~~-'-~~~-'-~~~_._~~~~ 20 40 60 80 100 CHANNEL 120 140 160 180 200 Figure 11 Demonstration that previously unobserved neutron groups correspond to 18 3 levels in Ne • The measured Q-value for the (He , n) reaction at laboratory angles between 0° and 150° is plotted versus laboratory angle. The data were taken at an 16 14 incident energy of 12. 5 MeV. Q-values were computed assuming targets of N , 0 , 17 18 0 , and 0 • The best fits to a single Q-value for both the 4. 55 MeV state (plotted 16 on the left) and for the 5. 14 MeV state (plotted on the right) are obtained with an 0 target. (See page 28.) The error bars are derived from estimates of the energy uncertainty and are not statistical. Hence the quantity "chi-square", while a measure of relative goodness of fit, has no interpretation in terms of probabilities. ....... t'-' t'-' -8.20 ~ ASSUMED TARGET MASS SYMBOL 0 14 16 18 6 0 -8.00 ~ f ~ ? ~ ~ > w x 2 9 6 f f 0 -8.60 0 -7.60 ~ > w ~ ~ f f § f f CHI-SQUARE MASS 14 MASSl6 MASS 18 20 40 1 f } t ~ ? f t r l ~ ~ 80 100 120 140 l 1 y If ....... J. f I "' !'-' l ~ ? CHI-SQUARE ' MASS 14 MASS 16 MASS 17 MASS 18 LAB ANGLE (DEGREES) I -aoo 13.4 .974 3.64 60 § f -8.20? ? - 1AO I- 0 -8.40 0 f y y f ~ 2 ? I - .f 14 16 17 19 0 -7.80 ~ ASSUMED TARGET MASS SYMBOL -8.80 160 180 0 20 40 6.09 .288 2.35 6.56 60 80 100 120 LAB ANGLE (DEGREES) 140 160 180 Figure 12 Time spectrum used in a measurement of the Q-value of the o 16 3 18 (He , n)Ne (4. 55) reaction. The time scale is about 1 ns/ ch and was calibrated using the 11 1 B \p, n)C (o. O) reaction. Note that the 1. 88 MeV state is very weakly populated iJ?. this spectrum. (see pages 30 and ·35). ........ N> ~ RUN 46 4/5/66 2500 E3H • 9.890 MeV 1 FLIGHT BL "0° I o.o PATH "2 .00 m I I I I ~ 2000 • • )( 1/3 ~ 1500 z z • ct :I: u ...... ....... N) U1 U> ~ z :::> 3.61 8 IOOO • '3.36 nI T 4.55 ~ 500 • !~, j· f\ J I ,..,..,_ e_, -~ (f)(), p •..,,....... '{!-'~· . ' • /l _r;f' ~('j ~~c.• I ..A " .... •1 I • . ~ .o~..c::>~• ,o~hf 'l·vl. I • 0 L--~~-'-~~~-'-~~~'--~~-'-~~~-L-~~~-'-~~---L~~~-J-~~~ 40 60 160 200 100 120 140 180 80 20 CHANNEL 126 Figure 13 Angular distributions of neutrons from the o 16 3 (He ,n) reaction at 9. 0 MeV incident energy. The error bars include contributions from counting statistics, and uncertainties in mean background, detector efficiency and beam current integration. The smooth curves are fits using the plane wave theory of Newns (1960) with the cutoff radius, r, and normalization treated as free parameters. (See pages 31, 33, and 35). The 3. 36 and 3. 61 MeV states were not fitted since they did not appear to be populated primarily by direct reactions at this energy. 100 arbitrary units of differential cross section correspond to 1. 4 + O. 3 mb/sr. 127 011 (He~ n) Ne'' (1.88) O"(He~ n) Ne'' (0.0) EH•' • 9.0 MeV ra 4.5f L •0 ~» • 9.0MeV L • 2 r • 4.0f 400 .,, ·2 :::> .!'.2 ·2 300 :::> ~ ~ ~ ~ :e :.0 0 300 >. 0 200 200 ~ ~ 100' t i 100 I 150 i 0 0~~~3~0=-----c6~0=--~9~0=-~=12~0~--,-~~-=- 180 8cM 0 16 (He! n) Ne18 (3.61) EHo3 = 9.0 MeV 0 16 (He~ n) Ne18 (3.36) EHos. = 9.0MeV .!'.! c .!'.! :::> => >. ·2 ~ ~ ~ 0 50 t If If ~ ~ :.0 ~ 0 blc: ~ 50 f I -0"0 00 ·.,_~~3~0,------,G~o,__~9 ~0 =-~~12~0~._.,15 ~0=----,,J180 8cM 0 0:;-~~3~0,------,6~0,---~9 ~0 =-~= 12~ 0,----,-15~0=-----,-,,J1so 8CM 128 Figure 14 Angular distributions of neutrons from the 0 reaction at 10. 5 MeV incident energy. 16 3 (He , n) The error bars include contributions from counting statistics and uncertainties in the mean background, detector efficiency, and beam current integration. In addition to the errors denoted by the flags there is an estimated uncertainty of± 10% in the absolute normalization. The smooth curves are DWBA calculations with only the normalization treated as a free parameter. Fits to the angular distributions of the 3. 36 and 3. 61 MeV states were attempted for L = 0, 1, 2, 3, and 4. ~he 3. 36 MeV state is fitted by L = 2, the next best fit (which is much poorer over the main peak) is found for L = O. The 3. 61 MeV state has been fitted with a mixture of L = 0 and L = 4 ·since it is suspected that this "level" may be an unresolved doublet. The pe rcentage refers to the ratio of normalizing constants needed to obtain the fit. The configurations of the residual nuclei indicated in this figure and in Figures 17, 38, 39, 40, 41, and 50 are believed to represent important components of the wave functions. However, the calculations do not distinguish between configurations which have the same values of 2n + l; for example, between ld and 2s or 2p and lf. and 34.) (See pages 31 129 12 r 18 18 2 d5/2 L•O 10 6 Ne (0.0) 5 8 4 6 3 4 2 I f E 3H• • 10.5 MeV 40 60. \ \ I f 2 .... \~o (/J 'E .D c; 'O 2.5 0 20 40 2 d:11i L • 2. E 3H• • 10.5 MeV 2 Ne (1.88) 0 100 60 80 18 Ne (3.36) 120 140 0 2.0 20 80 100 120 140 'b 'O 2.0 f\ 18 9.7%L•O} 90.3 % L• 4 d l.5N\ 2 512 EJH• • 10.5 MeV 1.5 1.0 l! 1.0 0.5 20 40 ~I f 60 80 100 2 d5/2 - -- L • 0 2 d5/2 EJH• = 10. 5 MeV \I\ \! ~ 0 0 Ne (3.61) - L •2 \ 0.5 \ \ ' ......... -..;: 40 60 i ~ 0 120 8cM 140 0 DEGREES 20 80 1 --100 120 ~ 140 130 Figure 15 Angular distributions of neutrons from the o 16 3 (He , n) reaction at 12. 5 MeV incident energy. The error bars include contributions from counting sta~istics, and uncertainties in mean background, detector efficiency and beam current integration. The smooth curves are fits using the plane wave theory of Newns (1960) with the cutoff radius, r, and the normalization treated as free parameters. Note the w1expectedly strong L = 1 transition to the 4. 55 MeV state. 100 arbitrary units of differential cross section correspond to 1. 4 ± O. 3 mb/sr. 31 and 35) (See pages 131 O" (He~ n) Ne'8 (0.0) EH13=12.52 MeV L =0 r = 4.0 f O"(He~n) Ne' 8 (1.88) Et,1 3=12.52 MeV 0 200 :.0 200 100 100 00 L•2 r = 4.75f 90 120 0 60 30 90 150 00 180 30 60 180 016 (He~n) Ne'8 (4.55) 0' 6 (He3, n)Ne11 (5.15) Et,13 =12.52 MeV - - L=2 r= 4.5f --- L = 0 r= 5.0f 15 150 BcM BcM EHt} = 12.52 MeV r = 4.5f L=I 150 ~ ·c:"':::> c: :::> >.... >.... ~ ~ :.0 :..0 .... 0 '\ ~;; 0 b ,~ \ "O "O ), 50 100 \ 50 \\ i ·1 ' ' :-... 00 30 60 90 BcM 120 150 180 00 30 60 90 eCM 120 150 180 132 Figure 16 Angular distribution of protons from the 0 16 (t, p) reaction at 10. 0 MeV incident energy (Middleton and Pullen 1964b). The curves are calculated from the plane wave theory (Newns 1960) using a cutoff radius a = 5. 5f, except for the 5. 33 MeV state which requires a = 5. Of. Compare 3 16 with angular dis tributions of the 0 (He , n) reaction presented in Figure 15. For a discussion of difficulties arising from this comparison see pages 33 - 38. 133 0 11 lO ; \ 1 GROUND STATE I L·O ~ r. tl. . . _. . . )0 I O• -;::- • l (/) .s 0 t)O t fv 60 10 1)0 l I L•Z lO ,., I t t .., ••• 110 I> IW )0 to to 110 1)0 11iG 1)0 tt0 '4 .'45 McV .. ....... to tO 10 lllO -llO I 0 3.92 McV \ \• • t .. •• 60 + I 0 llO 1.98 McV ....... ..... 1.0 t -~I "'.•'"""' )0 Y\.l ' l 0 L•O 1 ....___ .D llO 3 .63 McV \ 0 • '° to z '0 llO t)O 110 o )O to to 110 ID ~ t> 7 6 .., 8 5. 33 McV 5.25 McV 5.09 McV \ ••..•..•.. \ JO •:ie•tto1Z01ll0m .o I It t\ I0 1)0 1t0 L•3 ~.... \ t t \ .. •• 110 9 S.37 McV t "\ O·O to t .... • •• L•Z +tt •·l • )0 60 '° llO 1)0 ..0 Angle (c.m .) (deg) 0 JO '° .. llO llO - Figure 17 Angular distributions of neutrons from the o 16 3 (He , n) reaction at 12. 5 MeV incident energy. The smooth curves are DWBA calculations with only the ~ormalization treated as a free parameter. Compare with plane wave fits to the same data presented in Figure 15. (See page 34) ........ "".po. 500 500 .. 16o( 3 He ,n) 18 Ne(O.Ol E3 400 f-1 Ht 16 40J 12.5 MeV • L•O (d5/2 )2 Cl) 300 >- >a: < a: t: m a: a: < a: .... CD a: < I T Ht L•2 • 12.5 MeV (d5/2) 2 f 'b C::200 og \ 'b og 1• I < c:: 200 og ~ 100 0 E3 LoJ t z :l 16 3 o( He,n) Ne(l.88) 100 1 0 tG 1 30 • 1 "---60 I 1 90 BcM • 1n 120 I 1 150 I I ~ 180 I I O'--~~-'--~~-'-~~-'-~~-'-~~-'-~~~ 0 30 60 90 8cM 120 150 180 )-l (..;) C)l Figure 18 Isobar diagram of low-lying levels in the A= 18 nuclei. This diagram was 18 obtained by adding the information on Ne presented here to a diagram comparing 18 18 18 the low-lying levels of 0 and F (Ollerhead et al., 1965). T = 0 levels in F (except for the ground state) have been eliminated for clarity. The energy scales have been shifted to account for Coulomb energies and the neutron proton mass difference. Coulomb energies were calculated from the formula (Lauritsen and Ajzenberg-Selove 1966) E = O. 60 Z(Z-l)A-1/3 (MeV). Decay thresholds are shown, c but reactions leading to the nuclei under consideration have been omitted for simplicity. Spins and parities which are considered reasonably well established are indicated on the levels; values which are uncertain are enclosed in parenthesis . Isobaric analogs are connected by straight lines. Those which are considered well established are denoted by solid lines, tentative identifications are dotted. We suggest that the 3. 36 . Ne 18 may be a 0+, 4+ doublet. Ollerhead et al., argue that the 5. 59 and MeV "state" m 5, 66 MeV states in F 18 may be strongly mixed between T-:-Q; and T = 1. The identification 18 18 of the 4, 55 MeV state in Ne as the analog of the 4, 45 MeV state in 0 is especially uncertain. If correct, isospin conservation is blatantly violated. For a discussion see pages 35 through 37, ....... c,.:i (j) 7.527 160+d 6.227 14c+a i. :3+ 5.52 5.33_5.25 5.37 2+ o+/ 5.09 " 4.45 1- 3.92 2+ 3.55 3.63 o+ 4+ -----:=- 6.23 -·= ----~-==---=--=. -- 110 ... P -- -- ---- r - - ..=::- - 6 .64 1• .2 ·(1) :3+,4+,5+ 6.47 6 37 2(-) I ) ----- 5.59 5.66 1-12- 1- 2- ) - - - - - -- --- -- - 4.97 4.65 4 .74 ::::--..:::-4.41s---=..-_ 5 . 14 5.113 140+a 4.55 (i-) 4. 522 6 0+2 p 3.922 (2+) 17F + p (0++4+) 3.61 3 .36 1-4 14N+ a c.v -:J 2+ 1.98 rr.231 3.06 (2+) 1.88 2+ 1.05 o+ 0.11] o+ o+ 180 18Ne IBF Figure 19 1 3 Time spectrum of neutrons from the B \He , n) reaction at an incident energy of 7. 0 MeV. The excitation energies indicated above the neutron peaks 13 correspond to some of the lmown states in N • The prominent peak labelled 13 15. 07 corresponds to the lowest T = 3/2 state in N . Neutron groups arising 12 16 from c and 0 contaminants are labelled by the residual nucleus. This spectrum was used in the determination of the excitation energy of the lowest T = 3/2 state. The time scale is about 1 ns/ ch. (See pages 42 and 44) ..... C'-' co RUN 248 4/27/65 8 11 EHe3 = 6.976 MEV BL =0° FLIGHT PATH=2.054m 11.64 11.85 \ 014 3.51+3.56 ' ~0.0 2000 0=90µ.C ~ Neis 0.0 ' 1500 _J w 2 2 <l I u 9.48 _8.90 15.07 7.18 ' t ...... c.v CD .......... Cf) ..... 1000 2 ::,) 0 u 0.0 ' r------~~:-;:;:-;~~~-;-:-.-.;-:-:-:-=---=------1~ t••~ • 4't . EXCITATION IN Nl3 (MEV) -:--;::--- - -- I I I 15.0 14.0 12.0 10.0 - .. ! .. •.~ • I 5.0 0.0 oL_~----L~~~.J.._~~--1..~~~-'-~~--'~~~----'-~~~.l.._~---L~~~ 20 40 60 80 100 120 CHANNEL 140 160 180 200 Figure 20 Time spectrum of neutrons from the B 11 3 (He , n) reaction at 9, 00 MeV incident energy. Numbers above the peaks correspond to excitation energies of 13 12 some known states in N • The positions of neutron groups arising from C or 16 0 contaminants are labeled by the residual nucleus. The lines under the 3. 5 and . 15. 07 MeV groups indicate typical background subtractions used in computing the angular distributions shown in Figures 29 and 30. A small correction was made to 18 the peak area for a contribution from Ne (1. 88). The time scale is 1 ns/ch. (See pages 42 and 48. ) r-' t.f::.. 0 500 RUN 14 11/23/65 8 11 EHe3=9.00 MEV o' 15.07 t FLIGHT PATH 3.38m BL =0° Q=88.5J-LC 4 0.0 ~ Ne'a 1.88 11 .64 11.85~ 400 Ne's 0.0 3.51+3.56 ~ _J ' '- t 9.48 ~ w 2300 10.35 <I: t z I 7.18 ~ ~ CJ) ...... ~~ ...... ..__ z :::> 200 0 u 0.0 t •I ~.·• • •• EXCITATION IN N 13 ( MEV) 20 40 L___ I 15.0 14.0 60 __J 12.0 80 I _ _ 100 5.0 120 CHANNEL ,/ • • • _L___J 10.0 ....L.-.. . • ••,._.•• ~. 100 0.0 140 160 180 200 Figure 21 11 3 Time spectrum of neutrons from the B (He , n) reaction at 12. 5 Me V incident 13 energy. T = 3/2 levels in N are labelled by their excitation energy. The 18. 98 Me V state is clearly visible in this spectrum, which was used in a determination of the width of this level. A weak gamma ray peak from the out-of-phase beam burst is superimposed upon the neutron group from the 18. 44 MeV state. Gamma ray peaks are identified by measuring the change in flight time caused by a small change in flight path. The time scale is approximately 1 ns/ ch. (See pages 42 and 56) ....... >f:.. ~ RUN 6 4000 11/19/66 • 12.5 MeV E3 BL •0° PATH •3.3m FLIGHT Q• 270µ.C H -. 15.07 y t ~ 3000 x 117 _J 18.44 w z z y"ll <l :r: ...... 2000 l) .._ z (/) 0 18.98 ......... ~ (.;:> ~~ ::::> 0 l) CQ;,Ooo~ 1000 o~qf> oo o<-0 EXCITATION IN N 13 (MeV} 19.0 18.0 17.0 oO ~oo«f<>qp>&fb 16.0 14 .0 10.0 5 .0 0.0 0 0 0 ~~~_._~~~..__~~_._~~~-'-~~--'-~~~-'-~~--''--~~_,_~~~ 20 40 60 80 100 120 CHANNEL 140 160 180 200 Figure 22 Time spectrum of the B 11 3 (He , n) reaction at 13. 52 MeV incident energy. The T = 3/2 levels are indicated by their excitation energies. The peaks labelled y are due to gamma rays. The peak on the left is caused by the out-of-phase beam burst; the one to the right is due to the beam striking a slit. Gamma rays are identified by observing the time shift caused by a small change in flight path. (See page 42) ~ ~ ~ E 0 ~ C\J I Cl. ~ I_J I ~ l4. 0 0 ...J Q) "' ~ > CX) l.D oiri <;t" CX) (]')-- a:i- o.{) CX) N r0 ."'., J: UJ l.D l.D ....... ...... z CJ) :J .a:: 0 0 0 C\I • 145 0 0 0 • • 13NNttHJ/SlNnOJ or~ 0 0 • :· c 0 • • • 'b '3 Q) -> ~ z r0 z z 0 ~ 0 I- x w 0 0 0 Q 0 iri r-..: 0 0 c:ri 0 c;i 0 C\J 0 0 C\J 0 0 0 co l.D 0 <;t" 0 C\J 0 0 0 0 co l.D 0 <;t" 0 0 C\J _J w z z :r: <! 0 146 Figure 23 Demonstration that the previously unobserved 13 neutron group corresponds to a state in N . The measured 3 Q-value for the (He , n) reaction at laboratory angles between o0 and 135° is plotted versus laboratory angle. The data were taken at an incident energy of 9. 0 MeV and were computed . 10 11 12 assummg targets of B , B , and C . The data can be 11 fitted with a single Q-value only by assuming a B target. The error bars are derived from estimates of the energy uncertainty, and not statistical. Hence the tabulated quantity "chi-squared", while a relative measure of the goodness of fit, has no interpretation in terms of probabilities. page 43) (See 1'17 -5.20 D ASSUM ING MASS 10 T ARGET I::. ASSUMING MASS 11 0 ASSUMING MASS -5.10 TARGET 12 TARGET 0 0 0 0 -5.00 0 0 0 0 I -43J f f -w> ~ D 0 I 0 D 0 CHI - SQUARED -4.80 MASS 10 MASS 11 MASS 12 0 8.82 0.636 5.29 -4:70 D D D 0 - 4 · 60o'--~~~3~0~~~~6~0~~~-9~0~~~__.Jl2~0~~~-1~5-0~~~~180 LAB ANGLE (degrees) 148 Figure 24 Comparison of spectra taken with targets of B and natural carbon. 11 The· spectra were taken at the same beam energy and detector geometry. The prompt gamma peaks in both spectra have been superimposed. By using 14 the 6. 59 MeV state in 0 to normalize the amount of 11 carbon in the B spectrum one can readily see that the 18. 44 and 18. 98 MeV states cannot be attributed to a carbon contaminant. (See page 43) 149 RUNS 11 ANO 13 EXCITATION EHe3 = 13.5 MeV 1/11/66 BL =0° FLIGHT PATH = 3.30 m IN N 13 (MeV) 18.98 18.4 15.07 I I I x 1/4 ,,. I ~~~Cl:» .~o.; 7.78 6.59 5.91 5.17 EXCITATION IN 0 (MeV) 0 .0 14 g •• 150 Figure 25 Comparison of spectra taken with targets of B 11 and tungsten oxide. The spectra were taken at the same beam energy and detector ge01netry. The prompt gamma peaks in both spectra have been superimposed. It is readily seen that the 18. 44 and 18. 98 MeV states could not be produced by oxygen. (See page 43) 151 RUNS 14+ AND 15 EXCITATION MeV 18.98 1/11/66 IN EH e3" 13.5 MeV 8L " 15° FLIGHT PATH • 2.9 m N 13 18.4 15.07 I I )( 1/5 0 5.14 4.55 3.36 1.88 0 .0 + 3.61 EXCITATION IN Ne MeV 18 152 Figure 26 Demonstration that the 18. 98 MeV state is produced 11 3 in the B (He , n) reaction. In the upper part of this figure we have plotted the chi- square for fits of the experimental Qvalue determined at eL = 0°, 15°, and 30° to a constant. The graph displays chi-square as a function of assumed target mass. The data is best fitted by an A = 11 target. In the bottom part of the figure we have plotted the best fit of the experimental Q-value (MeV) versus laboratory neutron angle (degrees). The error bars are derived from an estimate of the energy uncertainty and are not purely statistical. Hence the "chi-square" displayed above has no interpretation in terms of probability, but is only a measure of relative goodness of fit. The best-fit value of Q was used in determining the excitation energy of the 18. 98 MeV state. (See page 44) 153 30 \ I N13 (18 .98) x x 25 20 I 15 1 10 0 x x 5 \_,/ 9 10 II 12 13 14 15 TARGET A - 8 .820 (/) (/) <! ~ n:: tJ u.. n:: -8.810 0 <.9 <! ~ t- -8.800 _J <! >I 0 -8.790 0 10 20 BLAB 30 Figure 27 11 Time spectrum from the reaction B (p, n) at an incident energy of 4 MeV. This spectrum was used to calibrate the time scale in Figure 19. The time scale is about 1 ns/ ch. (See pages 13 and 44.) 1-4 U1 .,p.. RUN 25 4/27 /65 8 11 Ep =3.996 MEV BL =0° FLIGHT PATH= 2.054m 5000 c" 4000 L 0.0 i I _J w z 3000 z <! I u ~ C.ll "z (J, (/) 1- 6 2000 u 1000 I y ~ I 0 ~--L·~"=~-,,..eo==o""'=-=~'"""""""'~·~·=='='==¥~-·A~="<-"• 20 40 60 80 100 120 CHANNEL 140 160 180 200 Figure 28 Time spectrum of neutrons from the B 11 3 (He ,n) :reaction at E He 3 = 9.0 MeV, · Blab = 120°. This spectrum was used in obtaining the angular distribution presented in Figure 29, (See page 48) .... CJl en 158 Figure 29 Angular distribution of neutrons from the B N 11 13 3 (He , n) reaction l eading to the lowest T = 3/ 2 level in . The error bars for points at eCM < 60° denote limits of error imposed by background subtraction. points the errors are statistical. For other The smooth curves are calculated using the plane wave theory of Newns (1960). The cutoff radius r = 5. 0 f was used in a successful fit of 11 the B (t, p) reaction (Middleton and Pullen 1964a). Our data require r = 3. 75 - 4.0 f. The sensitivity of the plane wave theory to the cutoff radius is graphically demonstrated. (See page 48) 159 8 (He 3 , n) N 13 (15.07) 11 EHe3 = 9.0 MeV FITTED WITH 200 exp(-K 2 /4y 2 lJ6 (kr) Y = 0.255 x 10 13 cm- 1 180 - - - r = 4.0f - - - r = 3.75f 160 (f) I- z 140 / I :::> >- 0:: I 120 1 I <I: 0:: I- '\ \ \ \ I 100 1 I OJ \ I \ I 0:: <I: \ I 80 \ I :2: u b,~ -... - - - - - - r = 5.0 f \ I \ 60 .A. TARGET 10 •TARGET I \ \ "'O "'O , ,,,,,-- ~\-;r-1 J_ _ ' ' ..... __ / 40 \ 20 0 ...... 30 60 90 120 150 -180 160 Figure 30 Angular distributions of neutrons corresponding to 13 the unresolved 3. 51 and 3 .. 56 MeV states in N , taken at 9. 0 MeV incident energy. Error bars have been omitted because the dominant uncertainty is due to a highly subjective background subtractiOn. Rather than make a totally arbitrary and meaningless estimate of the background uncertainty, we refer the reader to Figure 19, where he may form his own opinion of our taste in backgrounds. The smooth curve is an L = 0 fit using the same cutoff radius (4. 0 f) used in fitting the 15. 068 MeV state. The fit to the forward peak is quite good indicating that at forward angles the peak is almost purely due to the 3/2- state at 3. 51 MeV. The discrepancy between curve and data at back angles may be due to the presence of neutrons from the 3. 56 MeV state. (See page 49) l Gl 11 s c3 He n) 13 N (3.51+3.56) 1 E3 He =8.98MeV L•O 600 r = 4.0 f >- a:: ~ 400- ..... CD a:: c::x: q "O 'b "O 200 0 0 0 0 L-~~_JL-~~.......JL-.-::==:=::!==:::::::a----1~~~__J 0 30 60 90 120 150 162 Figure 31 B 11 Partial angular distribution of neutrons from the 13 (He , n)N (18. 98) reaction at an incident energy of 3 12. 5 MeV. The error bars include effects of counting statistics and uncertainties in background subtraction. (See page 49) 163 11 3 13 8( He,n) N ( 18.98) L =I r = 4.0 f Cf) 1- z ::> >0::: ~ 40 I-- co 0::: <! -b 20 0 ..__~---~~..__~__._~~--~--~~---~-0 10 20 30 40 BcM 50 . 60 70 164 Figure 32 13 T = 3/2 levels in c are 13 from Hensley and Barnes (1965, 1966), the 0 mass is . 13 from Cerny et al., (1966), and the T = 3/2 levels in N A= 13 isobar diagram. are from the present work. Correspondences which are considered to be well established are indicated by solid lines; those which are tentative are dotted. The corre3 spondences between the (He , n) and (He 3 , p) results are quite good. In both cases the lowest T = 3/ 2 levels are populated very strongly. The 18. 67 and 19. 13 MeV states 13 in c are populated relatively strongly and presumably 13 correspond to the 18. 44 and 18. 98 MeV states in N • In 11 3 the B (He , p) reaction the 18. 47 MeV state is quite weak and the 18. 70 MeV state is seen only as a shoulder on the 18. 67 Me V level. This is consistent with the suggestion that the 13 N 18. 44 MeV state may be an W1resolved doublet. (See page 51) T=3/2 ISOBARS- MASS 13 3.09 N'2•p 04 .91] T_::~/_2 __ 8'3 0'3 ~ G) u, 10.181 =--==-~-=- --J=l/2- c'3 3.56 3.51 ~..M- 2.367 112+ r:o.o~ J·! N'3 112r 166 Figure 33 0 Determination of energy loss in a 5000 A Ni entrance foil for the gas cell. The yield of high energy gamma radiation is plotted against nominal proton energy, 19 as the beam energy is swept over the 872 keV F (p,cx.y) resonance. The energy loss in the foil was taken to be the displacement of the centroid of the resonance when the foil was placed ahead of a thin fluorine target. and (See pages 56 1G7 868 KeV ___.. ...-- 5 Kev 937 KeV w 104 <..9 0:: <.( :c (.) rz :::> NO FOIL ......... (f) r- z :::> 8103 THROUGH FOIL 102 -----------.....____.____~-----~--_.__------_. 860 83 0 900 920 Ep (KeV} 940 9 60 9 80 Figure 34 15 3 Time spectrum of neutrons from the reaction N (He , n) at 10. 498 MeV 18 15 incident energ·y. The time scale was calibrated using the N (o.., n)F (o. 0) reaction 17 and is approximately 1 ns/ ch. The T = 3/2 levels in F are labelled by their excitation energy. (See page 56) ........ (j) co 15 3 8~-- - -FLIGHT !i_ (He_~--itt~J_Q~~98 _ _ -- - -PATH - - -• 2.60 - - m. - 7/26/66 2000 ~RU N 23 11.195 - - . I x T2 _J w z z <l I 12.544 ...... ( j) i 1000 (.) CD ' . (f) 1- z :::> 0 • (.) EXCITATION IN F I 13.0 0 20 40 17 (MEV) I 12.0 60 80 11.0 100 . .., . .,~ ·-· 180 200 -9 .o"eu;;;,"- ... . L~__._~~~~~~ 10.0 120 CHAN NEL 8.0 6.0 4.0 0.0 140 160 Figure 35 15 3 Time spectrum of neutrons from the N (He , n) reaction at 11. 88 MeV 17 incident energy. The T = 3/2 levels in F are labelled by their excitation energy. ....... -.::i 0 The time scale is approximately 1 ns/ ch. (See page 57) RUN 24 4000 7/26/66 81L • 0° EHe3• 11.88 Me V FLIGHT PATH • 3.00 m 11.195 I ~ I xi() _J w z z<( J: ....... -:i ....... ~ 2000 CJ) ~ • z :::> 0 u • I ... . e:a-• . .. . . . " -· .,,. ;. . ~. afl'o.... o.,.fo<!><a EXCITATION IN F 17 (MEV) • 1 . . • CIJ ""'"~?•.,.,~p!'w.,c · ~ ------'-------~----'----'-~'----~-~~ . 14.0 20 40 13.0 60 80 12.0 11.0 10.0 100 120 CHANNEL 8.0 5.0 14 0 0 .0 ~e • 160 T ~ "°' •" 180 200 Figure 36 15 3 Time spectrum of neutrons from the N (He ,n) reaction at 8. 255 MeV incident energy. This spectrum was used in a determination of the excitation 17 energy of the lowest T = 3/2 state in F . The time scale is approximately 1 n.s /ch and was calibrated using the spectrum shown in Figure 37. The peak marked SP (spurious) is due to gamma rays from the out-of-phase beam burst. Other 17 peaks are identified with known levels in F • (See page 58) ....... ~ NI N15 {He3 ,n) 7/26/66 RUN B 1600 E Ht 3 = 8.255 ~e V oo BL: FLIGHT PATH = 2.6 m 7.75 l 8.39 8.7~ xl 3.10 ' 1200~ II ' 9f8 ;~ \11 • 7 1 ~ 6.04 _, I ..J I ' I w z z <I I 0 ' .._ 800 .JV SP (j') z T =3/2 0 l :::> 0 I ' l ~J 11 1 l I V-- "• A 400 ~l • \. ... "''-~ · ~• • • EXCITATION IN F17 (MEV ) . .. ".· .°"' "a""' 160 200 ....... .,_.• .,_ "- ~--• • o • .,.. 11.3 20 11.0 40 10.0 60 80 8.0 100 120 CHAN NEL 6.0 • 4.0 2.00.0 14 0 180 ........ ~ c...:i Figure 37 15 17 Time spectrum from the N (a, n)F (0. 0) reaction at 8. 915 MeV incident energy. This spectrum was used to calibrate the time scale in the spectrum ~isplayed in Figure 36. (See page 58) f--l -J If::. E 0 <.D N 0 0 0 c z ~ <.D <.D <.D ' N ' r- N z ::> a:: ~ 0 0 -Iv >< 175 C\J 0 0 • • • • • •• • •• •• 'I:' .\ C\J 0 0 0 OJ (.!) 0 0 <;j" u <! I w C\J _J ~ 0 (.!) 0 OJ 0 0 0 0 • ••• z z .. • • • •• • •• • • ••• • •• •• • • • ~ • • • •• • •• • • •• • •• • •• ••• • ••• ~ ll • . • • •• • •"'•• • •• • • • • ••••' • •• • :·• i---.--1 . . • • • •• •••• ·• • • ..,_._.. • \ •• • • :• • • •• •• • •• • • • •• •• 13NN'V'H~/Sl.Nno~ Figure 38 15 17 3 L = 0 angular distribution of neutrons from the N (He , n)F (11. 195) reaction at 10. 36 MeV incident energy. In addition to the errors denoted by the flags there is an estimated uncertainty of± 10% in the absolute normalization, The curve is a DWBA calculation with only the normalization treated as a free parameter. (See page 60.) ...... -.J O':> 177 F 17 (11.195) L=O EHe3 = 10 ..36 MeV .01 0 20 40 60 80 BcM DEGREES 100 120 140 178 Figure 39 L = 0 angular distributions of neutrons from the . 15 3 17 react10ns N (He , n)F (11. 195) at E = 11. 88 MeV, and 3 16 3 18 He 0 (He , n)Ne (O. 0) at E = 10. 50 MeV. In addition to the 3 He errors denoted by the flags there is an estimated uncertainty of± 10% in the absolute normalization. Since both transitions may be thought of as the L = 0 capture of two protons into an 17 18 empty sd shell, the F and Ne angular distributions are expected to be very similar. The curves are DWBA calcu- lations with only the normalizations treated as free parameters. (See page 60) 1'79 100 - 2 F 17 (1 l.195) -- 1 Ne18 (0.0) 10 \ \ lo.- (.{) 'E ..0 -- L=O ~ \ \ 1.0 b 0.1 .0 1 ~~~~~~~~~~~~~ 0 40 80 8c M 120 160 180 Figure 40 L = 2 angular distributions of neutrons from the . 15 3 17 reactions N (He , n)F (12. 540) at E = 11. 88 MeV and 3 16 3 18 He 0 (He , n)Ne (1. 88) at E = 10. 50 MeV. In a ddition to 3 He the errors denoted by the flags there is an estimated uncertainty of± 10% in the absolute normalization. The curves a re DWBA calculations with only the normalizations treated as free parameters. Note that in both cases the DWBA curve fails to 0 reproduce the pronounced minimum at o • Since both transitions may be thought of as the L = 2 ca pture of two protons into an 17 18 empty sd shell, the F and Ne angular distributions are expected to be very similar. (See page 60) 181 100 - ~ F 17( 12.544) -- f Ne 18(1.88) 10 L =2 lo.- C.J) ........... _Q E -- 1.0 CD b 0 .1 40 120 - 160 182 Figure 41 N 15 Angular distribution of neutrons from the 17 (He , n)F (13. 059) at 11. 88 MeV incident energy. 3 In addition to the errors denoted by the flags there is an estimated uncertainty of± 10% in the absolute normalization. This level is unbound to diproton decay and cannot be treated by our DWBA code. (See page 60) 183 1.0 2 :I.... (/) 'E ~ 2 ...0 f f ~ 0.1 - ! b .01 0 40 120 160 184 Figure 42 Isobar diagram for the A ;:;; 17 nuclei. The notation and Coulomb corrections are described in the caption to Figure 18. For similicity only the low lying T ;:;; 1/2 levels are shown. The T;:;; l/2 levels are taken from Lauritsen and Ajzenberg-Selove (1962), 17 except for the 5/2+ assignments to the 3. 8 MeV states in 0 17 (Broude et al., 1963) and F (Segel et al., 1963). The T ;:;; 3/2 15 17 3 levels in-; have been taken from studies of the N (He , p) and 3 18 0 (He , a ) reactions by Hensley and Barnes (1966). The mass 17 indicated for Ne was estimated using the quadratic mass law, 17 which predicts a mass excess for Ne of 16. 478 ± . 032 MeV. (See page 62. ) 185 14 044 15N +d 13.647 ----- ;> "" 1.85 1.91 12.953 12 998 312- 1.37 ---- - r1 1. 163l 14.044 150 +d 13.782 16N+p 112- 12.473 11.086 13.059 112· 312- 12.540 312- 512- 12.726 15N+2p I I I I I I I I I I I I 112- 11. 195 112- 11N l[i 0.92J_ _ _J i1Ne ~=·: ~ 13c+a ~ 5.08 312- 4 .551 312- 16o+n 3.846 512 3.058 112- 0 .8 71 11?+ 13N +a 5.10 312• 4.69 312- 3.86 512- 3.10 112- 4 .143 0.500 512+ [- 0.191] 112 + .2:§.2!_ + 160+p (512 ) Figure 43 Time spectrum of neutrons from the 0 18 3 (He , n) reaction at 5. 204 Me V incident energy. This spectrum was used in determinations of the excitation 20 energy and width of the lowest T = 2 state in Ne • The time scale was calibrated 18 16 3 '1,1Singthe0 (He ,n)Ne (o.O) reaction and is roughly 1 ns/ch. (See pages67 and 69.) ....... cc (j) RUN 5 3000 9/24/66 EHe3 = 5.204 BL = 0° MeV FLIGHT PATH • 2.7m x 1/12 T•2 2000 j -' w z z <l: I 0 1-l (/) -.:i ........ ~ rz :::> 0 0 1000 EXCITATION IN Ne 2 o ~00,-::....~~o 0 0 oo '-'"" 17.0 16 .5 16.0 15.0 14.0 12.0 10.0 5.0 0.0 MeV oi--~~-'-~~~'--~~_._~~~.1.-~~-l.~~~_i_~~__J.~~~-1-~~_J 20 40 60 80 100 120 CHANNEL 140 160 180 200 Figure 44 18 3 Time spectrum from the o (He , n) reaction at 5. 714 MeV incident energy. 20 The lowest T = 2 level in Ne is quite prominent at this incident energy and appears to be on top of a broad "bump". This "bump" remains prominent at angles up to 45°, although the intensity of the T = 2 peak diminishes. The dotted line indicates our somewhat arbitrary choice of background subtraction. It is typical of those used in forming the angular distribution of Figure 49 • The sloping background to the right of the unresolved ground and first excited state group is composed of neutrons having a . . flight time, t, longer than one RF period, r, and which therefore have an apparent flight time t' = t - r. The time scale is approximately 1 ns/ ch. (See pages 67 and 71.) ....... OJ 00 RUN 18 9/24/66 EHe3 • 5.714 MeV BL= 0° FLIGHT PATH = 3.0 m 1600..-~~~~~~~-.-~--'=-...--~~~-y-~-=~-r---~~,--~~~,--~~~,--~~--, T•2 ' xl/12 • • _J w z z <[ • • I ~ 800 Cf) ,. 1- z 1-l co •to• ;· • ::l 0 <.) CD • •• • • EXCITATION IN Ne ~--------' 17.0 I 16 .0 • I 14.0 I I I 12.0 10.0 I I 5.0 0.0 140 160 " ~ 0 - _.-..-0 .... -~J ~ (:) 20 ! -6 MeV 0 20 40 60 80 100 120 CHANNEL 180 200 Figure 45 3 (He , n) reaction at an incident 20 energy of 6, 515 MeV, The lowest T = 2 level in Ne is clearly visible above the Time spectrum of neutrons from the o 18 intense continuum due to multibody decays. The time scale is approximately 1 ns/ch. (See page 67.) 1-l co 0 RUN 17 3000 9/0 I /66 EHe3 = 6 .515 MeV BL = 0° FLIGHT PATH = 3.0m o ~~----==--~~~~~~~~~~~~~~~~--. T• 2 ~ x 1/8 2000 _J w z z<{ .,.,••,,. I 0 ...... ..__ I 11 e Oe e . C> z ::> 0 0 1iV' •-"~ • (/) • 1000 EXCITATION I 17.0 0 20 40 60 IN I Ne 2 0 Me 16.0 V I I I 12.0 I 1610 15.0 14.0 . 80 100 120 CHANNEL ~.?~..Jt!'V' I -'• I I 5.0 0.0 140 • Cl ti c;:..' Oolo 160 180 200 ...... (0 ...... Figure 46 Time spectrum of neutrons from the o 18 3 (He , n) reaction at 9. 01 MeV incident energy. The lowest T = 2 state is labelled; the arrow labelled A marks the excitation of the 18. 5 MeV state reported by Cerny et al., (1964). This state is not seen in our spectra. At this incident energy the intense continuum is peaked at an excitation in ~e 20 close to that of the lowest T = 2 state. (See page 67.) ...... (.0 N> RUN 16 9/l/66 EH 8 3 = 9.010 MeV 3000 FLIGHT PATH = 3.0 m BL= 0° -----, T•2/! Xl/6 2000 _J A z z .•• • w +••• <l I 0 . ..,.'··· •• •• ' (/) ~ z '.:) 0 0 ••.A.o IOOO • • e'r.#' ........ co C,;j •••• • •fl" 'lte ~~~o• e 'lit o •" EXCITATION IN Ne 20 II" ~-V~,f (MeV) o~ eve. --20.0 0 20 19.0 40 60 80 18.0 100 16.0 14.0 12.0 5.0 0.0 120 140 160 CHANNEL 180 200 194 Figure 47 3 0 Goodness of fit of (He , n) Q-values obtained at eL = o , 10°, 20°, and 30° to a constant versus assumed target mass. The errors used in calculating the goodness of fit were not statistical, but taken from an estimate of the energy uncertainty. Hence the quantity " chi- squared" while a measure of relative goodness of fit, has no interpretation in terms of probabilities. From this graph we infer that the reaction was produced by a target having 16 < A ~ 26. (See page 67.) 195 0 (He 3 , n) Ne 2 0 18 FIT OF Q-VALUES 18 x OBTAINED AT 8L "0° , 10° , 20° , AND 30° TO A CONSTANT 16 14 Cl 12 w a:: <{ :::> 0 (/) 10 I :I: u 8 x 6 4 ·~ 2 X-_ --x-x 12 14 16 18 ASSUMED 20 --X ~·/' 22 TARGET MASS 24 26 28 196 Figure 48 In the upper right we have plotted chi- square as a . function of the assumed intrinsic width of the lowest T = 2 20 state in Ne . The procedure for calculating the neutron line shape is discussed on page 70. Note the offset scale on the chi- square axis. In the lower part of this figure we have plotted the line shape giving the best fit to the experimental points minus a linear backgrow1d. 197 ::i! 0 a 22 x w w E 20 LL 0 2 18 (/) WIDTH OF Ne 0 (T=2) FROM DATA OF 9/24/66 (/) w 16 0: (.!) w a 14 !-------~'-- 20% -- 12 0: 0 LL CIJ x x 10 Bx-___ _ / 61 0 I x I 10 20 f (KeV) - 0 600 w I(.) <t 0:: I- co BEST FIT ~ (/) 400 0 z ~ 0 0:: l9 :::.::: (.) • <t CD .- (/) 200 I- z ~ 0 (..) .----! 0 40 0 45 50 CHANNEL 55 198 Figure 49 o 18 Angular distribution of neutrons from the reaction 20 (He , n)Ne (16. 730) at 5. 70 MeV incident energy. In 3 addition to the errors denoted by the flags there is an estimated uncertainty of+ 10% in the absolute normalization. (See page 71. ) 199 10.0 I 18 I I I I 0( 3 He,n) 20 Ne{l6.73) E3He • 5.70 MeV 1.0 ,_ - 0.1 ,_ - ...en ...... .0 E -b ) -0.01 0 I I 10 20 I I I 40 50 60 200 Figure 50 Angular distribution of neutrons from the o Ne 20 18 (He3 , n) (16. 730) at 7. 33 MeV incident energy. The error bars include contribt-:.tions from counting statistics, and uncertainties in mean background, detector efficiency, and bEa m current integration. In addition to the errors denoted by the flags, there is an estimated uncertainty of± 10% in the absolute normalization. The smooth curves are DWBA fits for L = 0, 1, and 2, with only the normalization treated as a free parameter. The experimental distribution is obviously L = O. (See page 71.) 201 10.0 ... ell ....... J:l E -b 0.01 0 10 20 40 50 60 Figure 51 3 Energy systematics of higher isospin states accessible with (He , n) reactions on targets with 7 ~A~ 27. The Coulomb barrier in the laboratory system, and thresholds for production of the lowest T = 3/2 and T = 2_states are plotted versus A. The Coulomb barriers were calculated using the expression E c = 1. 03 A + 3 zl z2 A Al/3 + 31/3 • The open triangle and circles denote values obtained from an estimate of the excitation energies using a method described on page 39. The experimental implications of this graph are discussed on page 72. !:\:) 0 !:\:) SYSTEMATICS OF HIGHER ISOSPIN STATES THRESHOLD FOR LOWEST T = 2 STATE £. 410.0 • THRESHOLD FOR LOWEST T = 3/2 STATE COULOMB BARRIER 12 .0 \ ·~./\\ 48 .0 I ,,.. '6.0 ---x---------x- 4.0 ----t:.. 2.0 b 10 5 MASS OF 15 TARGET NUCLEUS 0 20 0 25 s: < (I) rv 0 w Figure 52 Time-averaged values of the pulsed beam and difference currents as a function of phase. The exact shape of these curves depends upon the detailed geometry of the beam handling system. For the Caltech Tandem cp l - cp 2 ~ 40°. (See page 74. ) ) ~ 0 If::.. . ......_ ......_ <fl (l) "O :::> ~ - 205 ,,/ I "'O --a. -- ......_ """- ............ (----- -- / I -----~ I I I Figure 53 Circuit diagram of the electronic phase-shifter used in the phase-stabilized beam-pulsing system. The feedback signal comes from the vacuum tube phase detector and is capable of varying the phase by 40°. Three back-biased silicon diodes are used as a voltage- controlled capacitor. {See page 74. ) ~ 0 Cl) PHASE SHIFTING NETWORK . I l l rr . RF IN .01 10.0 pt/1_________,_A mica~ IOOK 675V wv------<M•f----4> FEEDBACK j, SIGNAL IN 8 3.3K +22V 10n,l/4W I\) 0 8.2 K 47K ~ 56K ~I.SK 2.2K IOOn · T5 .01 .01 Ii::'. Ae>---J IK .01 f---¢ 8 RF OUT ~~ .01 47K ~2K IK 47K 15K~ 470n 330n ALL DIODES IN2070 Tl,T2,T3 2N3646 T4 2N3904 T5 2N339 1