An Investigation of the Compound Nuclei ⁷Li and ⁷Be Citation Spiger, Robert John (1967) An Investigation of the Compound Nuclei ⁷Li and ⁷Be. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/75XC-EF29. https://resolver.caltech.edu/CaltechETD:etd-10042002-143530 Abstract The differential elastic scattering cross section has been measured for the scattermg of 3 He from 4 He and the scattering of 4 He from tritium. Incident particle energies of 5 to 18 MeV and 4 to 18 MeV, respectively, were used. Gas targets were used and solid state silicon detectors were employed to detect the scattered particles. Data were also obtained for the reactions 4 He 3 He,p) 6 Li, 4 He 3 He,p 1 ) 6 Li*, 3 H(α,n) 6 Li and 3 H(α,n 1 ) 6 Li*. Levels are seen at 4.65, 6.64, 7.47 and 9.7 MeV in 7 Li and at 4.57, 6.73, 7.21 and 9.3 MeV in 7 Be. A phase shift analysis suggests assignments of 7 - /2 and 5 - /2 for the two lower levels in 7 Li, confirms the 5 - /2 assignment of the 7.47 level and suggests a 7 - /2 assignment for the new level at 9.7 MeV. Similarly in 7 Be, the assignment of 7 - /2 and 5 - /2 for the lower two levels is reconfirmed and an assignment of 7 - /2 is suggested for the new level at 9.3 MeV. The reduced widths for α and nucleon emission were determined by fitting the phase shifts near each level with a single and/or double level formula from the R-matrix formalism of Lane and Thomas (1958). The results of the analysis are discussed and compared with predictions of some recent nuclear model calculations. 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): Tombrello, Thomas A. Thesis Committee: Unknown, Unknown Defense Date: 27 October 1966 Record Number: CaltechETD:etd-10042002-143530 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-10042002-143530 DOI: 10.7907/75XC-EF29 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3898 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 07 Oct 2002 Last Modified: 20 Mar 2024 21:02 Thesis Files Preview PDF (Spiger_RJ_1967.pdf) - Final Version See Usage Policy. 11MB Repository Staff Only: item control page

AN INVESTIGATION OF THE COMPOUND NUCLEI hi AND Be Thesis by Robert John Spiger In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology’ Pasadena, California 1967 (Submitted October 27, 1966) ii ACKNOWLEDGMENTS It is a pleasure to acknowledge the generous assistance of the faculty, staff and students of the Kellogg Radiation Laboratory during the course of this work. Particularly appreciated was the assistance and guidance of my advisor, Professor Thomas A, Tombrello, who suggested the problem and was a constant source of help, advice and encouragement. in both the experimental and theoretical portions of the work. Credit for much of the design of the apparatus for the t+ a experiment goes to Mr. Vic Ehrgott. Also appreciated are the efforts of Mr. George Fastle, Mr. Don Woshnak and Mr. Harold Larson who constructed many pieces of this equipment. Assistance in performing the experiments was received from Mr. Andrew D. Bacher, who also introduced the author to many of the experimental techniques, and from Mr. M. Dwarakanath who constructed our current integrator. Many weeks of tedious data reduction were avoided through the use of a data display program developed by Mr. Michael Mahon. His efforts and the help of Mrs. Barbara Zimmerman in computer programming are greatly appreciated. To Mr. Reagan Moore, Mr. Martin Cooper and Mr. George Fox go credit for the many months of work spent helping me to plot and analyze the data. | To my wife, Pearl, goes much of the credit for preliminary typing and encouragement in the preparation of this thesis. The many others who have assisted in this work may be assured that their help is appreciated even though they remain unnamed. iii I should also like to thank the National Science Foundation and the California Institute of Technology for financial aid in the form of fellowships during the course of the work and the Office of Naval Research for financial support of the experiment. iv - ABSTRACT The differential elastic scattering cross section has been measured for the scattering of 3He from 4H and the scattering of 4He from tritium. Incident particle energies of 5 to 18 MeV and 4 to 18 MeV, respectively, were used. Gas targets were used and solid state silicon detectors were employed to detect the scattered particles. Data were also obtained for the reactions 4He(FHe, ») *La, 4te(7He, p))°nit, 2H(a,n)®Li and 3 4,65, 6.64, 7.47 and 9.7 MeV in Thi and at 4,57, 6.73, 7.21 and 9.3 MeV in "Be. A phase shift analysis suggests assignments of 7 ana 5 ment of the 7. 47 level and suggests as assignment for the new level at 9.7 MeV. Similarly in Be, the assignment of 4 and 2 for the - H(a, n)) ori, Levels are seen at for the two lower levels in ha, .confirms the 2 assign- lower two levels is reconfirmed and an assignment of 5) is suggested for the new level at 9.3 MeV. The reduced widths for « and nucleon emission were determined by fitting the phase shifts near each level - with a single and/or double level formula from the R-matrix formalism of Lane and Thomas (1958). The results of the analysis are discussed and compared with predictions of some recent nuclear model calculations, TABLE OF CONTENTS PART | PAGE L INTRODUCTION 1 I. EXPERIMENTAL DISCUSSION 3 A. The Elastic Scattering 3H(a, o)°H 3 (1) Apparatus 3 (a) The Chamber, Vacuum System and Safety Devices 3° (b) The Gas Handling System and Gas Cell 5 (c) Collimation and Particle Detection 6 (2) Procedure 7 (3) Results . 8 B. The Reaction SH(q, n)°Li 10 (1) Apparatus 10 (2) Procedure ~ 10 (3) Results . 11 C. The Reaction 3u(a, n)® yi 11 (1) Apparatus 11 (2) Procedure . 12 : (3) Results . 12 D. The Elastic Scattering *He(*He; °He)*He 44 (1) Apparatus 14 (a) Chamber ~ 14 (b) Electronics 14 (c) Target and Beam Below 14.8 MeV 14 (d) Target and Beam from 14.8- 18.0 MeV 15 (2) Procedure 15 vi PART PAGE (3) Results 16 E. The Reaction 4He(3He, p) °Li 17 (1) Apparatus 17 (2) Procedure | 17 (3) Results 18 F, The Reaction 4He(PHe, p)®1ix 18 (1) Apparatus 18 (2) Procedure 19 (3) Results - 19 i. . THEORETICAL’ ANALYSIS OF THE DATA 20 A. Introduction 20 B. The Phase Shift Analysis 20 (1) Method 20 (2) The Analysis of the "Be Data 23 (3) The Analysis of the ‘Li Data | 25 (4) Discussion of ‘the Derived Phase Shifts and Polarizations 28 “ C. Extraction of Level Parameters Using R- Matrix Theory — (32 (1) Method 32 (2) Extraction of the "Be Level Parameters 38 (3) Extraction of the Thi Level Parameters 40 (4) Discussion of the Derived Level Parameters 42 IV. § COMPARISON WITH NUCLEAR MODELS 46 A. Introduction 46 B. Modcl Comparison ) 47 PART vii (1) The Cluster Model (2) The Rotational Model (3) The Shell Model CONCLUSIONS APPENDICES REFERENCES TABLES FIGURES PAGE 47 48 50 53 56 86 88 199 I. INTRODUCTION In the past few years, several experimental studies of the : excited states of the compound nuclei "i and "Be have been made, The work to be described was designed to complement and extend the range of these studies. The tandem Van de Graaff accelerator was used to produce 4 He and He beams at energies exceeding 18 MeV. These energies allowed the compound nuclei to be inves- tigated over a fairly large energy range. The entrance channels employed in this investigation were t+a for Thi and 3 He + 4 He for "Be. From an experimental point of view these entrance thannels have the advantage of allowing the use of a gas target. This provided a target of uniform thickness for which the data obtained could easily be given an absolute normalization, The theoretical analysis was also made simpler by the fact that both entrance channels were cases of the scattering of a spin 5 particle froma spin 0 particle. In particular, the phase shift analysis to determine spins and parities of the various levels was considerably simplified. The entrance channels used lead to several reactions. For Li, the reactions 3 Ha, «)°H, 3x0, n) *Li and 3H(a, ny rae were investigated. For "Be the analogous reactions 4He(*He, 3110) *He, 4uePHe, p)® na and 4ueGHe, p84 were studied. An analysis of q the data obtained made it possible to compare a-widths and nucleon | widths of various levels with predictions of nuclear models (for example, the calculations of Barker, (1966) ). Several levels predicted by these calculations were investigated. The experimental details of this work and the data obtained are discussed in Part I. The data are listed in the tables and shown in the figures. In Part III, the theoretical analysis of the data is discussed. A phase shift analysis and R-matrix fitting are used to determine the level parameters. These are then compared with the predictions of nuclear models in Part IV. Additional experimental details and a discussion of the computer programs which were used are contained in several © appendices. | | Tl. EXPERIMENTAL DISCUSSION A. The Elastic Scattering 31a, o) °H (1) Apparatus (a) The Chamber, Vacuum System and Safety Devices The 3 done with a gaseous target of *Hy. The problems involved in pro- H(a, 0) °H elastic scattering experiment was tecting the laboratory from contamination by this radioactive gas - required the use of more elaborate safety precautions than were convenient with the available gas scattering chambers. To utilize the tritium target, a complete new beam tube and target station were added in the target room of the C. I. T.-ONR Tandem Van de Graaff accelerator, The scattering chamber was constructed of a cylindrical steel pipe with top and bottom of aluminum. The walls were 1,9 cm. thick and the inner diameter of the chamber was 27.9 cm. The top and bottom formed 0-ring seals with the walls. The chamber was provided with four ports set at 90° intervals around the chamber walls. A diagram of the chamber is shown in Figure 1. . The beam enters through a collimator formed by a series of tantalum discs pierced with holes 1.5 or 2.0 mm, in diameter. These serve to collimate the beam and provide resistance to the passage of gas from the chamber in the event of a leak in the gas cell. The opposite port leads to the Faraday cup used to catch the beam after passage through the target. The port opposite that containing the gas cell assembly leads to the main pumping station. It is also fitted with an ionization gauge which is used to monitor chamber pressure during the course of a run. The path to the pumping station is closed by a two inch butterfly valve when tritium is in the gas cell, The gas cell assembly is mounted on a brass flange and inserted into the fourth port. The flange is drilled to provide a vacuum passage to the gas handling system and has a threaded recess to attach the gas manifold. . Upstream from the beam collimator is a small charcoal trap followed by a second group of tantalum discs, which further increase the resistance to gas flow from the chamber. A bypass connects this trap to the main pumping system through a Circle-Seal valve. Upstream from the second set of discs is an electrically operated safety valve which can shut the main pumping station and beam tube off from the chamber. In operation with tritium in the gas cell, the following: procedure is used. The small charcoal trap and a large trap in the bottom of the chamber are cooled with liquid nitrogen. The bypass valves are closed. This.leaves open only the small passage through which the beam enters. The large charcoal trap then provides internal pumping of the chamber. Ifa leak from the gas cell develops, the rise in chamber pressure will be detected by the ionization gauge and the electric safety valve will be automatically shut. Most of the escaped gas will be pumped by the large charcoal trap in the chamber and most of that escaping through the beam collimator will be pumped by the small charcoal trap. These traps may then be sealed off under vacuum, detached from the station and disposed of. The large charcoal trap will normally hold the closed chamber at a pressure of about 5+ 10°° mm. of Hg. (b) The Gas Handling System and Gas Cell The gas handling system and gas cell were con- structed of hydrogen-free material, where possible, in order to minimize the contamination of the tritium target ‘gas by ordinary hydrogen. A schematic diagram of this system is shown in Figure 2. The gas cell is 4.45 cm. in diameter and 1.9 cm. high, It is constructed of brass and has nickel foil windows. The foils are sealed to the brass with Carter's Epoxy. The beam entrance foil is 8125 A thick. The three foils for the exit of beam and scattered particles are approximately 13, 000 A thick, They are arranged so that all laboratory angles from 12° to 90° can be reached by the counter collimators (see Figure 1). The cell is soldered to a hollow tube connected to the flange at the chamber port. This supports the cell and provides an entrance for the gas. The manifold is a brass block which screws into the threaded recess on the flange. The manifold has five interconnected outlets. One leads to the gas cell and another leads to a Wallace and Tiernan differential pressure gauge (0 - 50 mm, of Hg) by means of a length of 3.2 mm. copper tubing. Thc other three outlets are fitted with all metal Nupro bellows valves (model B-4H). One valve leads to a gas bottle which allows testing of the foils or the use of another target gas. The second valve connects to the vacuum passage through the flange and provides for pumping out the gas cell, the manifold and the vacuum chamber surrounding the tritium reservoir. The third valve is connected to the tritium reservoir. All the passages were kept as small as possible to maximize the pressure obtainable with our limited amount of tritium. The joints in the system were sealed with Tcflon tape or soldered. The tritium reservoir is shown in Figure 3. ‘To facilitate handling and storage, the tritium gas is stored in the reservoir in the form of uranium tritide. The gas is evolved into the cell by heating the uranium and is pumped from the cell by the cool uranium when the run is over (see Appendix C). The construction material is stainless steel with joints being silver soldered or sealed with Teflon, A nichrome wire coil is used to heat the uranium in the reservoir. (c) Collimation and Particle Detection Before performing the experiment, the chamber was optically aligned with the beam tube using a Brunson telescope. A bellows and support behind the Faraday cup are provided to keep the forces on the chamber in equilibrium when the system is under vacuum. The collimation slits for the particle detectors and the gas cell were also aligned in this manner. The zero positions were reproducible to about 3 minutes of arc. The slits were mounted in aluminum blocks which were suspended from two ground stainless steel tubes 1.27 cm. in diameter. The rods were press fitted into two concentric hubs which pass through the top of the chamber. This allowed the two collimators to be positioned independently. The positions were read with protractors on the top of the chamber lid. Nylon-tipped set screws hold the aluminum blocks in place on the rods and the slits in place in the blocks. | The slits are made of brass and are approximately 1.0 mm, thick, The front slit is defined in width and the rear slit in both width and height. The center slit is a wider anti- scattering slit designed to prevent particles scattered from slit edges and walls from reaching the detectors. The dimensions of the slits and their spacing in the chamber are given in Table 1 (see also Figure 1 and Appendix B). . The detectors were surface-barrier and Li- drifted silicon solid-state detectors. They were mounted in brass cans to shield them from electrical noise. The cans were held in place directly behind the slits in lucite blocks suspended from the stainless steel rods. Detector leads from one collimator were fed through the hollow rod and led out through the hub at the center of the chamber. The leads from the other collimator were led out near the side of the chamber top. A further discussion of the detectors and electronics is contained in Appendix A. (2) Procedure On a typical run the following procedure was used. Liquid nitrogen was used to cool the charcoal traps until lhey were cold enough to pump the chamber unaided. During this time the electronics were set up and checked. The beam was brought to a viewer just in front of the chamber. The valves to the diffusion pump were then closed and the safety valve in the beam line was coupled to the ion gauge. The tritium reservoir was opened to the rest of the chamber and the accumulated 36 was pumped off by briefly opening the main bypass valve. This valve was then shut as was the Nupro valve connecting the manifold to the chamber vacuum. Tritium gas was then evolved frum the uranium by passing current through the nichrome wire coil on the reservoir. When the desired tritium pressure (about 40 mm. of Hg) was reached the reservoir was shut off from the manifold and allowed to cool. The safety valve in the beam line was opened and the beam was focused on target. Data were then taken in the form of excitation curves at a number of laboratory angles. A separate spectrum was taken for each energy and angle on a 400-channel Radiation Instrument Development Laboratories multi-channel analyzer. For each spectrum the time for the run, the analyzer live time, the actual time of day and the nominal beam energy were recorded. The temperature and pressure in the gas cell were also recorded at frequent intervals. Energy steps of 50, 100, or 250 keV were taken, depending on the rate of variation of the cross section. The integrator was calibrated at several times during the day. Data were also taken in the same general manner in 500 keV steps for the elastic scattering tH, o) 1H. These data provided . a calibration to determine the hydrogen contamination in our tritium target gas. | The beam was obtained from the ONR-CIT tandem accelerator. For beam energies between 4.0 and 13.25 MeV the standard doubly charged 4Hett beam was used. For higher energies, a negative 4 He beam was extracted from the negative ion source. This beam was stripped to a double positive charge at the center terminal of the tandem and energies up to 18.25 MeV were obtained. Typical beam currents on target were 200 nano Amps for the standard beam and 5 - 15 nano Amps for the high energy beam. (3) Results A typical spectrum from the 400-channel analyzer is shown in Figure 6. The oa group is seen at channel 293, the triton group at channel 122 and the proton contaminant group at channel 80, The small group at channel 358 is composed of « particles scattered from the walls and foils of the gas cell. This is also the source of s) the low, continuous background in the spectrum. The shoulder at channel 40 marks the point at which the separation of charge one from charge two takes effect (see Appendix A). The data obtained were reduced to differential cross sections (see Appendix B). Excitation curves at 17 center-of-mass angles from 39° to 146° were obtained in the region of 4 to 13 MeV. These data are tabulated in Table 3 and are shown in Figures 9-17. The open circles are the data points. The solid lines are fits to the data from the phase shift analysis, which will be discussed in Part TI. These data show clearly three resonances. The lowest is the resonance near 5 MeV corresponding to the level al 4.63 MeV excitation energy in Thi The broad resonance near 5 MeV corresponds to the 3 level at 6.6 MeV excitation in "hi Note that excited dispersion curve near 11.5 MeV. This is of interest since 1,47 MeV level also appears in these curves as the weakly rin corresponding level in Be is not seen in the elastic scattering 4 He (fe He, 334¢)* He (Tombrello, 1963). In the range from 13 to 18 MeV excitation curves were taken at 8 center-of-mass angles from 54° to 135°. These show a resonance near 16,8 MeV corresponding to an excitation of 9.7 MeV in "hi (see Figures 18 - 21). These data are tabulated in Table 4, Figures 22 - 27 show angular distributions generated from these data. Once again, the solid line gives the phase shift analysis fit to the data. The angular distributions are shown at ~ positions below, at and above each resonance energy. A discussion of the experimental errors in the data is contained in Appendix D and the errors are tabulated in Table 5. 10 B. The Reaction Ha, n)° Li (1) Apparatus This experiment was done at 0° using a solid target of zirconium tritide on a .025 cm. thick platinum backing. The target contained about 2 - 1018 atoms of tritium per square centimeter in the form of a disc 2.54 cm, in diameter. This was placed in the center of a vertical quartz tube of approximately 3.75 cm. diameter, The target was oriented so that it was normal to the beam. A bias of 300 volts was used on the target for integration purposes. The tube was in the form of a T and was connected to the beam tube by its horizontal portion. A pressure of 5 - 10"! mm. of Hg was main- tained at the target. The beam current was integrated with an Eldorado Model CI-110 current integrator. A charge of 18.0 micro Coulombs was collected four each run, The neutrons were detected by a "long counter" placed very close to the quartz tube. This geometry was used so that all the neutrons in the cone about 0° would be intercepted by the detector. Pulses from the counter were amplified with a Hamner amplifier and counted in an Eldorado scalar. A bias was set on the scalar so that only pulses higher than those induced by gamma rays were counted. (2) Procedure The actual data for this reaction as well as for the reaction H(a,n") Li* were obtained by T. A. Tombrello. The neutron yield was taken at energy intervals of 40 keV except near threshold where 3 1,6 ) steps of approximately 10 keV were taken. The beam energy, length of time of the run and number of counts on the scalar were recorded for each run. 11 (3) Results The results are tabulated in Table 6 and are shown in Figure 28. These data show an s-wave behavior near threshold, ‘but the overall behavior is dominated by the effect of the 2 level at 7,47 MeV in "hai, These data were not used in the analysis, but do show good agreement with the data which were used. C. The Reaction 35(a, n2)® Lit (1) Apparatis The objective in this experiment was to obtain the total reaction cross section at beam energies between 12 and 18 MeV. Below 12.4 MeV, data were available from the inverse reaction Sr itn, 0) °H (Schwarz, 1965). Once again the negative helium beam from the ion source of the tandem was used. The target was a disc cut from the previously mentioned zirconium tritide target. Its diameter was approximately 0.95 cm. Figure 30 shows a schematic diagram of the target assembly and detector. The target is held at the back of a cylindrical aluminum target chamber by a liner of coiled tantalum sheet. The target chamber slips onto a metal tube and seals with an O-ring. The metal tube is fitted to a lucite plate at the end of the beam tube, This provides the insulation necessary for beam integration. For inlegralion, a wire is allached to the aluminum chamber and a 45- Volt bias is used between the chamber and integrator. The same El- dorado integrator is used. | The detection apparatus consisted of two parts. The first part was a large paraifin cylinder designed to thermalize the neutrons. 12 - The forward end was drilled to receive the target chamber so that a maximum number of neutrons from the target would be thermalized. The diameter of the cylinder was approximately 30 cm. and its length 41 cm. At the rear of the cylinder and on the axis, a hole was drilled to receive the second component. This was an Ne 402 phosphor mounted on a phototube. A standard Kellogg preamp: was used with the phototube. The wax block was insulated from the target chamber by wrapping the chamber with Teflon tape. (2) Procedure An Eldorado. scalar was used to count the pulses from the phototube. The pulse-height spectrum was a continuum and a bias was set at an arbitrary point in this spectrum. The scalar then counted pulses higher than the bias. Charge integrations of 2.7 44 Coulombs were taken. Runs were taken with beam energies from 11.0 to 18.0 MeV. Steps of 50 keV were used in the region of the resonance near 11.5 MeV. Near the 16.8 MeV resonance 100 keV steps were used, with 250 keV steps being used elsewhere, Runs were taken with the detector at the rear of the block and also with the detector on the side and near the front of the cylinder (see Figure 30). The side position was placed so that neutrons from this reaction | could not reach the phosphor directly. Thus the neutrons from the reaction SHH(0, n) Li are emphasized here if all the neutrons are not thermalized. (3) Results The number of counts on the scalar were recorded at each energy. Figure 31 shows the data recorded and reduced to 13 cross sections for the configuration with the phosphor at the back of the cylinder. The reduction was carried out in the following way. As was mentioned before, the cross section from 11,0 to 12.4 MeV was obtained from the inverse reaction. The neutron threshold for 3 H(a., ny 3 is approximately 16.3 MeV. Our data were normalized to the inverse reaction data (see Figure 29) in the 11.0 to 12.4 Mev region. The shape and normalization were consistent to about 5%. This normalization was then used to convert our data to cross sections al the higher energies. | To obtain the 2 H(a, n})® Lis cross sections a smooth back- ground, representing the ground state neutron contribution, was sub- tracted from the data. The remainder was attributed to the contri- bution of the 3H(a, nb) Lit reaction, | The method of reduction assumes a neutron detection efficiency which is constant over the range 11 to 18 MeV. Using this normalization for the first excited state neutrons is quite reasonable since they have approximately the same energy range as the ground state neutrons from 11.0 to 12.4 MeV. The problem lies in the normalization of the ground state neutrons at the higher energies. The difference in the excitation curves, obtained with the two phosphor positions, shows that this normalization is possibly quite inaccurate. As a result, the accuracy of the total reaction cross section above _ 16.0 MeV is probably no better than + 30%. The behavior of the ground state neutrons does seem to be smooth in this region, however, and thus, when separated from the background, the contribution from the first excited state neutrons may be expected to have somewhat better accuracy. 14 Siz \4 D. The Elastic Scattering 4ue(FHe, He) “He (1) Apparatus (a) Chamber In this experiment, a 4te gas target was contained in the gas scattering chambcr described by Bachcr (1967). To provide better angular resolution the slits in the moving counter telescope were replaced by a similar set with approximately one-half the width (see Table 1 for slit parameters). Beam collimation, charge collection, and the pumping system were not changed except for the addition of a liquid nitrogen trapped diffusion pump on the Faraday cup. (b) Electronics ‘As in the T(a,a)T experiment, a two-counter a ; E telescope was used to detect the scattered particles. The same rd charge integrator was also used (see Appendix A). (c) Target and Beam Below 14.8 MeV ‘In the range of 3 He bombarding energies between 4.6 and 14.8 MeV the neutral beam injector was used with the CIT tandem to produce a doubly charged 3 He beam. Beams of approx- imately 200 n A. were obtained on target. The beam entrance was sealed with a 1000 A Nickel foil and the entire chamber was filled with 4a gas. A pressure of approximately 13 cm. of oil on the oil manometer was maintained, 15 (d) Target and Beam from 14.8 to 18.0 MeV In this range of bombarding energies we were no longer able to attain the desired energy using neutral beam injection, Here, the negative ion source was used to produce a beam of negative He ions. These were then stripped to doubly charged positive ions at the center terminal of the tandem. This produced a doubly charged beam with three times the terminal voltage. After focusing, magnetic analysis and collimation, beams of 5 - 15 nano Amps. were obtained on target. Beams of this current range used with the low energy — target configuration greatly increase the length of time needed to take the desired data. Therefore, the 1000 A nickel foil was removed and the 4H target gas was cunlained in a small gas cell at the center of the chamber. The cell (see Figure 32) was inserted through the top of the chamber and was fitted with connections to a gas handling system and to a Wallace and Tiernan differential pressure gauge (0 - 800 mm. of Hg.). The thicker foil windows on the gas cell enabled us to use a target pressure of 15 cm. of Hg. The scattered particle exit window was of 1/6 mil Mylar and the beam entrance and exit windows were of 6250 R nickel foils. Temperature was monitored by a thermometer which was in contact with the gas cell. | (2) Procedure The general experimental procedures employed to gather the data are as follows. If the entire chamber is to be filled with tHe, the chamber is sealed off, filled with the target gas and the out- gassed charcoal trap is cooled with liquid nitrogen. If the gas cell is to be used, it is filled with target gas and the diffusion pump continues to pump on most of the chamber. Suppression and bias voltages are 16 applied to the Faraday cup and the electronics are checked for noise as the detectors are biased, ‘The integrator is calibrated and the beam is maximized in the Faraday cup by magnetic focusing and deflection. The discriminators are then adjusted to give proper particle separation using the ss counter signal anda pulser, The gains of the electronics for each counter are equalized. Spectra are then taken at each angle desired for a given _ energy. The live time of the analyzer, the clock time for the run and the time of day are recorded for each run. The temperature and ‘pressure of the target gas are recorded at frequent intervals. At the end of the day the integrator is recallbrated to check on possible drifts. (3) Results A typical spectrum is shown in Figure 33. The first 200 channels contain a proton group from the reaction channel 4He(7He, p)°Li in channel 84, a proton group from 4He( He, p2)°Lik, in channel 38, and a broad deuteron group from 4He(PHe, a) Li below channel 45. The Sie and “He groups are seen in the second 200 channels at channels 351 and 330, At forward angles the °He yield is much larger than the a yield while they are of more nearly equal size at the mid- range angles, The yields tend, in general, to drop off slowly with energy. The data reduction is discussed in Appendix B, The main portion of the data consists of angular distributions at 3He bombarding energies from 4.6 to 18.0 MeV. 36 and recoil tHe | groups give elastic scattering information at 14 center-of-mass angles below 14.8 MeV and at 10 center-of-mass angles from 14. 8 to 18.0 MeV. 17 The data are presented as excitation curves with angular distributions shown below, at and above each resonance (see Figures 34 - 45). The numerical values of the differential cross sections are tabulated in Table 8. The figures show the data points as open circles. The solid lines are the fits obtained with the phase shift analysis. They will be discussed later. The elastic scattering data clearly show the known 3 and 3 levels found at excitation energies in "Be of 4.55 and 6.51 MeV, respectively. The ; level at 7.19 MeV in "Be is not seen in the clastic scattcring data. It is seen, however, in the 4He(*He, p)PLi data (see Figure 46). The broad resonance in the elastic scattering data at 13,25 MeV lab energy is a new level corresponding to an excitation energy of approximately 9.3 MeV in "Be. It is also clearly seen in the 4He(?He, pt)’ Lik data (see Figure 50). The = level seen by Harrison (1966), at 9.9 MeV in TBe is not seen in our data, Experimental errors in the data are presented in Appendix D and Table 11, . 4, 3 6.. E. The Reaction “He(‘ He, p) Li (1) Apparatus The apparatus used in this experiment was the same as that used for the elastic scattering. (2) Procedure The procedure was essentially the same as that used for the elastic scattering measurements. Below 14.8 MeV, the only changes were. the use of 30 cm. of pressure on the oil manometer and the taking of data at more laboratory angles and at closer energies. Above 14.8 MeV, data were taken at the same time as 18 for the elastic scattering, Here too, more laboratory angles were covered, | (3) Results The data obtained are tabulated In Table 10. Dala were obtained at 5 laboratory angles for most energies; these data form excitation curves. At several energies, more laboratory angles were used. These additional daia allowed the formation of angular distributions. The data were reduced in the same manner as the elastic scattering data (see Appendix B). Two of the excitation curves are shown in Figure 46, They clearly show the resonance (near 9, 5 MeV) due to the 7, 19 MeV level in "Be. The 45° curve shows a weaker effect near the 9.3 MeV level in "Be. In this curve, the blackened circles are dala taken with the low energy configuration. The open circles are data taken with the high energy gas cell. (In all figures for this reaction and the reaction *He(FHe, p) Lit the lines shown serve only to connect the points.) Figure 47 and part of Figure 48 show angular distributions of the ground state protons. Experimental errors are discussed in Appendix D and shown in Table 11. F, The Reaction *He(PHe, p)° Lik (1) Apparatus The apparatus used in this experiment was the same as ‘that used in the elastic scattering. 19 (2) Procedure The data were taken at the same time and in the same | manner as the 4u0(3He, p)° Li data, (3) Results . The data obtained are tabulated in Table 10. Angular distributions of the first excited state protons are shown in part of Figure 48 and in Figure 49. Figure 50 shows two of the excitation curves obtained. Both show the effect of the 9. 3 MeV level in Be and they are similar to each other in shape. Experimental crrors are discussed in Appendix D and shown in Table 11, 20 Il, THEORETICAL ANALYSIS OF THE DATA A. Introduction The experimental data obtained in this work combined with data from other sources (to be discussed later) give a considerable amount of information on the compound nuclei "Be and "hi over 2 wide energy range. This analysis is primarily concerned with the two-body properties of the nuclear levels involving the following open channels: 4H + Sue, Slag p, and Oy ae + ot for "Be and 4 He + S31, 6h5 +n, and Ghat + nt for Thi, . The analysis is divided into two parts. In the first, the elastic scattering and reaction data for each compound nucleus are subjected to a phase shift analysis which separates the influence of the various partial waves in the scattering. This then determines the and J values pertinent to each of the levels seen. ' In the second part, the R-matrix formalism described by Lane and Thomas (1958) is employed to express the nuclear phase shifts in terms of parameters such as the reduced widths for the open channels, excitation energies, and nuclear radii. The phase shifts derived from the first part are then fitted with these expressions. This determines a best value of these parameters for each level. These parameters may then be compared with predictions of nuclear models for these nuclei. . B. The Phase Shift Analysis (1) Method The first step in the analysis of the reduced data was the phase shift analysis of both the "hi and "Be results. Both cases 21 represent scattering of a spin 1/2 from a spin 0 particle. This greatly Simplifies the analysis by allowing only one 4-value for a given value of the total angular momentum and the parity. The formula for the differential elastic scattering cross section is given as (Critchfield, 1949): ow 2 Go(8) - fp 1? + 14,1 (1) where f, (6) = SE csc" (3) exp Cinin csc” (3)] o Qi is, ib 1 % Lo. + boo. = +E Ze P, (cos 6) [(2+ le siné, + te sin 6, 1 and ye Bic dP, (cos 0) 16," _ iO)=E Ee Sin 6 - “ates Le sin 6, -e sin 6, 7 In these expressions: 8 =. the center-of-mass scattering angle, k = the wave number, n = e*/ av, V = the relative velocity of the two particles, b= 6, =65 = the phase shift for j= 4 1/2, m= (-1)* o, - 0. where o, is the Coulomb phase shift, and 4 oO 4 22 Zs and Zo are the charges of the bombarding particle and the target nucleus. The spin polarization of the scattered particles is given by: -2Im (f£. £.*) _ _ _ PB (8) = 2 S 2 in the direction of (K,, xk,,,) where k, and [f_ | +f. Cc 1 ou beams. E ; are unit vectors in the direction of the incident and scattered In both "Be and "hi the treatment of the reaction channels involving Sri + a nucleon must be considered. This can be done by allowing the phase shifts to become complex. We have: 2i6 Zane, 218 e ~ cos Ae 7" then e?° sin 8 > cos” Xe®® sin 6 +i >) , and the total reaction cross section is given by: 4. ° X12) R773 fg [(2%+ 1) - (2+ 1) (cos X,") - t cos k 2=0 og In our analysis, the real and imaginary part of the phase shifts from t = 0 to 2 = 4 were allowed to vary. This gives a total of 18 parameters, although these were not all varied at one time. The ° data were grouped into angular distributions at the various energies of the excitation curves. A program was written to fit the data of each angular distribution with a set of phase shifts from equation (1) (see Appendix E) by minimizing the quantity 23 do do 1 . (a2. Oe ~ da Peate) * x N, i-1 vie;) Here N, is the number of data points in the angular distribution and V(8;) is the experimental error associated with each point, No states of = 4 have been found in Li or Be; therefore, these phase shifts were not varied during the analysis. Upon completion of the analysis with phase shifts through ¢ = 3, the 2 =4 phase shifts were allowed to vary. Their variation from 0° was very small (+ 2°), and we therefore felt justified in not considering them further. (2) The Analysis of the "Be Data The phase shift analysis of *He(PHe, 3He)*He has been done from 2.5. to 5.7 MeV bombarding energy by Barnard (1964) and from 5.75 to 12.0 MeV by Tombrello and Parker (1963). Because the splitting of the p-waves of Tombrello and Parker differs in sign from those of Barnard, we obtained data and performed the analysis over both these lower regions. The results could then be accurately extrapolated into the region above 12.0 MeV as trial phase shifts. Below the first proton threshold at 7.0. MeV all values of Xy were held to zero and the real parts of the s,p,d, and f wave phase shifts were allowed to vary. The initial values of the phase shifts were determined from Barnard's data. The general procedure was to then use the computer program to search for a set of phase shifts for which only one would be resonant at the anomaly in the elastic scattering data. The selection of the fn /2. phase shift was quickly accomplished, both by supplying trial phase shifts 24 with a step in by /2- and by letting the program generate phase shifts at an energy using the phase shifts at the next lower energy > as starting values. Several orders of phase shift variation were tried with essentially the same result. The p and s wave phases were the most sensitive to the order of variation. Changing the order caused changes of.+ 5° in the s and p waves. The phase shifts finally selected were those for which the variation with energy was smooth and the yes were low. Above 7 MeV bombarding energy the reaction channel 4He(*He, ») °Li is open. Data on the inverse reaction 81 i(p, 3346) *He were available and we used that of McCray (1962) and Marion (1956) to calculate the values of Xs from the total reaction cross section, The analysis of McCray attributes the cross section to a 5 Yesonance and an s-wave background. We found that the background was too large to be accounted for by only the s-wave phase shift. Therefore, we set + _ Xi/2 = X3/2 part of the reaction cross section, This choice gave slightly better * and used the sum of both terms for the non-resonant fits pe essentially the same phase shifts as were obtained by using X,j. and Xy /2° With the values of X Jn then varied. The initial values were obtained by extrapolation from the lower region. The s,p,d, and f waves were varied and the 1/2 fixed, the real phase shifts were appropriate resonant phase shift proved to be 6, /2* As in the work of Tombrello and Parker, the state at 7.18 MeV excitation energy was not seen in the elastic scattering data or in the values found for the real part of the phase shift. Once again, several orders of variation of the phase shifts were tricd. The f-wave phase shifts were stable to + 2° and the s and p wave phase shifts to + 5° under the different variations. The solutions with good x's also provided good energy continuity. 25 Above 11 MeV both the *He(*He, p)°Li and the *He(*He, op?) Lit channels are open. Our data on the first channel were used in conjunction with Marion's to calculate values of X, J2 9 Ke Ja? and Ky /2. from 11 to 18 MeV. Data on the second reaction channel were limited to what we had obtained. These data were used to form angular distributions at several energies near the resonance, Smooth curves were then drawn through the data points. Our data extended only to 120° in the center-of-mass system; hence we were required to extrapolate the data to 180° and to 0° to obtain total cross sections from these angular distributions, This was done by assuming symmetry about 90° and by smoothly extending the curve to 0°. The resulting curves were then numerically integrated to obtain the total cross section. These values(and the fact that the excitation curves for first excited state protons all had a similar shape) were then used to generate the total reaction cross section as a function of the energy. An estimate was then made separating the curve into a resonant portion and a non-resonant background. The resulting resonance was too large to attribute to any one rcsonant Xt except Xy /2° The background was attributed to X, /2- because of the proximity of the state at 9.8 MeV excitation energy seen by Harrison (1966). Using these values of Ky, nd th fy /2. ‘phase shift would provide a fit low in y° and continuous in it was found that only a resonant energy. The features of the various phase shifts will be discussed in section (4). (3) The Analysis of the "Ti Data The target in these experiments was the lighter particle. This required a higher bombarding energy to observe the same resonances. In the region of 3.6 to 11 MeV bombarding energy, 26 there are no open reaction channels. This allowed us to set all the X, =0 inthis region. As trial phase shifts, we started with values Jtt from the "Be analysis taken below the first J resonance. We then allowed the s,p,d, and f wave phase shifts to vary and used the values obtained at a given energy as trial values for the next energy. The program selected by /2. as the resonant phase shift for the lowest level. it also selected & 5/2 as the resonant phase shift for the broad second level. Several orders of variation of all the phase shifts were used to obtain smoothness in the phase shifts and low values of x2. In the range from 10 to 11 MeV, some difficulty was encountered in obtaining good energy continuity in the Py /2 and fn /2 phase shifts. The Ps /2 and i. /2 phase shifts were quite stable when different orders of variation were tried. These latter two phase shifts were finally fixed at their preferred values in this region and the other phase shifts were varied until a reasonably smooth set of phase shifts was obtained. Values of 2 were about 25% larger, in general, when the smooth set was used instead ‘of a highly dis- continuous set (i.e. , jumps up to 30° in 250 keV for the Py /2 phase shift). The range of bombarding energies from 11 to 13 MeV was of particular interest. In analogy with the "Be data, we did not expect to see the 7.47 MeV level (corresponding to the 7.18 MeV level in Be) in the elastic scattering. However, the effect of this level is apparent in the data as a small dispersion shape in the - excitation curves. | - The reaction channel 3 H(a, n)°Li is open in this region. The inverse reaction has been investigated by Schwarz (1965), and his data (see Figure 29 and Table 7) were converted to our system 27 and used to generate values of X His analysis indicated that the main effect was due to the 3 resonance, with the nonresonant back- ground being due to s-wave scattering of channel spin 1/2. It was found that we could account for all of the background by the x, 2. parameter.. jheretore, we did not use the Xo 2. parameter as was done in “Be. Using the values obtained for X, 2 and X, /2? and extrapolating the real phase shifts from lower. energy, we used the program to see if 6 /2. would indicate a resonance behavior. No fit was obtained if we insisted on a step-type behavior such as is seen in the two lower resonances. It was found that a dispersion curve in the ; phase shift gave the best tit ‘This result was Similar to the high energy 3g vesonance in Be. Attempts to fit the resonance with other phase shifts (such as by /2- ) did not ~~ gueceed. The presence of the resonance in "Be near 13.5 MeV indicated that an analogous effect might be observed in Tha. Because the high energy beam was used, not as many data points were taken at each energy. All of the excitation curves indicated a more pronounced effect than was seen in "Be, however. Data on 3H(a, n®)®Lix, other than our own, were not available. These data were decomposed into a smooth background and a resonance peak. From 13.5 to 18.7 MeV the data of Murray and Schmitt (1959) on the reaction Sri(n, «)°H were used to determine values of xy /2. and Xe /2° The background in this region was too large to be accounted for by xy /2. alone. The resonance peak which we separated from our 3H(a, n1)6 15% data was of such magnitude that il could only be accounled for by Ry /2. . This was the same result as for "Be. The background 3 H(a, n4)6Li* contribution was attributed to the X 3/2 term. 28 Using these values of Xr , the real phase shifts were varied. Below the second neutron threshold, the resulting phase shifts were continuous with the lower results. At 12.8 and 13.1 MeV bombarding energy, separate angular distributions were obtained using the high energy beam and the low energy beam, respectively. Their separate analyses gave similar results, even though somewhat different values of the background Xs, were used. for each. Above threshold, the resonant real phasc shift was found to be bn J? as in the "Be case. However, ‘it was not possible to obtain a good fit and maintain smooth behavior with energy of the © supposedly non-resonant phase shifts. A variation of the X Jn Was tried to accomplish this, but without success. The final values obtained for the phase shifts were a compromise between the best fit and the smoothest phase shifts, with good fit being the major consideration. (4) Discussion of the Phase Shifts and Polarizations The phase shifts for 4He( He, SHe)*He are listed in Table 13 and shown in Figures 52 - 54, Phase shifts for *H(c,0)°H are. listed in Table 12 and shown in Figures 56 - 58. In both cases the various symbols represent values obtained from the phase shift program and the lines show fits to these data using the R-matrix formalism. S-wave Phase Shifts The s-wave phase shifts appear in Figures 52 and 56. The dashed lines are calculated hard sphere phase shifts for radii 29 2,8 Fermis He + a) and 2.6 Fermis (t+ a). There is a tendency in both cases for the phase shifts at higher energies to lie somewhat above the calculated curve. This effect has been noted previously in *He(*He, 3tie) “He by Barnard (1964) and by Tombrello and Parker (1963). McCray (1962) suggested a ; level which might account for this behavior. Such a level has not been seen in this work, however. The choices of X,_ for the representation of the reaction Jtt cross section do have an effect and may account for the discrepancy. P-wave Phase Shifts ; The ; phase shifts are shown in Figures 52 and 56. The ; phase shifts appear in Figures 53 and 57. With the exception of the f-wave phase shifts, these were the most difficult to determine. In the case of 4e(Pne, 3316) tte opposite splittings of the p- wave phase shifts were found by Barnard and by Tombrello and Parker. We therefore wished to investigate the sign of the splitting and to determine if there was a point at which the splitting reversed in sign. Both signs of the apne were tried and that “ee 8, /2- > 64 /2 He)*He. This result for "Be is in agreement with that of Barnard. was preferred in both 3H1(a, a) H and 4He(3 He, From the values in the tables, it is seen that these phase shifts have a very slight splitting at some energies. An example occurs near 11.5 MeV bombarding energy for 40H, 3310) 4He, Solutions with the opposite splitting were carefully investigated near these points and were found to be poorer than the solutions used. . Above 16 MeV bombarding energy in 3H(a, 0) °H, all the phase shifts, and the p-waves in particular are somewhat dis- continuous with energy. This is an effect of the suggested 4 level and probably reflects our lack of knowledge of the proper values of 30 Xs used to represent the reaction cross section. The general fluctuations of the p- waves elsewhere in both ~ H(a,a)°H and 4 He(* He, 3310) *He are probably due in part to the fact that they and the f-waves are the only negative parity terms used in the analysis. Thus the p-waves probably absorb a fair amount of any inaccuracies in the data which would tend to make the f-wave behavior less smooth, D-wave Phase Shifts There are no d-wave levels in this energy range. The d-wave phase shifts were allowed to vary, but remained small over the total energy range both cases. They are shown in Figures 52 and 88 for 4H0(° He, 2H)" He and in Figures 56 and 57 for 3H1(a, a)? H. Both the 5° and 3 phase shifts tend to remain near zero rather than decreasing at higher energy as for a hard sphere phase shitt. ‘he points which depart from a smooth line for these phase shifts occur near resonances and are still relatively small. These excursions probably are the result of inaccuracies in the data near the resonances. F-wave Phase Shifts The f-wave phase shifts for 4 He(PHe, S110) *He appear in Figure 54 while these for Sua, o) °H are shown in Figure 58, The most obvious features are the sharp steps in the Z phase shifts. These show the second excited states in "Be and Thi thus indicating a z assignment for this level in Tha, The broad step in the 5 phase shifts indicates an assignment of 5 for the level at 6.6 MeV in Tha and reconfirms 2 the : assignment of Tombrello and Parker (1963) for this level in ‘Be. 31 The upper 2 level was not seen in the *He(*He, 3 He) “He real phase shifts. It is seen in the parameter Xe /2? however. This result is not surprising since this level is also not seen in the elastic scattering data. Tombrello and Parker (1963) were also unable to see its effect in the elastic scattering. Note that this level does appear asa ausbersion shape curve in 6 5 /2- and as a peak in Xoo for Sua, a)? H. A Similar behavior is seen in the elastic scattering, _ The dispersion curve shape appears in the 4 pnas® shift for the level at 13.5 MeV bombarding energy in “eC” He, Se)4 He and for the level at 16.8 MeV bombarding energy tor SH(q, a)° H. The level in Be is much broader than that in Tha, The 2 phase shift is fairly smooth through the region of this resonance for "Be; how- ever, in "hi it varies by about 30° from a smooth curve. This effect . persisted in the phase shift analysis, despite efforts to eliminate it by adjusting other 6's or the Xy_'S. We have therefore concluded that it is probably due to our poor reaction data in this region. Another possibility is the presence of a nearby = ‘state analogous to that seen by Harrison (1966) in q conclusive evidence on this possibility. Be. Wechave, however, no G-wave Phase Shifts . No levels of 4 = 4 have been found in either TBe or Tha. . We did not vary these phase shifts during the analysis. At the conclusion of the analysis, we allowed them to vary and found that they remained small (< + 2°), Consequently, we felt justified in having neglected them in the analysis. The polarizations for the Ses and tritons were calcu- lated from the derived phase shifts. The results are shown in 32 Figure 55 for 4He(PHe, 3H1e) “He and in Figure 59 for 3H(a, «)°H, Polarization conlours are shown vs. center-of- mass angle and bombarding energy. The effects of the lower i and : levels are seen in both figures. As in the elastic scattering the effect of the higher 2 level is not seen in the 3He polarizations while it is for the triton polarizations. The higher 5 level is seen in both figures although it has a weaker effect for the. SHe's than the tritons. This agrees with the relative effects in the elastic scattcring rcactions. Of particular interest are the long regions of nigh negative polarization near 90°, These may be ‘of use in polarization experiments as sources or analyzers of polarized particles. . C, Extraction of Level Parameters Using R- Matrix Theory (1) Method The elastic scattering and reaction cross sections for two particle interactions have been treated by Lane and Thomas (1958). This formalism connects the observed cross section for a reaction or elastic scattering with a set of internal wave functions of the compound nucleus. Our phase shift analysis of the data provides the spins and parities of the states we have investigated in Thi and "Be, This knowledge and the Lane and Thomas formalism are used to determine excitation energies and some reduced widths for these states. We will use the following definilions (from Lane and Thomas): cc 1 ce 33 the cross section for formation of a particle pair cl from the scaliering of lhe particle pair c, The symbol ¢ denotes all information concerning the quantum states of the two particles, their spins, channel spin and relative angular momentum. the collision malrix for this inleraction. o ,a(U || au , 1s unitary and symmetric. ce ee ce the distance between centers of a-particle pair c. the effective interaction distance between the centers of a particle pair c. For r eo? % only Coulomb forces are active. * the center-of-mass energy of motion of the ' particle pair Ce the reduced mass of a particle pair c. the relative wave number of the particle pair c. Also given as (2M,|E,| Ja2yV/2 the relative velocity of the two particles. a Coulomb parameter givenas Z, oZoee /tV¥— where Za and Z,, are the two charges (in units of electronic charge) of the particles. the Coulomb phase shift. 34 Po = Kt Our analysis is concerned with two levels (at most) of the same spin and parity. We also consider an elastic channel and a reaction channel. Wave functions external to the nuclear surface are taken as the Coulomb wave functions. The following notations will apply: I, t = the incoming Coulomb wave in the elastic channel for angular momentum t. 0. L = the outgoing Coulomb wave in the elastic channel for angular momentum t, I. L = the incoming Coulomb wave in the reaction channel for angular momentum 2, | 0. L = the outgoing Coulomb wave in the reaction channel for angular momentum 4, x, = the coefficient of the outgoing wave for a given channel. Vo = the coefficient of the incoming wave for a given channel, The collision matrix U is then defined by: X,t-2U y ct oc cle © The R-matrix for our case has 4 components and is defined as: 35 r 20 2 Ye + Yee YteYir ‘ Y2e Yar _ Ree Per, | Biv# Eg BE’? Ey-E © EQ-E SER OR | vievir Yoovor Yip? Yor? re rr le ir 2e'2r ‘ir , Fr E,-& Ey-E , E,-# Ey-E Here r and e refer to the reaction and elastic channels, Ey and Ey are eigenenergies of the internal wave functions. E is the excitation energy of the nucleus. The y's are the reduced width amplitudes of the levels, For example, Vie. is the elastic reduced width of level 1. Note that Roy = R ne! The general form of the R-matrix considers all the eigenenergies of the in- ternal wave functions and has the form ‘el Yre =D yo 1° ETE ° R cc but we are only concerned with two levels in our analysis. We now obtain from Lane and Thomas the general relation relating the R- matrix to the collision matrix. We have: Vn Rig (D, ~ BV.) +R (D,, ~ BV.) (1) ve= R. (D, ~ B.V,) + Rey (,, ~ BV) (2) where Vo= ( *) a (o, ve On Xa t Py ve Te 4¥e) and Do: (toy (0,7 70 ot Xe * pn? Poe) 36 The primes indicate differentiation with respect to Po B, and 3. are boundary values (taken as real in this work) for the elastic and reaction channels and are proportional to the logarithmic derivative of the internal wave functions at the nuclear radius ao Using the relation of the x's and y's to the collision matrix and the fact that y, = 0 in our experiments, we can solve equations (1) and (2) for Vee: We employ the following definitions: L = Poo chy =S _+iP_, where Son is the (= = c On roa, ct ct ; shift function and P, z is the penetration factor -The solution then becomes: 2 = oe (1- R,[L,-B,0-R[hF- Bel) Rae (LS-B)(G-B,) - Vee et (1-R [L.-B1)(1-R_ [L.-B])-R,*(L.-B)\(L-B) Oper rt" “eet e We’ “re Se “er 6 2 Ww | 2i(w,, - ,,) Now re en & et et where We 2 Sives the Coulomb phase shift and et gives the hard sphere ohase “ shitt In our phase shift analysis we have separated the Coulomb phase shiit. Therefore, : -2i9 Q 216 : 2 . et _ eto _ 4 we define aro =e and Veco = iY Veo cos X,e ) et where 6 L and X , are real. These definitions then give: Im(zw* )) 6, =~, + arctan (Retaw) ) aa (3) 37 X, = arccos (|U 2/2) 4 eeo We thus wish to compare 6, and X, withthe 86. and X. from L L Jt oT the phase shift analysis. The relations are for a two-level problem with two open channels. If we take the limiting case of one channel (elastic) and _one level, then only Roe remains. Roe is then given by Yo AE, E). The relation for Veeco is then: -2i9,, 1-R 9 (h,* - B,) Veco © Cr R, te By) J . 2 ~ 21)» (1 - Roe (L* - B,) ° Ta aT q Um(L,*)] and b, = -¥y, + arctan > > TRetL SFR, Be 1 2 YY. P =-9., + arctan [ e SS ] Ey -E-y¥, (So, - B.) 9 (4) P = -ay + arctan [ pts ] where Ay == (See - B,) A fit of phase shifts to this single level formula can be approached as a linear least-squares fitting problem using Yo" and EH, as variable parameters. This will be done in our analysis for the second and third excited states of Ty and "Be. The other levels are treated as double levels or as single levels with an open reaction channel. 38 (2) Extraction of the 7Be Level Parameters The second excited state of "Be ( ) is well below the threshold for 4He(PHe, p) Li, Because of this, the single level formula (with only an elastic scattering channel open) was used to fit the z phase shift near this level. As was mentioned before, the problem can be approached as a linear-least squares fit for a given radius. Several values of radius were tried and 4,0 Fermis was chosen as a suitable value. Good fits were also obtained for higher values of radius, but 4,0 Fermis was more consistent with results for the other levels fitted in "Be, For lower radii, the values of the eigenenergy and reduced width change very rapidly and fall outside reasonable limits. The values obtained are shown in Table 14 and the fits are shown in Figure 54. The two s levels forming the third and fourth excited states in "Be have previously been analyzed as single levels because of the small reaction width of the “F /2 level and the small elastic width of the “P, 2 formula to fit the lower level and obtain an elastic reduced width and level. In our analysis we used the single level eigenenergy. We then used the reduced widths as given in Ajzenberg and Lauritsen (1965) for trial values for the higher state.’ The para- meters obtained for the lower state from the single level formula and the trial parameters for the upper state were then used in the double level formula for both an elastic and reaction channel, The trial parameters were found to give a good fit to the data. Variations of the eigenenergy or reduced width for the lower state produced poorer fits. Once again 4.0 Fermis was used as a radius for both states and both channels. Other radii were tried but the fits were not as good. With the eigenenergies and reduced widths fairly well 39 determined, the reaction width for the lower level was varied from the assumed vaiue of 0.0. The values obtained for the various param- eters are shown in Table 14 and the fits are shown in Figure 54, The boundary values used in the fitting (B, and B.) were set equal to -4% (the relative angular momentum of the two particles for each channel). This is a choice which is often used in the literature. Another common choice is to choose values which make the level shift zero at the resonance energy. For a single level, with or without a reaction channel, the two choices will give the same fit by simply adjusting the eigenenergy. For the double level formula, this is no longer the case. For lie Lwo 3 levels in "Be, it was found that the boundary value in the reaction channel still did not affect y a? using a radius of 4.0 Fermis. However, to obtain a good fit when the elastic channel boundary value was changed from -2, it was necessary to change the elastic reduced width of the upper level. For example, the use of the zero level shift boundary value required Ye to be approximately 2.4 times as large as for the -t case. The lower level was not appreciably affected. Some choices of boundary value and the best value of Ya are shown in Figure 60. The central region of B, in this figure indicates no fit for Yo up to 0.5. No fit appeared likely for values as high as 0.6 in this region. _ In the other computations involving these two levels, we raised the elastic width of the upper level until we could see it in the elastic phase shift. This sets an upper limit of Yor = ,09 for the elastic width of the upper level. The a level at 9.3 MeV in "Be was first analyzed as a 2 single level with a reaction channel and elastic channel open. A base line was determined from the 4 phase shifts below resonance. This corresponded to 0° in the analysis. The reduced widths for elastic 40 scattering and for the reaction leading to Oy is + pt were varied as was the eigenenergy of the state. A best fit was obtained for several radii and 4.0 Fermis was again found to give the best results. Changing the boundary condition resulted only in a change in the best eigenenergy. The values obtained for the various parameters are shown in Table 14 and the fits are shown in Figure 54. __ As a final step, we attempted to fit the two : levels with the double-level formula. To obtain a similar fit, it was necessary to reduce the reaction width of the top level and increase the elastic width. Unfortunately, the phase shifts above the lower level drop off - much like hard sphere phase shifts. At the energy of the upper level they were too low to give fits as good as the single level fits obtained previously. | . (3) Extraction of the "Li Level Parameters The extraction of the parameters for "a was carried out in essentially the same manner as for "Be. The second excited state (zs ) is below the 331(a, n)°Li threshold and was treated as a single _ channel single level problem. Again, a best fit to the 3 phase shift (for a given radius) was obtained. Here too, 4.0 Fermis was chosen as a suitable radius. The values of excitation energy and reduced width for this level are shown in Table 14 and the fit to the u phase shifl is shown in Figure 58. The two 2 levels forming the third and fourth excited states of Thi were analyzed as a double level. A single-level analysis of the broad lower level gave an eigenenergy and reduced elastic width. These and values of the reduced widths for the upper level (from Ajzenberg and Lauritsen, (1965)) were used as trial values in the double-level formula. From these starting values best 41 values of eigenenergies and reduced widths were found. Changing the elastic reduced width and eigenenergy of the lower level produced poorer fits. The radius chosen was again 4.0 Fermis. A variation of the reaction width of the lower level was also tried. The values obtained are shown in Table 14 and the fits to the > phase shifts are shown in Figure 58. The reduced a-width is in good agreement with that obtained in the analysis of the °Li(n,a)°H data by Schwarz, (1965). However, his nucleon width is ~30% higher than ours. The boundary values used in the fitting were again taken as -4. A variation of the reaction channel boundary value changed only the eigenenergy as in the "Be case. A change in the elastic channel boundary value required both an eigenenergy change and a change in the value of the elastic reduced width for the upper level. Some cases are shown in Figure 61. The behavior for central values of B, is similar to that for "Be, ; As in the Be case, the = level near 9.7 MeVin Li 2 was fitted using a single level with both an elastic and reaction channel. It was difficult to determine from the phase shift analysis whether this - level was best represented by a dispersion-shape or step-shape in the phase shift curve. Slightly better results were obtained with a dis- persion-shape in the phase shift analysis, but the R-matrix formalism gave a better fit using a step-shape. Once again 4.0 Fermis was obtained as the best radius. The fit is shown in Figure 58 and the values of the reduced widths are shown in Table 14. The vertical dashed line shows the point in energy above which 180° has been subtracted from the calculated phase shifts to compare them with the values obtained in the phase shift analysis. 42 (4) Discussion of the Derived Level Parameters The fitting of the s-wave phase shifts by hard sphere scattering phase shills has been discussed in Part I B(4). An attempt was made to determine the reduced widths of the ground state and first excited state in Thi and "Be by fitting the p-wave phase shifts. Reasonable fits were obtained at most radii used, but the values of the resonance parameters were not reasonable. Many of the reduced widths were negative and none predicted the proper location for the positions of the levels. There are no known d-wave levels in the two nuclei and the d-wave phase shifts remain small and inactive in the analysis. Therefore, no attempt was made to fit these phase shifts with the R-matrix formalism. . Good fits to the second excited state (3 )} of both "Be and "i were obtained with the single-level, single-channel R- matrix formalism. The reduced widths agree quite well between the nuclei. In addition, the use of the same radius as that used by Barnard (1964) (4.4 Fermis) yields a reduced width in agreement with his results to within the expected errors. The reduced widths for the states tend to increase fairly rapidly as the radius is decreased from 4.4 Fermis. _ The elastic reduced widths of the lower ; level in both nuclei were also obtained using the single-channel, single-level formalism. Good fits were obtained except for the regions on the upper edge of the lower 3 levels. Here the phase shifts calculated from the R-matrix formalism lie below those obtained from the phase shift analysis. This difficulty was not {as was previously hoped) resolved by analyzing the two 5 levels in each nucleus with 2 the two-channel, two-level R-matrix formalism. The nucleon 43 reduced widths of the lower 2 levels were determined from the _double-level formula and were quite small in both cases. The errors for these reduced width amplitudes are quite large, but the fits to the phase shifts indicate that they have a negative sign in both Thi and "Be, The agreement of the reduced widths of the lower = levels between the nuclei is very good. However, for TRe the reduced width obtained for this level is considerably larger than the value obtained by Tombrello and Parker (1963), even when the difference in radii is considered, This difference may be a result of the difference of sign in the p-wave splitting between the two analyses. , The analysis of the *P, /2 levels was done with the double-channel, double-level formula in both nuclei. Good fits were obtained for Be using values in agreement with those found in Ajzenberg, Lauritsen (1965). The fits obtained for "ha were a ‘compromise between a good fit to the elastic phase shift and a good _ fit to the x, /2. parameter. The values obtained are in agreement with those given in Ajzenberg, Lauritsen (1965). There is also good agreement between the two nuclei, The level at 9.3 MeV in "Be G ) was analyzed as a two-channel, single-level problem. The fits are least accurate on the high side of the resonance. This may well be a result of the possible errors in the reaction data used to fix the values of xy 2 for this level. The reduced width for Sy ix + p! is seen to be much larger than that for 3 He +a. This feature is also apparent in the scattering data itself. The decay of this level appears to proceed almost entirely by Sr y p as opposed to the channel Sri +p. Recent work by Christensen and Cocke (1966) has shown the presence of a 44. small f-wave admixture in the configuration of the 2. 43 MeV state in "Be. The decay of the 9.3 MeV level in ‘Be also offers an opportunity to determine such an f-wave admixture. The predominant mode is "Be (9. 3)" Li (2.184, 3+) + p by a p-wave decay. The decay of this level to 615 (g.s.) + p requires the Sr and p to be in a relative f-state of angular momentum. Thus the ratio of the reduced widths for these two channels is a measure of the relative f-wave admixture in the level. A small amount of yield in the ground state protons was attributable to the decay of the 9.3 MeV level. The effect was seen at three angles. These data were used to form angular distributions from which the total cross section . . 2 2 _ 2 was crudely determined. The ratio of y oS. /Vist ex. = Vt-wave! Yp-wave Was determined by the relation OF. s. P,/ O1st ex, P3 v gS. /Y ist ex. which applies at the resonance energy. P , gives the penetration factor for each decay. The value obtained for the ratio of reduced widths was (16 role The high errors reflect the small size of the effect and the small amount of data available. This figure represents a value of (1.3 5) MeV for the ground state reduced width. _ . The upper Z level in Tha was treated in the same manner as the corresponding level in "Be .. Although the phase shift analysis was not as satisfactory, the values of reduced widths agree fairly well between the two levels. From our data, it was not possible to obtain an estimate of the f-wave admixture in this level. The fits to the phase shifts were found to be consistently best for a radius of 4.0 Fermis. For the first and first : in both nuclei, a higher choice of radius gave a similar fit and required a smaller reduced width. For the *P. /2 levels, a larger radius 45 (4.4 Fermi) produced a poorer fit. For example, the parameters xX, /2- calculated for this level in "Be were too high below the level and too low above to fit the experimental parameters. The best results for the higher 3 levels also required a radius of 4.0 Fermis. The behavior of the reduced width as a function of | boundary value was of considerable interest. Figures 60 and 61 show the value of the elastic reduced width amplitude (Y,) asa function of the elastic boundary value B @ The value of Yo is that which best fits the phase shifts for that value of B.- The regions of B, near -1,6 are where the boundary value results in zero level shift. Note the region of very high Yo between this region and Be = -3.0 or -t. Weused Be = -2% in extracting the reduced widths. . The effect is similar in both nuclei and only occurs where the double-channel, double-level program is used. Fora radius of 4.0 Fermis, changing the value of the inelastic boundary value had the effect of changing only the eigenenergies. At other radii (such as 4.4 Fermis) the inelastic boundary value also had a Similar effect on the best value of y et 46 IV. COMPARISON WITH NUCLEAR MODELS A. Introduction The development of more sophisticated nuclear models and the extension of experimental knowledge of nuclei have a reciprocal effect upon one another. The purpose of the model calculations is first to attempt to fit known experimental data . with a number of parameters pertinent to the particular model. With these parameters determined, other quantities of interest may be calculated. T-se quantitics can be compared with ex- periment or used to predict future experimental findings. Pre- dictions of this sort then provide an incentive for the experimentalist to measure the quantities and thereby prove or disprove the model's predictions, These measurements provide, in turn, a basis for yet more complex models. Our part in this process has been the determination of the excitation energies and reduced widths discussed previously and shown in Table 14. We now wish to compare (qualitatively, at least) these measurements with the predictions of some of the more recent nuclear models, There are two major reasons for the qualitative nature of these comparisons. The first concerns the way in which the models are developed. it is customary to use, as a starting set of wave functions, those appropriate to a central potential such as an infinite depth harmonic oscillator potential well. The result is a series of bound levels. It has been pointed out that for low-lying levels of a nucleus, the difference between a finite and infinite depth makes onlya small difference in the levels and wave functions. However, in our case, the models are used to predict properties 47 of the nucleus far above the threshold for two-particle breakup. It does not seem unreasonable Lhat the prediclions of the models in this region should differ quantitatively from the experimental values. In fact, the degree of qualitative agreement is surprisingly good. The second reason for the qualitative comparison lies in the fact that the reduced widths for the various levels have not yet been calculated from the wave functions for the various configu- rations. The following discussion will compare our results with those of the cluster model, the rotational model and the shell model. B. Model Comparisons (1) The Cluster Model Several calculations have been made in an attempt to treat Thi and "Be as two clusters of nucleons such as an a particle and a triton (Tang, 1961). A variational procedure is used with trial wave functions to determine an upper bound to the energies of various levels. The wave functions consist of an internal wave function for each cluster and a wave function describing the relative motion of the clusters. The potential uscd is a finite depth central potential taken between each pair of particles. In the paper mentioned above a spin-orbit potential is also considered. The calculations were done for the @P and 2F levels in “Be and ‘Li which should be well represented by the a+ mass 3 cluster scheme. The calculated energy levels agree fairly well with the first and second excited states. The 25 5/2 level is predicted at a lower level than is found experimentally (as is the case in most of the model calculations) although it had not been identified at the time of these calculations. In a later paper (Khanna, 1961), a 61 44-n cluster calculation is made and an 48 approximate number is obtained for the position of the *P, /2 level. At the same time, it is shown that a positive parity level near 6. 5 MeV in "a is unlikely. The cluster model calculations are of interest for several reasons, They show that the grouping of the nucleons into these clusters is a reasonable approach to the problem. The number of parameters which are varied to obtain the energy levels is smaller than in the usual shell model calculations. Also an attempt is made to use two-body central forces (derived from nucleon-nucleon scattering) between individual particles instead of placing the p-shell nucleons in a common potential well. There are also some disadvantages. The calculations are mainly limited to the lowest levels of "Ti and "Be and are rather approximate in that a spin-orbit potential is not used in part of the work, Because of this and an approximate choice for some of the trial wave functions, the higher energy levels tend to disagree with the experimental values. In addition, the wave functions are suitable for bound states and hence do not provide information on the particle scattering. It would be interesting to have these calculations done for the continuum energy range allowing several configurations such as eri + nucleon, 8a i + nucleon and « + mass 3. (2) The Rotational Model _ Consideration has also been given to the rotational model as a description for the light nuclei. In particular, Chesterfield and Spicer (1962) have made calculations for Thi (and "Be) using this model. The model calculates the energy for a number of configu- rations using a Nilsson model potential. These energies are calcu- lated as functions of a deformation parameter ¢ which is a measure 49 of the non-sphericity of the harmonic oscillator well used in the potential. The energy minimum for each configuration is used to determine the best value of e. | . Each configuration is then used as a basis state for the formation of a rotational band. If the energy of a basis configuration is given by Ey then the energy of the other levels of the band is given by: . EQ) = B,°+ AlII+ 1) +6 a(-1)'* 2/24, 4/2)) K, 1/2 where A= n2/ aI, (I, is the nuclear moment of inertia), I is the total angular momenium of the nucleus, and a is a decoupling parameter defined by Nilsson (1955). K is the projection of I on ihe body z-axis. A is chosen to give a best fit to the data. Of the six bands considered in these calculations, three are of positive parity. Since no positive parity levels were found in this work, we will not consider them further. The band based on the 5 level at . 48 MeV seems to represent the ground state and first three excited states quite well. The second band based ona 3 level at 5.62 MeV predicts the *P. /2 level and has a 4 level near an energy appropriate to the position of the *D, /2 level. The 3 siale forming the basis for this band does not appear to exist and is thought to be a spurious representation of the ground state. The third band is based on a ; level which also has not been observed. A : level in this band could represent the level seen by Harrison (1966) at 9.8 MeV in a of this band have not been identified. The calculated levels which fit Be. The other members our current level scheme are shown in Figure 62b. This model reproduces the lowest five levels in Tha and "Be quite well (with the exception of the ; basis of the second band). 50 It also gives good agreement with experiment for the ground state electromagnetic moments, the de- excitation of the first excited state and the decay of "Be. The use of this model to calculate the wave nucleon decay of the “Dy /2 level gives values of Yew av of Yp-wave from .06 to .22 for values of ¢ from 0. 4 to 0.8, respectively. The energy minimum for the band occurs at « = 0.4, The calculations are relatively uncomplicated and it is interesting to see them produce such satisfactory results. The model has, of course, the problem of trying to represent a continuum situation with bound state wave functions. Thus the scattering of particles has not been considered, nor have reduced widths for various configurations for the levels been calculated. The basis states of the second and third bands are also a problem since they do not appear to exist. However, it -appears that these levels can be eliminated from the predictions without changing the remainder of the calculations. (3) The Shell Model Most of the calculations for "hi and "Be have made use of the shell model. The model normaly, considers negative (normal) parity levels formed by a (is) 4 (4p)3 configuration. Several surveys of the light nuclei (including "Be and "h3) have been made using the shell model (Inglis, 1953, Kurath, 1956). The most recent calculations are those of Barker (1966). We shall be primarily concerned with these calculations. The wave funclions used are those of an infinite depth harmonic oscillator potential well, | The L-S coupling limit is used in forming the total wave function of the three 1p shell nucleons. A residual potential between each pair of p- shell nucleons is then assumed. The potential 51 contains a spin-orbit term, as well as space, spin, and charge exchange operators. The energy levels are then calculated and ‘a best fit to the data is obtained by varying the parameters available. ‘Chis determination of the various parameters then allows predictions | of level positions and configurations to be made at higher energy. The energy levels obtained by Barker are in good | qualitative agreement with the schemes found by the earlier investigators mentioned at the beginning of the section, Data at higher energies have enabled him to extend his predictions with more accuracy than was possible before. These predictions for. the energy level schemes for "Be and ‘yare shown in Figure 62c. Also shown in Figure 62 are the rotational model predictions and the experimental results. The firstfour excited states of Thi and "Be show agreement in energy and configuration with experimental | observations. We have identified our highest level with his 3 level which consists mainly of the “Dy /2 configuration. Our relative nucleon and o widths for this level are in good qualitative agreement with the predicted configuration. The energy level predicted for the Dig ° a3 level below the + level, whereas the data on "Be from our work 2 and that of Harrison (1966) show the 3 level at a higher energy than the a level. 2 1- 1.3 3 The model calculations predict 5» T=5 and 5 T=5 for the 7th and 8th excited states, The , T =5 level has not been seen, but the 3 , v =4 level of Harrison's work is-in agreement with level also fits our experimental data. The calculation predicts the predictions. The predictions of this nuclear model appear to be quite good even though the problem is not considered in the continuum. Since the only configuration considered is (is)*(1p)°, the problem of the occurrence or non-occurrence of the positive parity levels does D2 not come up. The ground state magnetic moment, log ft values for the "Be decay and the lifetime of the first excited state are also calculated and agree with the experimental values. Quantities such as the quadrupole moments depend sensitively on configuration mixing and since this was not considered, the calculated values do not give a good fit to the experimental values. | The models discussed all make fairly good predictions for the lower levels. It is to be expected that the more recent shell model calculations of Barker will give better high energy agreement. This results from a greater abundance of experimental data and also from a larger number of fitting parameters than were used in the rotational model. None of the models, however, has attempted to describe the various particle scattering processes. A description of this sort would certainly be of great interest. 53 V, CONCLUSIONS The previous section has shown the good qualitative agree- ment between the predictions of nuclear models and the results of this work, It is also worthwhile to point out the high degree of agreement between the experimental results for the two nuclei. This is especially evident in the reduced widths for the various levels. The two 3 levels show excellent agreement between the two nuclei and thé agreement for the two 5 levels is also quite good. It is particularly nice to see the close agreement as to the structure of the nucleus for these levels (that is, the relative widths for nucleon versus a emission). One would expect this sort of agreement in mirror nuclei and it is gratifying to see it verified experimentally. - The agreement of the non-resonant phase shifts between the two nuclei is also very good. The p-wave phase shifts in particular show the same sign for the splitting and the same energy behavior in both nuclei. In our work, however, we were unable to account for the behavior of the p-waves in terms of the influence of the ground and first excited states in "i and "Be. Whether this behavior can be explained by high energy p-wave levels remains open to question. The existence of positive parity states in the range of this work has been a question for some time. For example, a paper by Lane (1960) uses configurations (1s)* (1p)? 2s, (1s)* (1p)? 1d and (1s)? (1p)* to predict many low-lying, positive parity levels. On the experimental side, the “Fr. /2 level in "Be was thought to be + a 3 level in some of the earlier work (c. g., see Marion (1957)). o4 Earlier experiments on "Be (Barnard, 1964), (Tombrello, 1963) as well as this work have found no evidence for a positive parity level within the energy range investigated. The work which has been described examines a large energy range for both "hi and 7 Be. While good agreement between the two nuclei and with the nuclear shell model has been shown, there are still several experimental and theoretical problems of interest. in the R-matrix analysis, the calculated phase shifts have a general tendency to lie below those obtained from the data on the high energy side of a resonance. It does not appear that one can account for this by errors in the phase shift analysis since the effect has the same sign for all the resonances. The behavior of the reduced widths as a function of the _ boundary value in the R- matrix analysis is also a matter of some concern (see Figures 59 and 60). These results indicate that in the double-level analysis, it is possible to fit the data with a range of Y,'8 which vary by a factor greater than five. Although this problem did not occur for the single-level analyses, it is still rather disturbing and should be investigated further. Fortunately, most analyses of data are done using single-level formulas and are there- fore safe from this trouble. The subject of an f-wave admixture in the predominantly p-wave decay of the *D, /2 level in’ "Be is another matter of con- siderable interest. A better determination of the f-wave decay width for this level in both "Be and Thi is needed and will be attempted in the near future. In analogy with the work of Harrison (1966), it would be of interest to investigate "i using Si +n as an entrance channel, at) Plans are currently being made to conduct an investigation of this sort. . In general, one can say that our work on "Be and "4 has been quite rewarding, due to both the knowledge we have gained about the nuclei from our investigations and to the number of interesting side-tracks which it has suggested for future exploration. : | 56 APPENDIX A ELECTRONICS (1) Beam Current Integration The method of beam current integration was essentially the same in both experiments. Electric and magnetic suppression were used on a Faraday cup (see Figure 1) which collected the beam after passage through the gas target. The magnet was annular in form and the field was in the plane of the ring so that electrons from the chamber would be deflected and not allowed to reach the Faraday cup. Electric suppression was supplied by a 300 V. battery on the 3H(a, 0) °H experiment and by a 300 V. bias supply in the 4He(PHe, 533e)*He experiment, The collected charge was fed through a BNC cable to an integrator of the type described by E. J. Rogers (1963) at Brookhaven. Our integrator was constructed by M. Dwarakanath. It was used in _ our experiments because of its high accuracy in measuring small currents, The error indicated by our calibrations was less than 0.5%. Calibration was accomplished by carefully measuring the voltage across a precision resistor through which current was fed to the integrator. A current was used which approximated the beam current to avoid inaccuracies due to leakage. Basically, the integrator works in the following manner. The input current is applied to a Miller integrator circuit which produces an output from -0.0 to -10.0 Volts. When this negative output voltage exceeds -1.5 V., an amplitude discriminator gates a charge pump which delivers negative charge pulses of a precise magnitude to the integrator until the output falls below -1.5 V.. The circuit is designed so that one charge pulse raises the integrator 57 output by 1 V. Hence the integrator output voltage will lie between -0.5 and -1.5 V. at the completion of an integration. The charge pump delivers charge pulses at a 500 cps rate determined by a continuously running multivibrator. An external scalar then simply counts the number of charge pulses delivered by _ the charge pump, thus determining the total integrated charge... In our work, integrations of 5000 to 10,000 charge pulses were used to minimize inaccuracies due to neglecting a fraction of a pulse. (2) Particle Detection and Charge Separation in both experiments it was necessary to separate the charge 1 hydrogen isotopes from the charge 2 helium isotopes. To accomplish this a counter telescope was used. The telescope | consisted of a thin (AE) counter and a thick (E) counter sandwiched together. The schematic diagram in Figure 5 shows the electronics configuration used in both experiments. The AE counter was a thin, silicon surface-barrier trans- mission detector, Detectors used were 26u or 39u in thickness. The energy loss in the thin 4H counter is roughly pr oportional to Z 2 iy? where Z is the charge of the particle and v is its velocity. for particies of the same energy passing through the AE detector, the charge 1 particles will lose less energy than those of charge 2. A bias level was set in the spectrum from the AE counter to make the desired separation. The E counter was a silicon surface-barrier or lithium- drifted detector of sufficicnt thickness to stop the particles. Detectors used ranged from 300u to 3mm in thickness. The pulses from the counters were amplified by Tennelec preamplifiers 58 and then fed into a summing amplifier to obtain a total energy pulse. The signal from the AE preamplifier was split for use in the charge separation. A bias level "b'' was set in this spectrum. If the pulse from this counter was greater than "'b'', then the | particle was charge 2 and the sum of the pulses E and AE was routed to the second 200 channels of the 400-channel Radiation Instrument Development Laboratories multi-channel analyzer. If the pulse was less than ''b", then the particle was charge 1 and the sum of the pulses was routed to the first 200 channels. In this way a Separate spectrum is obtained for each charge, The method works quite well down to the point where particles of both charges have the same energy and the charge 1 particles lose all their energy in the AE counter (about 1.5 MeV for protons). This technique was especially valuable in the 334(o,, a) °H experiment where the tritons and a's were often very close in energy. 59 APPENDIX B DATA REDUCTION Data obtained in the two elastic scattering experiments were very similar inform. The raw data consisted of spectra from the 400-channel analyzer. Figure 6 shows a typical spectrum for the SH, o) °H experiment and Figure 33 shows a typical 3550)“ He experiment. For each of these | spectrum for the 4He(*He, spectra data on length of time required for the integration (clock time), length of live time on the 400-channel analyzer and the time of day were taken. The gas temperature and pressure were also noted at intervals of one half to one hour. The next step was to obtain the yield of particles (Y) in each group by integrating the peaks observed in the spectra. A great amount of time was saved in this process by the use of a computer program written by Mr. Michael Mahon. The program uses the Burrough's 220 computer to display the spectra from the analyzer on a cathode ray tube. In Figure 7(a) we see a photograph of such a display. The data may be displayed on any desired vertical or horizontal scale. In particular, a logarithmic vertical scale was often used. In Figure 7(b), we see the use of a light pen to draw in ' a background under a peak, Figure 7(c) shows the spectrum after the peak has been integrated between two points flagged by the light pen and the background subtracted. The channel numbers of the horizontal integration limits are shown as well as the counts in each of these channels, Figure 7(d) shows the values of the total counts between the two channels; the counts in the background and the | difference between the two. This process can be continued for all the groups in the spectrum allowing one to extract yields for all the groups in about one to two minutes per spectrum. The quantities 60 displayed on the screen are also printed out on tape by the computer. ‘The yields (Y) for each group are then converted to dif- ferential. cross sections in the center-of-mass system by the relation P CT re) T CM . do(a__) gap) (a) Ca) a) SIN87 op cm = re) dan Qn Gy N, where: ss is the differential cross section in the center-of-mass system. Y = the yield of counts in a group on a spectrum. 77 = the ratio of actual integration time (clock time) to the live time on the analyzer. Po p * the ratio of standard pressure 76.0 cm. of Hy tu the gas pressure used in the target. < = the ratio of the target temperature to standard tempera- ° ture (273. 18°K. ). CM TAR = the ratio of the centcr-of~mass cross section to the laboratory cross section. SF ab = the laboratory scattering angle. 8 cm = the center-of-mass scattering angle. Qn = the number of incident particles. N 5 = the number of target nuclei per ecvhic centimeter et qT and P,. 61 G = A. w/Rh where A, is the area of the rear slit in the collimator, R is the distance from target center to the rear slit, h is the distance from front to rear slit, and w is the width of the front slit. This is essentially the target thickness at 90° in the laboratory multiplied by the solid angle subtended by the slit system. This form for G/ sin; 44 is a first order approxi- mation. A discussion of higher order terms is contained in the thesis by L. Senhouse (1964) and in articles by Breit, Thaxton and Eisenbud (1939) and by Silverstein (1959). See Figure 8 for a schematic of the geometry for G. 0 The following is a sample calculation for se at Ey = 7,953 hoe Bot! Seq yd He(“He, ’He)*He experi- _ 0 _ oO. MeV, Br ab = 31.6 8am 54. 7° in the ment. | 1.82,, 76.0,, 297.1 do(54. 7°) _ 888) (a-g7) (—gg59) ( a7g Fe) ¢ 3774) 52399) da Q_,, (4.842°10"*) (2, 687°107”) _ 8.8144. 1072 Qn vi Q = TT m R @, 14300 ——«1,3551_— 1 _ 4a 13 g., = 14800 . y= 9-035» 10 15.121-10° (1,602. 10°*”- 2, 0) $2 ¥ Where T is the time in seconds to complete an integration using a current determined by a voliage V acruss a resistance R. 2p is the charge per beam particle in Coulombs. Thus | do(54. 7°) _ 8.614107? 04 449-27 om? yoo 4 mb dn 13 “sr sr 6. 666 - 10 Calculations on the Ha, a) oy experiment are essentially the same. The only additional complication was in determining what fraction of the target gas was actually tritium, since the normal hydrogen contamination was of the.order of 27%. To make this determination we made calibration runs using the reaction 1 (a, a) H at 0.5 MeV steps at the same angles as the 3H(a, «) °H data. The values of do da do data were then used to determine the same aa assuming that all were computed as above. The proton groups in the 3 H(a, «)°H the tritium was hydrogen. The ratio of these two oo S was then used as a measure of the hydrogen fraction in the tritium gas. Data on el He, a Li was also reduced in the same manner as that on 4He(3 He, 346) tHe. Corrections were applied to the nominal beam energies to correct for the energy loss in gas cell foils and target gas. These values were calculaled from the slupping cross seclions of Demirlioglu (1962) using our data on pressure and foil thickness, In the case of the Ha, a) 3+ data the beam entrance foil was found to be considerably thicker (approximately 30%) than its nominal thickness. The thickness used in the energy corrections was determined by forcing the positions of the narrow ; resonance near 5 MeV and the narrow 3 resonance near 11,5 MeV to agree with the known positions of these levels in Thi, Values of the cor- rections for the several experimental configurations are shown in Table 2. 63 APPENDIX C TRITIUM TARGET PREPARATION Tritium, the mass 3 isotope of hydrogen, decays by 8 emission to 3 He. The end point energy of this decay is approxi- mately 18 keV. An 18 keV electron is stopped in the windows of most of the common radiation monitoring devices. For this reason, special precautions and monitoring devices are used with tritium. As an isotope of hydrogen, this gas readily exchanges with any hydrogen in a material to which it may be exposed. We have attempted to minimize this exchange by using hydrogen-free materials in our gas handling systems. Tritium was obtained in 2 cc STP lots (5 curies of radio- activity) from Oak Ridge. It arrives in a small glass vial and may or may not be mixed with a helium carrier (see Figure 4). To avoid dangerous leaks of tritium into the vacuum system or atmos- phere we store it in our apparatus in the form of uranium tritide. At room temperature, properly prepared uranium acts as a good pump for hydrogen isotopes. The reservoir was constructed of stainless steel and silver soldered at the joints. A schematic diagram is shown in Figure 3. Electrical feed-throughs carry current to the nichrome wire coil which is used to heat the uranium tritide and evolve the tritium gas. Asbestos cloth electrically insulates the wires from the tube, and an outer cloth layer directs more heat to the tube. Glass wool keeps the uranium chips in the heated portion of the reservoir. Uranium chips are cut from a rod on a lathe and cleaned with acetone. They are then deoxidized in a 30% solution of warm nitric acid, placed in the reservoir and heated to approximately 64 600° C with the heating coil while being pumped on with a liquid nitrogen trapped diffusion pump. When the uranium is thoroughly outgassed, it is cooled in a hydrogen atmosphere approximately 40 psi.). Reheating and cooling in this atmosphere is repeated several times, until approximately 40 atmospheric cubic centi- meters are absorbed and evolved with each cooling and heating. Heating and cooling in Ho causes the metal to powder and become porous, thus giving it a high effective surface area. Once this has been accomplished, the uranium is heated and pumped on while being agitated for approximately one day to evolve all the Hy so as to avoid contaminating the tritium. The prepared reservoir and gas vial are placed in a transfer manifold and the system is checked with a helium leak detector. A schematic of the transfer manifold is shown in Figure 4. The reservoir is opened to the manifold and leak checked. The manifold is then closed off from the leak detector and the internal pressure is monitored with a Hasting's vacuum gauge. Nuts holding the sylphon in an expanded position are backed off and the sylphon compresses. This allows the brass plunger to move in and break the neck on the vial. The tritium is quickly absorbed by the uranium in the reservoir. ' The valve to the reservoir is then shut off and the reservoir and valve removed from the manifold. The whole operation is carried out in the hot laboratory under a hood, An open ended ionization chamber (sniffer) is used to monitor the tritium level in the area. The tritium reservoir is then put in place on the chamber gas handling system. 65 APPENDIX D EXPERIMENTAL ERRORS (1) Types of Errors Errors in both the 3H(a, a) °H and 4He(2He, 3310) * He experi- ments were of two forms. Systematic errors are those involving inaccuracies in quantities related to the chambers and electronics. These errors are independent of the energy of the scattered particles. The second group of errors consist of relative errors such as those involved in subtracting background and statistics of counts in peaks, These errors are highly energy and angle dependent, (2) Systematic Zrrors (a) Target Particles The error in the number of target particles per cubic centimeter depends on the accuracy of the pressure and temperature ‘ readings and on the partial pressure of the target gas. In the 43 He, S310)4 He experiment the yet gas was not contaminated with other gases; however, in the 3H(a, a) 3H experiment the hydrogen contami- nation of the tritium rose to approximately 27%. The estimated error in the target particle density from this cause is 3%. The error in determining the temperature and pressure on both experiments * gotimated at less than .5% with the exception of the high energy 4H? He, He)4 He experiment where it is less than 1%, _(b) Incident Particles The error in the charge collection is less than .5% as determined by integrator calibrations. 66 (c) Detector Geometry The error due to approximating the differential cross section expression by the use of G, is estimated al less than . 1% using the calculations of Senhouse (1984). wine errors in the measure- ment of we Tae pvoived in G, = give errors ° less than .5% for 4ye(3 He, 3i40)4 He and less than . 25% for 33(a, 0)° «)H. The only anguler opbendent parameter in the list of systematic errors is sin 0; 44 (cM. Tap M. y | The error in both experiments for 8, is OM. | estimated at.1°. This leads to a maximum error in sin 8F ab —- Tap ab of less than . 8%. (d) Resultant Systematic Errors The resultant systematic error is then less than 3.2% for SH(c, 0) °H and less than 1. i for “He(He, 3310) *He below 14.8 MeV. For the high energy 4He( He, 3t¢)4 He data, it is less than 1.5%. (3) Relative Errors (a) Sources of Relative Errors The relative errors are those involving the differences between the individual spectra and the judgement of the experimenter in reducing the data. They arise primarily through the background subtractions and the statistics of the peaks. (b) Relative Errors in the 3 Ha, «)°H Experiment In the Sa, a) 3H experiment, these difficulties appeared in several ways. At the lower energies, the background of particles 67 scattered from the walls and foils of the gas cell became far larger than the group of particles we were trying to separate from it, This resulted in a poor background subtraction with the relative incon- sistency between neighboring points being quite high. The effect is most pronounced at low energies and/or at forward angles, where the Rutherford cross section is greatest. The error in the setting of the laboratory angle is significant only at forward angles where a( ge )/38 is large. Maximum errors due to the term A0@( ae )/3®) are approximately 1.5%. Over most of the angles and energies this error is less than 0, 5%. At the backward laboratory angles (mid-range center-of- mass angles) the recoil triton groups were quite difficult to distinguish clearly from the recoil proton contamination groups. This tended to provide poor background subtraction in this region, especially at the lower energies. The statistics of the counts in the groups begin to become relatively important at some of the low points in the excitation curves. All four of these sources of relative error are combined for each center-of-mass angle in Table 5. 4 (ce) Relative Errors in the He(?He, 3346) *He, *HePHe, p) Li 4 and He(“He, p4)°Lit Experiments The background in these experiments was, in general, less than on the 331(a, «)°H experiment. This results from the lower target pressures and thinner foils used for the low energy data. At the most forward angles the 3 He's are somewhat difficult to separate from the a particles in the spectra. The proton groups at the more 68 backward angles suffer from a lack of statistics and difficulties in separating the charge 1 particles from charge 2 at low energies. These errors are tabulated in Table 11. (4) Beam Energy The nominal energy of the beam from the tandem accelerator is accurate to approximately 20 keV. For the SHt6 +a work below 14.8 MeV, this number is a fair estimate of the total heam energy inaccuracy. For the 3 He +a work at higher energies, the width of the resonances did not allow us to determine whether there was an inaccuracy in the nominal thickness of the entrance foil to the gas cell. For the SH +a work, the entrance foil thickness for the gas cell was determined by positioning the low 5 level and the *P. /2 levels as near as possible to their known energies. The discrepancy in indicated foil thicknesses was about 50 keV. It seems reasonable to take 25 keV as a probable error due to the foil. This gives a total r.m.s. error of 32 keV, 69 APPENDIX E COMPUTER PROGRAMS (1) Phase Shift Analysis Program A Fortran IV program for the IBM 7094 was written to fit the elastic scattering data with the phase parameters of equation (1) (page 21). The fit was obtained by seeking a minimum value of 2 where N do do 2 | : (a2 (8) oxp ~ dQ (85) calc. \” 1 re vie) Ng The program is divided into a main program and a sub- routine, The function of the subroutine is to calculate the dif- ferential cross sections, polarizations, and 2 for an input set of phase shifts. The basic normal operation of the main program is as follows. (a) Several data cards are read telling the program how many different energies, angles, and variations of phase shifts it is dealing with. (bo) The laboratory energy, charges, masses involved in the scaitering, trial phase shifts, experimental cross sections, center-of-mass angles and estimated errors in cross sections are read in, (c) From this information the required Legendre functions are generated and the Rutherford scattering amplitude is calculated. (d) (e) (Z) 70 The main program then calls the subroutine which uses the trial phase shifts to calculate se , polar- izations, and 2. | The gradient of 2 with respect to those phase shifts being varied is then calculated, and a step in phase shifis is taken towards smaller Ma along this gradient do ; an x, the same procedure is repeated until a minimum vector. If the resulting values of do give a lower is reached. The cross sections, polarizations, and x" are then printed out and the program proceeds to the next energy. A listing is given at the end of this appendix (IBFTC DEL and IBFTC BEL). The following list defines or gives the equivalent of non- obvious parameters used in the phase shift program. KONG KING ZI, ZT AL AT a an integer giving the total number of angular distri- butions being analyzed. an integer code telling the program how it is to obtain trial phase shifts for an angular distribution. an integer giving the number of code word cards to be considered, laboratory energy in MeV of incident particle. charges of incident and target particles. masses of incident and target particles in atomic mass units. 71 NDEL- - the number of phase shifts being considered. MUT - a meaningless parameter to allow program expansion, NH - the number of points in the angular distribution. DELT() - for I= 1-9, these are bye bsg + baa bse? 63/2» ba/9 » 85/9» bo/Q > and 81/2. in that order. For I= 10-18, . DELT(]) gives the corresponding values of Xie . T() - these are the values of the center-of-mass angles. sD - these are the experimental values of do (85)/ da. D(D) - these are the percentage errors in do(6,)/da . FINC (I) - these are step sizes to be taken along the gradient of ye. CAY - «Kk, CHI - 2. SIGR - the total reaction cross section Op. | SIG(I) - the calculated values of da(8;)/ da. POL(]) - the polarization values for 6.. (2) Below the reaction thresholds the 2 = 3 phase shifts obtained were fitted using a single level R-matrix expression. (See equation (4), page 37.) A simple program was written to perform a least | squares fit to the phase shifts at a number of different energies. If the interaction radius is held constant, the problem can be expressed as a Simple linear least-squares fit. This program uses the sub-. routine COOL to calculate the Coulomb functions and desired 72 combinations thereof, and then employs a standard least squares- fitting program to obtain the best values for the reduced width and eigenenergy at a given radius. A listing is given at the end of this appendix (IBFTC SIN). (3) The data above the reaction thresholds was fitted with the more complicated two-channel R-matrix formalism (equations (3), page 36 ). A program was written to calculate the values of the phase shifts given the reduced widths, eigenenergies, boundary values, and interaction radii. A listing is given at the end of this appendix (IBFTC RMA). SIBFTC DEL DECK c 40 wen 101 57 58 102 59 1002 103 56 104 105 PHASE SHIFT ANALYSIS OF SPIN HALF PLUS SPIN ZERO ODIMENSION DELT(18)0T(75) 0V(75) 9S(75) pFINC(3) o TCw18943) sDEL (18) » LPOL( 75) »POL1( 75) sPOL2(75} sPOL3 (75) sPOL4&(75)}) sPOLS(75) sPOLS1(75) 5 2PO0LS2(75) sPOLS3(75) »POLS4(75) »RR( 75} oRI(75) sDELTA(18) sA(18) 5 3S1G(75) » D(75) DIMENSION APLOT(95)sSHIFT(80019) »ENERG(80) OCOMMON DELTA sDEL »DELT oT oVoSeF INC sSIGsCHI »sPOL »SIGR»POL1sPOL2 > LPOL3 »POL4»sPOLS »POLS51sPOLS2 »POLS3 »POLS4 a CAY aRReRI oCAl sCAZ sCA32CAS > 25A19S5A29SA39SA4s IT CWoNUMONTH DATA APLOT/ 95*1H /+STAR/IH*/s8LANK/1H / READ(5457} KONG JIT = 1 READ (5e40)KINGsNUM FORMAT(215) IF (NUM) 49402 READ (52105) (C(ICW(I5J)51=1918) sJ=1>sNUM) READ( 55103) (TCT) oVC1) +501) 9141935) READ (59101) EsZleZTsAl sATsNDEL sMUTeJTH NTH = JTH + 35 . FORMAT (F10e392F50292F1063/315) FORMAT(15) IF (KING)58558959 CONTINUE READ (59102) (DELT(1)s1=1518)} FORMAT(9F6e1/9F6e1) CONTINUE DO 1002 T=19018 DEL(I}=DELT(1)/57229578 READ(53103)(TCT) oV( 1) 5S¢1) 91236 sNTH) FORMAT (F10022F10039F10¢5) ‘ CONTINUE READ (559104) (FINC( I) 512133) FORMAT (3F5e2) FORMAT (1814) ASP =SQRT(E/ATI) CAY =0e06917*#AIL#ATH#ASP/(AI+AT) ETA =OelS76OT#ZIRZTSASP BAY=ETA/(2e0#CAY) ALF AQ=0 00 ALFA1=ATAN(ETA) ALFA2Z=ALFAL+ATANLETA/2 00) ALFA3=ALFA2+ATAN(ETA/3 0} ALFA4S=ALFA3+ATAN(ETA/400) CAL= COSCALFA1#260} CA2= COS(ALFA2#2 20) CA3= COSCALFA3*200) CAGe COS(ALFA4S#2 40) “SAL= SINCALFAL#¥200) SA2® SINCALFA2#200) SA32 SIN(ALFA3#200) 74 SAG= SINCALFA4*260) PO 21 I8lsNTH RAD =1(1)/57029578 POL1(1) =COS(RAD) POL2(I) =005%#(3e0*(POL1(I)**2) -160) POL3(1) = O05#*(5e00%( POLI{I1)¥**3) -3eO*POLL(I)) POL4(1) =00125¥*(35e0*(POLI(1)*#4) —3000*(POL1(1)**2)4300) POLS(I1) =SIN(RAD) POLSI(I} =SINCRAD) POLS2(I} = 3e0*POLS(I)*POL1(1) POLS3(I)= 7e5#POLS(I)*(POLI(1)*#2) —1e5*POLS(1) POLSG(I)= 00125*(14000#POLS( 1) *{POL1(1)*#*3)—-6000*POLS(1)*POL1(1)) BIN=SIN(RAD/200} BAN =120/(BIN*®*2) BUN = ALOG(BAN) RR(1) = -BAY*BAN*COS(ETA*BUN) 21 RICI) =-BAY*BAN*SIN(ETA*BUN ) CALL SNAG(-1ls-1} IF (NUM) 1591596 6 DO 14 IKE #1sNUM DO 13 JACK 2193 165 OCHI=CHI DO 7 1=1918 7 DELTA(I) =DEL(1) SUMP =020 DO 9 K=1918 IF CICW(UKs IKE) 199998 | 8 DEL{K) =DEL(K) +0005/57029578 CALL SNAG(—19K) A(K) =(OCHI=CHI)/0005 SUMP=SUMP +A(K)##2 DEL(K) =DEL(K) -0005/5729578 9 CONTINUE SUMPR=SORT (SUMP ) DO 11 K=1918 IF (ICW(KsTKE)) 11911510 10 DEL(K) =DEL(K) + FINC(JACK) *A(K)/SUMPR 11 CONTINUE . CALL SNAG (-1le-1) IF (CHI -OCHI) 165012912 12 DO 125 K=1918 125 DEL(K) =DELTA(K) CALL SNAG (1s=1) 13 CONTINUE 14 CONTINUE DO 1001 1=1918 1001 DELT(I) =DEL(1)#57+29578 15 WRITE(69112) 111’ FORMAT(30H1SPIGER» PHASE SHIFT ANALYSIS ) WRITE (69106)E . 106 FORMAT(//1X9F603//) 107 108 54 109 110 35 53 45 42 43 46 51 52 75 WRITE (69107)AT sZI1 AT 9ZT ; FORMATI1X 9 F603 9SXeF4el 95XaF 603 95XeF4el//) DO 54 121518 WRITE (60108) DELTCI) FORMAT ( 3XsF8e3 ) SHIFTCJITs})= DELTIN) ENERG(JIT) = €E CONTINUE WRITE (69109) CHI» SIGR FORMAT(//1X9E15e¢8//4X oF 803//) WKITE(60110) (TCL) s VEIT) sSCT) sSIG(T) sPOL( 1) sIT=lsNTH) FORMAT (1X 9 F602 9 5X sF502 9 5X 9F 903 95K 8F 903 95X 9 F 906) PUNCH 1025 (DELT(I),1= 1918) IF (KONG = JIT ) 53953555 CONTINUE JIT =JIT + 1 GO TO l DO 52 T=1918 WRITE (6945) FORMAT(17H1 DELTA VS E PLOT) DO 51 K=1sKONG APLOT(1) = STAR TF( SHIFTiKsT)) 42943943 SHIFT(KsT) = SHIFT(KsT) + 1806. IPLOT =SHIFTiKs1)*(05) + dle APLOT(IPLOT) = STAR WRITE (6946) ENERG(K}s SHIFT(KaT)s APLOT FORMAT (2X 9F60394X9F 7e3295Al1//) APLOT{IPLOT) BLANK CONTINUE END 76 SIGBFTC BEL DECK SUBROUTINE SNAG (ITs JAG) ODIMENSION DELT(18)9T(75)9V675) 95075) s9FINC(3) 9 ICW(18 943) sDEL (18) » 1POL(75) sPOL1(75) sPOL2(75) sPOL3 (75) sPOL4(75) sPOLS(75) »POLSI1(75)5 2POLS2(75) sPOLS3(75) sPOLS4 (75) aRR( 75) oRI CFO) SVELTACIS) xAC16)9 351G(75) » B75) OCOMMON DELTAsDEL sDELT oT oVeSeFINCsSIGsCHI sPOLsSIGR»POL1 »POL2s 1POL3 »POL4 sPOLS sPOLS1 sPOLS2 sPOLS3 sPOLS4 sCAY sRRORI sCAl] 1CA2sCA3 sCA4s 25A1sSA29S5A39SA491CW »NUM »NTH 1000 CONTINUE IF (JAG) 2029202960 6G0GO TO (201923192619291932193515361 poll veel 471 ¥501 53155615591 » 1621965196819711)% JAG 201 SSC0=SCO $SS0=SS0 202 SSO=(SIN(DEL(1))**2) SCO=COS(DEL(1) ) *SIN(DEL(1)) IF (JAG) 2329232861 203 SCO=SSCO $$0#5SS0 Gu TO 999 231 $8¢€1=SC1 $951=SS1 ; 232 SC1=(SA1*COS(DEL (2) )#CAL¥SIN(DEL(2)) 3 *SIN(DEL(2)) SS1=(CAL#¥COS (DEL (2) )=SAL*SIN(DEL(2))) *SIN(DEL(2)) IF (JAG) 2620262361 233 S$Cl=SSCl $$12SSS1 GO TO 999 261 $5C2-SC2 $3S2=SS2. 262 SC2=(SAL#COS (DEL (3) 2 +CAL*SIN(DEL( 32) 2 *SINCDEL (3) ) $S$2= (CAL *COS(DEL (3) }-SAL*SIN(DEL(3)) P¥SIN(DEL (3) ) IF (JAG) 2929292961 263 S$C2=SS5C2 $$2=S8S2 GO TO 999 291 SSC3=SC3 $$S3=SS3 292 SC3=(SAZ*COS(DEL (4) )+CA2*SIN(DEL(4))) *SIN(DEL (4) ) 9532 (CAZ®COS(DEL (4) I—SAZFSINIDEL( G4) ®SIN(DEL (4) ) IF (JAG) 3229322961 , 293 S$C3#SSC3 $$3=S5S3 GO TO 999 321 SSC4=SC4 $$S$4=S5S4 322 SC42(SA2*COS(DEL(5})4+CA2*SIN(DEL(5))) *SIN(DEL(5))} * S842 (CA2*COS (DEL (5) }-SA2*SIN(DEL(53) *SIN(DEL(5)) IF (JAG)3529352961 323 SC4=S5SC4 $$42SS5S4 351 352 353 381 362 383 411 412 413 441 442 443 471 472 473 501 502 503 531 77° GO TO 999 $SC5=SC5 $$5$5=S55 $C5=(SA3*COS (DEL (6) )+CAZ*SIN(DEL(6)))*SIN(DEL(6)) SS5= (CA3*COS (DEL (6) )-SA3B*SIN(DEL(6)))*SIN(DEL(6)) IF (JAG) 3829382961 SC5=SSC5 $S5=SS8S5 GO TO 999 SSC6=SC6 $$$6=SS6 5C6= (SA3*COS (DEL (7) )+CAZB¥SIN(DEL(7)) I #SIN(DEL(7)) SS6=(CA3*COS(DEL (7) )-SAB*SIN(DEL(7)) )*SIN(DEL(7)) IF (JAG) 4129412961 §C6=SSC6 SS6=SSS6 GO TO 999 SSC7=SCT7 SSS7=SST7 SC7=(SA4#COS( DEL (8) )#CAG#SIN(DEL(8)))*SIN(OEL (8) ) SS7= (CAG#COS (DEL (8) }-SAS*#SIN(DEL(8))) *SIN(DEL(8)) IF (JAG) 4429442961 SC7=SSC7 GO TO 999 SSC8=SC8 ' $$S58=SS8 SCB=(SA4*COS (DEL (9) )+CAG*SIN(DEL(9)) ) *SIN(DEL(9) ) SS8= (CA4#COS(DEL (9) )-SAG*SIN(DEL(9)))*SIN(DEL(9) ) IF (JAG) 4729472961 SC8=SSCB $S8=SSS8 GO TO 999 SHITO=FITO FITO=(COS(DEL(10)})*#2 IF (JAG) 5029502961 FITO=SFITO GO TO 999 SFIT1= FITL SFIS1= FIS1 SFICL= FIC1 FITI=(COS(DEL(11)})**2 FIS1= FIT1¥SA1 FIC1= FIT1*CAl IF (JAG) 5329532961 FIT1= SFIT1 FISl= SFIS1 FIC1=SFIC1 GO TO 999 SFIT2= FIT2 SFIS2= F1s2 SFIC2= FIC2 §32 533 561 562 $63 a9] 592 593 621 622 623 651 652 653 78 FIT2Z=(COS(DEL(12)) )##2 FIS2= FIT2#SA1 FIC2a FITZHCAL IF (JAG) 5629562961 FIT2= sFIT2 FiS2= SFIS2 FIC2=SFIC2 GO TO 999 SFIT3= FIT3 SFIS3= FIS3 SFIC3= FIC3 FIT3=(COS(DEL(13)))**2 FIS3= FIT3*SA2 FIC3= FIT3*CA2 IF (JAG) 5929592361 FIT3= sSFIT3 FIS3= SFIS3 FIC3=SF1IC3 GO TO 999 SFIT4= FITS SFIS4= FIS4 SFIC4= FICS FITS=(COS(DEL (14) ) ) #*2 FIS4= FIT4#SA2 FIC4= FIT4*#CA2 IF (JAG) 622 9622961 FIT4= SFIT4 FIS4= SFIS4 FIC4G=SFIC4 GO TO 999 SFITS= FITS SFIS5= FIS5 SFIC5= FICS FIT5=(COS(DEL (15) )) ##2 FIS5= FITS*SA3 ; FICS= FITS*CA3 IF (JAG) 6529652961 FITS= SFITS FISS5= SFIS5 FICS=SFICS GO TO 999 SFIT6= FIT6 SFIS6= FIS6 SFIC6= FIC6 FIT6=(COS(DEL (16) ))**2 FIS6= FIT6*SA3 F1C6= FIT6*CA3 IF (JAG) 682 3682561 FITS= SFITS FIS6= SFIS6 719 FIC6=SFICE GO TO 999 681 SFIT7= FITT SFIST= FIS7 SFIC7T= FICT 682 FITT=(COS(DEL(17)))¥*2 FIST= FIT7*SA4G FIC7T= FIT7#CA4 IF (JAG) 7129712361 683 FIT7= SFITT FIS7= SFIST FICT=SFIC7 GO TO 999 711 SFIT8= FITS SFIS8= FIS8 SFICS&= FICS 712 FIT8=(COS(DEL(18)))**2 FiS8= FIT8*SA4 FICc8= FIT8*CA4 GU TO 61 713 FIT8= SFIT8 FIS8= SFIS8 FIC8=SFIC8 GO TO 999 DO 998 I=1lsNTH OFCOR= RR(I)+ (CFITO*SCO)+ POLI(1)*(2e0*SS1*FITI+ FISI 1-1e5*SA1 + OoS*FIS2Z4+FIT2*SS2) +(POL2(1))*(3e0*SS3#FIT3+1 ¢5*F1S3 2-2 e5*SA2+ FISG +2e0*SS4*FIT4I+(POL 301) 1 ¥(GeO*SSS*FITS+2.0*#FIS5 3-3 e5*SAB +1 e5*FI1S64+360*SSO*FITE) + POL4S(IT)*(5e0*SS7T¥FITT+205*F IST 4-GeO*SAG +20¢0*F1S844 eO0*SSB*F ITB) ) /CAY OFCOT=RICI} +C(FITO*SSO+e5 #(1¢0-F ITO) )+POLI 01) *(2e0*SCI*FITI-FICI LTtleS*CA1L—Oe5#FIC2+ SC2*FITZ) +POL2(1I)*(3eO0*SC3*FITS -1e5*F ICS 242 05*CA2— FICK +200*SC4*FIT4) + POLZCII*¥(4e0*SC5*FITS -2e0*#F ICS 34+305¥*¥CAZ —-le5*FICE +300*SCOXFITE)+POL4(1)*(5e0*SCT#FITT -205*FIC7 4+4e5*CAG —2eO*FICB +40¢0*SCB8*FITB) I/CAY OFINR=(1e¢O/CAY)I *(POLSI CII #(SS2*FIT2 +005*FIS2 -Oe5*FIS1 I~SSI*#FIT1L) +POLS2Z¢01) *(SS4*F 114+ 0 D#F ISG “Oe DEF ISSHSOSFFITS) 2+POLS3( 1) *(SSO*FIT6+0 0 5*F 156-00 S*FIS5S-SSS¥*FITS) 3+POLS4(1)*(SS8*FIT8+005*FI1S8-00e5*F1S7T-SS7T#FITT7)) OFINI=(1e¢0/CAY) *¥(POLS1 (1) *(SC2*FIT2~Oe5*FIC2+0e5*FICL -SCL#FITI) L+POLS2(1)*(SC4*#FI1T4-0 05 *F1C44+0e5%#FIC3 -SC3*FIT3} 2+POLS3(1)*(SCO*FITE6-005*F 1 C6400 5*FIC5S-SCS*FITS) 3+POLS4(1)*(SCBE#FITB—Oe5¥*#FIC8+0e S*FICT-SCT*FITT)) SIG( 1) =FCOR**2+FCOL**2+FINR**X2+7FINIT#¥2 GLOP = NTH CHI = CHI +0 ¢(SCT)-SIGCIDZ( V¢1)))*#2)/GLOP JTF (NUM) 77797779345 345 IF (IT) 99899989777 777 POLI I) S—200*(FCOI*FINR -FCOR*FINI)/SIG(T) OSIGR =(BelGlSS/(CAYHCAY) D¥( (1 eO-FITO*FITON4+(300-c oOHFITI*FITI 80 L=FIT2Z#FIT2) +65 00-3 eO*F I TI#FITI—2 cO#F LTO*FIT4) + (700-4 e Oe FI TSHFITS 2-BeOPMFITG*FITE 4069 00-5 e O*F I TT*#FIT7—-4eO*F ITS*FITS8)) 998 CONTINUE 456 IFC JAG) 99939999234 2340GO TO (2039233 92635293532393539383 9413 9443 9473 0503 253395639593 16233653 36839713) sJAG 999 CONTINUE RETURN END % C ie c c IBFT 1001 101 889 207 199 17 888 81 c SIN _ DECK SINGLE LEVEL RESONANCE PARAMETERIZATION OF PHASE SHIFT PROGRAM BY SPIGER PROGRAM PERFORMS LEAST SQUARES FIT TO DATA COULOMB WAVE PROGRAM COOL REQUIRED DOUBLE PRECISION BETsALPsALPINV COMMON/ARR/C 9D COMMON Fs FPs Gs GP» PHIs ASs Ps Ss Sis CP COMMON/LSQ/ XesCHI2s SIGsRe ITESTsIAsIALPsIALINVsICOEs ICAL DIMENSION CHUNK(100) ODIMENSION ERR( 100) sDEL(100) sDELPHI (100) s8(100) » CALCU( 100) PeFSR6100)} «CALCUD(C10N03 «H(100) DIMENSION X(100) DIMENSION A(100925) 5Z(100) sERROR( 100) sWT( 100) ALP (25925) »BET(25) DIMENSION ALPINV(25925) sCOE(25) DELCO (25) sCAL(100) sDELCAL(100) ODIMENSION Tl4} 306100) sDELT(100} »FS(100)5 FGSQ(100)s 1PEN( 100) 9SH(100) »SANDL (100) sCOF (100) sDELTAR(100) sDELTA( 100)» 2 DIF (100) >SHIFT(100) 2ECM(100) , DIMENSION C(90) sD(90) EXTERNAL ARRAY READ(531001) ND FORMAT (15) READ (59101) ZIs ZT» Als ATe L FORMAT (2F5e192F1006/15) TA=5 IALP=5 IALINV=5 ICOE=5 ICAL=5 FORMAT (F1004) DO 1 121499 X(T) =I wRITE(69207) FORMAT (1H1) DG 199 I = 1s ND READ (55888) E(I)»s DELT(I)s ERR(1) CONTINUE READ (55889) RD DO 200 I = 1» ND FORMAT (2F70e39F 703) ASP = SOQRTC(ECI) ZAI) ETA = 0015767#ZI*ZT/ASP CAY=0 e06917#AL#ATHASP/(AL + AT) RO = (CAY )#30162278#RD ECM(1) = ECI)*#(AT/SCAI4AT)) CALL COOLtETAsROeL) FS(1) = PHI FGSQ(1) = AS "PEN(I) = P SH(I} = § SANOL(I) = SL 82 cor¢l) = CP DEL(1)) = DELT(1)/57029578 DELPHI(1) =DEL(I) + FS(T) BCE) =1le/TAN (DELPHI(1)) FAT = Le/(TAN(DELPHIC( LT) + ERRGI)) J CAT = Le /(TAN(DELPHI( 1) -— ERR(I)) ERROR(I) = ABS (FAT ~ CAT) Ctl) #le/PEN(T) D(1) = -ECMCI)/PEN(I) H(1) = (=SANDL(1))/PEN(T} 2{1) = Bll) = HT) WRITE(6 7209 ETA2RO2CAY 209 FORMAT(1H 3€15¢5) WRITE(6s210)FS(1) sPENC(T) oCOI) sO61) 9201) sH(T) SBC) 210 FORMAT(IH 7£15¢5) 200 CONTINUE WT(1) = 1006 O CALL LSTSQR(AsZ»NDo2sERRORsWT sALP BET sALPINVsCOEsDELCO CALs 1 DELCAL sARRAY) GAMSQ =le/COE(2) ELAM =GAMSQ*COE(1} DO 205 I=1seND CALCU(I) = ATAN (1Le/(CALCI4HCI)) 2 -FStT) FSR(I} = FS(1)*57e29578 IF(CALCUCT)) 31932932 31 CALCU(I) =CALCU(I) + 32614159 32 CONTINUE CALCUD(I) = CALCU(I)*57e29578 WRITE(691000} ECI1)sECM(1) sDELT(I) sCALCUD(1) sFSRI(1) LOOOCFORMAT( 7H ELAB= F70394Xs5HECM= F703s4X96HDEXP= F703s4X6HDCAL= F7o 1394Xs6HHDSP= F723) 205 CONTINUE WRITE (691002) ELAMsGAMSQ»s RDs CHI2 LOO2Z0FORMAT( 7H ELAM= £140e7s5Xs7HGAMSQ= El4e725Xs8HRADIUS= E140795X%s6HCH 112= El4e7) ; GO TO 17 END SIBFT Cc Cc 100 101 2 17 102 200 201 202 1 103 Cc RMA DECK PROGRAM TO FIT A DOUBLE LEVEL PHASE SHIFT BY A 2 LEVEL R-MATRIX THEORY» PROGRAMMER — SPIGERse PROGRAM REQUIRES COOL. COMMON FoF PsGsGP sPHI sASoP9SsSl CP REAL KYEC aKYE OCOMPLEX ELsELSTARsELRsELRSTRsOMEGAE sOMEGAR»> FEEsFERaXsY¥aUs 1VoWeZ »GUNK . ; ODIMENSION E£1SUB(50} »E2SUB(50) »GAM1E(50) sGAM1R(50) »GAM2E(50) » 1GAM2R(50) ODIMENSION EL (50) sELSTAR(50) sELR(50) s9ELRSTR(50) sOMEGAE(50) » LOMEGAR(50) FEE (50) sUEE(50) 9X(50) s¥ (50) 9V(50) 9W(50)-sGUNK(50) » PKYEC{50)eDEL TAC(50) sE (50) s9EEX(50) sDELTA(50) sKYE(50) sICW(50)+ 3DELTAR(50) «DELTRC(50) »FER(50) DIMENSION CAYE(50)sETAIN(50) +» ROIN(50)2 SCE(50) sPENE(50) s9EN(50) DIMENSION ASPR(50)0 CAYR(50) sETAQUT(50) »sROOUT (50) »SCR{(50) sPENR( 50) DIMENSION ASPE(50) READ (59100) ZIsZTsAIsATsZIOsZTOsAIOsATO FORMAT (2F5e292F100592F50e292F100¢5) OREAD (59101) LIN» LOUT sBEsBRsRIN»sROUT El 9E2 »GAMEL 1 sGAMEL2 »GAMR] » LGAMR2 sNE sKINGsQR9ED FORMAT (215/2F60e3/2F603/2F603/4F603/15/15/2F 704) IF (KING) 1791792 READ (59202) (CICW(I)sT=1910) CONTINUE FORMAT .(1014) WRITE (62200)21 sZT sAI sAT FURMAT (5X 9 3HZ1 =F 5 0284X%0 3BHZTHF 5 02 4X9 3HAI=RF 703 94X09 BHATHAFTe3/) WRITE(69201)Z10sZTOsAIOsATO FORMAT (4X 9 4HZ10=F50293X s4HZTO=F 502 33X s4HALO=F 7039 3X p4HATO=F 763/) OWRITE (62202) LINsLOUT » BE sBReRINsROUT sEl1 9E2 sGAMEL] sGAMEL2 sGAMR1 9 1GAMR2sQRsED OF ORMAT (5X os GHLINA1I5 94X 9 SHLOUT=15/5X 4 3HBE=F 6.63 94X09 3HBR=F663/5Xo4HRIN 1=F66394X 9 SHROUT=F603/5X 9 3HEL=F 603 94X 5 SHEZ=F603/5X9 THGAMELL=EF 6035 24X%s THGAMEL2=F 603 94X s96HGAMR1 =F 60 394X s6HGAMR2=F 663/5X s3HOR=F 6039 34Xs3HED=F653) DO. 3 I=loNE READ (55103) ECT) sDELTACI) sKYECI) FORMAT (3F 1004) DELTAR(I) = DELTACI)/57e29578 ASPE(T)=SQRT(ECI) ZAI) CAYE(1) =OcQO6917#AIFAT#ASPEC IT) /(AI + AT) ETAIN(I) =OolS767#ZI#ZT/ASPE(I) ROINCI) — = CAYE(T)4RIN®*32162278 CALL COOL (ETAIN( 1} sROIN(I) sLIN)} SCE(I) = § PENE(I} = P ELCI): =CMPLX(SCE(1) sPENE(I)) ELSTAR(I) 2 CONJG(EL(I1)) -FEECI) =«CMPLX(0.0sPHI) . EN(T) = (ECI)*#(AT/S(AL +AT})-OR)/(CATO/SIATO +AI0)) ASPR(I) = SQRT(ABS(EN(I))/AI0) 84 CAYROI) = OeQb91LTHALOXATOHASPRII)/(AIO +ATO) ETAOUT(I) = 0¢15767*#ZIO#ZTO/ASPR( I} ROOUT(I) = CAYR(1)*#ROUT#3 0162278 WRITE (69304) ETAOUT(I) sROOUT( I} sLOUT IF (ZI0O) 40940941 41 IF (ENCE) ) 18919919 18 PENR(I) =0.20 PHI =000 FLOUT = LOUT CSEE = SQRT((FLOUT+025 ) ##24+2.%ROOUT (1) *ETAOUT (1) +ROOUT( 1) ##2) SCRO 1) =-CS5EE+O oe S*(ROOUT CI) FETAOUT (I) +(FLOUT+H005) ##2) 4 ( CSEEXCSEE ) GO TO 20 ; 304 FORMAT(2E15e8s120) 40 IF (EN(C1T) 139938938 39 PENR(I) = 00«0 SCRCI) ==—(1e¢0+ROOUT (I )+ROOUT (1) **#2.0)/0120+ROOUTII)) GO TO 20 38 PENR(I) = (ROOUT(T) #*#3¢0)/01¢0+ROOUT(TI*#*#2e0 = } SCRE) = ~€1e0/¢1e0+ROOUT (1 )**200)) GO TO 20 19 CALL COOL(ETAOUT( I) sROOUT (I) sLOUT) WRITE (62303) SoP 303 FORMAT(2E1508) SCR(TI) = § PENR(I) = P 20 ELR(I) =CMPLX{(SCR(I) sPENR(I)) ELRSTR(I) = CONJG(ELR(I)) FER(I) =CMPLX{0eOsPHI) EEX(1) = ECI)*{AT/( AI +AT)) +ED WRITE (69203)E (1) sDELTACI) sKYE( I) sELC I) s9ELSTAR( 1) sFEE(T) 2030F ORMAT (5X o SHE (1) =F 70394X s9HDELTALC I =F 703 04Xo7HKYE (1 =F 703/5X 9 6HEL ( 11)=E150894X E1508 94Xs1 OHELSTAR (1) =E150894X% 9E1508/5X 9 THFEE (1 )=E1508 224X0E1548) WRITE (6s204)EN(T) sELR(I) s9ELRSTR(I) sFERCI) s9EEX(T) 2040F ORMAT ( 5X s6HEN (1) =F 703/5X 9 THELR (EF) =E15 0 894X0E150894X os LOHELRSTR(1)= 1E250894X9E1508/5X 9 7HFER( I) =E150894XsE1508/5Xs THEEX (1) F763) 3 CONTINUE READ(591202) NE1sNE2sNGE1 »NGE2 sNGR1 »NGR2 1202 FURMATCI5/I5/15/15/15/15) READ(541201) (E1SUB(I).1=16NE13 READ (591201) (E2SUB(1) oI =1eNE2) READ(591201) (GAMIE(1)91*1sNGE1) READ(591201) (GAM2E(1)sI=1sNGE2) READ( 59120172 (GAMIR( 1) 9121eNGR1) READ( 591201) (GAM2R( 1) ol *1 sNGR2 ) 1201 FORMAT( F603) DO 1300 IK=1»sNEi * ELZE1SUB(IK) DO 1301 J=1sNE2 E2=E2SUB(U) DO 1302 K*1aNGE1 1505 1401 34 35 1402 1305 1304 1303 1302 1301 ; 1300 85 GAMEL1=GAM1E (XK) DO 1303 L=l»NGR1 GAMR1ISGAM1IR(L) DO 1304 M=1»sNGE2 GAMEL2=GAM2E (M) DO 1305 N=leNGR2 GAMR2=GAM2R(N) WRITE (621508 )E1sE2sGAMEL1 +GAMEL2.GAMR1 «GAMR? OF ORMAT (5X 5 3HEL=F7 03 94Xs BHEZ=F 70 394X 9 THGAMEL L=F 703 94X 9 THGAMEL2 2F 703 1 04Xs6HGAMR 1L=F 703 94X sGHGAMR2=F 703) WRITE (691401) OPURMAT (3X sGHE (1) 98XsGHOELTAC I) 3GX sGHOLL TAC (CT) SX sGHKYEL I) »8X%> L7HKYEC( 1) 58Xs3HREEs10X»9 3BHRRE 9 10X9 3HRRR} DO & IT=1s5NE REE= ((GAMEL1*GAMEL1)/CE1-EEX(€1)))} +(GAMEL2#GAMEL2/ (E2-EEX(1))) RRE= (GAMELI*GAMR1/(E1-EEX(1))) + (GAMEL2#GAMR2/(E2—-EEX(1))) RRR=(GAMRI*GAMRI/(E1-EEX(I))) + (GAMR2*GAMR2/ (E2-EEX(1))) XOL)=¢160 — RRR*#(ELR(I)-BR)) YOCI3=01-0 — REEXCELSTAR(1}) =— BE)) VCI) = EL¢I) - BE W(I) = RRE#RRE*(ELR(1) — BR) OGUNKCID = OXCD)FYCT) = WOT) *CONJG(IVOT) DDS CXC LT #CONIGIY(1)) — WOTD* 1V(1)) KYEC(1) =(ACOS(SQRT (CABS(GUNK(1)))))*570e29578 HUNK = ATAN2 (AIMAG(GUNK(1)) sREAL(GUNK(T))) IF (HUNK) 34935935 HUNK = HUNK +20%3614159 CONTINUE DELTRC(I) =-AIMAG(FEE(I)) + O«5*HUNK DELTAC(T) 257229578#DELTRC(I) WRITE (691402) (1) sDELTACT) sDELTAC(I) sKYE( 1) sKYEC(I) 9 REE®RREsRRR FORMAT (F80397X 9F B03 96X9F 903 95X9E100494X E1104 94X93 (E100493X)? CONTINUE CONT INUE CONTINUE CONTINUE CONTINUE CONTINUE CONTINUE END 10. 11. 12, 13. 86 REFERENCES F, Ajzenberg-Selove and T. Lauritsen, Nucl, Phys. 78, 1 (1966). A.D. Bacher, Ph.D, thesis, California Institute of Technology, in preparation (1967). A.C.L, Barnard, C.M. Jones and G.C. Phillips, Nucl. Phys. 50, 629 (1964), F.C, Barker, Nucl. Phys. , to be published (1966). G. Breit, H.M. Thaxton, and L. Eisenbud, Phys. Rev. 35, 1018 (1939). C.M. Chesterfield and B. M. Spicer, Nucl. Phys. 41, 675 (1962). P.R. Christensen and C. L. Cocke, Nucl. Phys. , to be published (1966). C.L. Critchfield and D.C. Dodder, Phys. Rev. 76, 602 (1949). D. Demirlioglu and W.. Whaling, unpublished, (1962). W.D. Harrison, Ph.D. thesis, California Institute of Technology (1966). D.R, Inglis, Rev. Mod. Phys. 25, 390 (1953). F.C. Khanna, Y.C. Tang, and K, Wildermuth, Phys. Rev. 124, 515 (1961). D. Kurath, Phys. Rev. 101, 216 (1956). 14. 15. 16. 417, 18. 19. 20, 21, 22. 23. 24. 25, 87 A.M, Lane and R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958). A.M. Lane, Rev. Mod. Phys. 32, 519 (1960). J.B. Marion, G. Weber, and F.S. Mozer, Phys. Rev. 104, 1402 (1956), J.B. Marion, Nucl. Phys. 4, 282 (1957). J.A. McCray, Ph.D. thesis, California Institute of ‘lechnology (1962). R.B. Murray and H.W. Schmitt, Phys. Rev. 115, 1707 (1959), E.J. Rogers, Rev. Scientific Inst. 34, 660 (1963). S. Schwarz, L.G. StrOmberg and A, Bergstrim, Nucl. Phys. 68,598 (1965). L.S. Senhouse, Ph.D. thesis, California Institute of Technology (1964). E. A. Silverstein, Nucl. Inst. and Meth, 4, 53 (1959). Y.C. Tang, K. Wildermuth, and L.D. Pearlstein, Phys. Rev. 123, 548 (1961). T. A. Tombrello and P.D, Parker, Phys. Rev. 130, 1112 (1963). 88 Table 1 Detection Geometry Parameters This table lists the parameters pertinent to the solid angle subtended by the detectors and the target thickness seen by the detectors. Parameters are given for both the S(a, «)°H and 4He(*He, 3310)“ He experiments. (Pages 7, 14, 61) 89 Table 1 . Parameters on Slit Size and Positioning Used to Calculate G, 3H(a, 0) °H Experiment Collimator 1: (Used to take data for OF ab > 55°) Front Slit Width (w) - . 1558 cm. Rear Slit Width - .1577 cm. Rear Slit Height - .7179 cm. Rear Slit Arca (A,,) - . 1132 om’, Distance from Front Slit to - 4,068 cm. Rear Slit (h) Distance from Cenler of - 8.518 cm. Chamber to Rear Slit (R) 4 G, - 5.090-10 “cm. Collimator 2: Ww - . 1563 cm. ‘Rear Slit Width - 1559 cm. Rear Slit Height - . 7155 cm. A - ~ .1115 om’, r “oh - 4.085 cm. R - 8.533 cm. G. - 5.000+ 10" “cm. The half-angle seen by either collimator is 2. 2°, 90 Table 1 (cont. ) 4He(*He, SHe) “He and 4He(*He, p) °Li Experiments w . 1533 cm. Rear Slit Width . 1540 cm. Rear Slit Height . 7157 cm, 2 A, . 1102 cm”. 4.074 cm. R 8.567 cm. G, 4.842- 107 “cm, The half-angle seen by this collimator is 2. 2°, 91 Table 2 Foil Energy Losses This table shows the incident particle losses due to passage of the beam through the various entrance foils to the target gases. The nominal beam energies, energy losses and corrected energies are shown for several values of nom- inal beam energy. A smooth curve was drawn through these points to obtain energy losses for other energies. (Page 62) 92 Table 2 Energy Loss of a Particles in Tritium Gas and Entrance Foil (8125 &) for 331(,0)° 11 Experiment Nominal Beam Energy Loss | Corrected Beam _ Energy (MeV) . (keV) Energy (MeV) 4.0 388 3.612 8.0 261 ; 7,739 12.0 | 201 11.799 16.0 166 15. 884 20.0 141 19, 859 Energy Loss of Ste Particles in Entrance Foil (6250 A) and tHe Gas of the High Energy Gas Cell for the 4He(He, 3He) “He Experiment 208 7. 292 7.5 9.0 184 8. 816 10.5 165 10. 335 12.0 151 11. 849 18.5 136 - 13,364 15.0 128 14, 872 16.5 121 16. 379 18.0 111 17. 889 93 Table 2 (cont. ) Energy Loss of SHe Particles in Entrance Foil 0 (1000A) and 4ut6 Gas of tHe PHe, p)PLi Experiment Nominal Beam Energy Loss Corrected Beam Energy (MeV) (keV) Energy (MeV) 6.0 | 102 5. 898 9.0 74 8. 926 12.0 57 11. 943 15.0 49 14, 951 18.0 43 17. 957 Energy Loss of He Particles in Entrance Foil fe) (1000A) and 4yF6 Gas of 4He(FHe, SH) “He Experiment 6.0 58 «5, 942 9.0 43 8. 957 12.0 34 11. 966 15.0 29 14, 971 18.0 26 17,974 94 Table 3 Data for the 331(a,a) 2H Experiment This table shows the center-of-mass differential elastic cross sections (SIGMA),as a function of beam energy (LAB ENERGY). The energy range is from 4 to 13 MeV. The spaces marked by a series of asterisks are points for which data were not obtained. (Page 9) LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 4.343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 5-017 5.069 5-121 5.172 5.2224 5.276 5.2328 5.379 5.2431 5.482 52585 52689 5.946 6.203 6.460 6.717 62973 72228 72484 72739 72994 95 13.063 ) 39.23 TABLE 3 {TEXT 9 + FIGURE 9 CENTER OF MASS ANGLE = SIGMA LAB ENERGY eo teak ok 8.249 ae Rok ek kek 8.504 ek a ok te ok 8.759 ak OR ak 9.012 tok aR sok 9.266 ee oe ok aK 2 ok 9.520 He he ae oe Hk kk of 9.774 Oe ie he aK aye Xe 10.027 349.000 10.280 343.000 10.534 352.000 10.787 340.000 11-040 354.000 11-293 359.000 11.343 388.000 11.393 439.000 11.444 451.000 11.494 428.000 11.545 374.000 11.595 362.000 11.2645 338.000 11.697 335.000 11.747 324.000 11.798 329.000 11.848 320.000 11.899 313.000 11.950 312.000 12.001 313.000 12.051 311.000 12.101 315.000 12-6152 349.000 12.2202 336.000 12.253 327.000 12.304 339.000 12.558 301.000 12.2810 305.000 SIGMA 291.000 303.000 252.000 276.000 266.4000 292.000 284,000 287-000 258.2000 254.000 246.000 235.000 225.000 211.000 210.000 204.000 200.000 195.000 196.2600 204.000 211.000 208.C00 206.2000 208.000 208.000 202.000 203.000 201.000 203.000 196.000 197.000 194.000 192.000 181.000 176.000 159.000 LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 44343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 5-Ol7 5.069 5.121 5.2172 5.224 5.276 5.328 5.379 5.431 50482 5.585 5.689 5.946 6.203 6.460 6-717 6.973 74228 7.484 7.739 72994 96 TABLE 8 {TEXT 9, FIGURED } CENTER OF MASS ANGLE = 46.99 SIGMA LAB ENERGY He oe Oe ae 2 a 8.249 Ae Re tee 8.504 Weak ak ok ake ak a 8.759 me he of ae AK afc aie 9.012 eae ok aK oie ok ok 9.266 ae Me ah oe a fe 9.520 Re ake a af se ok Ac 9.774 REAR Ae He Ne Ie he 10.027 333.000 10.280 338.000 10.534 340.000 10.787 325.000 11.040 329.000 11.293 346.000 11.343 334.600 11.393 3204006 L1.-444 261.000 11.494 224.000 (121.545 211-000 11.595 226.000 11.645 227.000 11.697 233.000 11.747 233.000 11.798 248.000 11.848 24024000 11.899 257.000 11.950 258.000 12.001 264.000 12.051 260.000 12.101 262.000 12.152 268.000 12.202 275.000 12.253 263.000 12.304 274.000 12.558 253.000 12.810 254.0006 13.063 SIGMA 251.2000 248.000 2422000 233.000 225.000 205.000 189.000 171.000 164.000 151.000 144.000 134.000 154.000 156.000 156.000 154.000 153.000 155.000 153.000 148.0006 132.0006 142.000 144.000 144.000 145-2000 144.000 141.000 feof ate aie a a ok 145.000 145.000 140.000 141.000 142.000 139.000 139.000 116.000 LAB ENERGY 32612 3e717 3.822 3.916 4.031 4.135 42239 4.343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 52017 5.069 5.121 52172 52224 52276 52328 52379 52431 52482 523585 5.689 54946 64203 6.460 6.717 6.973 74228 72484 14739 71.994 97 13.063 TABLE 8 {TEXT 9, FIGURE.10) CENTER OF MASS ANGLE = 54.73 SIGMA LAB ENERGY 144.000 8.249 165.000 8.504 175.000 8.759 154.000 9.012 178.000 9.4266 188.000 9.520 184.000 9.774 188.000 10.027 193.000 10.280 214.000 10.534 214.000 10.787 226.000 11.040 233.000 11.293 229.000 11.343 212.000 11.393 165.000 11.444 77.300 11.494 57.500 11.545 84.500 11.595 . 107.000 11.645 122.000 11.697 139.000 11.747 142.000 11.798 147.000 11.848 146.000 11.2899 162.000 11.950 173.000 12.001 170.000 12.051 159.000 12.101 166.000 12.152 185.000 12.202 164.000 12.253 183.000 12.304 164.000 © 12.558 175.000 12.810 157.000 SIGMA 155.000 160.000 137.000 132.000 104.000 84.100 60.300 53.300 57-100 572400 65.300 75.000 79.200 81.200 83.400 88.000 90.400 92.000 86.600 71.800 68.700 68.600 70.2500 744000 734300 76.000 74.000 74.506 75.700 78.300 792900 76.900 80.400 83.600 81.500 83.200 LAB ENERGY 3.612 3-717 3-822 3.916 4.031 42135 4.239 4.343 4.447 4.551] 4.655 4.758 42862 4.913 4.966 5.017 5.069 5.121 5.172 54276 5.328 5.379 5.431 52482 5.585 52689 54946 6.2203 6.460 6.717 62973 7.228 71.484 7.739 10994 98 TABLE 8 (TEXT 9, FIGURE 10) CENTER OF MASS ANGLE = SIGMA LAB ENERGY 230.000 8.249 229.000 8.504 2282000 8.759 227.9000 9.012 219.000 9.4266 206.000 92520 211.000 9.774 199.000 10.027 187.000 10.280 194.000 10.534 194.000 10.787 193.000 11.040 191.000 11.293 186.000 “11.343 166.000 11.393 115.000 11.444 45.900 11.494 32.400 11.545 38.300 11.595 57.500 11.645 86.100 11.697. 103.700 11.747 112.060 11.798 115.000° 11.848 120.000 .- 11.899 137.000 11.950 138.000 12.001 147.000 12.051 135.000 12.101 134.000 12.152 141.000 12.202 145.000 12.253 139.000 12.304 145.000 12.2558 138.000 12.810 132.000 13.063 SIGMA 125.000 119.000 106.006 89.800 70.500 454300 29.800 24.600 252500 33.700 41.000 50.000 56-000 58.600 59.900 64.600 67.600 70.000 59.900 48.800 43.2600 44,700 45.000 472900 50.760 51.800 53.400. 552800 554400 55.400 57.200 57.2000 572900 60.200 60.900 63.4200 LAB ENERGY 3.612 3.717 3.2822 32916 4.031 4.135 4.239 4.343 4.447 4.551 4.2655 4.758 4.862 4.913 4.966 5.017 5.069 5.121 5.172 5.224 5.276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 6203 62460 66717 6.973 7.2228 T4884 7.739 72994 (TEXT 9 + FIGURE 11) CENTER OF MASS ANGLE = SIGMA 149,000 164.000 165.000 154.000 157.000 163.000 155.600 160.000 155.000 155.000 166.000 186.2000 178.000 171.000 142.000 94.100 27-600 10.100 252200 47.800 69.4800 79.4600 90.700 101.060 100.000 110.G00 116.000 126.000 132.000 Be ea IK a a WE RH I AR AE AE 2k AER KK A 141.000 140.000 137.000 129.000 99 TABLE 3 LAB ENERGY 8.249 8.504 8.759 9.012 92266 9.520 9.774 10.027 19.280 10.534 10.787 11.040 11.293 11.343 11.393 11.444 11.494 11.545 11.595 11.645 11.697 11.747 11.798 11.848 11.899 11.950 12.001 12.051 12.101 12.152 12.202 12.253 12.304 1225568 12.810 13.063 SIGMA 120.000 107.2000 97.600 77.100 53.700 33.700 18.800 15.200 17.4600 26.200 342000 43.900 51.500 55.200 562700 60.100 63500 61.100 49.400 38.500 372400 38.800 40.300 42-500 47.2700 46.000 47.000 48.200 48.400 51.600 51.600 522300 522900 572400 57.2200 59.000 LAG ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 42343 4.447 4.551 42655 4.758 4.862 4.913 42966 5.017 5.069 5.121 5.172 5.224 5.276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 6.203 6.460 6.717 6.973 7.4228 72484 7.739 7.994 100 TABLE 3 {TEXT 9 , FICURE I1) CENTER OF MASS ANGLE = SIGMA LAB ENERGY 122.000 8.249 143.000 8.504 146.000 8.759 149.000 - 9.012 144.000 9.266 132.000 9.5270 141.000 9.774 150.000 10.027 148.000 10.280 152.000 10.534 149.000 10.787 153.000 11.040 152.000 11.293 151.000 11.343 126.000 11.393 72.900 11.444 23.500 11.494 10.600 11-545 33.000 11.595 49.200 11.645 65-300 11.697 75.900 11.747 81.2006 11.798 90.800 11.848 90.100 11.899 - 103.000 11.950 105.000 12.001 112.000 12.051 112.000 12.101 115.000 12.152 112.000 12.202 113.000 12.253 114.000 12.304 108.000 12.558 106.000 12.810 103.000 13.063 SIGMA 100.000 97.2100 80.700 61.900 44,300 27.2200 14.2200 12.600 14.600 21.700 27.300 34.000 39.900 40.500 42.800 44.500 47.000 46.4800 38-100 29.400 26.700 2842500 30.400 31.800 33.000 34.2700 354300 36.300 37.800 37.900 37.600 39.200 392300 40.900 42.300 43.800 LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 4.343 46447 4.551 4.655 4.758 4.862 4.913 5.017 5.069 5.121 5.172 5.224 54276 5.328 5.379 5.431 5.482 5.585 5.689 64203 6-460 6-717. 6.973 74228 7.484 7.739 7.994 101 TABLE 3 (TEXT 9 , FIGURE 12) CENTER OF MASS ANGLE = 70.00 SIGMA LAB ENERGY 196.000 8.249 172.000 8.504 150.000 8.759 154.000 9.012 148.000 9.266 147.000 9.520 142.000 9.774 134.000 10.027 144.000 10.280 146.000 10.534 149.000 10.787 156.000 11.040 152.0006 11.293 148.000 11.343 128.000 - 11.393 92.400 11.444 45.300 11.494 38.900 11.545 48.300 11.595 62.100 11.645 72.400 11.2697 78.400 11.747 82.200 11.798 88.4200 11.848 90.400 11.899 95.400 11.950 97.100 12.001 98.600 12.051 102.000 12.101 101.000 12.152 100.000 12.202 100.000 12.253 97.400 12.304 95.500 12.558 94.400 12.810 88.900 13.063 SIGMA 82.300 18.2800 67.500 55.200 41.300 27.700 19.500 16.100 20.600 274200 334900 39.400 °45-2200 45.100 46.900 46.700 49.500 47.900 42.4000 32.600 30.2400 -31.800 34.000 34.800 37.800 39.000 40.2000 41.2400 42.300 432600 44.200 44.700 44.700 462200 47.800 48.900 LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 4.343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 5.017 5.069 5.121 5.172 5.224 54276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 64203 6-460 6.717 6.973 7.228 72484 7.739 74994 102 TABLE 3 (TEXT 9, FIGURE 12) CENTER OF MASS ANGLE = 75.95 SIGMA LAB ENERGY He RAE 8.249 we ak ee Foe oe 8.504 3K ak ae 2 a aK R759 He KR ea 9.012 He fe a te oe ak 9.266 94.400 9.520 101.000 9.774 94.300 10.027 103.0000 10.2R80 96.600 10.534 99.400 10.787 103.000 11.040 104.000 11.293 106.000 11.343 102.600 11.393 91.900 11.444 75.800 11.494 65.300 11.545 58.700 11.595 66.400 11.645 70.200 11.697 72.000 © 11.747 72.600 11.798 76.500 11.848 78.400 11.899 82.6000 11.950 80.100 12.001 81.300 12.051 80.600 12.101 78.100 12.152 81.900 12.202 78.300 12.253 762900 12.304 71.200 12.558 70.300 12.810 71.000 13.063 SIGMA 68.106 6445060 59.200 50.500 44.600 37.2500 33.000 32.000 23.500 36.600 40.2900 41.2900 44.400 44.700 43.700 45.300 44.100 42.000 34.700 31.200 32.300 334700 35.900 37.100 38.600 392200 39.400 40.400 40.800 41.600 41.000 41.400 41.900 43.300 43.300 43.100 LAB ENERGY 3.612 3-717 3.822 3.916 4.031 4.135 4.239 42343 4.447 4.551 4.2655 4.758 4-862 4.913 4.966 5.017 52069 52121 5-172 50224 52276 52328 5.379 52431 5-482 5.585 5.689 54946 62203 6.460 6.717 6.973 7-228 72484 72739 72994 103 TABLE 3 (TEXT 9, FICURE 19) CENTER OF MASS ANGLE = 84.75 SIGMA LAB ENERGY Fe HCH Ae Re 8.249 He RR IK I 8.504 die ate ale of atc ote ak 8.759 He RRR 9.012 ae ke eke otek ok 9.266 ok she ok ok ok 9.520 55.800 9.2774 57.200 ° 10.027 461.000 10.280 60.900 10.534 60.300 10.787 64.400 11.040 69-400 11.293 77.200 11.343 87.600 11.393 112.000 11.444 124.000 11.494 119.000 11.545 95.300 11.595 81.300 11.645 77.000 11.697 72-700 11.747 71.700 11.798 67.400 11.848 65.100 11.899 64.500 11.950 61.900 12.001 62-400 12.051 61.300 12.101 60.500 12.2152 61.100 12.202 59.800 12.253 59.400 12.2304 58.900 12.558 59.400 12.2810 59.500 13.063 SIGMA 60.700 61.200 64.7006 67.000 69.7006 72.300 72-2600 70.606 64.700 64.700 60.300 54.600 51.400 50.300 48.200 45.800 42.2600 38.2500 35.900 39.900 44.900 464300 46-800 47.900 47.700 472400 47.2300 47.600 46.200 462900 46.300 46.4500 45.2000 44.400 43.500 42.000 LAB ENERGY . 3-612 3-717 32822 3-916 4.031 42135 4.239 4-343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 5.017 5.069 52121 5.172 5.224 54276 5.328 5.2379 5.431 52482 5.585 5-689 52946 6.203 6-460 6.717 6.973 72228 72484 7.739 12994 104 TABLE 3 {TEXT 9, FIGURE 13) CENTER OF MASS ANGLE = 90.00 SIGMA LAB ENERGY 71.700 8.249 68.600 8-504 63200 8.759 65.300 9.012 64.000 9.266 624400 9.520 61.600 9.774 60.400 10.027 60.000 10.280 60.400 10.534 62.800 10.787 692400 11.040 86.100 11.293 108.200 11.343 150.000 11.393 201.000 11.444 216.000 11.494 174.000 11.545 133.000 11.595 106.000 11.645 90.000 11.697 81.300 11.747 75.200 11.798 69.900 11.848 67.200 11.899 62.800 11.950 58.400 12.001 52.600 12.051 52.400 12.101 49.300 12.152 49.600 12.202 49.700 12.253 48.700 12.304 49.600 © 12.558 52.400 12.810 54.500 13.063 SIGMA 57.700 624400 67.2800 772200 89.0606 954400 98.000 94.2300 88.400 79.300 69.4600 63.600 54.2400 51.400 47.100 46.400 41.900 34.2800 34.2900 40.500 48.500 50-000 512400 49.000 50.400 49.200 47.500 48.300 47.2600 48.300 47.000 452400 44.300 42.2500 . 38.400 39.200 LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 4.239 4.343 4.447 4.551 40655 4.758 4.862 4.913 4.966 5.017 5.069 5.121 5.172 5.224 5.276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 6.203 6.460 6.717 6.973 72228 T0484 7.739 7.994 105 TABLE 3 {TEXT 9, FIGURE 14} CENTER OF MASS ANGLE = 95.63 SIGMA LAB ENERGY He ak eae a ok 8.249 He aK RC aH ak 8.504 Heke Re a a a 8.759 We aK ak Re aR 9.012 2 ae ea ae 9.266 ao ea fk a 9.520 a ak ok oe ak 9.774 a a a AE aa 10.027 eM aR a a ok 10.280 Hef ROK ek 10.534 ee a aK ak OK 10.787 a ak a Xe ak 11.040 aie ea ak ee 11.293 He ie a RR a 11.343 eR ROCK 11.393 Hea CHK a 11.444 Be RR a a aK 11.494 He fe ae He a a 11.545 Ae Re ae Keak 11.595 ae Xe ae a ak 11.645 63.400 11.697 49.900 11.747 48.100 11.798 44.600 11.848 42.800 11.899 41.400 11.950 37.300 12.061 36.400 12.051 35.700 12.2101 34.700 12.152 334000 12.202 31.600 12.253 35.600 12.304 372200 122558 40.200 12.810 42.700 13.063 SIGMA 47.800 542500 65.4300 14.700 85.500 95.4300 95.300 91.900 80.100 75.500 664400 57.000 47.900 45.500 42.400 39.300 35-400 30.200 29-200 37.2800 43.900 45.800 47.200 45.800 44.400 43.500 422600 42-100 41.100 40.600 39.900 322900 34-2400 364200 39.400 106 TABLE 3 (TEXT 9, FIGURE 14) CENTER OF MASS ANGLE = 102.00 LAA ENERGY SIGMA LAB ENERGY SIGMA 3.612 HAE He ak He As Hs 8.249 45.2900 34717 Me Re He ak He He Xe 8.504 53.900 32822 Bea Nak Rea Ae 8.759 65.2700 3.916 372900 9.2012 80.000 4.031 37.600 92266 91.700 4.135 27.600 9.520 101.000 4.239 . 32.000 9.774 102.000 42343 36.500 10.027 93.900 44447 37.000 © 10.280 83.100 4.551 © 41.900 10.534 722100 42655 49.700 10.787 59.2900 4.758 59.300 11.040 50.500 4.862 91.200 11.293 °39.600 4.913 126.060 11.343 36.900 4.966 186.000 11.393 34.2100 52017 268.000 116444 30.500 5-069 292.000 11.494 26700 5.121 218.000 11.545 21.900 5el72 144.000 11.595 22-4700 50224 93.200 11.645 322100 5.276 70.100 11.697 38.300 52328 552800 11.747 39.800 5.379 47.800 11.798 40.100 5.431 39.800 11.848 39.300 50482 38.700 © 11.899 372800 5.585 32.600 11.950 37.000 5.689 31.300 12.001 352400 52946 28.2600 12.051 332800 64203 27.900 12.101 33.800 6-460 26.500 12.152 32.2600 66717. 29.2800 12.2262 ; 31.2700 6-973 29.300 12.253 30.2900 72228 29.400 12.304 222800 74484 30.700 12.558 25.2200 72739 34.900 12.810 27.800 70994 39.600 13.063 29-800 LAB ENERGY 32612 3.717 3.822 3.916 4.031 4.135 4.239 4.343 46447 4.551 4.655 4.758 4.862 4.913 4.966 5.017 5.069 5.121 §.172 5.224 54276 5.328 5.379 5.431 5.482 5.585 ° 5.689 5.946 6.203 6-460 6-717 6.973 7.228 72484 7739 7.994 107 TABLE 3 (TEXT 9, FIGURE 15) CENTER OF SIGMA 8.300 12.100 15.700 19.200 22.800 272700 29.860 35.300 39.800 44.900 54.700 73.2100 111.000 154.000 220.000 297.2000 301.000 216.000 126.500 78.000 53-400 39.2600 31.600 26.2400 234400 20.600 18.500 17.700 18.600 19.700 20-860 21.900 24.400 272100 31.500 35.900 MASS ANGLE = 109.87 LAB ENERGY 8.2249 82504 8.759 9.012 92266. 92520 9.774 10.027 10.280 10.534 10.787 11.040 11.293 11.343 11.393 11.444 11.494 11.545 11.595 11.645 11.697 11.798 11.848 11.899 11.950 12.001 12.051 12.101 12.152 12.2202 12.253 12.304 12.558 12.810 13.063 SIGMA 43.700 520100 63.300 74.2500 64.800 90.600 88.200 79.600 65.700 55.000 44.400 34.600 24-2400 222400 19.800 16.600 13.300 12.2400 16.2500 24.2300 262900 26.4000 252100 232900 22.2900 21.700 21.700 20.2500 19.500 19.000 16.300 17.600 17.100 14.500 13.200 11.600 LAB ENERGY 3.612 3.717 3.2872 4.031 4.135 4.239 4.343 4.447 4.551 4.655 4.758 4.862 4.913 4.966 5.017 5.069 5.121 5.172 5.224 5.276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 6.203 62460 6.717 6.973 7.228 72484 7.739 7.994 108 TABLE 3 (Text 9 , FIGURE 15) STGMA 24.2900 26.800 29.700 30.906 ae OK a ak ae oe koa gk ak ak ke a 27.2800 34.800 41.500 55.900 752400 113.000 154.000 211.000 285.000 276.000 190.000 103.000 59.800 37.700 264200 19.600 16.600 14.700 13.000 12.500 12.400 14.000 15.100 17.200 18.900 21.400 22.700 27.800 33.600 CENTER OF MASS ANGLE = 116.57 LAB FNFERGY 8.249 8.504 8.759 9.012 92266 9.2520 9.774 ~ 10.027 10.280 10.534 10.787 11.040 11.293 11.343 11.393 11.444 11.494 11.545 11.595 11.645 11.697 . 11.747 11.798 11.848 11.899 11.950 12.001 12.051 12.101 12.2152 12.202 12.253 12.304 12.558 12.810 13.063 STGMA 39.2600 472100 55.2700 63-500 742400 717-400 724200 61.700 49.400 384400 29.2600 19.800 13.700 11.900 10.800 82410 6-380 5-590 9-180 14.400 16.000 16.300 14.2400 13.800 12.2900 12.100 11.400 10.900 9.2930 92650 8.980 8.750 82150 6.780 5.610 42720 LAB ENERGY 3-612 3-717 3-822 4.031 4.135 4.239 4.343 4447 4.551 4.655 4.758 4.862 4.913 4.966 5.017 5-069 5el21 5-172 52224 5.276 52328 52379 5-431 56482 5.585 52689 52946 6.203 62460 6ef17 6.973 714228 12484 72739 72994 109 TABLE 3 (TEXT 9 , FIGURE 16) CENTER OF MASS ANGLE = 125.27 SIGMA LAB ENERGY 8.500 8.2249 12.200 8.504 21.800 8.759 24.2200 9.012 25.500 9.266 25.100 9.420 29.700 9.774 31.700 10.027 33.700 10.280 38.700 10.534 45.500 10.787 60.500 11.040 93.600 11.293 129.000 11.343 176.000 11.393 227.000 11.444 207.000 11.494 129.000 11.545 67.300 11.595 382400 11.645 24.600 11.697 17.100 11.747 13.500 11.798 10.800 11.848 10.000 11.899 10.000 11.950 10.000 12.001 11.500 12.051 13.300 12.1601 15.400 12.152 18.100 12.202 20.300 12.2253 24.100 12.2304 28.100 12.558 32.2400 12.810 36.900 13.063 SIGMA 44.00C 542900 63.200 68.100 742800 76.600 69.900 58.600 45.300 334400 24.2800 18.200 11.600 10.100 8-800 7.100 5.900 5.500 7.900 12.800 14.400 14.300 13.306 12.2400 11.700 11.100 10.000 9.800 9.300 9.000 8.400 8.400 8.100 6-800 6.100 5-500 LAB ENERGY 3.612 3.717 3.822 3.916 4.031 4.135 42239 40343 40447 4.551 4.758 44862 4.913 4.966 5.017 5.069 5.121 5.172 5.224 5.276 5.328 5.379 5.431 5.482 5.585 5.689 5.946 6.203 6.460 6.717 6.973 7.228 72484 7.739 7.994 110 TABLE 3 (TEXT 9 4 FIGURE 16) MASS ANGLE = 140.00 CENTER OF SIGMA He Me eof ok ae Hooke a ee kK ote he ak ate hk ok ok $k ego aK eR Moe ot ak ak Be eek ek ae ak ak tae ok dR tok xe 27.600 30.100 33.2500 40.600 62.2900 86.700. 129.100 195.000 224.000 185.000 129.000 93.800 72.700 59.100 51.900 46.400 43.800 39.4100 36.200 33.600 322400 34.400 352400 37.600 40.600 46.000 50.500 58.000 LAB ENERGY 84249 8.504 8.759 9.012 9-266 9.520 9-774 10.027 10.280 10.534 10.787 11.040 11.293 11.2343 11.393 11.444 11.494 11.545 11.595 11.645 11.697 L1.747 11.798 11.848 11.899 11.950 12.001 12.051 12.101 12.152 12.202 12.253 12.304 12.558 12.810 13.063 SIGMA 66.500 78.300 91.600 110.000 129.2000 141.000 147.2000 140.000 130.c00 121.000 117.000 Aka fe ake ok ek 73.4600 65.2200 64.100 569.4300 54.300 482400 49.2600 60.700 69.400 -4329006 73.200 71.600 71.600 70.2800 68.600 Se eae He ok oho 67.700 67.000 67.2100 66.500 65.600 64.700 57.000 54.700 LAB ENERGY 32612 3.717 3.822 36916 4.031 4.135 44239 4.343 4.447 4.551 4.655 4.758 4.862 42913 4.966 5-017 5.069 5.121 5.172 52224 54276 52328 52379 52431. 54482 50585 52689 5946 6.203 62460 6-717 6.973 72228 T2484 T2739 72994 (TEXT QO, SIGMA ok i gk ok a eae ak ake Xe ok ak ak ks ak tO Roe aka fe Re fe ak ae ok ok otek ake a ak 2 ae teak a ak ake ak ak ROR RE ek 2224906 232400 24-700 292200 50.400 82.9C0 139.000 239.000 306.2000 272.000 199.000 149.000 121.0006 97.900 85.300 742900 68.500 59.760 55.2600 47.2200 44.2300 43.800 432400 44,300 49.600 380400 - 61.800 71.700 111 TABLE 3 FIGURE 17) CENTER OF MASS ANGLE = 146.50 LAB ENERGY 8.249 8-504 8.759 9.012 94266 94520 9.774 10.027 10.4280 10.534 10.787 11.040 11.293 11.343 11.393 il 0444 11.494 11.545 11.595 11.645 11.697 11.747 11.798 11.848 11.899 11.950 12.001 12.051 12.101 12.2152 12.2202 122253 12.304 12.2558 12.810 13.063 SIGMA 85.100 96.100 118.000 147.000 177.000 195.000 213.000 218.000 208.000 177.000 162.000 144.000 130.000 126.000 121.000 111.000 103.000 86.600 86.800 107.000 122.000 132.000 124.000 127.000 125.2000 124.060 120.000 121.000 118.000 117.000 118.000 116.000 116.000 111.0006 109.000 109.000 112 Table 4 3 3 . Data for the “H(a, a)“ H Experiment This table shows the center-of-mass differential elastic cross sections in the same manner as Table 3. The energy range is from 12.8 to 18 MeV. (Page 9) — 113 TABLE 4 (TEXT 9 , FIGURE 18 ) CENTER OF MASS ANGLE = 54.70 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 85.900 160341 54.700 13.063 87.100 16442 43.700 13.315 86.500 16.542 34.700 13.568 86-800 16.643 28.700 13.820 85.600 16.743 27.000 14.073 85.300 16.844 28.900 14.325 86.700 16.944 32.100 14.577 85.400 17.046 38.100 14.829 86.300 17.146 40.500 15.082 85.900 17.247 42.000 15.333 83.800 17.347 45.800 15.585 81.900 172448 49.700 15.837 78.960 17.548 522100 15.938 78.500 17-648 524500 ~ 16.039 73.4300 17.849 55.600 16.139 72.100 18.100 58.000 114 TABLE 4 (TEXT 9, FIGURE 18) CENTER OF MASS ANGLE = 63.40 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 54.700 16.341 18.000 13.063 55.100 16.442 11.000 13.315 56.800 16.542 6.570 13.568 57.400 16.643 6.090 13.820 50.800 16.743 8-910 14.073 57.000 16.844 13.700 14.325 56.2100 16.944 18.500 14.577 54.300 17.946 23.100 14.829 54.800 17.146 28.300 15.082 50.100 172247 31-000 15.333 52.100 17.347 332600 15.585 47.800 17.448 372300 15.837 43.400 17.548 39.400 15.938 394400 17-648 39.306 16.039 35.700 17.849 42.400 16.139 31.300 18.100 44.600 16.241 25.000 18.500 HERB RH 115 TABLE 4 (TEXT 9, FIGURE 19) CENTER OF MASS ANGLE = 77.00 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 46.400 16.341 25.2400 13.063 45.400 16.442 21.700 L3.315 46.000 162542 19.300 13.568 43.700 16.643 18.000 13.820 44.200 16.743 17.2300 14.073 | 42.800 16.844 16.900 14.325 43.4200 16.944 18.900 14.577 41.700 172046 19.700 14.829 41.500 172146 21.800 15.082 39.900 170247 232200 15.333 39.400 17.347 23.900 15.585 36.600 172448 24.700 15.837 34.2906 17.548 254800 15.938 32-600 17.648 26.200 16.039 31.000 17.849 27.100 16.139 30.700 18.100 27.200 16.241 284500 18.500 RHRRRHE TABLE 4 (TEXT 9, FIGURE 19) CENTER OF MASS ANGLE = 91.39 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 38.900 16.341 48.2800 13.063 37.800 166442 - 47.700 13.315 37.100 16.542 46.600 13.568 . 362200 16.643 42.900 13.820 34.700 16.743 37.000 14.073 33.400 162844 33.700 14.577 32.600 17.046 24.200 14.829 327.700 17.2146 21.2900 15.082 33.300 17.247 20.100 15.333 33.900 17-347 18.300 15.585 35.200 17.448 16.300 15.837 38.300 172548 16.100 15.938 38.500 17.648 14.900 16.039 42.000 17-849 13.200 16.139 44.400 18.100 12.300 16.241 46.100 18.500 HEHE RH 117 TABLE 4 {TEXT 9 +» FIGURE 20) CENTER OF MASS ANGLE = 105.00 LAB ENERGY SIGMA LAG ENERGY SIGMA 12.810 19.700 16.341 37.300 13.063 18.700 16.442 44.000 13.315 18.300 16.542 48.300 13.568 16.900 16.643 50.600 13.820 14.806 16.743 50.700 14.073 142500 16.844 47.800 14.325 13.2900 16.944 43.600 14.577 132406 17.046 39.200 14.829 12.900 17.146 34.400 15.082 13.300 17-247 33-000 15.333 14.400 172347 30.100 15.585 14.600 17.448 26.100 15.837 17.700 17.548 242400 15.938 19.900 17.648 232109 16.039 23.100 17.849 202900 16.139 27.900 18.100 17.100 16.241 31.600 18.500 HEH 118 TABLE 4 (TEXT 9, FIGURE 20) CENTER OF MASS ANGLE = 115.80 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 52860 16.341 16.300 13.063 5.070 16.442 224400 12-315 4.140 16.542 28.000 13.568 42120 16.643 ; 32.2600 13.820 32470 16.743 354600 14.073 32120 16.844 35.4500 14.325 22570 16.944 33.000 14.577 2.680 17-046 31.500 14.829 2.480 17.146 28.900 15.082 2.2290 17.247 26.100 15.333 2.680 17.347 23.300 15.585 ° 34130 17.2448 22.800 15.837 4.250 17.548 21.700 15.938 5-500 17.648 20.600 16.039 62530 17.849 17.600 16.139 9.310 18.100 16.300 119 TABLE 4 (TEXT 9, FIGURE 21) CENTER OF MASS ANGLE = 126.50 LAB ENERGY SIGMA LAB ENERGY STIGMA 12.810 8.240 16.341 19.920 13.063 12470 162442 202510 13.315 7.070 16.542 20.180 13.568 74220 16.643 18.680 13.820 7-010 16.743 172146 14.073 6.600 16.844 14.980 14.325 72050 16.944 12.2400 14.577 72.100 172046 10.120 14.829 72290 17.146 8.560 15.333 8.760 17.347 66520 15.585 9.400 L7.448 5.970 15.837 10.600 17.548 52290 15.938 12.150 17.648 4.880 16.039 13.770 17.849 4.050 16.139 14.820 18.100 4.270 16.241 172440 18.500 ee TE 120 TABLE 4 (TEXT 9 + FIGURE 21) CENTER OF MASS ANGLE = 133.60 LAB ENERGY SIGMA LAB ENERGY SIGMA 12.810 24.2000 16.341 364300 13.063 224600 16.442 34.000 13.315 234400 16.542 28.800 13.568 23.100 16.643 2241006 13.820 - 23.300 16.743 16.300 14.073 23.000 16.8464 11.900 14.325 232190 162.944 7.8060 14.577 232100 17.046 5.360 14.829 242200 170146 4.000 15.082 252000 172.247 3.530 15.333 24.700 176347 2.960 15.585 28.000 172448 22420 15.837 30.300 17-548 22370 15.938 31.400 17.648 2.040 16.039 32.4600 17.849 2.320 16.139 34.2400 18.100 2.930 16.241 34.500 18.500 He a 121 Table 5 Experimental Errors in the 3H(a, o) 2H Data This table shows the systematic error and relative error at each center-of-mass angle. For some angles the relative error has been given separately for several different energy ranges. In general, the relative error tends to decrease with energy because of the lower backgrounds at higher energies. Statistics of the data are the major variation from this trend. (Pages 9, 65) 122 Table 5 - Tabulation of Experimental Errors 354(a, o)°H (3. 6-13. 1 MeV) Systematic Relative Error Energy Range °om Error (%) (%) (MeV) 39, 23 3.2 6- 12 3.6 - 10 4- 6 10 - 13 46. 99 5 - 10 3.6 - 11 3- 5 11 - 18 54.73 8 - 15 3.6- 8 4- 8 8 -13 60, 00 6- 12 3.6- 8 4- 6 8 - 13 63. 43 6 - 10 3.6- 9 4- 6 9 -13 64.97 3- 6 3.6- 8 15-3 8 - 13 70, 00 5- 8 3.6- 8 3-5 g - 13° 15. 95 5 - 10 3.6- 6 2.5-5 6 - 8 1- 2.5 8 - 13 84.75 4- 8 3.6- 7 2- 4 7 -11 1- 2 11 - 13 90. 00 3- 6 3.6- 8 15-3 g - 13 95.63) 6-10 5 - 7 3- 6 7 - 10 15-3 10 - 13 102. 00 1- 2.5 3.6 - 13 109. 87 1- 2 3.6-13 116. 125. 140. 146. 34. 63. 77. 91. 105. 115. 126. 133. CM 57 27 00 50 70 40 00 39 00 80 50 60 Systematic Error (%) 3.2 3.2 123 Table 5 (cont. ) Relative Error Energy Range (%) (MeV) 15-2 3.6 - 13 2 -8 3.6 - 13 - 2 3.6 - 13 1 -2 3.6 - 13 3u(c,c)°H (13 - 18 Mev) 2 13 - 18 1.5 - 3.5 13 - 18 2 -3 13 - 18 1.5 - 3 13 - 18 2 -4 13 - 18 4 -8 13 - 18.3 2-4 16.3 - 18 25-4 13 - 18 2 -4 13 - 17 4 -7 17 - 18 124 Table 6 Data for the Reaction 35a, n)°Li This table shows the data obtained using the zirconium tritide target. The number of counts obtained is shown for each beam energy. These data were not used directly in our analysis. (Page 11) Beam Energy 11, 11. 11, 11. 11. 11. 11. 11. 11. 11. 11. 11. 11, 11. 11. 11. 11. 11. 11. 11. 11. 11. 11. 1i. 11. 11. 11. 11. 11. 11, 11. 11. 11. 000 040 042 052 062 071 080 090 099 108 118 120 127 137 146 155 160 165 174 183 193 200 202 212 221 230 240 250 259 269 278 280 287 Data on the Reaction °H(q, n)°Li Counts 2488 2546 2670 2696 2732 27164 2740 2706 2880 2830 2920 2920 2950 2854 2936 3250 3302 3592 3942 4490 5028 5238 5498 6252 7014 7730 8498 9356 9918 10938 11614 10854 12178 125 Table 6 Beam Energy 11. 11. 11, 11, 11. 11. 11. 11. 11. 11. 11. 11. 11, 11. -14, 11. 11, 11. 11. 11. 11. 12, 12. 12. 12. 12. 12. 12. 12. 12. 12. 12, 297 308 317 320 327 360 400 440 480 520 560 600 640 680 720 760 800 840 880 920 960 000 040 080 120 160 200 240 280 320 360 400 Counts 12546 13070 13824 12920 14342 15140 18176 22840 28394 38676 53812 82448 111590 127678 118468 92702 74016 56515 48124 42262 38102 34504 31942 30472 28632 27546 26468 25822 25026 25218 25020 24514 Table 7 Data for the Reaction 33a, n) Li This lable shows actual reaction cross sections obtained from the data of Schwarz, et al. (1965) on the inverse reaction. The cross sections and energies are shown for our system. The data above 12,5 MeV were obtained from those of Murray (1959). (Pages 26, 27) | 127 Table 7 Data on 3u(a, n)°Li Obtained from the Inverse Reaction 61 s(n, a)°H (Schwarz, 1965, Murray, 1959) Lab Energy Total Reaction Cross Section 11, 329 13. 96 11. 348 15, 53 11. 369 17, 29 11. 408 21.62 11, 448 27. 71 11, 488 36, 90 11. 527 51, 15 11. 567 73. 18 11. 609 104. 31 11. 649 137.1 11. 688 154.1 11. 728 147. 3 11. 768 127, 2 11. 807 107. 0 11. 847 90. 84 11. 889 78, 90 11. 929 70, 24 11. 968 63. 63 12, 008 58. 91 12. 048 55. 08 12. 087 52. 35 12.127 50. 13 12, 169 48. 33 12, 209 46, 90 12. 248 45, 78 12. 228 44,87 12.328 44.13 12. 367 43, 50 13.530 72.4 — 13. 630 84. 7 13. 750. 78.9 14. 009 80,5 14, 248 85.7 14, 406 97.0 14, 567 95.7 14, 746 $7.2 14, 965 106. 15, 205 105. 128 Table 7 (cont. ) Lab Energy Total Reaction Cross Section 15, 444 104, 15. 903 110. 16. 959 98. 7 18, 751 78. 2 129 Table 8 Data for the Reaction 3H(a, nt) ®Li* This table shows the total reaction cross section for the two reactions 331(a, n)°Li and Sa(a, n)) Li asa function of beam energy. ‘I'he data below the 350, ny Li threshold was due only to the SH(c, n)°Li reaction and pro- vided a normalization of the cross sections and the means to separate the effect of the two reactions. (Page 12) 130 Table & Data on 35(a, n) 915% Lab Energy Total Reaction Cross (MeV) Section (millibarns) 11. 00 4.4 11. 05 4,3 11. 10 4,4 11.15 4,5 11, 20 8.4 11.25 12.7 11, 30 15.6 11, 35 18,2 11. 40 22.2 11, 45 30,0 11. 50 40.9 11. 55 68.8 11.60 103, 4 11.65 140. 11. 70 156. 11.75 133. 11, 80 102, 11,85 78.3 11. 90 - §9.8 11. 95 60. 4 12. 00 58. 9 12. 05 53. 2 12. 10 51.4 12.15 52. 1 12, 20 51.7 12. 25 50. 1 12, 50 49.4 12. 75 53.1 13. 00 55.4 13. 25 66.5 13. 50 71.4 13.75 75.7 14. 00 84. 6 14, 25 95.7 14, 50 108. 14, 75 113, Lab Energy (MeV) 15, 15. 15, 15. 16, 16. 16, 16. 16. 16. 16. 16, 16. 16, 17, 17, 17. 17. 17, 17. 17. 17. 17. 18. 00 25 5 75 00 10 20 30 40 50 60 70 80 90 00 10 20 30 40 50 60 70 80 00 131 Table 8 (cont. ) Total Reaction Cross Section (millibarns) 116. 126, 128. 140, 141, 145. 152. 166, 199. 247, 294, 346. 365, 379, 377, 379, 376, 358. 366, —384i, 338, 341, 327, 337, 132 Table 9 Data for the *He(*He, 3136) *He Experiment This table shows the center-of-mass differential elastic cross sections (SIGMA) as a function of beam energy (LAB ENERGY). The energy range is from 4.6 - 17.9 MeV. The spaccs marked by a scrics of asterisks are points for which data were not obtained. (Page 17) LAB ENERGY 4.434 4.735 4.836 4.936 4.986 5.037 5.087 5.137 5.188 5.238 52288 5.339 52389 5.439 5-691 52942 62194 60445 62696 62948 72199 72450 7-702 72953 8-204 82455 8.706 8.957 92208 133 TABLE 9 {TEXT 17, FIGURE 34) ' CENTER OF MASS ANGLE = 39.420 SIGMA LAB ENERGY 542.600 94459 542.000 9.710 543.0CC6 9.961 534.000 10.211 538.000 10.462 549.000 10.713 574.000 10.964 598.000 11.214 654.006 11.715 6422000 11.966 606.000 12.217 575.2000 126467 559.000 12.717 492.000 12.968 467.600 13.218 454.00 134469 437.000. 13.719 427.000 13.970 417.000 142220 401.060 14.470 397.000 14.721 394.2000 14.872 4032000 15.375 413.060 15.878 397260600 162380 394.0600 16.883 373.2000 17.386 349.000 17-888 STGMA 325.2000 308.000 293.000 285.000 268.000 258.000 252.000 240.000 229.000 2292000 220.000 217.000 210.000 2032000 206.000 194.000 180.000 180.000 180.000 1692000 158.000 153.600 152.800 141.000 131.600 118.400 114.700 109.300 103-200 LAB ENERGY 42634 4.735 4.836 42936 4.2986 5.037 5.087 52137 52188 5-238 5.288 5.339 5.389 50439 52691 5942 60194 62445 62696 6.948 7.199 7.450 7.702 7.953 8.204 8.2455 8.706 8.957 92208 134 TABLE 9 {TEXT 17, FIGURE 34) SIGMA 350.000 349.000 345.4000 339.4000 333.4000 333.000 305.000 292.000 258.2000 227.000 218.000 227.000 244.2000 251.2000 277.2000 278.000 28.000 272.2006 266.000 2608000 255.000 246.000 240.000 226.000 216.000 195.00C 180.006 164.000 154.2000 CENTER GF MASS ANGLE = LAB ENERGY 92459 9.710 9.961 10.211 10.2462 10.713 10.964 11.214 11.465 11.715 11.966 12.217 12.467 12.717 12.968 13.218 130469 13.719 13.970 L4e220 14-470 14.721 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGHA 148.000 145.000 144.000 149.000 143.000 139.000 137.000 134.2000 135.000 133.000 132.000 1272000 121.000 109.000 103.000 94.000 90.000 91.000 92.000 892000 90.000 86.2100 sok tek ea dete fe ote ako IKK alee ae sie ae Se ea ak seg eke sete ak a ak xe ste she vk ah 2h ate LAB ENERGY 42634 4.735 4.2836 4.936 4.986 5.037 5.2087 5-137 5.188 5.238 5.288 5.339 5.389 5.2439 5.691 52942 6.194 64445 6-696 64948 72199 72450 72-702 71.6953 8-204 8.455 8.706 8.957 9.208 135 TABLE 9 {TEXT 1%. FIGURE 35) CENTER OF MASS ANGLE = 54.70 STIGMA | LAB ENERGY 2452400 92459 2452160 9.710 244.200 9.961 2322660 1oO.211 188.600 10.462 214.006 10.713 187.860 10.96% 154.000 11.2214 97.800 112465 58.100 11.715 58.400 11.2966 82.200 12.217 105.406 124467 130.2100 12-717 175.800 12.968 180.006 13.218 189.500 13.469 180.306 134719 182.800 13.970 175.900 14.220 165.700 14.470 158.460 14.721 126.300 15.375 164.500 15.878 . 80.600 ‘16.380 67.2100 16.883 58.400 17.386 62.906 17.888 SIGMA 70.100 752000 78.400 78.000 61.600 85.100 88.700 88.300 86.2600 85.800 81.2800 75.800 69.2500 61.2100 52-000 50.800 52.600 55.800 58.000 58.600 61.000 60.600 58.300 58.900 53.300 49.2400 47.600 44.2900 41.2900 LAB ENERGY 4.735 4.836 4.2936 4.986 52037 5.087 5.137 5.188 52238 5.288 52339 5.389 50439 5.691 5.942 60194 66445 6.696 626948 7-199 76450 7-702 7-953 8.204 B.455 8.1706 8.957 9.208 136 TABLE 9 (TEXT 17, FIGURE 35) CENTER OF MASS ANGLE = 63.40 SIGMA LAB ENERGY 159.000 9.459 156.100 9.710 151.860 9.961 141.200 10.211 135.700 102462 123.406 10.713 100.300 10.964 68.800 11.214 Be AK OK fe ie Ae aK 11.465 4.200 11.715 10.900 11-966 33.900 12.217 57.200 12.467 73.600 12.717 107.300 12.968 120.400 13-218 1212300 13.4609 118.200 13.719 115.400 13.970 105.900 142226 104.000 146470 90.400 14.721 75.700 14.872 58.900 15.375 37-960 15.878 20.2700 16.380 12.660 16.883 14.600 17.386 23.400 17.888 SIGMA 322700 39.2300 42 2600 48.600 51.000 55.800 58.200 562500 562100 54.100 51.700 44.2100 38.2300 31.600 39.500 30.400 342900 42.200 442900 45.800 48.100 46.800 47.200 46.300. 43.500 42.000 41.300 38.600 LAB ENERGY 4.634 4.735 42836 44936 4.2986 5.037 5.087 5.137 5188 5.2238 52288 54339 5.389 50439 5.691 6.194 64445 64696 62948 7.199 716450 7-702 7.953 8.204 8.455 8.957 9.208 137 TABLE {TEXT 17, CENTER OF MASS SIGRA 112.206 111.200 103.100 98.3G0 90.400 81.400 70.500 51.2100 292800 202400 32.006 46.1006 60.700 70.2300 90.000 93.100 88.5800 88.800 85.2500 (%e300 71.200 65.100 542400 392300 266300 © 16.900 12460 18.000 - 252000 9 FIGURE 36) ANGLE = 70.10 LAB ENERGY 9.459 9.2710 9.961 190.211 10.462 10.713 10.964 11.214 11 0465 11.715 11.966 12.217 126467 12/17 12.4968 13.218 136.469 13.719 13.970 142220 1404/0 14.721. 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGMA 31.4700 34-800 38.700 42.2600 46.500 47.2900 49.2100 47.900 46.2000 45.100 41.2600 34.800 30.200 Z2te raele) 244700 25.2600 30.300 32.2100 34.900 362300 41.300 40.600 394400 40.100 39.600 39.2200 37.400 37.2400 3262300 LAB ENERGY 4.2634 4.2735 4.836 42936 ' 4.986 52037 5.087 5.137 5.188 5.2238 5.288 5.339 5.389 52439 5.691 52942 62194 6.445 6.696 62944 72199 72450 T2702 12953 82204 8.455 8.706 8.957 92208 138 TABLE 9 {TEXT 17, FIGURE 36) CENTER OF SIGMA 80.600 772100 73.800 71.2300 68.500 66.400 624200 56.000 572200 60.100 68.500 752100 78.800 79.600 79.400 762600 71.28CC 66.300 65.300 6352100 6024G0 54.5006 4629700 41.960 37.2900 334200 334400 35.260 40.000 MASS ANGLE = 77.00 LAB ENERGY 92459 9.710 9.961 10.211 10.462 10.713 10.954 11.214 11.465 11.715 11.966 i2.-217 126467 12.717 12.968 ‘13.218 130469 13.719 13.2970 14.2220 146470 14.721. 14.872 15.375 15.878 16.380 16.883 17.386 17-888 SIGMA 40.2400 42.700 44.2100 43.300 43.300 42.500 39.500 38.800 362400 34.300 294400 26.900 24.300 232400 252600 262100 28.200 302100 292900 28.2700 28.000 28.700 28.600 272400 272600 26.600 262400 LAB ENERGY 4.634 4.735 4.2836 4.936 4.986 5.037 5.087 5.137 5.188 5-238 5.288 5.2339 5.389 54439 §.691 5.942 6-194 62445 . 66696 . 64948 7.199 7-702 7.953 8.204 8.455 8.706 8.957 92208 139 TABLE 9 (TEXT 17, FIGURE 37) MASS ANGLE = CENTER GF SIGMA 66.400 65.460 61.900 6?.060 60.700 62.700 62-160 63.000 772500 65.2460 89.900 92.300 866400 82.500 75.000 71.800 67.500 65.800 62.000 59.2400 564300 54.060 47.2800 462600 47.6C0 460206 47.160 47.100 48-2400 80.00 LAB ENERGY 9.459 9.710 9.961 10.211 10.462 10.713 10.964 11.214 11.465 11.715 11.966 12.217 12.467 12.717 12.968 13.218 134469 13.719 13.970 144220 14.2470 14.2721 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGMA 45.100 44.200 45.100 44.800 452200 43.2000 44.500 40.900 37.500 37.800 35.2300 33.500 31.900 262900 23.2700 we oie ate he oh he he SRE Mee AE Re aR Hee A ok He He Ne Re ake afc ae aie NE KK See Ae ae oe a ae Sk ea a ae eke Wek dete ak Xe He he oe ae He eof He 3K EK Ak aie fs hc ahs he ok a ak os of ale as afs ake erie Ak Hk oie He a sk he Xe HK a eK ste eos ese He Re LAB ENERGY 4.4634 4.4735 4.836 4.936 4.986 5.037 5.087 52137 5.188 5.238 5.288 5.339 5.389 5.4439 5.691 52942 60194 64445 6.696 62948 7.199 72450 7.702 7.953 8.455 8.706 8.957 9.2208 140 TABLE 9 (TEXT 17, FIGURE 37) CENTER OF MASS ANGLE = 685.26 SIGMA LAB ENERGY 55.160 94459 51.900 9.710 55.400 9.961 57.5060 10.211 56.600 10.462 646400 10.713 70.400 10.964 84.100 11.214 105.000 1106465 118.80C 11.715 114.400 11.2966 109.400 12.217 96.500 120467 88.900 12.717 70.400 12.968 61.4800 13-218 568«e300 132469 56.100 13.719 52.600 13.970 5920400 14e220 51.000 142470 492900 14.721 $2,700 14.872 55.160 15.375 57.500 15.878 59.906 16.380 61.100 16.883 59.700 17.386 522900 17.882 SIGMA 48.600 46.700 462600 46.300 44,200 402800 38.300 36,400 36.2900 35.700 33.4400 30.900 30.2000 272800 21.500 202000 18.400 16.900 15-2800 16.300 17.2100 ME Re Ae ae ae ae Ke SIE 2g OK ce Bee oe ok ak eH ok ls ok de Hele 3 He ac He steals he Ee FE ake he he ake oh ok ak ok LAB ENERGY 42634 4.735 4.836 4.936 4.986 5.037 5.087 ° 52137 5.188 5.22738 5.288 52339 52389 52439 5.691 56942 64194 62445 62696 62948 72199 T2450 7.702 72953 8.204 8.455 8.706 8.957 9.208 141 TABLE (TEXT 175 CENTER OF MASS SIGMA 49.2400 46.2000 52.2600 88.600 65.906 74.790 87.100 116.2G00 141.900 151.606 142.2300 118.200 101.160 90.200 59,600 53.906 47.800 46.800 43.700 47.2300 462100 50.800 542306 62.2600 68.500 (04400 4244600 67.2500 612400 9 FIGURE 38) ANGLE = 90.006 LAB ENERGY 9.459 9.710 9.96) LN.?71)4 10.462 10.713 10.964 11.214 11.2465 11.715 11.966 12.217 12.467 12.717 12.968 13.218 134469 13.719 13.970 14.220 14.470 14.721 14.872 15.375 15.878 16.380 16.2883 17.2386 17.888 SIGMA 53.500 47.B00 43.500 40.2000 392400 36.2700 34.2600 342000 32.2006 30.600 30.700 302600 29 400 28.300 24.2900 20.900 19.900 15.000 13.700 LieZO0 11.000 10.500 - 90480 8.450 72500 62650 62260 54900 54740 LAB ENERGY 4.634 4.735 4.2836 4.936 4.986 5.037 5.087 5.2137 5.2188 52238 5.2288 5.339 5.389 520439 5.691 5.942 6.194 6.445 62696 6.2948 72199 72450 T2702 7.953 B.~204 8.455 8.706 8.957 92208 142 TABLE 9 {TEXT 17, FIGURE 38) CENTER OF SIGMA 45.400 49.2400 54.600 69.200 832600 101.569 1652300 196.360 194.500 159.100 120.200 95.2100 7842006 40.200 35.060 322600 32.2000 33.600 34.3600 38.500 41.800 48.100 59.700 72.2200 76.2606 74.4900 70.600 59.000 MASS ANGLE = 968.40 LAB ENERGY 94459 9af10- 9,961 10.211 102462 10.713 10.964 116214 112465 11.715 11.966 12.217 12.4467 12.717 12-968 13.218 13.469 13.719 13.970 14.220 14.470 14.721 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGMA 462900 41.800 36.4400 34.400 312100 27.2300 24.100 24100 222900 222100 21.700 21.800 23.2200 21.900 212200 19.500 16.100 13.300 11.000 10.100 8.800 6.800 62980 52520 3.970 32780 3.2160 22650 22190 LAB ENERGY 4.634 4.735 4.836 4.2936 4.986 5.037 5.087 5.137 5.188 54238 5.288 5.339 5.389 52439 5.691 52942 62194 6.445 62696 62948 7.199 72450 72702 7.953 8.204 82455 8.706 8.957 9.208 143 TARLE (TEXT 17, CENTER CF MASS SIGMA 49.200 54.2160 644100 87.400 102.200 123.100 156.300 196.200 ae he ake ae de aie 3K 204.700 15621C0 105.000 74.000 552/00 23.4660 17-300 172800 20.660 232600 232900 28.400 366300 420300 50.4660 60.500 644900 66.4700 56.2200 45.700 9 FIGURE 39) ANGLE = 106.40 LA8 ENERGY 9.459 9.710 9.961 10.211 10.462 10.713 10.96% 11.465 11.715 11.966 12.217 12.467 12.717 12.968 13.218 136469 13.719 13.970 140220 14.470 14.721 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGMA 344 780 28.900 26.000 222200 1/2600 16.306 14.700 14.000 12.500 10.700 11.2000 12.200 13.600 l+.e600 15.2800 16.900 15.500 14.600 12.500 10.700 10.200 8.600 Ba 140 8.000 7-030 6.2810 62500 5.920 5.460 LAB ENERGY 4.634 4.735 4.836 4.936 4.2986 52037 5-087 5-137 5.188 5.238 5.288 5.339 52389 52439 5-691 50942 6.194 64.445 6-696 6-948 72199 72450 7.702 72953 8.204 8.455 8.706 8.957 9.208 144 TARLF 9 (TEXT 17, FIGURE 39) CENTER (iF SIGMA 51.000 58.200 > 71.900 92.400 100.800 130.500 160.700 186.700 203.4800 179.4100 125.500 76.360 44.000 29.2400 t«700 8.300 12.000 13.400 17.300 19.800 24.100 28.100 32.2600 39.100 45.000 48.000 46.800 35.2200 26.600 MASS ANGLE = 116.80 LAB ENERGY 94459 9.710 9.961 10.211 10.462 10.713 11.214 11.465 11.715 11.966 12.217 12.467 12.717 12.968 13.218 13.469 13.719 13.970 142220 144470 14.721 14.872 15.375 15.878 16.380 16.883 17.386 17.888 SIGMA 17.200 13.500 11.200 8.700 72000 5.600 42500 3.600 32200 22800 2.300 22600 3.200 42900 64900 72600 8.300 9.000 9.4800 9.800 9.300 9.2500 8.21/80 8.840 8.630 8.510 8.230 9.2050 8.3406 LAB ENERGY 4.634 4.2735 44836 4.936 4.986 5.037 5.087 5-137 5.188 54238 52288 5-339 5.389 52439 5-691 52942 606194 64445 62696 6.948 72199 74450 7.702 7.953 8.204 6.455 8.706 8.957 92208 145 TABLE 9 {TEXT 17, FIGURE 40) CENTER GF MASS ANGLE = 125.20 SIGMA LAB ENERGY 46.2800 92459 52.566 9.710 62.2400 9.961 19.2400 10.211 92.400 "10.462 111.400 10.713 129.900 10.2964 154.4060 11.214 165.200 11.465 145.2800 11.715 98.000 11.966 61.300 12.217 39.900 126467 262000 120717 11.2300 12.968 13.060 13.218 16.600 134469 202600 13.719 20.900 13.970 26.800 14.220 30.260 14.470 35.400 14.721 39.500 14.2872 44.500 15.375 50.600 152878 52.000 16.380 47.100 16.883 36.800 17.386 27.300 17.888 SIGMA 18.900 14.500 12.600 10.400 8.206 8.000 72700 72200 62900 7.2900 2400 6.500 6.2400 5-300 4.200 4200 4.2100 3.800 34900 4-900 5-300 4400 Be Re He He 3K Ae fereok ak doko sede ake kook se sks ok the ak ie 3c Be aR oie OK 3K aK ac Me ae Me He a A IK sek ea ak ak LAB ENERGY 44634 4.735 4.4836 4.2936 4.986 5.037 5.087 5.2137 5.188 5.238 5.288 52339 5.389 5.439 5.691 5.2942 6.194 6.445 6.696 6.2948 72199 726450 7.702 72953 8.204 8.455 8.706 8.957 9.208 146 TABLE (TEXT 17> CENTER OF MASS SIGMA 36.100 38.700 44.860 55.000 64.300 754800 94.100 121.606 143.000 147.4006 122.100 98.000 74. 100 662200 43.760 37.500 35.2400 362500 41.100 45.2100 462700 56.800 65.4500 754800 882206 89.200 862900 79.200 68.400 9 FIGURE 40 } ANGLE = 125.00 LAB ENERGY 9.459 9.716 9.961 10.211 10.462 10.713 10.964 11.214 11.465 11.715 11.966 12.217 124%67 12.717 12.968 13.218 13.469 13.719 13.970 14.220 14.470 14.721 14.872 15.375 15.878 16.380 16.883 17.2386 17.888 STGMA 53.200 472900 434600 39.900 37.2000 34.600 33.500 32.600 322300 30.700 31.300 29.2900 29.500 24.700 21.000 16.100 14.000 10.500 10.700 10.800 . 11.000 8.900 82940 8.100 62630 64050 6.080 52670 52850 147 Table 10 Data for the 4ye(FHe, p)° La and 4He(8He, p2)*Lit Reactions Table 10A shows the laboratory differential reaction cross sections for the reactions 4He(FHe, p)°Li (SIGMAO ) and 4He(*He, pt)’ 1a (SIGMA1) as a function of beam energy ~ (LAB ENERGY) for each laboratory angle investigated. A row of asterisks indicates that the data for that point were not obtained even though the energy was above the required thresh- old. Table 10B and 10C show angular distributions of the ground state and first excited state protons. The cross . sections are listed as a function of the center-of-mass angle. (Pages 18, 19) , . Oe 148 TABLE 10° LABURATGRY ANGLE = 15.00 LAB ENERGY SIGMAQ SIGMA1 7.919 5.2790 8.171 8.740 8.422 9.570 8.523 10.400 8.624 10.700 8.725 10.800 8.825 , 12.700 6.926 12.300 9.027 146290 9.127 15.900 9.228 17.700 9.328 20.900 9.429 2346500 9.530 272400 9.630 29.4100 9.731 30.400 9.832 28./00 9.932 272900 10.033 252600 10.133 226006 19.2340 21.4200 10.335 17.500 10.435 - 17.800 10.666 15.900 106.938 164100 HE Ae aC ae 3K 3K 115.189 12.4100 25 He ae He ie aK xc 114.441 15.700 eI 2 Ak ae ak 3c 11.692 12.300 9.670 11.943 © 11.400 13.800 12.194 10.100 204100 124445 94540 252900 12.2696 7.610 31.900 12.946 , 6.770 36,700 13.197 64440 35.4500 12.448 5.4740 32.2500 13.698 5.200 36.300 13.949 4.390 45.900 149 TABLE 10 LABORATGRY ANGLE = 20.00 LAB ENERGY SIGMAG SIGMAL 8 6422 10.200 9.731 29.206 10.435 16.300 10.938 146.500 Bek a a ak 11.441 16.000 62150 12.354 12.910 25.540 12.445 11.500 29.900 13.111 11.310 42.060 13.197 8.740 43.900 13.866 12.340 33.380 14.872 11.310 282170 150 TABLE 10 LABORATORY ANGLE = 22.50 LAB ENERGY SIGMAQ SIGMAL 7.805 5.570 8.311 8.9706 8.817 12.410 9.323 19.460 9.829 28.170 10.335 19.070 10.840 16.920 11.345 15.550 ae kee ake ake ak oe 11.850 Ld.U50 11.960 12.102 15.050 . 23.180 12.354 14.490 29.5680 12.607 13.2940 ; 412660 12.859 13.890 604120 13.111 13.290 49.400 13.363 13.850 65.2890 13.614 13.700 52.170 13.866 13.270 36.330— 14.118 13.580 312970 14.369 13.240 — 28.670 14.872 12.680 34.340 15.375 12.480 33.650 15.878 - . 12.060 33.020 16.380 12.110 29.840 16.883 124410 29.4640 17.386 11.230 32.260 17.888 10.140 30.280 LAB ENERGY 7.919 8.171 8.422 8.523 8-624 8.725 8.825 8.926 9.027 9.127 92228 9.323 9.429 $2530 9.630 G.731 9.832 $932 10.033 10.133 10.234 10.335 10.435 10.686 10.938 Al.189 11.441 11.692 11.943 12.19% 12.445 12.696 12.946 13.197 13.448 13.698 151 TABLE 10 LABORATORY ANGLE STGMAO 1.030 72510 9.180 9-740 9.980 10.600 11.500 12.300 13.100 14.100 16.500 18.500 21.2900 25.200 27.100 27.4300 27.2200 254200 234100 21.700 20.700 18.700 17.700 17.100 16.200 15.2C0 16.500 15.000 14.000 13.900 13.200 12.600 12.100 10.906 10.300 9.010. 25.00 SIGMAL 30.2700 41.300 462200 56.600 44.100 462100 LAB ENERGY 12.354 13-111. 13.866 14.872 152 TABLE 10 LABORATORY ANGLE = 27.00 SIGMAQ 14.370 14-470 ‘ 13.870 13.510 SIGMAL 27.100 45.890 37-340 322920 LAB ENERGY 8.422 9.731 10.435 10.938 11.441 124445 13.197 153 TABLE 10 LABORATORY ANGLE STGMAO 8.420 2424200 17.700 15.900 17.000 14.900 12.800 = 30.00 SIGMAL He MO AC 5.560 33.2400 56.300 154 TABLE 10 LABORATORY ANGLE = 31.460 LAB ENERGY SIGMAO SIGMAL 7.805 5.070 8.311 8.620 2.817 10.910 9.323 16.240 9.829 232430 10.335 17.730 10.840 15.480 11.345 ; 142950 eae ak x ale ake Xe 11.850 14.850 12.800 12.102 15.770 23.880 12.354 15.860 33.180 12.607 16.530 45.430 12.859 14.950 50.870 23e111 16.680 52.100 13.363 15.130 42.4370 13.614 ; 15.680 46.840 14-866 14.450 42.670 14.118 — 14.570 40.230 14.369 13.990 34.2710 14.872 14.G00 so 32.020 15.375 13.2310 28.2120 15.878 12.440 25.2820 A6.380 13.040 244560 16.883 12.230 232790 17.386 ; 10.740 — 2221750 17.888 9.890 18.130 TABLE 10 LABORATORY ANGLE = 35.00 LAB ENERGY SIGMAQ SIGMA] 8.422 6.850 92/31 222000 10.435 16.C00 10.938 14.600 aie Ae Xe Hea Mee L1.441 16.C00 He Me He He Re He Ac 12.445 16.300 34.400 A319T7 | 15.100 56.700 156 TABLe 10 LABORATORY ANGLE = 36.80 LAB ENERGY SIGMAO ° SIGMA1 7.805 3.4640 8.817 10.070 9.323 14.820 9.829 19.930 10.335 15.870 10.840 14.540 11.345 15.590 We whe kee ae ake 1r.850 16.070 11.610 12.102 * 164460 246490 12.2354 16.520 28.910 12.607 16.550 46.670 12.859 16.590 50.950 43.111 15.530 51-180 13.363 16.090 55.320 13.614 © 15.910 53.320 13.866 15.020 48-470 14.118 15.400 42.050 14.369 14.280 37.630 14.872 14.050 OS 29.680 15.375 13.420 264320 15.878 13.260 23.210 16.380 11.780 20.930 16.883 9-860 — 20.040 17.386 10.090 18.010 17.888 . Be390 17.480 LAB ENERGY 8.422 9.731 10.435 10.938 11.441 12.445 13.197 157 TABLE 10 LABORATORY ANGLE SIGMAQ 1.980 19.600 14.400 14.700 16.000 16.800 15.900 40.00 SIGMAL RoE RO ak Mee eee Ss 2. 25.4300 59.300 158 TABLE 10 LABORATORY ANGLE = 40.80 LAB ENERGY SIGMAO SIGMAL 7.805 He i a OK 8.311 6.850 8.817 9.700 9.323 13.650 9.829 18-710 10.335 14.000 10.840 13.870 11.345 14.860 se Me oe Be le ale He 11.850 15.290 13.450 12.102 16.400 21.100 12.354 16-690 26.860 12.607 17.430 41.380 12.859 17.050 51.200 12.111 15.570 55.110 13.363 16.360 53.790 13-614 15.040 52.500 13.866 14.850 48.830 14.118 13.630 40.930 14.369 13.620 38750 14.872 12.950 oo 31.580 15.375 12.960 25.4480 15.878 12.470 23.250 16.380 10.970 20.870 16.883 10.880 19.400 17.386 9.700 17-130 17.888 8.180. 15.840 159 TABLE 10 LABORATORY ANGLE = 45.00 LAB ENERGY SIGMAQ SIGMAL 7.805 BIC HAC A 8e311 : ie Xe aK Ae a aK ok 8.523 0.540 8.624 1.730 8.725 3.920 8.817 8.980 8.825 6480 8.926 72930 9.027 9.390 9.127 10.100 9.222% 11.2600 9.323 | 13.000 9.328 13.300 92429 142300 9.530 16.300 9.630 18.300 9-731 17.000 9.829 15.690 9.832 16.300 9.932 15.300 10.033 15.100 10.133 14.200 10.234 14.100 10.335 132650 10.435 - 12.600 10.686 13.700 10.840 : 14.400 . 10.938 14.C00 ROI Ra A a ir.189 14.300 Ae ae ak ak ak a 160 TABLE 10 LABORATORY ANGLE = 45.00 LAB ENERGY SIGMAQ SIGMAL 11.345 14.080 Hem fe ak a L1l.441 15.000 Aa OS 2B ds ois als is 11.692 14.300 (REM ae fe a de 11.850 14.980 — 7.570 11.943. 14-300 14.100 12.102 14.380 16.390 12.194 15.600 17.300 126379% 154100 23.2890 12.445 16.6000 30.200 12.607 16.570 39.830 12.2696 15.600 43.200 12.859 16.990 51.110 12.946 15.000 52.400 13.111 15.270 546.650 13.197 14.600 49.900 13.363 15.360 54.880 13.443: 14.100 54.200 13.614 14.090 48.390 13.698 13.900 50.300 13.866 - 14.070 oe 46.940 14.118 12.730 42.540 14.369 12.130 * 36.870 14.872 11.970 30.410 15.375 ~ 11.390 " 25.960 15.878 11.130 21.330 16.380 10.680 21.040 16.883 9.160 17.520 17.386 8.110 16.260 17.888 7.780 14.570 161 “TABLE 10 LABORATORY ANGLE = 50.00 LAB ENERGY SIGMAQ SIGMA1 9-731 14.300 10.435 11.900 10.938 12.100 MARR Rea ae ae L1L.441 14.500 Me eRe ak a he 12.354 14.890 20.140 12.445 14.700 29.900 13.111 13.650 51.000 13.197 14.200 50.700 13.866 11.940 44.220 14.872 10.720 28.760 LAB ENERGY 9-630 9.731 10.435 10.938 11.441 12.354 12.445 13.111 13.197 14.872 162 TABLE 10 LABORATORY ANGLE = 455.00 SIGMAO 12.600 122/00 11.000 11.700 13.600 Be ae a ak ae ae 13.100 12.2160 11.900 8.930 SIGMA1 He He He Ae Ae ade ote ae ofe ake afe aie Heke do 9k 23.4600 50.210 47.100 272760 LAB ENERGY 9.630 9.731 10.435 10.938 11.441 12.354 12.445 13.111 13.197 14.872 163 TABLE 10 LABORATORY ANGLE STGMAO Bok Re gokok ak 10.100 9.570 10.400 11.600 ake He ae eke ok 11.400 10.630 10.900 7.740 SIGMAL KOK Rta Be Be ie Hea eas fe teak a 18.900 59.400 39.800 26-060 164 TABLE 10 LABORATORY ANGLE = 65.00 LAB ENERGY. SIGMAO SIGMA1 9.630 1.440 g9.73k 22390 9.832 4.430 9.932 64150 10.033 7-510 10.133 8.700 10.234 8.030 10.335 8.060 10.686 9.330 10.938 9.420 | Me BC Re Re ae ae 1r.t89 74.810 ’ het a ate eae 11.441 . 10.900 Be Bee He a A He A 11.692 9.290 We 3 a a aK 2 11.943 9.770 BE IE HE HE RENE HE 12.194 10.200 ak Feo oe ak oe 12.354 Mok ae oe ak oie aK ; ae Re ake fe ak ake ok 12.445 10.600 Be Pk Ae a ae ae Os 12.696 11.060 20.200 12.946 10.200 an 27.000 13.111 8.590 49.760 13.197 9.370 324400 13.448 94160 34.800 13.698 8.670 32.2900 14.872 44370 18.350 LAB ENERGY 10.435 10.938 11.441 12.445 13.197 165 TABLE 10 LABORATORY ANGLE = 70.00 SIGMAO 7.700 ok KOK 8.440 9.020 8.530 SIGMA Fe aK AR He ae A Sedo ROR IK ek ak feoke ft ak 25.800 LAB ENERGY 10.435 10.686 10.938 11.441 122445 13.197 166 TABLE 10 LABORATORY ANGLE = 75.00 SIGMAO 7.180 6.690 Sok a sok 7.200 62910 7.350 SIGMAL ek AO aK ak He Ok ea Rea Xe ate ste te ate Se ae ote HORI eae ak 167 TABLE 10 LABORATORY ANGLE = 80.00 LAB ENERGY SIGMAO SIGMAL 10.435 5.140 10.938 Bob Ok a Atk Rete ae ee 2 11.441 6.660 © Reg ae ake ak ake 12.445 6.500 © We He fe ee as ak 13.197 6.860 Re fe he he ofc a ke LAB ENERGY 10.234 10.335 10.435 AI.189 11.441 11.692 11.943 12.194 12.445 12.696 122946 13.197 13.448 13.698 168 TABLE 10 LABORATORY ANGLE SIGMAO 4.890 5.610 5.190 5.680 6.350 5.630 5.290 661/090 6.320 5.860 6-100 5.560 5.750 4.390 85.00 SIGMA] ee ae Be ae ae ak Neate Xe took ak ak Kee Xe ake a a ke eC aC He aK aK ae DKK NEE CK OK We af CRE ea aK ete ae ote ake a a Op FE AS As 2s He aK Ae Rok fete ak 9.620 11.300 169 TABLE 10 LABORATORY ANGLE = -90.00 LAB ENERGY SI.GMAO SIGMAL 12.445 5.160 Mw He a a ak 12.696 5 0440 Be Re ACT a a 13.197 4.690 © Ree ca ak as 170 TABLE 108 GROUND STATE PROTONS LAB ENERGY = 10.938 CENTER OF MASS CENTER OF MASS ANGLE GROSS SECTION 23.9 6.50 31.8 , 6.82 39.6 6.89 4703 7.02 5540 6.73 62.5 | 7.13 6909 7219 17.2 6.64 8402 6.92 91lel . 6268 97.7 6.63 171 TABLE 108 GROUND STATE PROTONS LAB ENERGY = 12.445 CENTER OF MASS CENTER OF MASS ANGLE CROSS SECTION 23-0 4.13 30.6 5.09 38.2 6.01 45ef FeOl 53.0 7299 60.3 . 8.63 67.4 9.00 1404 Be46 81.2 Be 07 8769 7o57 94.3 7264 100.5 | 7.10 10664 5298 112.1 . 6022 117.5 | be 72 122.7 6.13 172 TABLE 108 GROUND STATE PROTONS LAB ENERGY = 13.197 CENTER OF MASS CENTER OF MASS ANGLE CROSS SECTION 2207 2236 3023 3-96 37.7 5-08 45el 6.16 520% _ 1256 5926 8.33 6626 8.06 1365 8.31 80.2 7244 6606 Te32 9342 6.81 99.3 6-74 10542 6436 116.2 5-86 121.4 5049 173 TABLE 10C FIRST EXCITED STATE PROTONS LAB ENERGY = 12.445 CENTER OF MASS CENTER OF MASS ANGLE "CROSS SECTION 30.0 6269 40.0 7.294 501 8.45 60.1 9262 70.1 10.50 80.1 8.24 90.1 10.70 100.2 11.60 110.2 10.30 120.2 , 9243 174 TABLE 10C FIRST EXCITED STATE PROTONS LAB ENERGY = 13.197 CENTER OF MASS. CENTER OF MASS ANGLE CROSS SECTION 27.7 10.80 36.9 13.70 46.0 18.20 5541 19.00 64.1 20.10 73.0 22-40 81.9 20.40 90.5 . 22.260 99.0 23-30 107.3 22220 115.2 20.80 122.9 - 19.50 175 TABLE 10C FIRST EXCITED STATE PROTONS LAB ENERGY = 14.872 CENTER OF MASS. CENTER OF MASS ANGLE CROSS SECTION 3326 10.47 3707 12.95 4502 12.81 52.7 12-397 6lel 12.67 67.5 14.14 7420 14.39 81.7 14.67 89.2 15642 96-5 15.94 103.4 12-49 176 Table 11 Experimental Errors This table shows the experimental errors associ- ated with the 3 He +o scattering. The first column shows the laboratory or center-of-mass angle in question. The second column gives the systematic error for the angle and the third column gives the relative errors. The reactions 4. Sqr, Srz,\4 4... /3 6.. 4... Sez, 187 sx He("He, "He)“He, “He("He, p) Li and “He(* He, p ) Li* are considered. (Pages 17, 18, 19). CM 39, 2 47.0 54.7 63.4 70, 1 77,0 80. 0 85. 3 90.0 177 Table 11 Experimental Errors for the *He(*He, SHe)*He, 4He(He, p) °Li and *He(*He, p')°Lix Experiments Systematic Error — (%) Prep PP PP PPP PPP PRPPPrP Pep PPR Pp eR ee ee OTe OO OO Re BOOT RS OT Ro pe 4He(PHe, 3H) *He (%) Pet len on! on! oo! my, way 1 wo 1o bo ns 1 Oy go ge gig yoo yee ty NND WN WH RYN BPWN PNW WP NEN NNN Pb aan an an aon a! a | t aa oi bo Relative Error oro on oo oor om ol oa Energy Range (Mev) 178 Table 11 (cont. ) ®om Systematic Error Relative Error Energy Range | (%) (%) (MeV) 98, 4 1.1 15-3 4.7- 8 1.1 2-4 8 - 13. 25 1.1 4-6 13,25 - 14.7 1.5 3-5 15 - 18 106. 4 1.1 1.5- 3.5 47-8 1.1 2.5-5 8 - 14.7 1.5 2.5 - 3.5 15 - 18 116.8 1.1 1- 2.5 4.7 - 5,5 1.1 25-5 5-8 1.1 2-5 8 - 10 1.1 5-9 10 - 14.7 1.5 2.5 15 - 18 125, 2 1.1 1.5 - 3.5 4.7- 8 1.1 2-5 8 - 14.7 1.5 2.5 - 3 15 - 18 135. 0 1.1 1-2 4.7- 8 1.1 2-4 8- 14.7 Laboratory Angle 15 20 22. 25 27 30 31. 35 36, 40 40. 45 50 a5) 60 65 70 | 75 80 85 90 179 Table 11 (cont. ) 4H0(PHe, p) Li Systematic Error % 1.1 1,1 i * on Be PR Pe PP PP eon oe oF oe eM a an Pr ee s e . * e e e cf e or orwrntana oa o Relative Error % 2.5- 4.5 25-45 2-4 38-5 4 3-5 2.5 - 4.5 4-6 3.5 - 6 4-8 4-6 5-10 (8-13. 8 MeV) 4-6 (14-18 MeV) { - bo bo 1 (Oo be 180 Table 11 (cont. ) 4e(PHe, p!) Lit Laboratory Angle Systematic Error % Relative Error % 15 1.1 6 - 10 20 1.1 16 22.5 15 15 25 : 1.1 15 27 15 30 1.1 15 31.6 15 35 1,1 15, 36.8. | 15 40 1.1 15 40,8 | | : 15 45 L500 12 50 1.1 10 55 ee oe 10 60 , 1.1 65 1.1 70 1.1 85 1.1. 10 181 Table 12 3HH(a, «)°H Phase Shifts in Degrees This table shows the phase shifts obtained from the 334 +a scattering data. The laboratory energy is shown in the first column (ELAB). The quality of the fit at that energy is indicated by 2 in the second column (CHI2). The number at the top of cach of the next 7 columns gives the value of Jn for the phase shifts listed below. The letter 0 indicates the real phase shifts 6 In used in the analysis. Tables 12A and 12C show the real phase shifts and X5_'s obtained from data below 13.1 MeV. Tables 12B and 12D show the real phase shifts and X,_'s obtained from data above 12.8 MeV (data obtained using negative ion injection). 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The laboratory energy is shown in the first column (ELAB). The quality of the fit at that energy is indicated by 2 in the second column (CHI2). The number at the top of each of the next 7 columns gives the value of Jn for the phase shifts listed below. The letter D indicates the real phase shifts 6 In The letter X indicates the param- eters Xx used in the analysis. Table 13A shows the real phase shifts and Table 13B shows the parameter X5 (Page 28) 3 191 12°28 0o0°SL L9" 9 EL°EG B6°T? CErCE 9e°92 SL°6T TS°9T TL°ET Te" tt 6S °6 oT*Ss GL°S LS°S Qg°*s 90° eve? YO"TT Be°s T2°s eT"? SL°9 Te "s cL°S 0Z2°S oy" lt ce °¥ -c/sd B6°OLT Oe°elt 6L°tlt eo°cLt ol? 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OS ‘Tt oo'T 0S ‘0 -2/GX 06° 84 00° 4S 0S° 6S 00° €9 CG" Eo 00°LS 00° ey 0S ° 82 OSG*6T 00° eT OS°8 00% "0 "0 "0 "a 00°0 "0 "0 “a "0 *0 *0 00*0 "OQ oat) "0 *a ~E/LX OS°9E 00°9€ OS°GE OO°SE QS°vE 00° %E OS*EE OO°EeE OS°CE 00°¢E OO°TE OS°62- OS"82 00°22 0S°S2 cS*e2 00°22 06°02 CO°st oo°ZLt os"9T OS*sSt oo*SsTt o0°yT QOS*cTt Co°TT 00°6 00°9 +Z/€EX Os°6T OS°st Os*itl Og°91 o0°9T OS*T OS*ET os*dt OO°TT 0S°6 OO°L 00°S “0 "0 "0 "0 "0 °0 *O *O "0 “0 “0 0 "0 °O “0 “0 +Z2/S% SL4IHS 3SVHd 239 ‘0 ‘Od ‘oO a8) ‘0 ‘0 ‘Oo ‘Oo "0 "0 "0 ‘0 °O ‘0 ‘Oo me) ‘O ‘0 ‘0 ‘O- ‘0 me) ‘Oo ‘0 ae) "0 ‘0 ‘0 —c/1Xx GET 3ATaVE OS*6T 0S°8T Os*lt os°9T oo°sT OS°4sT oS’°eT .06°2T Oo° TT OS "6 0o°L 00°s *Q *Q “Qa *C “QO *Q “OC “a 0 “0 °O na 0] *Q “0 “Cc *O —c/€X 0S°9€ 00°9E 0G °GE 00°SE 0G °7E 00° ¥v7€ 0G °EE OO°EE 0S°*2Ee corze corTe 09°62 09°82 00°22 0G6°SZ OS*E? 00°22 0S °02 oo'st OO°LT OS*9T OS*ST 00°ST OO*+T os*2zt OO°TT 00°6 00°9 +Z2/1X S06*T G6¥°*T 96L°T T60°T coc °T Z4E °% 9Ef°T 86 °T wl2°T 912 °T OLO‘? TTO°T G7L°O 0S6°O 65%°0 £éL°O T9%7°O Zl9o°0 998°O 92T°T OT9°O Sst9°0 6LT°T 418°O £59°O cv8°0 e89°0 S90°T cIH9 O22°rT Ol6°CT 6TL*ET 697°ET 8Tc°ctl 896E°2T ZTL°2T L97°2T L1z°2T 996°TT STL°Tt S97°TT FIZ°Tl ¥96°OT etl*ot 299° OT T1z2°o! 196°6 OTL°S6 667°6 802°6 166°8 901°8 GG?7°S 702°8 €S6°L cooled OS7"L SV13 195 “0 “9 ae) °0 "0 "0 "0 "0 "0 -2/5% a6) 0S°OI oo°9oT 09°02 00°S2 OO*0E 00° 9E QG6°S8E OO" ec? -c/ LX 0S*8E 0S°8E 0S°8E oo°se 00°8E 0o°BE OS*LE OSstle OO"LE +2/€X 00°92 OS°S2 OS° He oO*#e oSs*e? OS*e2 OS°T2 00° T? 00°02 +2/G&X SLAIHS ASVHd L398 *0 "0 "0 "0 *O "0 "0 °0 —c/ Ix get ateve 00°92 0S°S2 OS*v? 00° ¥2 OSs°€2 OG*¢e Os*te oo*ted 00°02 —~c/€X OG *8E 0S ’°8E 0G°SE oo°ee OO°Se 00° 8e OS*LE OS*LE oorle +2/ 1X Tes°oO 6icS°0O 92S°0 iTe°O 265 °O 4E9°O 6S °O 00¢6°T ocT*T éLH2 gascLt 98€°LT €8a°ot oge°gT @L8°ST GLE*ST ZL9°%T T2ZL"4T Oley avi3i 196 Table 14 Resonance Energies and Reduced Widths This table shows the resonance energies and reduced widths obtained for Thi and ‘Be. A radius of 4,0 Fermis was used for the analysis of all the levels. ‘The subscripts Ny and Po refer to the decay of the level to 6r 5 + nucleon, The subscripts ny and Py refer to the decay of the level to 61 is +nucleon. (Pages 40, 41) 197 of ‘0 + 19°6 60 OF LPL Or 0 + 79°9 G0°0 F499 $ (A931) ota T u . eng 2d ated ajornaed Z 9Y} JO SSBUI poonpe. oy} ST nl pues ug 5 UOTJOVIOJUT JO SNIPSA 94} ST B TOM 4 5 = 28 XN G _ oO + 0° +9°OT - - €$°0 GO FST 60 °0 + _ T0000 * ¢€00°0 F - 92°0 T'O0+ @'T ft0°0 7c0 0 200 ‘0 * gt ‘Oo + - 000°0 T0'0*00'0 98 T EC OFT'S 700 + - - - LS‘0 «TOF E'T qu ou gu 2 ve) =) A 3 A fe) h (A®IN) z 2° (A®N) Z 29 (A IN), T rl, vT STdeL t/h @/ Lg v 2/5 2/s 5 alg W/Sq : o/h aq o/h Z up ayes 198 OT “0 F12°6 90°O F18°L OT ‘0 F€L°9 G00 LSP sor (A°W) =F [o0) wt +i €°0 - 9¢'0 + EO+T+ET OLT0 9°OF9'T _ T00’'0 * S000 F T‘O0* ZT OT0°O €20°0 STO F _ 100 7F00°0 9E'T SOFT’S v0'0 F | - 0L°0 T'OF9'T od Be) be) 3 A FS) A (A2IN) Z 2° | (ASI) Z od, (*}U09) FT P1GeL _0/L _8/S a/¢ t/L up B/h 2/¢ AS o/h ayers 199 Figure 1 The Tritium Chamber The tritium chamber is shown as seen from the top ona horizontal plane through the beam line. The numbered items are listed below, me) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) . (20) (21) (22) (23) (24) (25) (26) Blank off flange connecting to the force equalization bellows. Outer body of Faraday cup. Brass Faraday cup body. Tantalum liner, ; Teflon insulator. Electrical feed through. Suppression magnet. ; Lucite insulator. Tantalum aperture. Brass insert. Chamber body. Brass can for counters. Lucite can holders. Counter collimator, Gas cell windows. Brass counter collimator slits. To main pumping system. Gas cell body. Typical O-ring seal, Vacuum passage to gas handling system. Receptacle for gas manifold. Spacers for collimation disks. Tantalum collimation disks. Gas cell support, Beam collimator. To upstream pumping and second set of slits. (Pages 3, 4) 200 S| SN Oo - = ¥ SSitt] WNT Se: i! f Wnts R hy DELLE GE ETOCS ELITELS: é i SSE ASO MEIGS: SASSI (6) ae RR > hs PAN RNS RS SS Seeks = => z = 2 oa a = om, pe CSD SLE LE LESSEE: Lele MD es EME GEOL TST E OG: = = (2) lan QQ QM e @) Ke E aati 201 Figure 2 Gas Handling System A schematic diagram of the gas handling system used in the 3 H(a., «)°H experiment. (Page 5) 202 SCHEMATIC DIAGRAM OF GAS HANDLING SYSTEM FOR T{a,a)T EXPERIMENT GAS CELL MANIFOLD ,—NUPRO VALVE NUPRO TO MAIN TO TEST VACUUM <— — x» GAS SYSTEM SUPPLY DIFFERENTIAL PRESSURE | "GAUGE TRITIUM RESERVOIR VACUUM CHAMBER SURROUNDING RESERVOIR CIRCLE SEAL VALVE 203 Figure 3 Tritium Reservoir A schematic diagram of the reservoir used to store the tritium as uranium tritude. (Pages 6, 63) MIOAYMASSY WANILIYL 40 WVYSVId SILVAWSHOS “WAS SNIW-O \ LEMAR MMMM Me Le HLOT9D SOLSAESV LVAH dVY¥L OL GSNOAN SdIHO “excraracalel iNior uaq70S Y3ATIS Nag - =—\ ; N3LSAS ONd NN a 00M Ve gS ees a WNNOVA OL > dadvayHt & . SSAIHQHHy - Le LL ALLL A LL 2 y KS perez taker y 4 7 5 7. auIM y AGOG YIOANAS AY NIV “We —yoromntoutons ; Sssvug Z HONOX H 1q3a3 4 i Vy i, WoIN19373 NO YSEWVHO WANOVA “WNYALXSA 205 Figure 4 Transfer Manifold A schematic diagram of the manifold used to transfer the tritium gas from the glass shipping container to the reservoir. (Page 64) GQIOJINVA, YSASNVYL WNILLIYL 4O WVYSVIC IILVWSHOS YIOANSSSAY WNAILIGL SdIHOD ANINVYN SAIVA O8dNN- TWIA NO vas yOaN atavyvayg— «9 NIN-0 Gou Ga0vayHL 206 YAONNId 3B NOLSId WALLIEL SSVUS YOs WIA SSVT19 LINA cans A9NNVS WNNOVA YOLIS LAG HVAT OL 207 Figure 5 Electronics A schematic diagram of the electronics used with the = , E counter telescope. (Page 57) 208 SCHEMATIC DIAGRAM OF ELECTRONICS AE COUNTER ——> <—— E COUNTER RA. RA. AE SUMMING AMPLIFIER E+AE NO AE>b? YE wn E+AE E+AE Ist 200 CHANNELS 2nd 200 CHANNELS |. 400 CHANNEL RIOL ANALYZER 209 Figure 6 Typical Spectrum from the 3H(a, 0) °H Experiment A spectrum obtained using the ge , E telescope and ax the 400-channel analyzer. The first 200 channels show charge 1 particles and the second 200 channels show charge 2 particles. (Page 8) 210 O8e OSE CDCONQy pbaGEORLRIOAII, ° Go 00, 0 © Y3SEWNN TANNVHO He HE hd SLNNOD 30 UIOWNN 211 Figure 7 Data Reduction Display This figure shows a sequence of photographs of the cathode ray tube used (with the Burroughs 220 computer) to display and partially reduce our data. (Page 59) 212 ’ ° é “ : i af ‘ $ a ios Pan z i 4 a ve - .o% seg. © ’ . we Te - od A 2 . < j eet ee « -— ee 2 ame . - Hy . 4, ae “* 2 “ees” $ ae wm oo : : we . - 7Sil 7089 CH 285 = CH 328 = 213 Figure 8 Slit Geometry A schematic diagram showing the slit arrangement in the detector collimators and the relevant parameters for determining solid angle and target thickness. (Page 61) 2 AYLAWOSS LIS YOLOALAG 40 WVYSVIC SILVAWSHOS LAVAL. 215 Figure 9 Excitation Curve from the 3u(a, 0) a Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 520 440 360 Au — 280 als 200 140 J i J | | ! 4 5 6 7 8 9 LAB ENERGY (MeV) I } | | 1 } | | | | | | 4 5 6 7 8 9 LAB ENERGY (Mev) 217 Figure 10 Excitation Curve from the 3H(o, a) Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 240 200 | 120 |- 80 |- 40 F- } | | 290 7: gs) 9 LAB ENERGY (MeV) 220 200 [- 180 -- 160 + 140 | QQ) bIG ulo 100 -- 60 AOL 20 t- I | I | | L T 8 9 LAB ENERGY (MeV) l2 13 14 ! Bey = 60.0° + | | \ in i263) (4 219 Figure 11 Excitation Curve from the Sua, 0) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) Of} ag 200 180 160 140 - 120 t- 100 j—- g0 [- 40+ 20 -- | | 1 180 7 8 9 LAB ENERGY (MeV) 160 140 F- 120 |- 100 |- 80 ;-- 40 F- 20+ { 1 | 7 8 9 LAB ENERGY (MeV) 221 Figure 12 Excitation Curve from the 5a(a, «) °H Experiment The open circles show the experimental points, The lines show fits to the data from the phase shift analysis. (Pages 9, 25) mb sr bIG 250 200 150 tele) 50 120 110 100 90 80 TO 60 50 40 30 20 222 Gem = 70.0° 7 8 9 ! i I } | | | 6 7 8 9 LAB ENERGY (Mev) 223 Figure 13 3H(a, 0) °H Experiment Excitation Curve from the The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 224 160 TT TT i40}- 6cm = 84.8° “| 20 ~ 100+ 4 a el3 bIS clo 60l- 29%000002 = 40 4 20 ~ 0 ! l | | l l | | 2 3 T 6 A] tO H l2 IS I¢ LAB ENERGY (MeV) 300 l l l l 250K Bem 2 90.0° 4 200+ 4 oo EI! iso _ b/G ojo 100+ - 50+ _ 6 l l l | ! | | | 2 3 7 8 9 10 il 12 13 14 LAB ENERGY (MeV) 225 Figure 14 Excitation Curve from the Su(c, 0) H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) (F) do do 220 200 160 140 120 100 80 60 40 20 | | | | l ! | ak (o>) “Ni 8 9 0 UU LAB ENERGY (MeV) 320 280 240 200 160 120 “80 40 | | | ] j | i | Bom =102.0° LAB ENERGY (MeV) 227 Figure 15 Excitation Curve from the 33(a, o) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 320 280 240 200 ~— 160 120 80 40 300 250 200 Poly ££); 150 Sis alo i00 228 7 8 9 LAB ENERGY (MeV) T i | 9ou = 116.6° 7 8 9 LAB ENERGY (MeV) 229 Figure 16 Excitation Curve from the 3H(a, «) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) roll Ey” dIG uo 240 220 200 180 160 140 j20 Tore) 80 60 40 20 240 200 i60 i20 80 40 230 >> | Som # (25.3° 7 8 9 | \ } | | l 7 8 9 LAB ENERGY (MeV) 231 Figure 17 Excitation Curve from the SH(c, 0) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 232 vl Ol (A®9W) AOYSANS 8VI 8 6 Op 08 oz! cal a0z ovz 092 oze Ove o9¢ 233 Figure 18 Excitation Curve from the SH(a, a) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) ‘100 bIG . 80 60 40 20 60 50 40 iN 15.0 LAB ENERGY 1 16.0 (MeV) 1 170 18.0 1 Sou =65.4° 1 13.0 L 14.0 1 15.0 LAB ENERGY 16.0 (MeV) 17.0 L 18.0 235 Figure 19 Excitation Curve from the Sua, a) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) — A] ela ag aod 236 te) 40+ 30, 20+ Gem2 77.08 50 L 13.0 n 14.0 L 15.0 FA 16.0 LAB ENERGY (MeV) 40 T 13.0 L 14.0 i5.0 LAB ENERGY 16.0 (MeV) 170 18.0 237 Figure 20 Excitation Curve from the SH(c, 0) °H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) OD] & Ea biG ‘ojo 60 50 40 30 20 40 30 238 150 160 120 18.0 LAB ENERGY (MeV) UJ U t $ 1 135.0 i 14.0 15.0 6.0 120 18.0 LAB ENERGY (MeV) 239 Figure 21 Excitation Curve from the S35(c., o)°H Experiment The open circles show the experimental points. The lines show fits to the data from the phase shift analysis. (Pages 9, 25) 240 20r i 13.0 1 14.0 5.0 16.0 LAB ENERGY (MeV) 40 20r F q 13.0 14.0 15.0 16.0 LAB ENERGY (MeV) i7.0 18.0 241 Figure 22 Angular Distributions for the 33a, 0) ?H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle. The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 242 08! 091 STONY SSVW 4O YALNAD Ort Oe! OOo! o8 og Ov 02 LIOG = BF” T T 0 ool 002 ala 2 “—s “B o0o¢e OOF 00S os] og ATION Ovl Od! SSVW JO YSINAD ool 08 og Ov 02 T ] T T cere} | 002 oo€ OOP 00S a8 243 Figure 23 Angular Distributions for the SH(a, «)°H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle. The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 244 ost 091 JIONV Or! Od! SSVW 40 Y3ALNSD ool 08 09 Ov Oz 6be28 = 2g T T oo! Leler4 lole}-3 oor 00S O81 O9l FIONV Ovi Oz SSVW JO ool 08 431N49 09g | | cZiG = 03 U 002 OO€ oOb 00S 245 Figure 24 Angular Distributions for the Sa5(c., 0) H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle. The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 246 JIONV SSVW 40 Y3LNI9 JTONY SSVW 40 Y3LN39 ost O98 Obl Oz OOl C8 O98 Ob oz Cc os! O91 Ori Oz! OO! os 098 Or of oO T 1 T T T T T T 0 T T T T T T T T ie] ° ° - + 00! — ~| 00l - + 002 + 002 aja. 5iq ca) ns of *e — + 00€ + o0¢ 4 00p 7 + 00% Pesol = DF OzZG’6 = 23 1 i l L l 1 00S l ! I — | l 005 247 Figure 25 . Angular Distributions for the SH(a, 0) 3H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle. The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 248 ost og! JIONV Ovi Odi SSVW 40 YSLN3ID- 001 o8 09 Ov 02 46911 = 93 T T T T ool 002 oo€e OOb 08! JIONV SSVW 4O Y3LN39 Oo} Obl Oz OO! O08 09 OO o2 T T I T T T T GPS Il = 93 oO 02 Ob og 08 ool Odi Ovl 09 O8l O22 Ove 249 Figure 26 Angular Distributions for the Su(a, 0) °H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle, The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 250 ' O8t FIONY SSVW 30 YALNI9 og) Ou Oo2t ool 08 09 Ov 02 UJ J J I t I i 6Elsi = PF 02 0 Ol oe Ov OS 09 OL 08 06 ool SIONV SSVW 40 YSLNI9D oo3|. =6OFl «60d! =—00k S08 0S Oh qT i} L lJ i T ] ose = 93 ~| 0% Ov og Ovi os! oal Ove 251 Figure 27 Angular Distributions for the Su(c, 0) 3H Experiment This figure shows the center-of-mass differential elastic scattering cross section as a function of center-of-mass angle. The open circles show the data points and the solid line shows the fit from the phase shift analysis. (Page 9) 252 08! 09! TIONV SSVW 40 YSLN3Q os Obl Od! ool og Ob 02 T T 9pOZ2I = 23 T T U T Aa) 91 02 $e 82 ef 9¢ Ov bb ob os! os! JIONV SSVW 4O Y3ALN3D 09 Ov © Ort Odi col 03 i J U Epo9i = &F T 00! 253 Figure 28 Data for the Reaction SH(a, n)°Li This figure shows the data obtained with the zirconium tritide target. The number of counts are shown as a function of beam energy (E,). The open circles represent the actual number of counts. The closed circles are the number of counts multiplied by 10 to show the threshold behavior. (Page 11) 254 L. 2 H3(a,n) Li® lOOK |- ° a “x10 50K F ° ° 9 ° Q t+) @ we, _ 929005 ov - Threshold 12.5 11.0 WS nN Eq (MeV) ——> 255 Figure 29 Data Obtained for the Reaction 3H(a, n)°Li from the Inverse Reaction This figure shows the total reaction cross section for the reaction 33a, n)*na as a function of laboratory energy. ‘The line serves only to connect the points. These data were obtained by converting data on the reaction Sr i(n, 0) 2H to our system, The data on the inverse reaction were obtained by Schwarz, (1965). (Page 26) | 256 160 -— 140; 120/- 100/- © oO j m oO I op (millibarns) 20/-- oll I l I l l 11.0 WZ 11.4 KS) 11.8 12.0 12.2 12.4 LAB ENERGY (MeV) 257 Figure 30 Schematic Diagram of the Detection Geometry for the 3H(a, n° Lit Reaction This figure shows the geometry and apparatus used to detect neutrons for the 337(0,,n2)° Lex reaction. The paraffin moderator is cast in the form ofa cylinder with the target and detector shown on axis. The diameter of the cylinder is 31 cm. and its length is 38 cm. The distance from the target to the detector is 19 cm. (Page 11) AYLAWOAS NOILIALAG NOYLNAN YOLVYOSZLNI | J “OL av37 j MASWVHD LIOUVL — WIANIAINTY Yy OES | 8 . . dO ASSASAS ARMAS 4 li YANID NIVIN Si NOILISOd 4 YALNNOD 4 WOINODYIZ | SLA9YMVE SOILIML | 259 Figure 31 Excitation Curve for the 3H(a, n) ix Reaction This figure shows the total reaction cross section for the SH(a, n)° Li and 3H, n)) 813+ reactions. The data on 37(a,n)°Li below the °H(a,n)°Li* threshold provides normal- ization and background subtraction data thus allowing the effect of the SH(c,, n))6y 5x reaction to be separated. (Page 12) 260 ogi 021 091 (A®W) AOYSNA BVI OSI Ovi Olt [e} + 0o| 4 002 gig Bl ——— o|3 io ~~ + 00€ + 00F 261 Figure 32 Diagram of the High Energy Gas Cell This figure shows a diagram of the gas cell used to obtain the 4He(PHe, S10) “He data for energies above 14.7 MeV. (Page 15) St/t, “ip Tf 6, 4 oN YY WNAZZZ Ul <\ GY“, GH OLL iin: Ys bi ih bjs YK, Witty WHE) CHAMBER TOP GLYIYG fj CHIH OES \ CHL, BRASS BODY Yjfyy GGG YY YY Syed yy WN Ui, f/4 YY hii, YYW}. }y iy i, HIGH ENERGY GAS CELL RING FOIL WINDOWS CENTER WINDOW IS MYLAR 263 Figure 33 Typical Spectrum from the *He(*He, 3110) *He Experiment This, figure shows a typical spectrum from the 400-channel analyzer. The first 200 channels show charge 1 particles. The second 200 show charge 2 particles. The highest group (in channel number) is the 3 He group. Just below it is the a group, The group near channel 80 is a proton group from the reaction *He(*He, p) Li. The sharp group near channel 40 is a proton group from the reaction 4H0(FH0, pty Sz, The background under this group is due to deuterons from the breakup of Sri, (Page 16) : YSEWON TSNNVHS fen®) O02 OOP 009 SLNNOD 30 Y3A8WNN 008 000) 00¢! 265 Figure 34 4 Excitation Curve for the He(?He, 3 He) *He Experiment This figure shows an excitation curve for the 4He(PHe, 3340) *He experiment. The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17) 700 ) Co do da 266 600;- 500;- 400!l— 300}- 200;-- i00;- | | | Ben #39.2° | \ pO 400 7.0 80 90 100 HO 120 LAB ENERGY (MeV } 130 140 50 169 170 18.0 ij T T J | T | H ] Oey 2 470° 40 50 60 70 80 30 ! 100 «110 s*120 LAB ENERGY (MeV) 130 140 15.0 l 16.0 170 180 267 Figure 35 3 He) tue Experiment _ Excitation Curve for the 4He(PHe, This figure shows an excitation curve for the *He(PHe, 3110) “He experiment, The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17) () Ale El? ag 250+ 150 - 100 50 | | | | | | | | | 200 50 60 70 80 90 100 110 120 130 140 150 160 i170 LAB ENERGY (MeV) 18.0 150 }- 100 F 50-- T i i i T if T I a u? 63.4° 60 90 100 110 120 130 #4O 80 160 170 LAB ENERGY (MeV) 18.0 269 Figure 36 wt 4s 4... (3 347.\4 . Excitation Curve for the “He(“ He, He) “He Experiment This figure shows an excitation curve for the 4He(FHe, 3340) “He experiment, The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center- of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17). 150 270 100 - am (ar) SO f- | 100 70 80 90 100 10 i120 LAB ENERGY (MeV) 13.0 14.0 15.0 j 16.0 70 18.0 T | T ] T i q | 70 80 90 00 HO 120 13.0 LAB ENERGY (MeV) 14.0 15.0 16.0 As) 18.0 271 Figure 37 4 3 Excitation Curve for the Ho(*He, Ho) *He Experiment This figure shows an excitation curve for the 4He(FHe, S140) *He experiment. The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17) 100 120+ 272 fons) | ! ! ! i ! | ! 93.0 100 «~=110) «120—s*13.0 LAB ENERGY (MeV) 14.0 150 160 170 100 }- {00 F Ae Ej — ae | I I I 8cm 7 953° re | 40 50 60 70 8.0 3.0 100 ~=11Q «120 « 130 LAB ENERGY (MeV) 14.0 - 150 160 {70 18.0 273 Figure 38 3 Excitation Curve for the 4He(FHe, He) “He Experiment This figure shows an excilation curve for the 4e(PHe, 3H) “He experiment, The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17). 274 200 150 - 50 |- 100 110 120 130 140 150 160 LAB ENERGY (Mev) 200 l T l T T T 170 §=180 , 150 i00.- 40 50 60 70 80 90 100 110 120 130 I40 150 160 70 §=180 LAB ENERGY (MeV) 275 Figure 39 4 Excitation Curve for the He(?He, 3 He) “He Experiment This figure shows an excitation curve for the *HePne, 3H) "He experiment. The differential elastic scattering cross section (in the center-of-mass system) is plotted as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17) 200 |- i 7 100 60 40 50 60 70 80 90 100 |10 120 130 140 150 160 170 180 LAB ENERGY (MeV) l q T qT T T T T i T I i { i Boy # 116.8" b r 100 -- 4 60 EF 40 50 60 70 80 930 100 ii0 320 130 140 150 i60 170 180 LAB ENERGY (MeV) 277 Figure 40 Excitation Curve for the 4 He(?He, S110) *He Experiment This figure shows an excitation curve for the 4He(FHe, 3H) “He experiment. The differential elastic scattering cross section (in the center-of-mass system) is plotled as a function of laboratory energy for the center-of-mass angle. The open circles are the data and the solid line is a fit from the phase shift analysis. (Page 17) | 200 100 278 5.0 i Boy = 125.2° 200 6.0 Ae) 80 90 100 HO 120 LAB ENERGY (MeV) I T T 1 1 13.0 14.0 5.0 i | 1! 60 170 180 150 Fr 100 "50 4.0 50 8cy * 135.0° 6.0 7.0 8.0 9.0 100 WO 120 LAB ENERGY (MeV) 13.0 14.0 15.0 279 Figure 41 Angular Distribution for the 4H0(7He, Ste) *He Experiment This figure shows the differential elastic scattering cross section (in the center-of-mass system) as a function of center-of- mass angle. The open circles are data points and the solid line is a fit from the phase shift analysis. (Page 17) 280 08! JIONV SSVW 40 Y4LN39 O91 OF Og! ool o8 09 Ov oz T ] I | T T T 280'¢ = e°Hy j ool 002 00€ OOF 00S 009 081 Ogi JIONV SSVW 4O Y3iN39 Ovl O¢} OO! og og Or O02 ] I I ! \ I ge7s = 27H 06 08! Ole O9€e OS? Ovs O¢9 281 Figure 42 Angular Distribution for the 4He(He, Ste) “He Experiment This figure shows the differential elastic scattering cross section (in the center-of-mass system) as a function of center-of- mass angle. The open circles are data points and the solid line is a fit from the phase shift analysis. (Page 17) 282 JIONV SSVW 40 Y3ALNAD . FJIONV SSVW 40 Y3INS9D ogi O98! Ob Og OO! 08 08 OF of a Og! O91 Obl Oz! OO! og os OF of oO I ] T T T T T T | I T T - 001 |. 4 oo! = 4 002 a 002 Qa olq |. + 00¢ Pin ala ajo ——— z -o00¢ L— -1 0Ov = oop | + 00S 5 9H ry ¢ ZOLi = S°HQ 6Eeps = £°HQ ~ -4 009 ! | { i L { ! | | i | i | I i | 283 Figure 43 Angular Distribution for the 4He(PHe, 3310)“ He Experiment This figure shows the differential elastic scattering cross section (in the center-of-mass system) as a function of center-of- mass angle. The open circles are data points and the solid line is a fit from the phase shift analysis. (Page 17) 284 os! JIONV SSVW 4O 43LN39 ost Ov! Oz! OOF 0&8 09 Op oz T I T I T I T T g0z6 = S°Hy 002 OO€ OOP Osi 091 JTONV Ovt Od SSVW ool JO Y3ALNAS 09 08 Or 02 pCe2g = £°HQ T ool 002 oo 0Ob 285 Figure 44 Angular Distribution for the 4He(*He, S10) “He Experiment This figure shows the differential elastic scattering cross section (in the center-of-mass system) as a function of center-of- mass angle. The open circles are data points and the solid line is a fit from the phase shift analysis. (Page 17) 286 08! ogi JIONY SSVW 4O YAIN39 Obl = Od! ool 08 03 Ov O02 ie) T alge| = £943 | I I qT i + ool 1 OI 1 O91 - 08] | 002 ajQ 5/9 o|3 “lo os JIONY SSVW 4O YSLNAD os} «=OFl Odi =O! os Og Or O02 Q J I i T I I l Zig]er = 49 0¢ Ov 08 ool 02! Ovi ost ost 002 O2ze Ove 287 Figure 45 Angular Distribution for the 4 He(PHe, Ste) *He Experiment This figure shows the differential elastic scattering cross section (in the center-of-mass system) as a function of center-of- mass angle. The open circles are data points and the solid line is a fit from the phase shift analysis. (Page 17) 288 osl FIONY SSVW JO YS.LNI9 os oo! «Obl COI ool o9 Ov 02 T I T gseul= e743 T I T Se OS GL ree)| S2l ost ogi JIONY SSVW JO Y3LN59 ool Ovl Od 08 09 Ov 02 fe) T | Oz2'pl = £°H3 J J I I oz Ob 09 o8 oo! oz! Obl 091 ost 002 289 Figure 46 Excitation Curves for the 4He(PHe, p) Li Experiment This figure shows the differential reaction cross sections for the “He (PHe, p) °Li reaction at 2 typical laboratory angles. The open dots are the data obtained using the gas cell. The closed dots are data obtained by filling the whole south 20° chamber with target gas. Thc lincs scrve only to connect the points. (Page 18) 32 28 T ft ! a Lop = 22.5° J io 612 BS LAB ENERGY (Mev) 1 ! 1 | 10 Ho 612 B14 LAB ENERGY (Mev) 291 Figure 47 Angular Distributions for the 4He(FHe, p) Li Reaction ‘This figure shows 2 angular distributions of the protons from the 4He(*He, p)°Li reaction. Center-of-mass differential cross section is plotted against center-of-mass angle. The lines serve only to connect the open circle data points. (Page 18) 292 og! Ogi JIONY SSVW 40 Y3.LN39D Ovl Od! OO! 8 0g Ov O02 T T r 1 T T T SNOLOYd 3ALVLS GNNONS Srl = ¢743- 2 ) 2p (ai Os! Ovi T STONY SSVW JO YSLN3) ogi ool os 09 Ov _ 02 T T og! T l T i T SNOLOYd 3LVLS GNNONS eco'o1 = 243 L ol al 1 i | | nn Oa i ) 2p (aa 293 Figure 48 Angular Distributions for the *He(*He, p) *Li and 4He(FHe, p)®Lix Reactions This figure shows another angular distribution for the ground state protons and also an angular distribution for the first excited state protons, The quantities plotted are the same as in Figure 47, Here too the line serves only to connect the data points. (Pages 18, 19) 294 SIONV SSVW 30 ¥31LN39 . JIONV SSVN SO YSLN39 og! O98: Ov! oOzl oo! Of 09 OF 02 0, os! Og! Obl OZ! OO O8 09 Ov 02 qT q q q T i t t J i ] | J T J i L st s =2 — SNOLOYd SLVLS GNNOUS _ 4€ = 4 = a 4g aja. plq * 49 -——™ — a rE in To 4 ; al - SNOLOUd 31VLS A3LIOX] 4S! q4 - 4g = a 46 = 401 = 4 a it ° i aH ‘>) . 2H 26rel= o°9 | Gbprai = @ 43 doy . - i l i i { i 1 i i j { { ji I J i 295 Figure 49 Angular Distributions from the 4He(?He, pt) or 3 Reaction This figure shows two more angular distributions of the first excited state protons. The quantities plotted are the same as in Figure 47 and the lines serve only to connect the points. (Page 19) 296 ogi _ JTONV SSVW JO Y31LN30. ool Ovi Oz! oo! 08 09 Ob 02 T T | im I T dq I SNOLOYd ALVLS G3ALIDX3 IS! ziepi= 243 0g! og! Ovl JISNV SSVAN JO Y3LN39 oz! OO! O08 09. Ov Og q 1 q LJ SNOLOUd JLVLS G3L19X3 4s] oI 22 ve oz 297 Figure 50 Excitation Curves for the 4ye(FHe, p)®Li* Reaction This figure shows excitation curves of the first excited state protons for two laboratory angles. The shape is quite similar for other angles investigated. The laboratory differential cross section is plotted versus beam energy. The lines serve only to connect the points. (Page 19) 75 298 SOF . 257 i 12.0 it 1 14.0 15.0 LAB ENERGY (MeV) 75- 50 25+ l J 14.0 15.0 LAB ENERGY (MeV) 299 Figure 51 Energy Level Diagram This figure shows the energy levels of Thi and "Be. The spins, parities and isospins of the levels are also shown. 300 Be’ VO ek Aah sad PIAS V6 Bh hh ht A) Oe ly ph ol & 4 4.6 W2.5_ [1.13 (372);32 ~~ — — _[10.79 3/27;3/2 110.678 9.685 EPPO PLL NEE a 9.9 alata Sen We Be® +n He® ta | ~ 077774" HOO +P (QB Wee 9.046 Lid + 7.47 5/27;1/2 ¢ _¢.253 | _—— 7.2) 5/27 -1/2 Li®é +n. 6.64 | 25/2752 | — SSPT TIT TI | 6.73 °° © 5/27;1/2 5.608 465 ewe} lags weryve| Lie te 2.467 He* +t 1.587 -. 3 4 0.478 1/27;1/2 _____|0.431 verse He’+ He J® 3/27 € J $3/27 -7 [-0.24] = Li 301 Figure 52 4He(*He, 3110) “He Phase Shifts in Degrees This figure shows the phase shifts rT /2. ; rT /2 and b4 2 asa *unction of energy. It also shows the parameters ~ + xX, /2 and Xe 2. . The dashed line is a fit to the phase shift 6, /2 and corresponds to the s-wave scattering from a hard Sphere of radius 2.8 Fermis. (Page 28) | 302 (A29W) AOYAN3 Gv1 O61! Ost O21 ogi oscil Ori o¢l ord! Ol (exe) O6 o8 OL O09 OS Ov Fa q ] I L T } I ] I ] I j J i I _ ahe Po 4 5 ms rele} - P0900 OT eS + 0g- PO GAHAQO OO, ~~ 00 = “WO 06 —7 03- ~~ 06 ° ~~ i +R, | o- - + 02- ° fe) % 0 °o ° Lt +g o 9° 0 6 0 0 o9D5 2909090900555, 9°°* 200000009 M om +0 goo” . & a gog9aot poG + 02 oa ogooo9% _ poo oo 8 oo ogo op3g800098 4 Ov Xa+"" = “fgiza"ly 25092 “fg 409 — + 08 . ° 2029900 ° _ “he 02 0 o ° ° 5 ool So g000 0°09 - 9° ° 021 { N L ! | I l | j | Rae OPo 7 OF SONV 3SVHd 303 Figure 53 *He(PHe, 3 He)*He Phase Shifts in Degrees : : . - + This figure shows the phase shifts $3 /2 and 65 /2 asa function of energy. It also shows the parameters X, /2- and x, / (Page 28) + 9 . 304 O6! os! (A®9W) ADMANS 8V1 Ob < I | i T 90 99 00550000009 °OR”” oO Qa aooa® noe aoa® 5000000? fo} Osi Ovi io} 4) Odi oi! roxe]| 06 08 coy 09 OS T L T I T T ° ° [o} ©9900? 99 0002029999 Leproere argzo4l x 2500 = 4fs Ot- 409! 4 col 4 cst coZd SIONV 3SVHd 305 Figure 54 4u0(2He, 2He)*He Phase Shifts in Degrees This figure shows the phase shifts by /2 and 6. /2° It also shows the parameters xX, /2- and x, /2° The lines show the fits to the phase shifts from R-matrix theory. (Page 28) 306 (A®9W) ADYSN3 9V71 o6!| O8! oll 6O8l = = Ost Ovl Of! OI OH ood 06 o8 Oz 09 OS Ov I I I I T T I T | I | T T I | Ov- | oO wo | o @ - s0giza4ly 2509 = Mfg | [o) oO rs 099900° > — Ovi ° ~| 09! ° 509009 gee 999000990 -g + 081 9° 0900 1 { I | | ! | 002 SJIONV 3SVHd 307 Figure 55 3 He Polarizations This figure shows the spin polarizations of the scattered Sie particles from the 4He(*He, 3 polarizations are calculated from the phase shifts obtained in the He) “He experiment. The phase shift analysis. The Basel convention for the sign of the polarizations is used and the contour levels are plotted as a function of center-of-mass angle and laboratory energy. (Page 32) 309 - Figure 56 3H(q, o)°H Phase Shifts in Degrees This figure shows the phase shifts rT 2 ; by /2- and 3 jr asa function of energy. It also shows the parameters . /2 * and Xe 2 The dashed line is a fit to the phase shift 1 8/2" and corresponds to the s-wave scattering from a hard sphere of radius 2.6 Fermis. The change of symbols near 13 MeV indicatcs that the phase shifts and xy 'g obtained above this energy used the high energy beam data. Below this energy ts) the low energy beam data were used. (Page 28) 510 (A9W) AQYSNZ 8V7 ogi O21 o>) Os! Ovi o¢!l ors | oll oo} O6 os OL 09 OS Op oe T T T 1 T T T T I T T T I T T — = 7 4 Ve tas z WO RY ym Ae To TTA ~ Vv You goon +4 Be % TT LO 6 ~~ ee L xe) © 82002000 TB BH 4 “O°0~o~5.6, ~ORRD ORG. 9 zZ ; 3° rv pore ovevaverr eg a%%9 | ° 9 fBR GMO, 4 vw CAF Ce 5° oo 0 9000 fs) 5 2 Go fone) oO fo] Vv °o shy wahy gogo” wo, 5 oa gao +fly B Corto O89 4 Atgizettfy zs00 = Hts oy = - % VV¥eg . 4 kee v VV oe vg 0 GUA % og [~ “8 ° 7 ° ° 09909 L 0900000°° nor | _ OPM Oa9 0 { i L ! ! \ i I L ? Odi- ooi- 08s- o9- Ov- O¢- 02 OF 09 08 ool oz! Ovi ost SONY ASVHd 311 Figure 57 Ha, a) °H Phase Shifts in Degrees gs . - + This figure shows the phase shifts bo /2 and 6. /2 asa function of energy. It also shows the parameter Xs /2- The change of symbols near 13 MeV indicates that the phase shifts and Xy'S obtained above this energy used the high energy beam data. Below this energy the low energy beam data were used. (Page 28) 312 (A8W) ASYAN3 av osl OLI o9l Osi Ov! oO¢l or! Ol OOl 06 T ! 7 T 1 ] T T T { hg Q fo] z, Ry Vv Ww ya WF v0 gy Vv 2 Vvg co ~hg VIM gg Mets EI VVVIIIVVVIVITY 0° SH ° oO PY ig er 2 0 9 WRN Gg 5 099000099000 aan teizatly 2800 = 4s oo : “SCG G0O Gg 9 6 o°0 99006 fone) RR arc + 02 4 OF + 001 + 02 - Ori 4 ogi 4 08! elers JIONV 3SVHd 313 Figure 58 331(a, a) H Phase Shifts in Degrees This figure shows the phase shifts 6,, 2 and 6, /2, as a function of energy. Also shown are the parameters xy /2 and X. /2° The change of symbols near 13 MeV indicates that the phase shifts and X5,'s obtained above this energy used the high energy beam data. Below this encrgy the low energy beam data were used. (Page 28) 14 os! O21 ost os! ov! Ol oe! ol (A8W) ASYSN3 BV oo! os of 09 OS Ov of is) q I T I zZ, hy fs] gp Tamoo@qgg05909 | | | | Y wy | | | | | | | gvvvvvvvy T 8 eq 9.90 Bangi o zZ . “Ag oe? 000 O° ° 59 °°? argizatly 2509 = “fs P 90090090"? ° 90 0 FSP 3 Or- 001 L i oO oO lo} @ = A JSIONV 3SVHd i o ao -] 002 O22 ~Ovr2 +092 os2 OO€ 315 Figure 59 Triton Polarizations This figure shows the spin polarizations of the scattered tritons from the 35a, o) °H experiment. The polarizations are calculated from the phase shifts obtained in the phase shift analysis. The Basel convention for the sign of the polarizations is used and the contour levels are plotted as a function of center-of-mass angle - and laboratory energy. (Page 32) STONY SSVW 40 YSLNS9 LAB ENERGY (MeV) 317 Figure 60 "Be Boundary Value Variations This figure shows the value of the elastic reduced width amplitude for the *P. /2 a given value of the boundary value B.- The line is a smooth state in "Be which gives the best fit for curve connecting the calculated points. (Page 45) 318 Set T I ] | 7Be 4 = 3 2b A ol ! 1 l i | | ~3,5 ~3.0 -25 -2.0 -1.5 1.0 -05 319 Figure 61 "hi Boundary Value Variations This figure shows the value of the elastic reduced width amplitude for the *P. /2 state in "i which gives the best fit for a given value of the boundary value B.. The line is a smooth curve connecting the calculated points. (Page 45) Sm T r? T T TL oe 7 ott i ! L -35 -3.0 -25 -2.0 -{.5 ~1.0 -05 @) 321 Figure 62 Nuclear Model Predictions This figure shows the energy levels for "hi or "Be with their spins, parities and isospins as predicted by the rotational model (Chesterfield, 1962) (b) and the shell model (Barker, 1966) (c). Parts (a) and (d) show "hi and "Be energy levels determined by experiment. The isospin is 5 except for those levels listed as T= . (Page 51) Hi3 3727:3/2 060 aye 3/27:3/2 10.79 3/2-:3/2 _ -|99 3/27 o7 727|9.80 we" |9.8O., ven) 9.43 172* 9 17 e993 7/27 7.67 - PAT yor TS RBE17.48 5/27 7.2\ 5/27 6.64 5/27 6.27 5/27 6.56 sye- |O.f3 5/27 | 4.91 7/27 465 7/27 463 7/27|4.57 7/27 048 1/2-|0.48 yo [O84 219 43 yee 3/27 -0.| ! 3/27 . 3/27 3/27 i ROTATIONAL SHELL "Be MODEL MODEL. (a) (b) (c) (d)