A Study of the ⁹Be Nucleus Citation Cocke, Charles Lewis, Jr. (1967) A Study of the ⁹Be Nucleus. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2DBM-0G92. https://resolver.caltech.edu/CaltechTHESIS:11022015-145724587 Abstract The reaction 7 Li( 3 He, p) 9 Be has been used to measure excitations and intrinsic widths of levels in 9 Be below the 7 Li + d threshold. Previously unreported levels have been found at excitations of (13.78 ± .03) MeV and (16.671 ± .008) MeV with widths of (590 ± 60) keV and (41 ± 4) keV respectively. Two overlapping levels have been found at (11.81 ± .02) MeV and (11.29 ± .03) MeV with widths of (400 ± 30) keV and (620 ± 70) keV respectively. Branching ratios from 9 Be levels populated in this reaction to the ground and first excited states of 8 Be have been measured by observing the associated protons in coincidence with the decay neutrons. Branching ratios were found to be: Excitation in 9 Be .... Branching Ratio.......... Final Nucleus......... (MeV) .......................... (percent) ..................................... .. 2.43 ........................... 7.5 ± 1.5 .............. 8 Be(g.s.) .. 3.03 ........................... 87 ± 13...................................... .. 4.65 ........................... 13 ± 4....................................... .. 6.76 .............................. ≤ 2 ...................................... .. 11.29 ...............................≤ 2 ...................................... .. 11.81 ...............................≤ 3 ...................................... .. 6.76 ........................... .41 ≤ B.R. ≤ .69 ....... 8 Be(2 + ) .. 11.29 ........................... 14 ± 4 ....................................... .. 11.81 ........................... 12 ± 4 ....................................... Corresponding reduced widths for neutron emission are calculated and a comparison of the results with the expectations of current nuclear models is made. In particular the measured branching ratio to 8 Be(g.s.) from 9 Be(2.43 MeV) corresponds to an f-wave reduced with θ 2 f = 2.1 x 10 -2 , in units of ħ 2 /mR 2 , with R = 4.35 fm. A comparison of this value with that predicted by a Nilsson model calculation, in which 9 Be is taken to be a deformed nucleus, is discussed. The measured value for θ 2 f is found to be consistent with that expected on the basis of measured E2-transition rates between rotational levels in 9 Be. 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): Lauritsen, Thomas (advisor) Whaling, Ward (advisor) Thesis Committee: Unknown, Unknown Defense Date: 5 May 1967 Record Number: CaltechTHESIS:11022015-145724587 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11022015-145724587 DOI: 10.7907/2DBM-0G92 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9268 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 04 Nov 2015 22:07 Last Modified: 15 Mar 2024 19:05 Thesis Files Preview PDF - Final Version See Usage Policy. 32MB Repository Staff Only: item control page

A STUDY OF THE 9 Be NUCLEUS Thesis by Charles Lewis Cocke, Jr. In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1967 (Submitted May 5 , 1967) ii ACKNOWLEDGMENTS I would like to express my sincere gratitude to all of the members of Kellogg who have created the excellent conditions which make working in the laboratory both stimulating and enjoyable. I am especially grateful to Dr. T. Lauritsen for supervision, encouragement and education during the course of this work. I am indebted to him not only for enlightening discussions and fruitful suggestions but also for the sense of excitement with which he endowed the project. The branching ratio measurements were carried out in collaboration with Dr. P. R. Christensen. I am grateful to him both for education in the laboratory and for the stimulation generated by his interested and adventurous approach to the work. I would like to thank Dr. W. Whaling for supervision 6 during the Li studies. I am grateful to Dr. F. C. Barker and to Dr. D. Kurath for providing me with their reduced width calculations, and to Dr. G. J. Stephenson, Jr. for helpful discussions. Financial assistance has been provided by the National Science Foundation and the California Institute of T echnology. The research was supported by the Office of Naval Research. iii ABSTRACT 9 7 3 The reaction Li( He, p) Be has been used to measure 9 7 excitations and intrinsic widths of levels in Be below the Li + d threshold. Previously unreported levels have been found at excitations of (13. 78 ± • 03) MeV and (16. 671 ± • 008) MeV with widths of (590 ± 60) keV and (41 ± 4) keV respectively. Two overlapping levels have been found at (11. 81 ± . 02) MeV and (11. 29 ± . 03) MeV with widths of (400 ± 30) keV and (620 ± 70) 9 keV respectively. Branching ratios from Be levels populated 8 in this reaction to the ground and first excited states of Be have been measured by observing the as_sociated protons in coincidence with the decay neutrons. Branching ratios were found to be: 9 Excitation in Be (MeV) Branching Ratio (percent) 2.43 7.5±1.5 3.03 87 + 13 4.65 13 ± 4 6.76 < 2 11. 29 :s. 2 11. 81 < 3 6.76 11. 29 .41 ~ B.R. :::;. .69 11. 81 14 ±4 12 ± 4 Final Nucleus 8 Be(g. s.) iv Corresponding reduced widths for neutron emission are calculated and a comparison of the results with the expectations of current nuclear models is made. In particular the measured branching 9 8 ratio to Be(g. s.) from Be(2. 43 MeV) corresponds to an f-wave 2 2 2 reduced width of = 2. 1 xl0- , in units of 1i /mR , with 8; R = 4. 35 fm. A comparison of this value with that predicted by 9 a Nilsson model. calculation, in which Be is taken to be a deformed nucleus, is discussed. The measured value for e; is found to be consistent with that expected on the basis of measured E2-transition 9 rates between rotational levels in Be. v TABLE OF CONTENTS PART I TI TITLE PAGE INTRODUCTION 7 Li(3 He, p).9Be SINGLES :MEASURE:MENTS 1 4 A. Introduction 4 B. Experimental Apparatus 6 (1) Beam 6 (2) Proton Detection 7 C. Targets 8 D. Contaminant Problem 10 E. Results 12 9 (1) Below 10 MeV in Be 12 (2) 11.29 and 11.81 MeV States 12 (3) 13. 78 MeV State 13 (4) 16.671 MeV State 14 (5) Peak Identification and Q-value Determination m 15 BRANCHING RATIO MEASUREMENTS 16 A. Outline of the Problem 16 B. 2.43 and 3o03 MeV Regions 17 (1) Introduction (2) Kinematics 17 18 (3) Experimental Apparatus 19 (a) Targets 19 (b) Target Chamber 20 (c) 21 Proton Detection vi TITLE PART C. PAGE (d) Neutron Detection 22 (e) Neutron Detector Efficiency 23 (4) Experimental Procedure 24 (5) Results 27 Higher Excitation Regions 28 (1) Introduction 28 (2) Experimental Apparatus 29 (3) Kinematics and General Features 30 (4) Experimental Procedure and Results 33 (a) 4.65 MeV State 33 (b) 11.29 and 11.81 MeV States 35 (c) 6. 76 MeV Level 39 N CALCULATION OF REDUCED WIDTHS 43 v DISCUSSION 46 A. Introduction 46 B. Non-normal Parity States and the Shell Model 46 (1) 6. 76 MeV State 47 (2) 11.29 and 11.81 MeV States 48 C. Positive Parity Levels 49 Do Configuration Mixing and Nilsson Model 51 E • . Conclusion 57 APPENDICES A. B. Conversion of Magnetic Spectrometer Spectrum to Excitation Spectrum 60 Energy Spectra from a Two Stage Breakup 64 vi TITLE PART C. Branching Ratio Calculations D. Calculation off-wave Components of Nilsson E. Orbital #2 6 7 3 The Li( He, a.) Li Reaction PAGE 70 74 80 REFERENCES 86 TABLES 91 FIGURES 107 1 I. INTRODUCTION The development of a consistent picture of the nucleus has come to involve not so much the solving of a complex equation of motion as the direct guessing of the solution. At the heart of current efforts to understand nuclear structure lie attempts to build models of the nucleus which can account for its various properties. In this context the nuclear theorist must have at his disposal considerable experimental information on the properties of nuclear 7 levels. Experimentally, the excitation region below the Li+ d 9 threshold at 16. 693 MeV in Be has been, until recently, quite poorly known. This is due in part to the absence in this region 9 of two- body particle channels through which Be may be formed as a compound nucleus, and to the relatively simple structure of the excited levels which makes them broad and difficult to study experimentally. This thesis finds partial motivation in filling in some of the experimental facts necessary for the theorist to 9 formulate a consistent picture of Be. 9 Of more specific interest in the case of Be is the possibility that this nucleus may exhibit collective features. In the region of light nuclei with 4 s. A s. 16, the most widely used nuclear model has been the independent particle shell model, 4 4 using the configuration (ls) (lp)A- _ The success of this model in describing level spacings, spins and parities, beta-decay matrix elements, Ml transition rates and magnetic dipole moments has been impressive (Barker, 1966; Inglis, 1953; Kurath, 1956; Cohen and Kurath, 1965). A notable failure of the model has been its prediction of quadrupole moments and E2 transition rates which are often several times lower than those observed experimentally 2 (Warburton et al., 1963; Warburton et al., 1963 a; van der Merwe, 1963). As has been found in intermediate- and high-A nuclei, such large quadrupole matrix elements may be indicative of collective nuclear modes of excitation. The idea that nuclei as low as the lp- shell may exhibit 8 . collective features is not new. Be is well known to have an energy spectrum interpretable as a rotational band based on its o+ ground state. Chesterfield and Spicer (1963) have found rotational bands in the energy spectrum of 7 Li, and have given a successful description of its ground state magnetic dipole and electric quadrupole moments and the lifetime of its first excited state using a rotational model. 9 The Be nucleus lies far enough from the ends of the lpshell that it may be expected to display a large equilibrium deformation. This suspicion is strengthened by the rotational character of its neighbor, 8 Be. Blair ·and Henley (1959) have 9 proposed an alpha-particle model for Be to explain the selective population, in the inelastic scattering of alpha-particles, protons 9 and deuterons from Be, of rotational levels based on the ground state. They observe that the ground state, 2. 43 MeV state, 6. 76 MeV state and 11. 3 MeV state display a level spacing and population in inelastic scattering experiments consistent with their belonging to a K = 3/2- rotational band. Kunz (1960) has extended the use of this model to include a K = 1/2- band, and has found that the quadrupole moment predicted by the model is about a factor of two greater than that predicted by the shell model. Kunz also points out that overlap of the wave functions of the nucleons in the alpha-particles with a ls-wave function decreases as the nucleus becomes more elongated. The result is that a neutron in a nominal 3 2s- orbit is allowed a greater component of the ls-wave function, and a correspondingly lower ~nergy. The low energy of the 1. 7 MeV positive parity state may be due to this characteristic. Nguyen Ngoc et al. (1963) have observed that the ratios of the E2 9 widths to the B-; ground state from levels at 2. 43 and 6. 76 MeV are in excellent agreement with rotational model predictions. 9 This thesis presents a rather open ended study of the 9 Be nucleus. As described below, the level scheme of Be is not well known. Consequently the first stage of the experimental work was concerned with measuring level positions and total widths of 7 3 9 the levels. To this end the reaction Li( He, p) Be was used. While considerable information on the spins and parities 9 and electromagnetic matrix elements of Be levels is now becoming available, very little is known of the wave functions. The second stage of the work was concerned with measuring the 9 branching ratios in the decay of excited levels of Be to the ground 8 and first excited states of Be. This information, when combined with the measurement of the total widths of the levels, allows one to calculate neutron reduced widths into these two outgoing channels. 4 IL 7 Li(3 He, p) BBe* SlliGLES MEASUREMENTS A. Introduction At the outset of the present work, the energy level diagram of Ajzenberg-Selove and Lauritsen (1959) showed only eight excited 9 levels of Be below the 7 Li + d threshold. The small number of such levels allows a brief level-by-level summary of some of the experimental . information on their properties: (1) The ground state is known to have spin 3/2 from the quad- rupole splitting of its magnetic resonance absorption line (Schuster and Pake, 1951). The 1. 7 MeV state has been assigned 1/ 2+ from analysis of (2) 9 the Be( y, n) reaction (Guth and Mullin, 1949). Its spectral shape has been adequately represented by Spencer et al., (1960), and by Barker and Treacy (1962). Both analyses assume that the state 8 consists of a neutron in an s-wave orbit about Be(g. s.) core, confirming the 1/2+ assignment. (3) The 2. 43 MeV state has been assigned spin 5/2 from a direct interaction interpretation of inelastic scattering angular distributions (Summers-Gill, 1958; Ribe and Seagrave, 1958; Benveniste et al., 1956). This spin is supported, and an unambiguous negative parity assignment is made, on the basis of its excitation by E2 (Nguyen Ngoc et al., 1963) and Ml (Edge and 9 Peterson, 1962) transitions from the ground state in Be(e, e') scattering. 5 (4) The 3. 03 and 4. 65 MeV levels are both assigned positive 9 parity on the basis of their strong excitation in Be( y, n}, both supposedly being electric ·dipole transitions (Jakobson, 1961). These assignments are supported by the absence of both levels 9 in Be(e, e') at 180° (Edge and Peterson, 1962), which excites negative parity levels by Ml transitions. The anisotropic 9 Be( y, n) neutron angular distribution from the 3. 03 MeV level is consistent with d-wave neutron emission, supporting 3/2+ or 5/2+ for this level (Jakobson, 1961). This assignment agrees with the analysis of Spencer et al. (1960). (5) The 6. 76 MeV level is interpreted as the third member of the ground state rotational band, having as such spin and parity 7/2- . (Benveniste et al., 1956; Blair and Henley, 1959; Kunz, 1960). This interpretation is based on its strong excitation in inelastic scattering experiments (Summers-Gill, 1958; Ribe and Seagrave, 1958; Benveniste et al., 1956; Schrank~ al., 1962), which should favor transitions within a band. Pinkston (1959) has shown that the inelastic scattering results can also be 9 explained using the shell model for Be, the 6. 76 MeV level remaining 7/2-. The interpretation of this level as a member of a ground- state- based rotational band is supported by the 9 observation of this level in Be(e, e'}, where it was found to be strongly excited by an E2 transition from the ground state (Nguyen Ngoc et al., 1963). (6) 9 Levels at 7. 94 and 11. 3 MeV have been reported in Be(p, p') (Benveniste et al., 1956; Hasselgren et al., 1965; Britten, 1952). No spin and parity assignments have been hazarded. 6 (7) A level at 9. 1 MeV has been only tentatively reported in 9 7 3 Li( He, p) Be (Almqvist et. al., 1955), and has failed to appear in other reactions. The first T = 3/2 level has been found at 14. 392 MeV (Lynch et al., 1965), and has been identified by its extremely narrow width, r = O. 8 ± O. 3 keV (Griffiths, 1965), which it owes to the absence of T-allowed particle decay channels. Its spin and parity are 3/2- according to the shell model, an assignment consistent with the observation of its Ml excitation from the ground state in inelastic electron scattering (Edge and Peterson, 1962), and with its strong electromagnetic decay to both the 2. 43 MeV state and the ground state, supposedly also by Ml (Griffiths, 1965). 7 3 9 The reaction Li( He, p) Be has previously been used 9 primarily to study low excitations in Be. Population of the everpresent 1. 7, 2. 43 and 3. 03 MeV levels has been reported (Almqvist et al., 1955; Moak et al., 1958; Careaga and Mazari, 1963). In addition, Almqvist et al. (1955) and Moak et al. (1958) report a broad level at approximately 4. 8 MeV. At higher excitations, Lynch et al. (1965) have used this reaction to populate the first T = 3/2 9 level in Be. This section of the thesis presents the results of a 9 7 survey of the entire excitation region in Be below the Li+ d threshold. B. Experimental Apparatus (1) Beam 3 . A doubly charged He beam of energy ranging from 6 to 12 MeV was provided by the Caltech-ONR Tandem Van de Graaff 7 accelerator. The beam energy was determined by a 90 ° magnetic analyzer to a precision of ap_Proximately 20 keV. A typical beam spot was a 2 mm square, to which currents ranging from O. 1 to O. 3 µa were delivered. The beam charge was measured by an Eldorado model CI-110 current integrator. (2) Proton Detection 3 7 He on Li can give rise to a host of charged particles through such reactions as: 7 9 Li(3 He, p) Be 7 8 3 Li( He, d) Be 7 6 Li(3 He, a.) Li 7 3 7 Li( He, t) Be • It was therefore important to be able dearly to distinguish protons from other types of particle. For a particle of mass number A, charge Z, and energy E, traveling a fixed orbit at a fixed field in a magnetic spectrometer, E = canst. x z2 A Thus a magnetic analysis of particle momentum, together with an energy sensitive detector, provide an excellent means of particle identification. If any ambiguity remains, as in the case of doublycharged alpha-particles and protons, thin foils placed over the 8 detector can utilize the differing energy loss rates of the various particles for further identification. A magnetic analyzer has the additional advantage of higher r e solution than that which is available with the best alternative particle detectors. T his characte ristic allows accurate Q-value and width measurements of narrow levels. In the present experiment it also allowed . . 12 3 14 16 3 18 narrow contammant Imes from C( He, p) N and 0( He, p) F 9 . . to be resolved from broader Be proton groups. For these reasons, the singles proton spectra were taken using a 61-cm radius double-focusing magnetic spectrometer. The spectrometer target chamber has been described in detail by Groce (1963). The chamber is evacuated by an oil diffusion pump system with a liquid nitrogen cold trap located immediately below the target. The detector at the focus of the magnet was a single surface barrier solid state detector for low resolution work (p/ t. p = 360 was used). For higher resolution (p/ t. p = 720), an array of sixteen such counters in the focal plane of the magnet was used, allowing simultaneous counting at sixteen different momenta. The details of this array are described by McNally (1966). C. Targets 7 The targets were Li metal (99. 99%) evaporated onto commercially made nickel foils. The targets ranged in thickness 2 18 from 1 to 20 x 10 atoms/ cm (energy loss 4 to 80 keV for a 10 (energy loss 11 to MeV 3 He); the nickel foils, from 500 to 5000 X 3 110 ~eV for a 10 MeV He). Since lithium nitrides and oxidizes 9 on contact with the atmosphere, it was necessary to evaporate the target w1der vacuum in the spectrometer target chamber. The chamber is equipped with an arrangement whereby the nickel foils can be lowered into the furnace area for evaporation and subsequently raised to the beam level for bombardment. Hand formed boats of 0.08 mm tantalum were loaded with cubes of lithium approximately 2 mm on an edge. The boat temperature was initially raised high enough to melt the shell of hydroxide and nitride which had farmed during the loading of the boat, and to evaporate a visible amount of lithium onto the chamber walls. The boat temperature was then lowered for the actual target evaporation. For a given boat, it was found possible to reproduce target deposition rates within about 50 percent by noting the current through the boat. Targets were initially made somewhat thinner than desired, the yield from the lithium measured, and subsequent layers evaporated as necessary. The high vapor pressure of lithium at low temperatures, relative to that of, for example, Ni and Li 0, makes evaporation 2 of the target by heating from the beam a problem. At the low target temperatures required most of the energy deposited by the beam is conducted to the target rod through the nickel backing and lithium layer. Since the ratio of energy loss rate to thermal conductivity for lithium is much lower than that for nickel, a high ratio of lithium to nickel favors a lower target temperature. Thin nickel backings were therefore used for thin lithium targets. Frequent runs at checkpoints on the proton spectra were made to ensure the stability of the target. For a 10 MeV doubly-charged 10 3 He beam and 10 19 2 atoms/cm lithium on 5000 Anickel, no deterioration was noticed at beam currents less than O. 3 µa. D. Contaminant Problem A major experimental problem was the buildup of carbon and, to a much lesser extent, oxygen, on the target surfaces. Since the momentum range covered by the array is only 1/26 of momentum at the center counter, it was necessary, with both the array and the single counter, to scan the proton spectrum in several steps to cover a region of interest. This process inevitably 12 3 14 16 3 18 allowed proton groups from c( He, p) N and o( He, p) F time to grow. The oxygen was found to build up only on the surface of the lithium layer. Runs on oxidized nickel targets were taken and normalized to the obvious contaminant peaks in the lithium spectra. The oxygen content in a freshly evaporated lithium target was found 18 to be sufficiently small that the proton groups from F did not 9 significantly interfere with the Be groups. The growth rate was low enough to allow several hours running on the same target before 16 0 became a problem. The carbon, presumably cracked by the beam onto the target from organic vapors from sources such as diffusion-pump oil and 0-ring grease, was deposite d on both t he lithium layer and the back side of the nickel foil at rates approximately equal and proportional to the beam current. At an ambient pressure of 10- 6 mm of mercury, this rate was found to be approximately 1. 6 x 10 3 atoms of carbon per micro-coulomb of doubly-charged He. 12 11 For completeness, it should be mentioned here that runs on an oxidized lithium target carried out on the Kellogg 3 MV Van de Graaff accelerator also showed a carbon deposition rate proportional to the beam current. The target chamber was very similar to that used for the tandem work, with a major addition being a cylindrical cold trap extension, of 2 cm inner diameter, which surrounded the target. The target chamber and a cold trap extension very similar to the one used here are described by Cusson (1965). The target in this case was made by evaporating 2 18 a layer of approximately O. 5 x 10 atoms/ cm of lithium onto a O. 05 mm tantalum blank and exposing it to moist air for ten 6 minutes. At an ambient pressure of 10- mm of mercury, a O. 5 µa beam of 900 keV 3 He was found to deposit approximately 12 5. 5 x 10 carbon atoms per micro-coulomb of singly charged 3 He on the target. The hydrogen content in the lithium metal targets, in evidence for example in fig. 6, was also found to grow in time. Two procedures were fallowed to minimize the contaminant problem: First, runs on a carbon foil were made to locate the size and relative intensities of 14N lines. Points at expected locations of these lines were then taken immediately fallowing evaporation of the lithium target before contaminants had time to grow. The remaining spectrum was then scanned at comparative leisure. This procedure is illustrated in fig. 4. Second, the beam energy and proton angle were chosen in a way such that the contaminant groups appeared in as favorable 9 locations as possible with respect to the Be states. In order both to avoid crippling contamination and to find spectra in which the 12 9 Be groups stood out clearly above the continuum, it was necessary · to tailor the proton angle and beam energy 9 region of excitation in Be being studied. selectively to each E. Results (1) Below 10 MeV in 9 Be The region below 10 MeV was surveyed at three combinations of energy and angle (figs. 1 - 3). In agreement with previous studies of this reaction, proton groups appear from states at 0, 1.7, 2.43, 3.03 and 4.6 MeV. h1addition, the 6.76 MeV level is populated strongly in the two spectra taken at 90°. Th.e 9. 1 MeV state tentatively reported by Almqvist, et al. (1955), is not in evidence. The extraction of widths for the broad 4. 6 and 6. 76 MeV levels is inherently inaccurate due to the uncertainty in subtracting the background. Using only the criterion that the background be smooth and "reasonable", upper and lower limits were placed on the widths for these states, and are given in table L The coincidence work later provided better spectra from which to extract both of these widths (see pages 34 and 42 ). (2) 11. 29 and 11. 81 MeV States 9 The region of excitation in Be around 11. 5 MeV revealed two overlapping levels (fig. 4). It was felt that the. difficulty both of establishing that the qualitative interpretation of the proton spectra in this region was correct and of extracting the widths and excitations for the levels warranted a more detailed analysis than was given the region below 10 MeV. Consequently 13 the magnet spectra obtained for this region at three combinations of angle and bombarding energy were converted to excitation spectra (see appendix A for procedure) and a two-level fit to the data was made. The shape of the spectrum in this excitation region was assumed to have the form of two non-interfering Breit-Wigner resonances superimposed on a linear background: 2 2 2 2 Y(E) =A/[ (E-ERl) + r 1/4] + B/[ (E-ER2) +r 2/4] +C +D xE (13, 1) where C and D paramaterize the background. An eight-parameter non-linear least-squares fit was made to the data, allowing A, B, C, D, ERl' r 1 , ER 2 and r 2 to var:y in each spectrum. The minimization of chi-squared was done on the CIT-IBM 7094 computer by the familiar technique of numerically calculating the eight-dimensional gradient of chi-squared, then stepping along this gradient toward decreasing chi- squared until a minimum is reached. For each spectrum several sets of initial trial parameters were used to ensure that the minimum finally reached was not a sensitive 3 function of the starting point. Spectra taken at [ E( He) = 10 MeV, 8 0 3 = 1.7 ], [E( He)= 10 MeV, 9 0 3 . = 60 ] and [E( He)= 7 MeV, 8 p = 10°] were fitted in this man:er. Corresponding values of the p resonance energies and widths are summarized in table L Fig. 5 shows two of the fits so obtained. (3) 13. 78 MeV State The excitation region between 12 and 15 MeV revealed a previously unreported level at 13. 78 MeV with a width of 590 keV. 14 Two clean spectra of this level were obtained from runs on thick, 7 freshly evaporated Li targets, one of which is shown in fig. 6. The group also appeared in eight other spectra, but in most of these the presence of contaminant lines made the reliable extraction of excitation and width impossible. (4) 16. 671 MeV State Fig. 7 is a magnet spectrum showing a previously 9 unreported Be level at 16. 670 MeV. ,The experimental resolution for this spectrum was calculated to be 18 keV (FWHM) proton energy, being composed of 8 keV from the spectrometer resolution, 15 keV kinematic broadening and approximately 6 keV from target thickness and beam resolution. The experimental width of the curve in fig. 7 is 55 keV. After extracting the finite experimental resolution, the natural line width is left as 52 keV, corresponding 9 to a Be center-of-mass width of 40 keV. A similar analysis on a spectrum taken at 10 degrees, also with 18 keV experimental resolution, gave a center-of-mass width of 42 keV. Taking into account the errors involved in the background subtraction, and in determination of the half-width of the proton group, we adopt an average width of 41 ± 4 keV for this level. The resolution functions at both angles were checked using the proton group from the 14. 392 9 MeV level in Be, which is known to have an intrinsic width of (. 8 ± • 3) keV (Griffiths, 1965). 3 For Q-value measurements, the energy of the He beam at the target center was determined from the energy of the 9 proton group from the 14. 392 MeV Be level [ Q = (-3. 192 ± • 005) MeV]. The average Q-value found from four spectra (table I) was 15 Q = (-5. 472 ± . 008) MeV, corresponding to an excitation in 9 Be of 16. 671 ± . 008 MeV. (5) Peak Identification and Q-value Determination Each level was observed at several angles and bombarding energies. In order to ensure that the observed protons were in fact coming from a mass 7 target, a chi-squared fit to the Q-value for each level was done assuming the target masses 6 and 9 as well as 7 (table I). The chi-squared for mass 7 is, in the worst case, a factor of fifteen lower than that for the better neighboring mass, eliminating the possibility that the observed groups came from target contaminants. The possibility that a group may come from some more complex mechanism than the 9 population of a level in Be, for example by a two-stage sequential decay, is unfortunately not excluded by the determination of the target mass. The behavior with changing bombarding energy of groups produced by two- stage mechanisms is quite different from 9 that of Be groups, however. Precautions were taken to vary both the beam energy and the proton angle in all cases. The current version of the mass 9 isobar diagram is shown for convenience in fig. 35. 16 III. BRANCHING RATIO MEASURE:MENTS A. Outline of the Problem 9 Be has the unfortunate characteristic that the nucleus 8 to which it neutron-decays, Be, is itself particle unstable. This fact excludes the possibility of using this channel as an entrance 9 channel in measuring partial neutron widths from Be excited states. The situation is further complicated by the absence, below 7 9 the Li + d threshold, of any two- body channels through which Be may be formed as a compound nucleus, with the exception of the 9 Be + y channel. The measurement of the partial decay widths 8 9 to states in Be thus requires the population of the Be levels by a more complicated reaction, and the measurement of the branching ratios into the various outgoing channels. In the present experi9 9 ment, levels in Be were populated in the 7 Li(3 He, p) Be reaction. 9 The neutrons emitted in the subsequent decay of the Be levels were detected in coincidence with the populating protons, and the number of such coincidences was divided by the number of populating protons to find the branching ratio. The measurement of the energy and angle of the proton from the first stage of the reaction, for a well defined bombarding energy, determines kinematically the excitation and vector velocity of the recoiling 9 Be nucleus. The subsequent emission of the neutron to 8 a sharp state in Be will then result in a well defined neutron energy at each laboratory angle. The energy of this decay neutron is the 8 signature of the level in Be through which the decay is going. Measurement of both neutron and proton energy is thus necessary. In the present experiment, the proton energy was 17 obtained from a surface barrier solid state detector. Since the neutron is emitted promptly, typically within 10- 21 sec of the proton, the time between the detection of the proton near the target and of the neutron some distance from the target, typically 10 -8 sec, can be used to measure the velocity of the neutron. Thus a time-of-flight spectrum of the neutrons coincident with protons can be obtained. The coincidence work historically was done in two separate parts, and accordingly will be described as two separate experiments with liberal references from one to the other. The first part, carried out on the Kellogg 3MV Van de Graaff generator at a beam energy of 2. 2 MeV, was concerned with measuring the 9 neutron widths from Be states at 3. 03 MeV and 2. 43 MeV. The second part consisted in measuring neutron widths from higher 9 Be levels at 4. 65 MeV, 6. 76 MeV, 11. 29 MeV and 11. 81 MeV and was done on the tandem at bombarding energies between 5 and 10 MeV. B. 2. 43 and 3. 03 MeV Regions* (1) Introduction The major interest in this excitation region focused 8 9 on the decay of the Be (2. 43 MeV) level to Be (g. s. ). Two-body channels open for this decay are (see fig. 36): * Portions of this section have been taken from a paper by Christensen and Cocke (1967). 18 9 Be (2. 43 MeV) ... 8 Be {g. s.) + n ... 8 Be (2+) + n .... ... 5 9 He (g. s.) + a. ... 2a. + n (1) ... 2a. + n (2) .... 2a. + n (3) Be (g. s. ) + Y • (4) _.a. Sincer d/r,_ t =(l.16+.14) x 10 ... (PurdQmet.itl.,1966),partLcle decay ra • LO. dominate~ Channels (2) and (3) are available only through the tails of the 8 5 broad J?e (2+) and He (g.s. ). The spin ~d p;rity, 5/2-, 0£ the 9 Be (2. 43 MeV) level require that mode (1) proceed by f-wave neutron emission. Thus the size of the reduced width for this decay provides a direct measurement of the amount off-wave configuration present in the wave function for this state. 9 The branching ratio of the 3. 03 Me V level in Be through (1) was originally measured for use in analyzing the 9 Be (2. 43 Me V) decay. It soon became apparent, however, that this number was interesting in its own right. The single particle nature of this level served as partial motivation for extending the neutron decay measurements to higher excitations. (2) Kinematics The velocity diagram for the sequence 7 Li(3 He, p) 9 Be 8 (2. 43 MeV)(n) Be (g. s. ), at a bombarding energy of 2. 2 MeV, is shown in fig. 8. The proton, detected at a laboratory angle of 150°, 9 leaves the Be recoil travelling at 15. 7° with respect to the beam axis. After travelling a mean distance of approximately 5 x 10-lO 9 cm, the Be nucleus breaks up, sometimes emitting a neutron to 19 8 the grow1d state of Be at an angle e with respect to the c,n 9 laboratory Be velocity direction. The laboratory neutron velocity, 9 V L , is the vector sum of V , with respect to the Be, and the ,n c, n 9 laboratory velocity V 9 of the Be. Since the vector velocity L, Be 9 of the Be recoil has been defined by the proton detector, the final neutron energy is a unique function of laboratory neutron angle. If the reaction proceeds by the emission first of an 5 5 alpha-particle to He (g. s. ), then of a neutron by the He, the resulting neutron spectrum will be a continuum. This result is 5 due in part to the lack of definition of the He recoil velocity, and 5 in part to the range of excitation in the broad He (g. s.) through which the reaction may go. time spectrum at e L ,n The shape of the expected neutron = -15. 7° for the conditions used in the present experiment, calculated assuming isotropic angular distributions for both the alpha and neutron decays, is shown in fig. 9. 8 (See appendix B for calculation.) The Be (g. s.) neutrons appear at sufficiently high energy to be easily separated from this decay 8 mode. Decay neutrons to the tail of the Be (2+) will also give a 8 continuum, due to the breadth of Be (2+)~ (3) Experimental Apparatus (a) Targets 18 7 2 Li atoms/ cm 7 7 in the form of Li 0 were prepared by evaporating Li (99. 99%) 2 in vacuum onto O. 025 cm tantalum backings and then exposing them Targets of approximately 10 to air for approximately twelve hours. Carbon contamination again loomed as potential problem, in this case the offending reaction 20 being 12 c (3 He, a.) 11 c. decay of Annihilation radiation following the positron 11 c caused a high counting rate in the plastic scintillator used for detecting the neutrons, thus contributing to the random coincidence rate. The oxidized targets had the advantage of stability 3 at high enough beam currents (O. 5 - 2. 0 µa He+) both to provide a good coincidence rate and to keep the target temperature at a level where carbon buildup was not important. (b) Target Chamber The target chamber used for the associated particle work is shown in fig. 10. The proton detector is located 3 cm from the target, and is movable over the angular range 150° to -150°. Neutrons leaving the target must pass through the • 317 cm brass walls of the chamber en route to the neutron detector. For neutrons energies between 2 and 10 MeV, approximately 3 percent of the outgoing neutrons are inelastically scattered and 5 percent elastically scattered by the walls. When the yield from a monoenergetic neutron line is being measured, all neutrons whose energy has been changed sufficiently by scattering in the walls or whose flight path has been sufficiently lengthened by travel to the neutron detector via the walls to cause them to fall outside the expeI'.imental 2 ns time resolution are effectively removed. The inelastically scattered neutrons are immediately excluded. There is some chance that neutrons may be elastically scattered into the scintillator within the allowed 2 ns, after leaving the target at an angle other than the scintillator angle. The size of this effect depends in a complicated way on the neutron angular distribution, the kinematic change with angle of the neutron energy and the detailed geometry of the chamber. An estimate of its size, 21 assuming a spherical target chamber, isotropic neutron angular distribution, isotropic scattering without energy loss from copper and zinc nuclei in the walls and kinematics appropriate to 7 9 3 8 3 Li( He, p) Be (2. 43 MeV) (n) Be (g. s.) at E( He) = 2. 2 MeV, 8L = 150°, 8L = -15. 7° and d = 1 m, gives the result that ,p ,n only 3 percent of the neutrons elastically scattered by the walls will contribute to the observed neutron peak within the 2 ns resolution. It was therefore assumed that the neutrons elastically scattered by the brass walls were entirely removed. The observed yields were correspondingly multiplied by a correction factor of 1. 08. (c) Proton Detection The protons were detected at 150° to the incident beam in an 850 µ surface barrier detector. Aluminum foils of O. 025 and O. 23 mm thickness were placed over the counter to stop the elastically scattered beam. The resolution of the proton counter, limited il). the case of the thicker foil by straggling, was 125 and 225 keV respectively for the two foils, for 8 MeV protons. The thicker foil had the advantage of shifting the deuterons from 8 7 9 7 3 3 Li( He, d) Be (g. s.) below the protons from Li( He, p) Be (3. 03 MeV). The timing signal from the proton counter was derived from a commercially made ORTEC model 260 time-pickoff circuit. This unit consists of an inductive pickoff followed by a fast two-stage amplifier and a tw1nel-diode discriminator. The quiescent bias of the tunnel-diode may be adjusted externally, allowing a variable setting of the triggering level on the counter 22 signal. The time slewing of the proton-counter-time-pickoff unit was such that lowering the triggering point on the counter signal from approximately 90 percent to 50 percent shifted the neutron time spectrum by 4 ns. The signal from the time pickoff was used to start an ORTEC model 263 time-to-height-converter (TTHC). The linear signal from the counter was detected by a Tennelec model 100 A charge-sensitive pre-amplifier, and was followed by a Hamner model N-328 double-delay-line ·amplifier and single channel analyzer. The analyzer was used to select the region of interest from the proton spectrum. A sample spectrum from the proton detector is shown in fig. 11. (d) Neutron Detection The neutrons were detected at 60 to 100 cm from the target in either a (12. 7 cm dia. x 5. 08 cm thick) NE 102 or a (12. 7 cm dia. x 1. 91 cm thick) Naton 136 plastic scintillator, coupled to an XP-1040 phototube. The neutron counter could be rotated around the target in the plane defined by the beam axis and the proton detector. The scintillator was tilted with respect to the target scintillator axis at an angle such that the kinematic change in neutron energy over the finite angle subtended by the scintillator was compensated for by the change in flight path over this same angle. A timing signal was derived from the zerocrossing of the 2 ns delay-line-clipped anode pulse. The zerocrossover pickoff was built after the circuit design of Brafman (1965). The signal from the pickoff was used to stop the TTHC. The best neutron time resolution observed was 1. 2 ns (FWHM). 23 A slow linear signal was taken from the 13th dynode of the phototube, and was used to trigger a low-level discriminator. The signal from the TTHC was stored in a RIDL 400 channel analyzer when it was coincident with signals from the discriminator and from the proton detector single channel analyzer. A block diagram of the electronics is shown in fig. 12. (e) Neutron Detector Efficiency The efficiency of the neutron detector depends on the geometry and composition of the detector and on the setting of the low-level discriminator on the linear signal. The discriminator was set, using a 137cs source, to reject pulses of amplitude less than half-way down on the Con~pton edge from the 662 keV gammaray. . The amplifier gain was then raised by a factor of eight before taking neutron spectra. The relative efficiency of the thick (5. 08 cm) scintillator was measured as a function of neutron energy with the CIT-ONR tandem pulsed-beam-time-of-flight system, using the 3 3 reaction T(p, n) He. The discriminator cutoff was found to come at a neutron energy of • 45 MeV. The theoretical expression for the efficiency ( e) is given by (1 - e - crH NHL ) (23, 1) 3 where NH is the number of hydrogen atoms/ cm , cr H the n-p scattering cross section, L the thickness of the scintillator and B the discriminator cutoff. This formula is derived neglecting 24 scattering from carbon atoms in the scintillator, and is found to be adequate in the region of 6 MeV neutron energy (Swartz and Owen, 1960; Rybakov and Sidorov, 1960). For Ne 102, 24 3 NH=. 0525 x 10 /cm • With B =. 45 MeV, E = 6. 0 MeV, cr H = 1. 45 barn and L = 5. 08 cm, expression ( 23, 1) gives e (6. 0 MeV) = O. 295. The relative efficiency data were normalized to this point. An absolute efficiency measurement made at 3 E = 6. 23 MeV using the reaction D(d, n) He agreed within 10 n percent with expression ( 23, 1). Figure 13 shows both measured and calculated values for e as a function of E . n The efficiency of the thin scintillator (1. 91 cm) was measured relative to that of the thick scintillator. For neutron energies between 1 and 2 MeV it was found that e; (thick) = 2. 21 x e; (thin). Table ID summarizes the neutron efficiencies used in the calculations for each part of the experimental work. (4) Experimental Procedure The procedure followed was to record a time spectrum, using the single channel analyzer on the protons to define the region 9 of interest in Be. Figure 14 shows a time spectrum recorded with the proton window accepting protons corresponding to excitation 9 energies in Be between 2. 2 MeV and 3. 9 MeV. Figure 15 shows the same spectrum converted to an energy spectrum. Before converting the time spectrum the random coincidences, indicated by the dashed line in fig. 14, were subtracted. 9 The neutron group from the Be (2. 43 MeV) to 9 Be (g. s.) stands out clearly. The group at E = 2. 77 MeV is due n 25 9 8 to the decay of Be (3. 03 MeV) to Be (g. s. ). E n Neutrons below = 1. 7 MeV are due mainly to decay modes (2) and (3). The background beneath the 2. 43 MeV peak and the 3. 03 MeV group may be attributed to neutron decay from the continuous background in the proton spectrum. 9 9 Since the tails of the Be (3. 03 MeV) and Be (1. 7 MeV) 9 states extend below the Be (2. 43 MeV) peak in the proton spectrum 9 (see fig. 11), a narrow window around the Be (2. 43 MeV) proton group will always produce a peak in the time spectrum corre8 sponding to a Be (g. s.) transition. As the branching ratios to 9 8 9 Be (g. s.) from Be (3. 03 MeV) and Be (1. 7 MeV) are factors of 9 ten greater than that from Be (2. 43 MeV), this contribution may be appreciable. The proton window for fig. 14 and fig. 15 covered a 9 wide range of excitations in Be. The neutron group labeled 2. 43 therefore cannot have been produced artificially by a narrow proton 9 window, but must come from a narrow state in Be. The corre9 sponding excitation energy in Be calculated from the measured flight time is 2. 44 ± O. 05 MeV. Because of counting rate and resolution problems at lower neutron energies, it was found impractical to distinguish the 9 Be (2. 43 MeV) neutrons by their flight time alone at all eL • The ,n procedure then followed was to set a narrow proton window around 9 the Be (2. 43 MeV) proton group and to correct the observed neutron 9 yield for the contribution from the Be (3. 03 MeV) state and the 9 Be (1. 7 MeV) state. A typical time spectrum obtained by t his procedure is shown in fig. 16B. The region marked "p-window" 8 r efers to Be (g. s. ) neutron energies corresponding to the region 9 of Be accepted by the proton window. The part of the spectrum 26 marked "3. 03" indicates the neutron contribution from that part 9 of the Be (3. 03 MeV) state falling inside the proton window. 8 To calculate the contributions to the Be (g. s. ) neutron 9 9 group from the Be (3. 03 MeV) and Be (1. 7 MeV) states, the 9 populations of these states relative t o that of the Be (2. 43 MeV) state were needed. These were obtained by fitting the observed proton spectrum with appropriate "density of states" functions, as described by Barker and Treacy (1962), assuming t = 2 and t = 0 8 9 9 neutron decays to the Be (g. s.) for the Be (3. 03 MeV) and Be (1. 7 MeV) states respectively. The resulting fits, after folding in the proton counter resolution function, are shown in fig. 11. The relative population of the three levels inside any proton window could then be calculated. 8 Using the measured yield of Be (g. s. ) neutrons from 9 the 2. 9 - 3. 5 MeV region in Be (see fig. 17), and assuming that 9 these neutrons came entirely from the Be (3. 03 MeV) state, the 8 contribution of this state to the Be (g. s.) neutron group was calculated for the case where the proton window was narrowed 9 around the Be (2. 43 MeV) protons. The size of this contribution 8 to the Be (g. s.) neutron peak was less than 20 percent of the total number of neutrons in the peak at all angles. 8 9 The Be (g. s.) contribution from the Be (1. 7 MeV) state was calculated assuming a branching ratio of 100 percent and an isotropic center-of-mass angular distribution (s-wave neutrons). This contribution to the 8 Be (g. s.) neutron peak was never larger than a few percent of the total number of neutrons in the peak. = -15. 7° neutron yields obtained by this ,n procedure agreed within statistical error with those obtained from At eL spectra such as fig. 14. 27 (5) Results The angular distribution of neutrons from the decay 8 of Be (2. 9 - 3. 5 MeV) to Be (g. s.) was measured from e = o0 9 ·C n to e = -80°. The result is shown in fig. 17. The vertic~ scale c,n 3 is the number of neutrons per steradian per 10 protons in the proton window, after converting from laboratory system to centerof- mass system, dividing by the neutron detector efficiency, and correcting for scattering in the backing and target chamber wall. Figure 18 shows the angular distribution of neutrons 9 8 for the decay of the Be (2. 43 MeV) state to Be (g. s.) from 9c ,n = -90° to eC·, n = 80°. The vertical scale is neutrons per 9 steradian per 103 protons leaving the Be in its 2. 43 MeV state. To obtain the branching ratio for this decay mode, one should measure the neutron distribution over the entire sphere. Parity conservation requires that the angular distribution have even parity, so a measurement over any hemisphere is sufficient. There is in general no axis of symmetry, however. The angular distribution of the neutrons from the 8 Be (2. 43 MeV) state to the Be (g. s.) is within the experimental 9 errors symmetric about the Be (2. 43 MeV) recoil axis in the 9 reaction plane. By assuming rotational symmetry about this axis, 9 one finds that 7. 5 ± 1. 5 percent of the Be (2. 43 MeV) decays go by an .e, = 3 neutron to the 8 Be (g. s. ). Similarly, one gets that 61 ± 9 percent of the 8 excitation region 2. 9 MeV to 3. 5 MeV decays to the Be (g. s. ). Only 70 ± 5 percent of the protons corresponding to this region 9 leave the Be in its 3. 03 MeV state. Assuming that it is only the 9 8 Be (3. 03 MeV) state which contributes to the Be (g. s.) decay, one 28 finds that 87 ± 13 percent of the time this state decays by an 8 t = 2 neutron to the Be (g. s. ). It may be mentioned here that a number of previous measurements of the branching ratio for the 2. 43 Me V state in 9 8 Be to Be (g. s.) + n have been reported. Bodansky, Eccles 9 9 and Halpern (1957) did the experiment Be (a,a. 1) Be(2. 43 MeV) 8 4 (n) Be(g. s. )(a.) He, looking for the alpha particles in the breakup 8 . . of Be(g. s. ). Their result was that less than 10 percent of the 9 decay of the 2. 43 MeV state in Be goes by mode (1). A branching ratio of 12 ± 5 percent for the ground state has been reported by Marion, Levin and Cranberg (1959) from a study of the reaction 9 8 Be(n, 2n) Be. The lack of vector-momentum definition of the 9 Be(2. 43 MeV) nucleus in this experiment, however, makes a unique interpretation of the data impossible. The neutron energies 9 from the Be(2. 43 MeV) decay overlap considerably the energies of the neutrons from the initial population of this state. Messner, Schmidt and Schintlmeister (1965) have reported a figure of 13 ± 5 percent for the branching ratio from a study of the reaction 9 4 12 8 c(n, a.) Be(n) Be(g. s. )(a.) He. The interpretation of the data is again ambiguous, as recog11ized by the authors. In their experi8 ment it was impossible to distinguish between Be(g. s.) decays 9 from the 2. 43 MeV state in Be and those from the tails of the 3. 03 MeV state and the 1. 7 MeV state. C. Higher Excitation Regions (1) Introduction The primary interest in the 9 8 Be(g. s.) neutron width from the Be(2. 43 MeV) level was in the small f-wave components 29 of the wave fw1ction. The strong d-wave neutron decay from the 9 Be(3. 03 MeV) level suggested that much information on the major 9 components of the wave functions of other Be levels might be available from the neutron decay widths. Consequently the experi- ment was moved to the tandem accelerator where the greater beam 9 energy allowed the population of higher states in Be. Neutron 9 decay from levels in Be at 4. 65, 6. 76, 11. 29 and 11. 81 MeV 8 was studied. Since the stability of the Be nucleus is not a requirement with the associated particle teclmique, it was possible 8 to extract information on neutron decays to Be (2+) as well as to 8 9 Be(g. s.) from the 6. 76, 11. 29 and 11. 81 levels in Be. The relevant decay energies are shown in fig. 36. (2) Experimental Apparatus The associated particle time of flight spectrometer described in Section B was transferred as a whole to the tandem and, with only a few exceptions, the teclmiques described above were employed. Only the exceptions will be discussed below. 3 Doubly charged He beams of 0. 1 - O. 2 µa, of energy ranging from 5 to 10 MeV, were· provided by the tandem. It was 7 not possible to use Li 0 targets at these beam energies, since 2 16 3 the o( He, a,) 15o reaction now proceeded much more strongly than it had at low bombarding energies. Annihilation radiation 15 from the positron decay of the 0 created a high counting rate in the plastic scintillator, thus adding to the random rate. Con18 sequently, lithium metal targets of approximately 5 x 10 atoms/ 2 7 cm , enriched to 99. 99% Li, were evaporated onto O. 050 - 0.075 mm tantalum backings and transferred under vacuum to the target 30 chamber. The target transfer system is shown schematically in fig. 10. detector. The protons were detected in a 1000 µ surface barrier 0 3 For work at 0 , the He beam was ranged out by the tantalum backing, while the protons passed through into the counter. A Nuclear Data 4096 channel analyzer, operating in a two-dimensional mode, was used to record neutron flight time versus proton energy. (3) Kinematics and General Features In the measurement of the branching ratio to 8 Be(g. s.) 9 Be(2. 43 MeV), one was dealing with a sharp state in Be. 9 At higher excitations in Be the levels become broader, and lie on from 9 large backgrounds. To interpret the spectra in this region requires that one measure neutron time spectra over a wide range of proton energies. For this. reason, a two-dimensional analysis of neutron flight time versus proton energy was made. The discussion on pages 18 and 19 treats the kine8 matics for the reaction 7 Li+ 3 He -+ Be(g. s.) + n + p for the case where the reaction proceeds sequentially through a sharp state in 9 9 Be. At the higher excitation regions the breadth of the Be levels and competition from other reaction mechanisms require that one adopt a view of the kinematics not restricted to sequential decays. If the total momentum and energy of a three-body final state are given, and if two of the particles are detected in coincidence at fixed angles, a measurement of the energy of one of the detected particles supplies enough information to determine the final vector momenta of all three particles, using only conservation of energy 31 and linear momentum. Thus a plot of the energy of one detected particle as a function of the energy of the other will result in a kinematic line. As an example, a plot of calculated proton energy 7 3 8 versus neutron flight time for the process Li+ He .... Be(g. s.) 3 0 + n + p with E( He) = 10 MeV, eL, P = 90°, eL, n = o is shown in 8 fig. 19. The .kinematic line for the case where the Be is left in its first excited state is also shown. Since each point on a kinematic line corresponds to completely determined final momenta for the three particles, the excitations in systems comprised of any two of the particles are also determined. For example, in fig. 19 a point on either kine9 9 matic line specifies definite excitations in Be, B and d. An enhanced population .along the line may appear whenever a resonant excitation in one of the above three nuclei is encountered. In the case where such a resonance is very strong, the process is said to proceed sequentially through the corresponding intermediate state. In the present experiment interest was focused on those 9 resonances for which the reaction proceeded through states in Be. The excitation range in the n-p system was sufficiently high that no pronow1ced structure from this interaction was expected. The same 9 could not be assumed in the case of B, however. The reactions 7 Li(3 He, p) 9 Be(n) 8 Be and 7 Li(3 He, n) 9 B(p) 8 Be can both produce 8 8 resonant groups along Be(g. So) and Be(2+) kinematic lines. Only by tracking such groups as the beam energy or detector angles are changed can the processes be distinguishedo Fortunately, the 9 relevant excitation region in B showed sufficiently little structure 9 that the Be groups c ould be separated. Individual cases are discussed with the description of the analysiso 32 Figure 20 shows an oscilloscope display of the experimental data corresponding to fig. 19. A few general features of this spectrum are easily discernible, and are indicated on fig. 19: 9 5 1) The decay of the 2. 43 MeV state in Be to He + a appears as a horizontal line. The proton energy from population of 9 5 the state is fixed, while the two stage process Be -+ He + a -+ 2a. + n produces a continuum of neutron energies. 9 2) The 3. 03 MeV state in Be is seen to decay strongly 9 8 8 along the Be(g. s.) line. The decay of Be(4. 65 MeV) to Be(g. s.) appears as a considerably weaker but still easily discernible group. 9 3) The 6. 76 MeV state in Be is seen to decay strongly along the 8 Be(2+) line. There is little, if any, sign of the decay of 8 this state to Be(g. s. ). If the proton from the population of a state is observed at an arbitrary laboratory angle, the differential decay probability for the associated neutrons must be measured over the whole sphere. 0 When the proton is observed at o , however, the corresponding angular distribution of the decay neutrons must have axial symmetry about the beam axis. Furthermore, if the decay is from a single 9 state in Be with a well defined parity, the corresponding neutron angular distribution must have a positive parity. In the pre sent experiment population protons from the 4. 65 MeV, 11. 29 MeV and 9 0 11. 81 MeV states in Be, were observed at o and the associated ° neutron angular distributions were measured only out to 90 in tile 9 Be center-of-mass system. 33 (4) Experimental Procedure and Results (a) 4. 6 5 MeV State Figure 21 shows a singles spectrum from the 0 3 barrier counter taken at e L = o , E( He) = 5. 0 MeV. The 7 3 ,p + deuteron yield from Li( He, d)8Be(2 ) completely obscures the 9 proton yield in the region around 4. 65 MeV in Be. For this reason a singles spectrum was taken with the mag11etic spectrometer at the same angle and energy, separating protons from deuterons. The resulting proton spectrum is shown in fig. 22. 9 The number of times the 4. 65 MeV state in Be was populated was derived from this data, using the proton yield to the 2. 43 MeV 9 state in Be to normalize this spectrum to that from the solid state counter. The deuterons present no problem to the coincidence spectra, since they cannot be accompanied by neutrons. Two-dimensional coincidence spectra were taken 0 at thirteen neutron angles between e L = o and 130°, for 3 ,n 0 eL = o , E( He) = 5. 0 MeV. The procedure followed to obtain the ,P8 9 Be(g. s.) neutron yield from the Be(4. 65 MeV) state was the following: 1) For each coincidence spectrum, time spectra from each proton channel were plotted. Fig. 23 shows an example of such a spectrum for a proton energy corresponding to 4. 75 MeV . 9Be. m 8 2) The Be(g. s.) yield was extracted from each spectrum and plotted as a function of proton channel number. Fig. 8 24 shows a sample of such a sum along the Be(g. s.) line. The 34 9 8 decay of the 4. 65 MeV state in Be to Be(g. s.) appears as a resonant group along this line. 3) The number of neutrons in this group was divided by the neutron detector efficiency, corrected for scattering in the chamber walls and target backing, divided by the number of populating protons and plotted as a function of neutron angle. The o0 yield from the 7 Li(3 He, d) 8 Be(g. s.) was used to normalize the coincidence spectra to the singles spectrum. The measurement of the yield from the 9 Be(4. 65 MeV) level in both the singles and coincidence spectra depends on knowing the width and excitation of the level. This is especially important in the case of the singles spectrum where the size and shape of the assumed background depend sensitively on the width ta.ken for the proton group. It was found that an excitation energy of 4. 65 MeV and width of 900 keV provided consistent fits to both singles and coincidence spectra without requiring the assumption of unreasonable backgrounds. The resulting fits, taken to be of the form Y(E) = (const.)/[ (E - ER) 2 2 + r /4] are shown as solid lines in figs. 22 and 24. , (34, 1) It was found that the branching ratio decreased by only 10 percent if the width used was increased to 1000 keV, as long as this width was used in fitting both the singles and the coincidence spectra. To confirm that the group being observed in 9 9 the coincidence spectrum came from Be and not B, plots were 9 9 made of the excitation in Be versus that in B for the reaction 35 7 Li+ 3 8 He ultimately proceeding to Be(g. s.) + n + p. The relationship is given in fig. 25 for several values of e L for 3 o ,n E( He) = 5 MeV, e L = 0 • The heavy dots are the experimental ,p points, with their associated errors. The excitation of the 9 Be(4. 65 MeV) group is seen to remain constant at e c n :5. 90°. ' for The deviation in excitation of this group from 4. 65 MeV 9 e cn> 90° may be an indication of a contribution from a B level 9 9 at :_., 9. 8 MeV. Since the excitation in Be of the Be(4. 65 MeV) group appeared constant in the forward hemisphere, and there are 9 no known levels between 9. 7 and 11. 6 MeV in B, the region o0 $. e L n ~ 70° was used for branching ratio measurements for ' this stateo The differential branching ratio of neutrons to 8 Be(g. s.) from the e c,n· in fig. 26. 9 Be(4. 65 MeV) state is shown as a function of Integration of this angular distribut ion gives a total branching ratio of (13 + 4) percent. (b) 11. 29 and 11. 81 MeV States The 11. 29 and 11. 81 MeV levels were populated 3 at E( He) = 10 and 9 MeV, e L = o0 • Seven coincidence spectra 'e: were taken in the region o ~ n $. 80°. The extraction of 8 branching ratios to Be from the;e states required the solution 0 to several new problems: 1) Since these levels overlap considerably, ( r (11. 29 MeV) = 620 k:e V, r(ll. 81 MeV) = 400 keV), a detailed knowledge of the composition of the proton spectrum was necessary. Fig. 27 shows a solid state counter spectrum corresponding to this 3 region of excitation, for E( He) = 10 MeV, e L = o0 • The ,p 36 experimental resolution in this spectrum is approximately 380 keV, primarily due to the straggle of the protons through the target backing. The widths and relative intensities of the two levels from this reaction had been measured previously at the same bombarding energy and proton angle with a resolution of 50 keV, using a magnetic spectrometer (Fig. 5, page 13 ). The solid curve through the data points in fig. 27 is a fit to the experimental points of the form given in eq. ( 13, 1) • The parameters ERl' r l' ER 2, r 2 and A/Bx r 2/r1 are consistent with the values used in the fit of fig. 5, after taking into account the poorer experimental resolution. A comparison of the parameters used in the two fits is made in table II. The background in the solid state counter spectrum is due to deuterons and to protons not stopped in the counter, as well as to the proton 12 16 1 continuum. Some sign of c, 0, and H target contamination is seen. 2) The large energy release in the decay of these 8 states to Be produced much faster neutrons than did the lower 9 8 8 lying Be states. In order to resolve the Be(g. s.) from the Be(2+) the neutron counter had to be removed to a distance of about one meter. The corresponding reduction in solid angle, and thereby in counting rate, made it impractical to gather sufficient statistics 8 8 to make a meaningful plot of either Be(g. s.) or Be(2+) sum versus proton energy, as was done for the 4. 65 MeV state. The alternate procedure adopted was to evaluate the sum at only four different proton energies. For each coincidence spectrum, time spectra were summed from four strips of the two dimensional spectrum, each strip having the same width along the proton energy axis. The locations of the.strips were chosen in such a way that they represent 37 9 time spectra from excitations roughly centered at Be(11. 29 MeV; 9 9 region ill), Be(ll. 81 MeV; region II), Be(10. 5 MeV; region IV) 9 and Be(12. 5 MeV; region -). A sample of the raw data is shown in fig. 28 with the appropriate regions outlined; the regions are also indicated on the singles spectrum of fig. 27. Corresponding summed time spectra are shown in fig. 29. By summing over the several proton channels , it was possible to obtain enough counts to make practical the 8 8 extraction of the Be(2+) and Be(g. s.) yields from each region. 8 8 The variation in time of the Be(g. s.) and Be(2+) neutrons across 9 such a region, due to the change in excitation in Be and to slewing in the proton timing, was approximately • 8 ns, as compared to the experimental time resolution of about 2 ns. Crudely speaking, time spectra from regions I and IV represent a background on which the decay from the 11. 29 and 11. 81 MeV levels, regions III and II respectively, is expected to lie. By linearly interpolating the behavior of this background between regions I and IV, the resonant behavior in regions II and ill could be determined. 8 For quantitative e:h.1:raction of the Be(2+) 9 9 8 yields to Be(l1. 29 MeV) and Be(11. 81 MeV), the Be(2+) neutron yield per proton channel as a function of proton energy was assumed to be of the form of eq. ( 13, 1 ) at each e L . For each ,n coincidence spectrum, the four unknown parameters in this equation, 8 A, B, C and D, were evaluated from the measured Be(2+) yields in the four regions. From the values of these parameters the 9 8 number of Be(2+) neutrons in the 11. 29 MeV and 11. 81 MeV Be groups could be calculated at each e L n· ' This procedure was 38 checked by e:h.'tracting A, B, C and D in fig. 27 from the yields in the four regions. The values of these parameters so obtained agreed with those obtained from the curve fitting. A similar 8 procedure was followed for the Be(g. s.) neutrons. The importance of including the background terms (C and D) of eq. ( 13, 1) in the coincident neutron yields 8 cannot be overemphasized, since by no means all of the Be(2+) 9 neutron yield in regions II and ill comes from Be(ll. 81 MeV) and 9 Be(ll. 29 MeV) respectively. 3) The determination of the 8 Be(2+) yield from each time spectrum required a knowledge of the shape of the neutron continuum. This continuum is supposedly due to decays 8 5 through Be(4+) and through He + a - 2a. + n (see level scheme in fig. 36). Fig. 30 shows a time spectrum from region II taken at e L = 30°. The dashed curve is a calculated shape 8 assuming a d~cay through Be(4+). The solid line is a calculated spectrum assuming isotropic breakups through the ground state of 5 He. (See appendix B for calculations.) The representation of the observed neutron spectrum by the latter shape is sufficiently good to lead us to use this continuum shape consistently in the 8 extraction of Be(2+) yields from all the spect ra. The continua shown in fig. 29 are of this form, for example. The errors quoted in the final branching ratios are largely due to the uncertainty in this background shape. The angular distributions of neutrons, divided by the neutron efficiency, corrected for scattering in the chamb·~ r 9 wall, and converted to the Be system, from the 11. 29 MeV and 39 9 8 11. 81 MeV states in Be to Be(2+) are shown in figs. 31 and 32. As no pronounced structure in the compound nucleus has been seen at E(3 He) in the vicinity of 10 MeV, the polarization of the 9 Be nucleus was not expected to change sig11ificantly when the bombarding energy was lowered from 10 to 9 MeV, and thus points from the two bombarding energies are included on the same graph. 7 3 9 8 Since the kinematics for the sequential processes Li( He, p) Be(n) Be 9 8 7 3 and Li( He, n) B(p) Be, vary quite differently as the bombarding energy is changed, the consistency of results at different bombarding energies provides a good check against any possible perturbing 9 influence of decays from levels in B. The branching ratios obtained from the integrated 8 9 angular distributions are: Be(ll. 81 MeV) to Be(2+), (12 ± 4) per9 8 cent; Be(ll. 29 MeV) to Be(2+), (14 ± 4) percent. Only upper 9 8 limits could be placed on the Be(g. s.) decay: Be(11. 81 MeV) to 9 8 8 Be(g. s. ), $. 2 percent; Be(11. 29 MeV) to Be(g. s. ), $. 3 percent. (c) 6. 76 MeV Level The extraction of the neutron decay probabilities 9 for the 6. 76 MeV state of Be was hindered by two major difficulties: 1) Since the state is quite broad, it is necessary to operate at a proton angle for which this group stands out strongly above the background in the singles spectra. Whereas the 4. 65, 11. 29 and 11. 81 MeV states were strongly populated at e L ,P = 00 , the 6. 76 MeV level was relatively weak at this angle, standing out strongly at e L = 90°. This made it experimentally impossible ,p 0 to use the axial symmetry gained at e L = 0 • ,p 40 2) While the neutrons from the decay of the 6. 76 8 MeV region to Be(g. s.) were easily separable, those to the broad 8 Be(2+) were difficult to separate from those coming from the 5 8 He + a. decay. Accordingly, the analysis of the Be(2+) decay of 9 the 6. 76 MeV level in Be was directed toward placing limits on the decay probability, rather than extracting a number for the branching ratio. In fig. 33A is shown the result of projecting onto the proton energy axis the coincidence spectrum of fig. 20, 8 excluding neutrons from the Be(g. s.) line. This spectrum will 8 contain neutrons from both Be(2+) and 5 He + a. decays. The 6. 76 9 MeV level in Be stands out strongly above the background, an essential point in the interpretation of its decay spectrum. The neutron time spectrum corresponding to decay from a 600 keV 9 wide region in Be centered at an excitation of 6. 8 MeV was taken 9 to represent the decay from the Be(6. 76 MeV) level, the implicit assumption being that the background decay mode is the same as that for this level. Since the background at this point is less than 20 percent of the peak height, this assumption is not expected to introduce a large error into the results. Fig. 34A shows the 6. 8 MeV decay spectrum from the coincidence spectrum of fig. 20, converted to a center-of-mass energy spectrum and divided by the neutron detector efficiency, plotted versus excitation in the a. - a. system. For the choice of e L ,p and e L ,n in this figure, the neutrons are being emitted at o0 with respect to the laboratory 9 velocity of the recoiling Be nucleus. Any attempt to extract a branching ratio from a measurement at a single neutron angle is dangerous, as is evident, for example, from fig. 18. Consequently 41 a 6. 8 MeV decay spectrum taken at e L = 25° is also shown 9 (fig. 34B), corresponding to an angle of ~9° in the Be system 8 for decays through the center of Be(2+). The angle is measured 9 with respect to the laboratory direction of the Be recoil. These spectra amount to a poor-man's two-point neutron angular distribution. The solid curves represent the expected shape 8 of the Be(2+) level, folded into the experimental resolution. These curves are taken to represent upper limits on the amount 8 of Be(2+) decay at the two neutron angles. If a branching ratio in this case is taken, at each angle, to be the number of 8 Be(2+) neutrons divided by the total number of neutrons, upper limits of 68 and 69 percent are found in figs. 34A and 34B respectively for 8 9 the branching ratios of Be(6. 76 MeV) to Be(2+). The lower limits for this decay mode are more difficult to deduce. The dashed curve in fig. 34A represents the spectral shape expected from neutrons from the ground state 5 5 of He for isotropic angular distributions of both the He' s and the 5 neutrons from the subsequent He decay. If an angular distribution 2 9 5 of the He's given by W(e ) = 1 + cos e in the Be system is c, n c, n taken, a somewhat better representation of the spectrum at high 8 Be excitations is obtained, although the general features of the spectrum are not drastically affected. Dash-dotted curves in figs. 9 0 34A and 34B represent spectral shapes at o and 90° in the Be 5 system, respectively, using this He angular distribution. The 8 height of these curves under the Be(2+) peak has been taken to 5 represent the maximum contribution from He d·~cay to this peak. 9 The corresponding lower limits on the Be(6. 76 MeV) decay to 8 Be(2+) are 41 and 44 percent for figs. 34A and 34B respectively. 42 8 Fig. 33B shows the Be(g. s.) yield from the spectrum of fig. 20, plotted versus proton energy. No resonant effect is seen at 6. 76 MeV. The corresponding ~pper limit on 9 8 the branching ratio of Be(6. 76 MeV) to Be(2+) is 2 percent. 9 The width of the Be(6. 76 MeV) level, taken from fig. 33A, is r = 2. 3 ± .4 MeV. A similar spectrum taken 0 at e L n = o gave r = 2. 2 ± .5 MeV. The width used in calculating ' the partial neutron widths is r = 2. 3 + .4 MeV. 43 IV. CALCULATION OF REDUCED WIDTHS: In order to compare our experimental results with nuclear model predictions it is convenient to extract from our data the 9 reduced widths for single neutron emission from the Be states under investigation. Following the R-matrix formalism, the line 9 shape of a Be state is assumed to have a "generalized density of states" function (Barker, 1962) of the form (43,1) where = 2kRP-t (kR) y -t 2 t. (E) k = center-of-mass wave number R = channel radius are the regular and irregular coulomb wave functions, respectively = P-t(p) o 1 P - 2 - oP ( P-t(p)) = Reduced width in channel denoted by .i . 44 If b. is assumed to have a linear variation with E across the resonance, this expression can be written (Thomas, 1.951) p (E) = con st. 2 2 x r TO (E)/ [ (E - ER,) + (rTO(E)/2 J where ( 44, 1 ) Although r TO itself is a function of energy, due to the dependence . of r T on energy, a good representation of the curve shape is obtained by taking r TO to be a constant, and to have the value which it has at E = ER,. Let rTO = rTO(ER,) rT = r T(ER,) r;e, = r-!- (ER,) . The line shape is then given by p (E) = const. - 2 - )2 x r TO/[ (E - ER,) + (IT 0 / 2 J • (44, 2) 45 9 r TO was obtained for each level by fitting the observed Be line shape to expression ( 44, 2 ). f T was then obtained using expression ( 44, 1 ). Since the evaluation of ( 44, 1) involves 2 knowledge of y t , an iterative procedure was used. Table N shows values of f T and f TO so obtained. The 3. 03 MeV level shows the greatest difference between fT and f TO" The 6. 76 MeV level has been taken to decay entirely through the channels ( 2) and ( 3) (see page 18 ). No shift function correction has been made for the levels at 11. 29 and 11. 81 MeV. Al~hough the branching ratios from a broad level through various decay channels vary, in principle, with excitation within the level, the approximation has been made here that 2 2 Reduced widths, expressed in units of ti /mR , are then given by et 2 2 = rT x (B. R. )-0 x [ 2kRP-l (kR)ti /mR 2 -l J (45, 1) 2 Table V shows the values of et so obtained. The reduced widths for 8 Be(2+) decay from the 11. 29 and 11. 81 MeV states have been tabulated assuming both p- and f-wave emission, as discussed below. 46 V. DISCUSSION A. Introduction In this section we attempt to interpret our results in the light of current nuclear models. Our choice of model is directed not solely by the agreement which it affords with our results, but also by the availability of detailed theoretical calculations. The problem naturally divides itself into separate discussions of negative or normal parity states and positive or non-normal parity states. For the former, we compare our results with lpshell model calculations; for the latter, with calculations based on a single particle model which in some sense approximates a shell model with higher configurations. A discussion of the 9 applications of the Nilsson model to Be is reserved for separate consideration. B. Non-normal Parity States and the Shell Model Recent shell model calculations for the A = 9 system, 4 5 using the (ls) (1p) configuration, have been done by Barker (1966) and by Cohen and Kurath (1965). The level scheme of Barker, very similar to that of Cohen and Kurath, is shown in fig. 37. The corresponding wave functions are in most cases near the pure LS-coupled wave functions, and, accordingly, the levels in fig. 37 are labeled with the spectroscopic notations of their major LS 9 components. The Be ground state, 2. 43 MeV state and 6. 76 MeV 22 22 state are taken to be the higher J components of the P, D and 22 F doublets, respectively. The lower J components of these doublets have not been seen experimentally. 47 Positive parity levels at excitations as high as 11 MeV are expected to be quite broad (see page 50 ). We accordingly choose to interpret the relatively narrow 11. 29 and 11. 81 MeV 9 states in Be as negative parity levels, and to include them in the present discussion. The reduced widths for single nucleon emission by levels of A = 9 to states in A = 8 have been calculated by Barker (1966a), ustng his intermediate coupling shell model wave functions (Barker, 1966), and by Kurath (1966) using the wave functions of Cohen and Kurath (1965), and are shown in table VL Si.nee only lp configu- rations are used in both sets of wave fw1ctions, only reduced widths for p-wave neutron emission are non-zero. The absolute values of calculated reduced widths depend sensitively on the radial wave functions for the emitted nucleons. As discussed by Lane (1960), it is difficult to calculate this wave function accurately enough for the widths derived from the calculation to be meaningful. consequently theoretical reduced widths are generally normalized to an empirically determined single particle reduced width, 2 esp • Lane (1960) finds, from a survey of lp-shell reduced widths, that a e 2 = .6 gives an adequate fit to the experisp 2 mental data. The values of e given in the table were calculated using this value for e!p· P single particle value of (1) 6. 76 MeV State The spin and parity of this level, 7/2-, forbid its 8 decay to Be(g. s.) except by f-wave neutron emission, and it is therefore not surprising that this decay mode was not observed. The upper limit s. 6 x 10- 2 is greater than the positive result e; 48 2 = 2. 1 x 10- 2 found for the 2. 43 MeV level of 9 Be. f 2 8 + 2 The calculated value of e to Be(2 ), e = .126 p p is somewhat smaller than the lower limit of e 2p < - .28 found of e experimentally. There are several states predicted by the p-shell model in this excitation region which have never been seen experimentally. It is certainly not possible to rule out that the very broad 6. 76 MeV level may contain contributions from more than one level. (2) 11. 29 and 11. 81 MeV States There are at least four theoretical candidates for these two experimental levels, namely the [ 4, 1] 22 G 7/2 - and 9/2 2L!- - levels, and the [ 3, 2] ·p 1/2 and 3/2 - levels. It is possible to get some feeling for what to expect from these levels by looking at these states in the LS-coupling limit. The first three levels in 8 9 Be have a [ 4 ] symmetry in this scheme; only states in Be of symmetry [ 4, 1] have non-zero parentage for a single nucle on 8 coupled to these Be levels. The [ 3, 2] levels would be expected to have zero reduced widths for the emission of neutrons to the 8 first three l evels in Be in LS coupling. Continuing in the LS-coupling limit, the doublet G, L = 4, levels cannot be formed by coupling a p-wave nucleon to 8 8 Be(g. s.) (L = 0) or Be(2+) (L = 2). Neutron decay to these levels is thus also forbidden. Decay to 8 Be(4+) is not forbidden from these levels in the LS-coupling limit. The calculated values in intermediate coupling 2 8 (a/k = 2. 25 ; . see Barker, 1966) for e to Be(g. s.) and 8 ' p Be(2.,..) are small for all four shell model states, as would be 2 expected from the above discussion. The finite values for e p 49 come from small components of the wave functions which are mixed in as one departs from LS coupling. We conclude that 9 the small observed reduced widths for the decay of Be(ll. 29 9 8 8 MeV) and Be(ll. 81 MeV) to Be(g. s.) and Be(2+) are in general agreement with the expectations of the shell model. For any of the suggested assignments these decay modes are sampling only the minor components of the wave functions; consequently, we feel that it is not possible to make shell model assignments for the observed levels on the basis of our observations in these decay channels. The 9/2 - level can decay to 8 Be(2+) only by f-wave neutron emission, from conservation of spin and parity. The sizes of the reduced widths necessary to account for the observed 8 ( 2 -2 -2 branching ratios to Be 2 ·) are only e P = 4. 0 x 10 and 1.8 x 10 ..L.. for the 11. 29 and 11. 81 MeV levels respectively. In view of the observed f-wave reduced width of 2. 1 x 10 -2 found for the 2. 43 MeV level, it is not possible to eliminate a 9/2- spin assignment for 8 either level on the basis of its non-zero branch to Be(2+). C. Positive Parity Levels In the shell model description, non-normal parity levels cannot be formed by a lp-shell configuration, but require the excitation of at l east one particle into a higher shell. The lowest 4 5 energy configurations so formed are expected to be (1s) (lp)A(2s), (ls) 4 (1p)A- 5 (1d or ld ) and (1s) 3 (lp)A- 3 . Lane (1960) 512 312 has noted the computational difficulties of diagonalizing a Hamiltonian in the basis for med by the inclusion of all possible states belonging to these configurations, and has suggested that 50 a good approximation for the lowest lying non-normal parity states of a nucleus A may be fow1d by limiting the basis to states formed from coupling a single 2s or ld particle to the lowest , ld 112 312 512 states of the A-1 nucleus. In this way he was able to account with some success for the low-lying non-normal parity states in many of the lp-shell nuclei. . Barker (1961) has made detailed calculations based on this 9 13 9 . model for Be and C. In the Be case, he uses a basis formed 8 8 by coupling 2s and ld neutrons to Be(g. s.) and Be(2+) cores. He then diagonalizes a Hamiltonian of residual interactions, similar to that used in intermediate coupling calculations, to find energy eigenvalues and wave functions, and, from the latte r, neutron decay widths. The resultant level scheme is shown in fig. 37. Only relative energies are given by the model, the absolute placement of the scheme being adjusted to fit the 1. 7 and 3. 03 MeV levels. Since all of the positive parity levels have strong single particle character, they become quite broad as their excitations rise above 8 8 Be(g. s.) and Be(2+) decay channels. The three lowest, and narrowest, levels of the model, at 1. 7, 3. 04 and 4. 84 MeV, are to be associated with the experimental 1. 67, 3. 03 and 4. 65 MeV - states. Since Barker has tabulated partial neutron widths, it is at this l evel that we make our comparisons in table VII. Reduced widths are included for convenience. The s-wave single particle character of the 1. 67 MeV state is inferred from the success of 9 this structure in the analysis of the Be( y, n) reaction, and in accounting for the spectral shape of the level (see page 4 ). The strong d-wave single particle character of the 3. 03 MeV level is in agreement with the model, though the total widths are in disagreement by almost a factor or two. The agreement of partial 51 neutron widths from 9 8 Be(4. 65 MeV) to Be(g. s.) is almost within the experimental error bars. It appears that Barker's model gives at least a qualitatively valid description of the positive parity 9 levels in Be. D. Configuration Mixing and Nilsson Model The most directly relevant part of this thesis to the 9 question of whether Be may be thought of as a deformed nucleus 9 is the measurement of the f-wave neutron width of Be(2. 43 MeV) 8 to Be(g. s. ). The eigenfunctions of a single nucleon in an axially def or med potential well are not eigenstates of the orbital angular momentum, but may be expressed as some linear combination of eigenfunctions with different values of orbital angular momentum. The most often used formalism for describing the motion of a single nucleon in an axially def or med potential well is that of }filsson (1955). Kurath (1965) has used this formalism to predict 7 configuration mixing in the case of Li, taking a deformation sufficiently large to account for the observed value of the static 7 quadrupole moment of the Li ground state. His result is that the ground state wave function contains, in addition to a major 4 3 component of approximately 80 percent (ls) (1p) (in intensity), 2 4 an admixture of approximately 4 percent' of the (ls) (1p) (1f) configuration, the remainder being comprised of the configurations 4 2 3 3 (ls) (1p) (2p) and (ls) (1p) (2d). In view of the many successes 4 4 of the (1s) (1p)A- shell mo:lel, it is particularly gratifying to see that he was able to account for the quadrupole moment while maintaining such a large component of the normal shell model configuration. 52 Stephenson (196G) has used the Nilsson model to calculate 8 the expected f-wave width to Be(g. s.) from the 2. 43 MeV state 9 in Be. A summary of the steps involved in this calculation follows. Nilsson gives, for the Hamiltonian of a nucleon in an anisotropic harmonic oscillator potential with spin-orbit coupling, 0 = H 0 + H 0 + C -1 • -s + D -2 .f- H o H tiwo = 2 0 2 , where 2 [ - "Vr + r J , and r is related to the spatial coordinate r' . by x = VMw0 I h x'' etc~ . . M :;:: the partide-r.a.asp, 4 /TT 2 Ho = - oti wo 3 .J 5 r Y 20 o = a parameter characterizing the deformation (o = 0 corresponds to a spherical potential), C · = strength of spin orbit potnetial, D = strength of term which depresses higher angular momentum states, to be adjusted to give the proper shell order. ti w 0 = is the energy separation needed to reproduce the · observed shell structure of nuclei. If the nucleus is required to have a constant volume under deformation, w 0 becomes a function of o: o 4 w0 ( 0) = w0 (1 - 3 0 2 16 - 27 0 3 -l/G ) • The representation used by Nilsson in the main body of his 0 paper is that in which E 0 is diagonal. The basis states are eigen- 53 2 states of Z , t z and s z with eigenvalues t (t + 1), A. and ~ respectively, and are designated by l Nt/\ ~), where N is the number of oscillator quanta. 0 H , 0 I NtJ\L:) = (N + 3/2)tiw I NtJ\L:) • . 0 The quantum number o = J\ + 1:, the eigenvalue of projection on the symmetry axis of the total angular momentum, is conserved by H. The 1 · s term mixes states with different A. and L: , while H has off-diagonal matrix elements between states differing 0 in .e, by 2, and between states differing in N by 2. Since shells separated by t. N = 2 differ in energy by 2 ti w , and matrix elements 0 of H are usually much smaller than 2ti w , mixings between major 6 shells were not considered by Nilsson. 0 As shown by Nilsson in an appendix, however, if the spatial coordinates x, y and z in the functions obtained by diagonalizing H, neglecting t. N = 2 terms, are replaced by x', y' and z', where · -2cx. z' = ex. = e: e z 1 2 tn(l + e:/3) and = 6 + 6 2 /6 + 0( 6 3 ) the resulting deformed orbitals are much better approximations to the true wave functions of H, a..11d, in particular, contain the · effects of major shell mixing. 54 9 The Nilsson configuration for the ground state of Be should consist of 4 particles in orbit #l(ls, in orbit #3 (lp, o = 1/2), 4 particles o = 1/2) and 1 remaining particle in orbit 4fo2(1p, o = 3/2). The 2. 43 MeV level should be the first member of a rotational band based on this state, having as such the same configuration. The wave function for orbit #2, although designated by the spectroscopic notation "p" above, has, when written in the deformed coordinate system, non-zero projections onto the spherical wave functions with principal quantum numbers higher by 2, namely the 2p and 1f orbits. The procedure followed by Stephenson was to explicitly evaluate the overlap between deformed orbital #2 and the spherical lp, 2p and 1f orbits. Writing I (#2 orbital)) = e 1p j lp ) + e 1f j lf > + e 2 p l 2p > , . his results are 2 1/2 -1 = [cos h (a) cos h (2a.)] - (54, la) elf=ls x [tanh(2a.)+tanh(a.)J x e 1p (54, lb) e 2P.=Jfo x [tanh(2a.) - 4tanh(a.)J x e 1P • (54, le) e 1p A derivation of e 1p and elf is given in Appendix D(l). An alternate procedure to using Nilsson's deformed representation is to calculate the size of major shell admixtures to the wave functions in the spherical representation usingfirst order perturbation theory. This is done f or Nilsson orbital #2 in Appendix D(2). 55 To complete the analysis, the reduced widths for single 9 nucleon emission by f- and p-wave decays by the Be(2. 43 MeV; - 9 - 8 5/2 ) and Be(g. s.; 3/ 2 ) levels, respectively, to Be(g. s. ), are ta.ken by Stephenson to be proportional to the squares of the expansion coefficients: (55, 1) The evaluation of the equilibrium value of o for a given Nilsson configuration may be obtained by finding that value which minimizes the total energy of the configuration. Alternatively it may be found from an observed quadrupole moment or E 2 transition rate. The latter methoa is perhaps to be desired, since it relates the deformation directly to a measurable property of the nucleus. Nilsson (1955) gives for the intrinsic quadrupole moment of a nucleus of charge Z, mass number A and a deformation characterized by o : Q = • 8 x z x Rz 0 2 x 0 (1 + 2 3 o) (55, 2) where 1/3 fm Rz ~ - 1. 2 x A (55, 3) Nguyen Ngoc et al. (1963) evaluate Q from the observed E2 0 9 9 9 widths to Be(g. s.) from Be(2. 43 MeV) and Be(6. 76 MeV), assuming collective transitions. Their value is 56 Q0 = (. 2e ± . o 1) b • Substituting this value for Q , Z = 4 and A= 9 into eqs. ( 55, 2) 0 and ( 55, 3 ), one finds 6 .8 Evaluating Stephenson's expression ( 54, lt] for 6 = .8 gives e lf - - ::: .244 . clp 2 9 The value for e calculated for the ground state of Be to 8 p Be(g. s.) from the shell model wave function of Cohen and Kurath is given in table VI as 2 e P = .348 • If one inserts these values into expression ( 55, 1), the f-wave reduced widt h is predicted to be e ~~ = 2.08 x 10-2 ' J.. a value to be compared with that found experimentally, 2 ef = 2.1 x 10 -2 • 57 9 9 The proton decay from the B(2. 71 MeV) and B(2. 34 8 MeV) states to Be(g. s.) has been .measured by Wilkinson, Sample and AJ.burger (1965). These states are the analogs of the 9 9 Be(3. 03 MeV) and Be(2. 43 MeV) states, respectively. Their 9 8 results were that B(2. 71 MeV) goes almost entirely to Be(g. s. ), a result consistent with the branching ratio of (87 ± 13) percent 9 8 for Be(3. 03 MeV) to Be(g. s.) obtained in the present experiment; however, they found only an upper limit for the f-wave decay of 9 B(2. 43 MeV): 2 8f ::;. .5 x 10 -2 • The sensitivity of the reduced width to the radius R for the 9 Be case is such that a 10 percent decrease of · R changes 8; by a factor of 1. 84, while a 10 percent increase of R changes f by a factor of •58. A 20 percent increase in R is therefore e necessary to change the reduced width by a factor of four; it is 9 furthermore very unlikely that the radius of Be should be larger 9 than the radius of B where the coulomb repulsion is more important. The disagreement between the two experimental results is at present unresolved. E. Conclusion 7 3 9 The Li( He, p) Be reaction has been found to populate all 9 7 known levels in Be below the Li + d threshold, with the exception of the 7. 9ll and 9. 1 Me V levels, neither of which has been well established. Of those found here, the levels at 16. 671, 13. 78, 11. 81 and possibly 11. 29 MeV have not been seen previously. It 58 is interesting to notice that the widths of the 11. 29 and 11. 81 MeV 9 levels in Be are quite small (620 and 400 keV respectively) compared to the width of 2. 3 MeV found for the 6. 76 MeV state 9 in Be. This characteristic is due at least in part to the small reduced widths of the former states for neutron emission to 8 8 Be(g. s.) and Be(2+); however, their main decay must be 8 attributed to neutron emission to Be(4+) or to alpha-channels, and it is the small widths in these channels which must be explained. 8 8 The neutron decay widths to Be(g. s.) and Be(2+) from 9 normal parity states in Be have been found to be in fair agreement with shell model predictions. The expectation that states at high 9 excitations in Be have small parentages for low-lying states in 8 Be plus a neutron is fulfilled. 9 Unfortunately it has not been possible to 9 Be(ll. 29 MeV) and Be(ll. 81 MeV) levels observe the decays of the 8 to Be(4+), since only the tail of this level is energetically available. 8 8 Measurements of decays in the Be(g. s.) and Be(2+) channels have 9 provided details concerning the Be states without producing needed information on their major constituents. 8 The observation of the large reduced width to Be(g. s.) 9 from the Be(3. 03 MeV) level supports the suggestion by Lane (1960) 9 that the lowest non-normal parity states in Be should be formed by promoting a single neutron into a 2s- or ld- orbit and taking the eight 8 remaining nucleons to form a Be core in a low excitation. The extension of this idea by Barker (1961) into a more detailed model has provided satisfactory agreement also with the observed decay 9 8 rate to Be(g. s.) from the Be(4. 65 MeV) level. The success of this model is especially interesting in view of the very simple structure which it ascribes to the non-normal parity states in the lp-shell. 59 Although large quadrupole moments and E2 widths strongly suggest such admi.A'tures, the non-zero reduced width 8 8 found for the Be(2. 43 MeV) decay to Be(g. s.) provides the first direct evidence for f-wave mixing in the lp-shell. quantitative agreement of the measured value for The precise i e with that predicted by the simple Nilsson calculation, though pleasing, is 2 almost certainly fortuitous . Uncertainty in the value of e used p in the calculation, and of the channel radius chosen, to which the reduced width extracted from the observed branching ratio is very sensitive (p. 57 ) , leave room for variation in both values. be said, however, that the value of e; It can measured here appears to 9 be accounted for by assuming a deformation of Be consistent with observed E2 transition rates between rotational levels of the nucleus. The disagreement of the value of e: 9 Be(2. 43 MeV) decay with the upper limit on 0 found here for the e; reported by 07 Wilkinson et al. for the B(2. 34 MeV) decay is viewed as serious and indicates that further experimental work is needed. 60 APPENDIX A Conversion of Magnetic Analyzer Spectrum to Excitation Spectram We adopt the conventional notation m 1 + m -. m + m 2 3 4 where m 1 is incident with energy E 1 upon the stationary target m , and m is observed at a fixed laboratory angle e L. m , m 2 3 1 2 and m have definite masses, and m , the residual nucleus, is 4 3 left at an excitation Ex above its ground state. If m is observed 3 in a magnetic spectrometer, there is a one-to-one correspondence between the momentum of m , as measured by the spectrometer, 3 and E . The conversion of the spectrometer spectrum to an x excitation spectrum consists of two steps: (1) The momentum axis must be re-labelled with the corresponding values of E . x (2) The number of counts at each momentum must be multiplied by the appropriate factor to convert it to counts per unit excitation interval. Step (1) has been covered extensively in the literature (e.g., see Brown et al. , 1951). Quantities which must be measured in order to calculate the excitation are E (the energy 3 is related to the frequency of the nuclear of m ), E and e . E 1 3 3 3 magnetic resonance probe used to measure the magnetic field of the spectrometer by the expression x [1- 61 where k is the calibration constant of the spectrometer, and m is the proton mass. p k has been determined, using a Thorium-B alpha-source, to be . 01139 MeV-(MC) -2 (Groce, 1953). Corrections for the dependence of k on frequency (McNally, 1965) were made. The observation angle e3 , was taken from the spec- trometer track calibration made by Groce (1954). The energy of the incident beam at the center of the lithium layer was calculated from the observed position of the proton groups from either 9 9 Be(g. s.) (Q = 11.199 MeV) or from Be(14. 392 MeV) (Q = -3. 192 ± .005 MeV). By this procedure effects of energy loss by the out- going proton in the target (typically less than 10 keV) were 9 implicitly taken into account. For the Be(l6. 671 MeV) state, small corrections for the variation of this energy loss with outgoing proton energy were made . Step (2) consists of two stages: (a) Conversion of Spectrometer Spectrum to Laboratory Energy Spectrum For a fixed magnetic field strength, the finite radial extent 6 r of a counter at the spectrometer focus subtends a finite window 6 E in particle energy. For the 61 cm radius magnetic spectrometer, the relationship is (Groce, 1963): where D = the dispersion of the magnet, approximately independent of field, = 3. 75, 62 r = the mean radius of the particle trajectory, = 61 cm, E = the mean particle energy. To obtain an energy spectrum one must divide the number of counts t.N at each field setting by the corresponding t.E: dN dE = t.N x (D r ) E 2 t.r • (b) Conversion of Laboratory Energy Spectrum to Excitation Spectram As shown by Williams (1961), it is true relativistically that 1 = p c 2 d N ( dE do c c ) where = laboratory momentum of m 3 = center-of-mass momentum of m 3 2 ct N dELdOL = laboratory energy spectrum of m 3 2 ct N dE dO c c = center-of-mass energy spectrum of m 3 • 63 In the non-relativistic approximation, this expression gives = where EL and Ec are related by From E x where Q 0 Ex = = Q-value to the ground state of m 4 = excitation in m 4 , one finally obtains - - dE .d o c c 64 APPENDIX B Energy Spectra from a Two Stage Breakup 9 7 The particle decay of Be levels below the Li + d threshold ultimately results in the three particles a. + a. + n. In the foregoing analysis it has been assumed that the mechanism by which this decay occurs is well approximated by an incoherent superposition of twostage decays in which the final state is dominated by either the a. - a. interacti on or the a - n interaction, referred to in the text as decays 5 through 8 Be and through He respectively. The calculation of neutron energy spectra used in the analysis is described below for the cases of dominant a. - a and a - n interaction. Using the factored wave function representation, as discussed for example by Gillespie (1964), it is possible to write the transition probability for a three- body decay, in which the interaction between particles 1 and 2 dominates the final state, as the product of a term T , representing an unenhanced transition 0 probability, with an enhancement factor F, representing the interaction between particles 1 and 2: T = T 0 x F . Following Barker (1962), we represent the enhancement factor by a "generalized density of states" function of the form . 2 Sill where i3.e, 65 o.e, = t-wave nuclear phase-shift parameterizing the (1, 2) interaction, k 12 = center-of-mass wave number in the (1)-(2) channel, R 12 = interaction radius of (1)-(2) channel, 2 2 p.e, (p)= 1/[ ~ (p) + G.e, (-e, )] , where F.e, and Gt are t he regular and irregular coulomb wave functions, respectively, We use for T 0 where k 3 = center-of-mass wave number in the (3)-(1, 2) channel, R 3 = interaction radius of (3)- (1, 2) channel. The factor k R 3 3 is proportional to the density of final states of the (3)-(1, 2) system, while P(k R ) takes into account the 3 3 dependence of T 0 on centrifugal and coulomb barriers in the (3)-(1, 2) channel. 66 8 (1) Neutr on Energy Spectrum from Decays Through Be The center- of- mass neutron spectru m for the dominant a - a interaction is given by . 2 dN (E ) _ ... dE n - COnSL. x [ kRP, (kR)] 8 n where E v Sln Be- n \3 x [ fu.-qp (l~) ] -t a-a This expression 8 was used in calculating neutron line shapes for decays to Be(2+) 8 (fig. 34) and Be(4+) (fig. 30). The parameters used were: n is the center-of- mass neutron energy. a - a channel: R a-a = = 2 or 4 ,e, n - 8 4. 0 f m Be channel: R ,e, n = 4. 35 f m = 1 The experimental a - a phase shifts were used for o,e, (Tombrello and Senhouse, 1963). 5 (2) Neutron Energy Spectrum from Decays Thrrugh He(g. s. ) The neutron energy spectrum in this case owes its 5 continuum shape both to the width of the He(g. s . ) and to the 67 emission of the neutron in the second stage of the decay. The shape of the spectrum depends on both the variation of the transition 5 matrix element with the excitation of the He produced in the first stage and the angular distributions of particles emitted in both stages. The shape of the expected spectrum for a two-stage decay proceeding through a sharp intermediate state, for arbitrary angular distributions of both stages, is given in closed form by Morini.go (1963). We summarize only those results relevant to the analysis described in the text. For an angular distribution of 5 the He in the first stage given by 2 W(e) = 1 + ~ cos e 5 and an isotropic He decay, the center-of-mass neutron energy spectrum is given by 2 3b + 4 gc const. dE (En,EJ = -vw- x [ 1 + ~ J dN n where 5 v = velocity of w = velocity of emitted neutron with respect He after the first stage, 5 to the He, g = resulting center-of-mass neutron velocity, b = gz (o-2 _ w2 + v2) v t:> ' 68 2 2 2 2 = w (1 - y 0 ) - g z ' c = o·2 - v2 - w2/2vw b E ' = excitation in the a. - n system. x The velocities are implicit functions of E • x T his expression is valid for \v-w\ ::;_g~ \v+w\ otherwise dN dE ::: O 0 n The transition probability for the process as a function of E x is given by dT dE x ::: const. x [ kRP.e, (kR)] 5 x F(E) He - a a -n The enhancement factor F was approximated for the calculations by the expression F(E \ x a-n where E x is in MeV. 2 1 I ( (E - .7) + .16) x x = (E ) 3 2 69 The parameters used in the a. R = 4. 0 ,('., 5 He channel were: fm = 2 The final neutron spectrum is obtained by integrating over E : x E scm dE n (En' E~ dEdTx dEX' dN = const. x 0 where E is the total center-of-mass energy available to the cm ex. + ex. + n system. 70 APPENDIX C Branching Ratio Calculations (1) Differential BranchiI1g Ratio The differential branching ratio at a single neutron angle, 9 expressed in the Be center-of-mass system, is given by (70, 1) where N n = Observed number of neutron counts through the decay mode of interest, N = Corresponding number of populating protons, C = Correction factor for neutron scattering in p target backing and chamber walls, = Neutron detector efficiency, 60. L = Laboratory solid angle subtended by neutron counter, C. M. F. = Factor for converting the laboratory solid 9 angle into the Be center- of- mass system. Referring to the velocity diagram in fig. 8, 71 2 . 2 1/2 2 . 2 1/2 - 2 [xcos e + (1 - x Sill e ) J (71, 1) C. M. F. = [l - x Sill e J where e = I1 e L,n - e X=V 9 I and L, Be g /V • L, Be c, n As an example, the branching ratio from 8 0 9 Be(2. 43 MeV) = o , will be calculated below. c,n time spectrum for this case is that shown in fig. 14. to Be(g. s. ), at e The neutron 8 The background under the Be(g. s.) decay peak 11 9 from the 2. 43 MeV state in Be was estimated by linear extraN : polations of the low energy side of the group marked "3. 03" and the high energy side of the decay from modes (2) and (3) (see page 24). Integration of the peak gives N n 9 N : p = 601 cts. The proton window for this run included excitations in Be between 2. 2 and 3. 9 MeVo From a spectrum similar to that of fig. 11, it was calculated that 54 percent of the protons in 9 this window populated the 2. 43 MeV state in Be. During the taking of the neutron spectrum in fig. 14, a scaler (fig. 12) recorded 6 15. 47 x 10 counts in the proton window, giving the number of population protons as 6 N = 8. 38 x 10 cts. p 72 C: Apprm..imately . 2 percent of the neutrons are scattered passing through the . 05 cm tantalum target ba cking. T ::king this as the removal percentage and adding an 8 percent correction for removal by the chamber walls gives C : ;:; 1. 10. The thin scintillator was used for this run. e: : From table m, e: ::;:; • 19 60..,. : .LI A 12. 7 cm diameter scintillator at 100 cm from the target subtends a solid angle of M2L ::;:; 1. 26 x 10 C. M. F.: e 9 L, Be -2 ster. Expression 71, 1 above gives, for I : ;:; o, x::;:; • 702, C. M. F. ::;:; • 345 • Evaluation of expression ( 70, 1) yields ~~ (0°) : ;:; 11.4 x 10- 3 neutrons per proton per steradian. (2) Total Branching Ratio 9 In all cases axial symmetry about the laboratory Be recoil 9 direction and symmetry about 90° in the Be center-of-mass system was assumed. Under these conditions, the total branching ratio is g,i.ven by 73 n /2 B. R. = 4n J 0 dB ( ) . de d o 8 c, n sme c, n c, n 74 APPENDlX D Calculation off-wave Components of Nilsson Orbital 4/:2 (1) Def or med Representation: For a spherical potential, Nilsson orbital #2 is given by the pure basis vector I 111+), in the I N-iJ\I:) notation, where the + signifies positive projection of the nucleon spin along the z-axis in the body coordinates. In Nilsson's spherical representation, neglecting major shell mixing, this basis vector remains an eigenstate even when the nucleus is deformed, since there are no other basis vectors in the same major shell with o :: f\. + L: = 3/ 2 which can be mixed in. To obtain the deformed Nilsson orbital which implicitly contains the effects of major shell mixing, one need only write the vector I 111 + ) in the deformed coordinate system. Overlaps of this deformed wave function with spherical solutions can then be evaluated to find the coefficients in the expansion The coefficients C 1p and C 1f are evaluated below. In spherical coordinates, the properly normalized solutions for a particle in an isotropic harmonic oscillator potential well for lp and 1f orbits, with m-e, = 1, are 75 where A. = m w/ h • Spin functions are suppressed throughout this section. In Cartesian coordinates, *1p, 1 = 3 [ A. l/ 4 0r] ( TT 9 1lt lf '1 =[ A. lOOrr 3 J . ) x + iy e l/ 4 - A./ 2 (x 2 2 2 + y +z ) 2 2 2 (x+ iy . ) (4 z 2-x2-y2) e - A./ 2 (x + y + z ) . The spatial wave function for Nilsson orbital #2 is obtained by making the substitutions (cf. p. 53) x _, ea. x = xT x _, ea. Y = yT z _, e -2a. z = zL into the above expression for .lL2 or b"tal) 1)r (rr i = [ A.1i 5 l/ 4 3 J *lp, 1, giving 2 2 2 2 2 T(x.,-1y . . ) e - A./2 [ (x +y )T + z L J . 76 Evaluating the overlaps, 5 l/ 2 C lp = [ A. 3 ] co Jdx J dy J' ro ro 2 2 2 dz { (x-iy) e -t../2 [ x +y +z ] TT 2 2 2 2 2 . ) -A./2[(x +y )T +z L ]} • T( x x+ iy e Setting 2 2 2 dxdy = pd pd e and x + y = p -oo The 1f overlap is evaluated in a similar way, giving The ratio C 1f to C lp is then given by 77 == Jf [tanh (2et) + tanh (et)] (2) Perturbation theory: The major shell mixings can also be calculated in first order perturbation theory using Nilsson's spherical representation. The total Nilsson Hamiltonian can be written as where, H 1 0 == H 0 + Ct · -s + D -2 t . Here we take H to represent that part of H which does not 0 01 include matrix elements between major shells, and H 02 to represent only that part of H which has matrix elements between 0 major shells. Nilsson has diagonalized H + H ; the problem 1 01 here is to evaluate the size of major shell mixing caused by H . 02 The f-wave admixture into Nilsson orbit #2 is considered below. The explicit form of H 0 is given by The eccentricity € of the deformed shape is related to o by E: = o + 61 o 2 + O(o 3) • 78 The relative scales in the x- and z-directions are given by zo = ( 1 + 8 / 3 ) x 1 - 2 E: /3 where x 0 0 and z 0 are the distances along the x- and z-axes respectively to an equipotential surface. The shape is prolate for positive e. conserves the quantum numbers A. and L: , and 6 connects states differing in N and t by 2. In the major shell H two quanta above the lp shell there is only one basis vector with t = 3 which will be mixed into Nilsson orbit #2 by H 6 , namely the I 331 + ) vector. In first order perturbation theory (331+ I H 1111+ > 0 I (#2 orbital)) = 1111 + > + Relevant matrix elements of r 2 (N-2, t-2lr IN, t ) = 2 2 tiw and Y I 331 + > + --- • 0 20 are given by Nilsson: (n+ t + 1/2)(n+ t - 1/2) 2t+l 2t'+l < t2A.0 I t2.f-'A') x < .i200 \ -e..2-e..' o > where n = N-2 t Evaluating the perturbation matrix element above gives 79 0 I (#2 orbital) ) ~ I 111+ ) + jfO I 331+) + ---- This result may be compared with the results of section (1) for small values of o: j2 elf o C = 5 [tanh(2a.) + tanh(a.)] .... .,;!2 3a. .... JfO 5 lp For a value of o = .6, the perturbation expression gives while the deformed representation expression gives 80 APPENDIX E 7 This section describes work done on the reaction 6 Li( He, a. ) Li. Its relationship to the main body of the thesis 3 is technical only, the target and bombarding particle being the 9 same as those used in the study of Be. The incentive for this work was quite independent and will be reviewed briefly. Of the various reactions which have been used to explore 6 7 3 6 the level structure of Li, the reaction Li( He, a. ) Li has been one of the most prolific. In 1960 Allen et al. (1960) published an 3 alpha-particle spectrum, taken at E( He) = .9 MeV, which showed 6 levels in Li at excitations of 0.0, 2.19, 3.56, 4.3, 5.35, 5.6, 6.63, 7.40, 8.37 and possibly 9.3 MeV. Alpha-deuteron scattering had previously revealed levels at excitations of 2.187 MeV (Lauritsen et al., 1953), 4.53 MeV and 5.4 MeV (Galonsky et al., 1955; Galonsky and McEllistrem, 1955); Day and Walker (1952) had found a Y-emitting state at 3.58 MeV. For the levels above 6 MeV, however, the spectrum of Allen et al. was the sole evidence. Linck et al. (1961) subsequently published an alpha-particle 3 spectrum-:- taken at E( He) = 5 MeV, which had little in common with that of Allen et al., and which later proved to contain numerous spurious peaks. In 1963 Linck et al. (1963) published a revised 6 7 3 version of the Li( He, a.) Li reaction, including several spectra 3 at He energies between 1 and 5 MeV. Their results were in general agreement with those of Allen et al. , with one conspicuous difference: none of their spectra showed any levels above 6 MeV excitation. Groce and Whaling (1963) had similarly been unable to 81 observe the population of levels above 6 MeV in the reaction 8 6 Be(p, a.) Li. Senhouse and Tombrello (1964) have found some indication of negative parity levels in this region in alpha-deuteron scattering, although they feel that more extensive measurements are necessary to establish the order and position of the levels. The present work was undertaken to resolve the conflict between Allen et al. (1960) and Linck et al. (1963) with respect to 6 levels in Li above 6 MeV. Target preparation, beam handling and particle detection procedures were very similar to those described 9 in the singles phase of the Be work, (pp. 6-10 ) , the only difference being the detection of alpha-particles instead of protons. 3 Alpha spectra have been taken at He energies between .9 6 and 12 MeV. In none of these has any evidence of levels in Li above 6 MeV appeared. At bombarding energies above 8 MeV alpha 8 groups from sequential decays through Be have been identified. (1) Studies at TanC.em Bombarding Energies 7 18 Targets of Li metal ranging in thickness from 6 to 40x10 2 atoms/ cm were evaporated in situ onto nickel backings, and were 3 bombarded with He beams ofenergies between 3. 78 and 12 MeV, at typical currents of 0.2 µa. The alpha particles were detected in surface barrier counters at the focus of the 61-cm radius magnetic spectrometer, using a foil arrangement to identify the particles. (a) Spectra for E (3 He) Between 3. 78 and 5 MeV: A total of ten spectra were taken at angles from 15 3 to 150° and He energies from 3. 78 to 5 MeV. 0 In all of the spectra the 0.0, 2.18, 3.56 and 5.35 MeV levels are seen and perhaps a 82 broad level at 4.4 MeV, though the last group is too broad and weak to be w1ambiguously interpreted. In none of the spectra is there evidence for levels above 6 MeV. A sample spectrum, taken at a bombarding energy of 3. 78 MeV, is shown in fig. 38. The data was taken with the magnetic spectrometer and subsequently converted to an alpha- particle energy representation. Positions of the levels found by Allen et al. are indicated. (b) Spectra for E(3 He) = 10 MeV The alpha continuum increases rapidly as the bombarding energy is raised, due at least in part to the increasing availability of processes whiCJ.'1 emit alpha-particles in a second 9 9 8 stage. For example, highly excited states in Be, B and Be, 3 3 3 populated by ( He, p), ( He, n) and ( He, d) reactions respectively, may produce secondary alpha particles by their decay. The alpha spectra taken at E(3 Ee) near 10 MeV are characterized by an intense continuum which complicates the search for 6 Li levels considerably. A sample spectrum is given in fig. 39. The levels 6 at 0.0, 2.18, 3.56 and 5.35 MeV in Li are clearly discernible. Also prominent are groups at frequencies of approximately 33 and 23 MC/S. These groups represent dramatic evidence that a bump on the spectrum of c particles from a reaction of the type A(b, c)D does not necessarily correspond to a state in the nucleus D. The group at 33 MC/S, which was studied in some detail, comes not 6 7 3 from a state in Li but from the two stage process Li( He, d) 8 Be(16.62MeV)(a.) 4 He. This identification of the group .was established from two types of experimental information, as discussed below. The first was the agreement between the measured energy 83 distribution of the alpha particles and the shape predicted from the angular distribution of the deuterons populating the 16.62 MeV state 8 in Be; the second was the kinematic behavior of the group as the bombarding energy was changed. The lack of definition of the 8 Be recoil velocity in the above two stage process will result in the alpha particles' presenting a continuum distribution at given laboratory angle, kinematically constrained to lie within some energy limits which are functions of the bombarding energy, angle and Q-values. These limits are 7 3 indicated, for example, in fig. 39 for the sequences Li( He, d) 8 4 8 7 4 3 8 Be(16,62 MeV)(a,) He and Li( He, d) Be(g. s. )(a) He. If the Be nucleus is emitted preferentially in some laboratory direction, its momentum becomes more nearly defined, and the resulting energy distribution of the alpha particles will reflect this characteristic by tending to form a peak in their energy spectrum. 7 The angular distribution for the reaction Li(3 He, d) 8 Be(16.62 MeV) was measured for the purposes of verifying that the 33 MC/S alpha-particle group in fig. 39 did in fact come from the 8 breakup of this state in Be. Fig. 40 A shows a sample spectrometer deuteron yield in the vicinity of the 16.62 and 16.92 MeV 8 levels in Be; Fig. 40 B shows the center-of-mass angular distri8 bution of the deuterons to the 16.62 MeV level in Be. The angular 8 distribution from the 16.9 2 MeV state in Be was found to be roughly isotropic. . 8 The effect of the strong forward peaking of the ~e(l6.62 MeV) deuterons on the energy distribution of the sub- sequently emitted alpha-particles may be qualitatively understood 8 by noting that the Be recoil nucleus is preferentially emitted at e = 180°. If the alpha particle is observed at a forward angle the 84 8 recoil velocity of the Be is preferentially directed against the laboratory alpha velocity, tending to group the alpha energies at their low energy limit. A quantitative evaluation of the alpha spectrum 8 expected was calculated from the observed Be(16.62 MeV) deuteron 8 angular distribution, assuming isotropic Be decay. The result is shown as a shaded group in fig. 39, with its ·expected intensity. The formulae of Morinigo (1963) were used in the calculation; the width 8 of the Be(l6.62 MeV) level was taken to be 100 keV. An independent check on the interpretation of this alpha group is provided by tracking the position of its lower edge as the bombarding energy is changed. Fig. 41 shows that this edge 7 8 3 follows nicely the kinematics expected for the Li( He, d) Be(l6.62 4 MeV)(a.) He process, and not at all the kinematics expected for a 6 group leaving a state in Li. Although no such exhaustive study has been given the group at 23 MC/S in fig. 39, it is believed to come from the process 4 8 7 3 Li( He, d) Be(g. s. )(a. ) He. This interpretation is based solely on the agreement of the location of its high energy edge in this spectrum 8 with that expected for the Be(g. s.) process. 3 (2) At E( He) == 900 keV The failure of attempts to find levels above 6 MeV in 6 Li at higher beam energies suggested that an alpha-particle spectrum should be taken under conditions as similar as possible to those used by Allen et al. For this phase of the work the Kellogg 3 MV · Van de- Graaff generator provided a 900 keV singly-charged beam 3 of 0. 5 µa of He. The alpha particles were detected at the focus 85 a 40- cm double focusing magnetic spectrometer, using a surface barrier solid state counter and foil arrangement for particle identification. The target used was of Li 0 on a tantalum backing, 2 and is described on page 11 • The buildup of carbon on the surface of the target was such that, by the end of the fourteen hours required to complete the run, the beam energy was degraded by 50 keV in passing through the carbon layer. Because of the high coulomb barrier in the incident channel, this energy loss resulted in an observed 16 percent decrease in counting rate. A correction factor proportional to total charge delivered to the target was applied to the observed number of counts to compensate for this loss in counting rate. No corresponding corrections were applied to the energy scale. The use of a Li 0 2 target, E (3 He) = 900 keV and e = 90° were conditions common to the experiment of Allen et al. 6 The resulting spectrum is shown in fig. 42. Li recoil ions 6 6 from Li(O.O MeV) and Li(3.56 MeV) were also seen. Fig. 42 shows the same spectrum converted to an alpha-particle energy representation. The states above 6 MeV are not observed, and we must conclude that these states in the spectrum of Allen et al. were spurious. Thinking it not impossible that these peaks could have resulted from proton or deuteron beam contaminants in the experiment of Allen et al., we have run proton and deuteron beams on 7 Li 0 targets. No peaks which could have been mistaken for 2 6 these states in Li were observed. 6 Average values of excitations and widths of Li levels found in the present work are given in table VIII. 86 REFERENCES F. Ajzenberg-Selove and T. Lauritsen, Nucl. Phys • ..!.!, 1 (1959). E. Almqvist, K. W. Allen, and C. B. Bigham, Phys. Rev. 99, 631A (1955). K. W. Allen, E. Almqvist and C. B. Bigham, Proc. Phys. Soc. 75, 913 (1960). F. c. Barker, Nucl. Phys. 28, 96 (1961). F. c. Barker and P. B. Treacy, Nucl. Phys. 38, 33 (1962). F. C. Barker, Nucl. Phys. 83, 418 (1966). F. C. Barker, private communication (1966a). J. Benveniste, R. G. Finke, and E. A. Martinelli, Phys. Rev. 101, 655 (1956). J. S. Blair and E. M. Henley, Phys. Rev. 112, 2029 (1959). D. Bodansky, S. F. Eccles and l Halpern, Phys. Rev. 108, 1019 (1957). H. Brafman, Nuc. Inst. and Meth. 34, 239 (1965). R. Britten, Phys. Rev. 88, 283 (1952) . . A. B. Brown, C. W. Snyder, W. A. Fowler and C. C. Lauritsen, Phys. Rev. 82, 159 (1951) . . J. A. Careaga and M. Mazari, Bull. Am. Phys. Soc. ~' 124 (1963). C. M. Chesterfield and B. M. Spicer, Nucl. Phys. 41, 675 (1963). P.R. Christensen and C. L. Cocke, Nucl. Phys. 89, 656 (1967). S. Cohen and D. Kurath, Nucl. Phys. 73, 1 (1965). 87 R. Y. Cusson, Ph.D. Thesis, California Institute of Technology (1965). R. B. Day and R. L. Walker, Phys. Rev. 85, 582 (1952). R. D. Edge and G. A. Peterson, Phys. Rev. 128, 2750 (1962). A. Galonsky, R. A. Douglas, W. Haeberli, M. T. McEllistrem and H. T. Richards, Phys. Rev. 98, 586 (1955). A. Galonsky and M. T. McEllistrem, Phys. Rev. 98, 590 (1955). J. Gillespie, Final State Interactions, Holden Day, Inc., San Francisco, California, pp. 2-13 (1964). G. M. Griffiths, Nucl. Phys. 65, 647 (1965). D. E. Groce, Ph.D. Thesis, California Institute of Technology (1963). D. E. Groce and W. Whaling, Phys. Rev. 132, 2614 (1963). E. Guth and C. J. _M ullin, Phys. Rev. 76, 234 (1949). D. Hasselgren, P. U. Renber, O. Sundberg, and G. Tibell, Nucl. Phys. 69, 81 (1965). D.R. Inglis, Rev. Mod. Phys. 25, 390 (1953). M. J. Jakobson, Phys. Rev. 123, 229 (1961). P. D. Kunz, Ann. Phys. (New York)_!..!, 275 (1960). D. Kurath, Phys. Rev. 101, 216 (1956). D. Kurath, Phys. Rev. 140, B1190 (1965). D. Kurath, private communication (1966). J. Linck, S. Nicolas, R. Bilwes and D. Magnette- Valette, J. Physique Rad. 22, 581 (1961). 88 J. Linck, L Nicolas-Linck, R. Bilwes and D. Magnette-Valette, J. Physique 24, 983 (1963). A. M. Lane, Rev. Mod. Phys. 32, 519 (1960). T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 78, 1 (1966). T. Lauritsen, T. Huus and S. G. Nilsson, Phys. Rev. 92, 1501 (1953). B. Lynch, G. M. Griffiths, and T. Lauritsen, Nucl. Phys. 65, 641 (1965). J.B. Marion, J. S. Levin and L. Cranberg, Phys. Rev. 114, 1584 (1959). J. H. McNally, Ph.D. Thesis, California Institute of Technology (1966). J. H. Van der Merwe, Phys. Rev. 131, 2181 (1963). C. D. Moak, A. Golonsky, R. L. Traughber, and C. M. Jones, Phys. Rev. 110, 1369 (1958). F. B. Morinigo, Ph.D. Thesis, California Institute of Technology (1963). J. Mtlsner, G. Schmidt and J. Schintlmeister, Nucl. Phys. 64, 169 (1965). H. Nguyen Ngoc, M. Hors and J. Perez y Jorba, Nucl. Phys. 42, 62 (1963). S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955). W. T . Pinkston, Phys. R ev. 115, 963 (1959). P. Purdom, Jr., P.A. See ger and R. W. Kavanagh, Nucl. Phys. 83, 513 (1966). 89 F. L. Ribe and J. D. Seagrave, Phys. Rev. 94, 934 (1958). B. V. Rybakov and V. A. Sidorov, Fast-neutron spectroscopy, ed., N. A. Vlasov (translated from Russian, Consultants Bureau, New York, 1960). G. Schrank, E. K. Warburton and W.W. Daehnik, Phys. Rev. 127, 2159 (1962). N. A. Schuster and G. E. Pake, Phys. Rev. 81, 886 (1951). L. S. Senhouse, Jr. and T. A. Tombrello, Nucl. Phys. 57, 624 (1964). R.R. Spencer, G. C. Phillips and T. E. Young, Nucl. Phys. 21, 310 (1960). G. J. Stephenson, Jr., Proc. of the Int. Conf. on Nuclear Physics, Gatlinburg, Tennessee, Sept. (1966). R. G. Summers-Gill, Phys. Rev. 109, 1591 (1958). C. D. Swartz and G. E. Owen, Fast neutron physics, part I, chapter II B, ed. , J. B. Marion and J. L. Fowler (Interscience Publishers, New York, 1960). T. A. Tombrello and L. S. Senhouse, Phys. Rev. 129, 2252 (1963). R. G. Thomas, Phys. Rev. 81, 148 (1951). E. K.. Warburton, D. E. Alburger and D. H. Wilkinson, Phys. Rev. 129' 2180 (1963). E. K. Warburton, D. E. Alburger, D. D. Wilkinson and J.M. Soper, Phys. Rev. 129, 2191 (1963). D. H. Wilkinson, J. T. Sample andD. E. Alburger,Phys. Rev. 146, 662 (1966). 90 W. S. C. Williams, An Introduction to Elementary Particles, Academic Press, New York, New York, pp. 356-378 (1961). 91 Table I 9 7 3 Summary of Data from Li( He, p) Be Singles A summary by individual spectrum is shown of the data 9 from which the average excitations of levels in Be were found. For each level and for each spectrum the beam energy, observation . angle, calculated excitation and estimated excitation error are given. The value of chi-squared, divided by(the number of degrees of freedom minus one), was calculated for the best fit to a single Q-value for each proton group, using the listed error estimates, and assuming target masses of 6, 7 and 9. Average level positions 9 and intrinsic widths, both expressed in terms of excitation in Be, are presented. See pages 12-15. '. ;~. , •• j -~ 9 7 3 TABLE 1. Summary of Data from Li( He, p) Bc* Proton Group 3 E( He) Lab.Proton Angle (MeV) (degrees) Excitation 9 in Be (MeV) Chi-squared/ {Number of degrees of freedom minus one) Assuming Target Mass: Value Error 6 7 9 Average Excitation 9 in Be (MeV) Intrinsic Width 9 in Be (MeV) pl 10 8 8 90 90 15 1.626 1. 650 1. 653 0.02 0. 02 0.02 518. • 55 901. 1. 64 p2 10 8 8 90 90 15 2.418 2.436 2.432 0.02 0.02 0.02 496. • 23 930. 2. 429 ± 0. 012 p3 10 8 8 10 90 90 15 90 3.029 3.034 3.009 3.051 0. 02 0.02 0.02 0.02 259. • 7-2 605. 3. 031 ± o. 010 o. 274 ± 0. 015 p4 8 10 8 15 90 90 4.46 4.60 4.64 0.2 0.2 0.2 3. 56 • 23 23. 4 4. 57 .± o. 1 o. 6 ::;_ r s. 1. o p5 10 8 8 90 90 15 6.7 6.7 6.8 0.1 0.1 0.2 5. 73 .12 10. 9 6. 7 ± 0.1 1. 7 s:. r : ;_ 2. 2 pS 10 10 7 1. 7 60 10 11.31 11. 27 11. 28 0.02 0.03 0. 03 59.6 • 75 86. 8 11. 29 ± 0. 03 o. 62 ± o. 07 p7 10 10 7 1.7 60 10 11. 81 11. 81 11. 83 0.01 0.03 0.02 59. 5 • 42 109. 6 11.81 ± 0.02 o. 40 ± o. 03 p8 9 10 10 12 50 90 13. 78 13.78 13.6 0.04 0.03 0.15 17. 9 • 72 22. 9 13. 78 ± o. 03 0. 59 ± o. 06 p9 10 10 12 10 10 30 45 15 16.670 16.665 16. 678 16.670 0.01 0.02 0.01 0.01 59. 9 • 20 137.1 16. 671 ± o. 008 o. 041 ± 0. 004 $:. 0.035 \D I\) 93 Table II Comparison of Spectrometer and Surface Barrier Counter Spectra A comparison is made of the parameters of eq. ( 13, 1) 7 3 9 used in fitting proton spectra from Li( He, p) Be taken with the magnetic spectrometer (fig. 5, upper curve) and with a barri3 er counter (fig. 27). Both spectra were taken at E ( He) = 10 ~ 0 MeV, ep - 0 . All energies are expressed as excitations in 9 the Be system. The quantity A/B x r /r is the ratio of 9 92 1 intensities of the Be(ll.29 MeV) and Be(ll.81 MeV) levels. The greater values of the widths used for the solid state counter spectrum reflect the poorer experimental resolution in this case. See text, pages 35 and 36. 94 Table II Comparison of Spectrometer and Solid State Spectra Parameter Spectrometer Surface Barrier Counter (MeV) 11.81 = 11.81 ERl - ER2 (MeV) .. 52 - .52 rl (MeV) .620 .644 r2 (MeV) . 400 .550 A r2 .608 .562 ERl B x rl 95 Table ID Neutron Detector Efficiencies The neutron detector efficiencies used in this calculation of branching ratios, with the corresponding assigned errors, are given. See text, pages 23 and 24. 96 Table ill Neutron Detector Efficiencies E(3 He) Excitation Range .111 9B e Neutron Energy Range Scintillator Thickness (MeV) (MeV) (MeV) (cm) 2.2 2.4· - 1.0 - 3.3 5.08 .42 ± .04 1.9 .19 + .02 1.9 - 3.6 1.9 .18 ± .02 - 8.6 5.08 .28 ± .04 5.0 9.0 - 10.0 3.8 - 3.5 5.4 12. 5 - 10.3 5 Efficiency 97 Table IV 9 Be Level Widths 9 The observed intrinsic widths of Be levels, the level widths, rTO' and f T' which were used in the calculation of partial neutron widths are shown. All widths are given in terms of 9 excitation in the Be system. The difference between f TO and f T is explained in the text, page 44 • Where no value of r T is given, f T was set equal to f TO in the calculation of partial neutron widths. Unless otherwise indicated, values listed for excitations and observed widths are taken from table L Experi- mental values for Jn are taken from the recent compilations of Ajzenberg-Selove and Lauritsen (1966). See pages 43 and 44. 98 Table IV 9 Excitation Be Level Widths Ji:r,. (MeV) rTO rT (keV) (keV) . . 2.43 5/2- . 1 0 -+ 2(b) 3.03 (5/2)+ 265± 17 433 ± 28 4.65(a) 5/2+, 3/2+ 900 ± 250(a) 930 + 258 6.76 7/2- 2300 + 500(c) 2830 ± 615 11.29 640 ± 11.81 410 ± 30 (a) Text, page 34. (b) Purdom et al., 1966. (c) Text, page 42. 70 99 Table V Partial and Reduced Neutron Widths A summary of the partial widths, rt , and reduced 2 8 8 widths, et , for neutron emission to Be(g. s.) and Be(2+) 9 from states in Be found in the present experiment is shown. Values of the assumed t-value of the outgoing neutron, the corresponding penetration factor, the measured branching ratio and the deduced values of partial and reduced neutron widths are given. All calculations have been done for a channel radius R = 4. 3 5 fm. The reduced widths are expressed in units 2 2 of ti /mR = 2.47 MeV. See pages 43-45. Table V Partial and Reduced Neutron Widths 8 Decay to Be (g. s. ) Excitation tn kRP (MeV) - Branching Ratio rt (percent) (keV) e2 .t 2 (x 10 ) 2 -3 • 703 x 10 -1 .921 x 10 87 ± 13 377 ± 61 81 4.65 2 .407 13 ± 4 121 ± 50 6.0± 2.5 6.76 3 .241 < 2 :s. 56 < 6 11.29 1 2.47 < 2 < 13 ~ 1 11.81 1 2.55 < 3 :s. 12 $. 1 2.43 3 3.03 .075 ± 7.5 ± 1.5 .021 2.1 ± .6 ± 13 Decay to 8 Be(2+) Excitation tn kRP (MeV) e2 Branching Ratio rt (percent) (keV) (x 102) l 6.;76 1 .849 .41 :s_ B. R. $. .69 1160 $. r l ~ 1950 .28::;. et2 ~ .47 11.29 1 1.964 14± 4 90± 27 .93 ± .28 3 .464 1 2.064 3 .540 11.81 4.0 12 ± 4 49 ± 16 ± .12 .48 ± .16 1.8 ± .6 ....... 0 0 101 Table VI Theoretical Reduced Widths Reduced widths to 8 Be(g. s.) and 8 Be(2+) from levels in 9 Be, calculated from the lp-shell wave functions of Cohen and Kurath (1965) and Barker (1966) are shown. All reduced widths are calculated for p-wave neutron emission, and are normalized 2 to a single particle reduced width esp = .6. The excitation values are those calculated by Barker (1966), while the spectroscopic designations refer to the main components of the wave functions when they are expressed in an LS coupled basis. See pages 46-49. 102 Table VI Theoretical Reduced Widths Level Jrr eP2 ( x 10 2) Excitation (MeV) Kurath 8 [ 4, 1J22p [ 4, 1] [ 4, 1] [ 4, 1] 22 D 22 22 F G [3,2]22p Barker Be(g.s.) 8 Be(2+) 8 Be(2+) 3/ 2- o.o 34.8 43.5 1/2- 2.02 43.2 27.6 5/ 2- 2.41 o.o 68. 7 3/2- 4.60 3.0 69.3 5/2- 5.90 23.7 7/2- 6.14 9/ 2- 10.46 7/ 2- 11.35 o.o o.o o.o o.o 1/ 2- 11.88 0.07 3/2- 12. 76 0.11 12.6 o.o o.o 1.5 2.2 103 Table VII Positive Parity States A comparison between the present experimental results 8 for neutron decay widths to Be(g. s.) by positive parity levels 9 in Be is made with the theoretical calculations made. by Barker (1961). Theoretical calculations of the observed total widths and partial neutron widths which are enclosed in parentheses are not expected by Barker to be reliable, but are included for completeness. Unless otherwise indicated, experimental values - - for r TO are taken from table N, and values for r .t and e 2 are taken from table V. Experimental values for J _rr are taken from .' the recent compilation of Ajzenberg-Selove and Lauritsen (1966). See pages 49-51. 104 Table VII Positive Parity States 8 Decay to Be(g. s.) Theoretical Excitation - Jn 1 TO tn (keV) (MeV) r-t (keV) 1.75 1;2+ (530) 0 (560) 3.04 5/2+ 150 2 230 4.84 3/2+ (1000) 2 180 1 .tn r -t 8 2 (keV) (x 102) Experimental Excitation Jn (MeV) TO - .{, 1.67 1;2+ (keV) 224 ± 25(a) 3.03 (5/2)+ 265 ± 17 2 377 ± 61 81 4.65 3/2+, 5/2+ 900 + 250 2 121 + 50 6.0 ± 0 (a) Ajzenberg-Selove and Lauritsen (1966). ± 13 2.5 105 Table VIII 6 Excitations and Widths of States in Li from 7 Li(3 He,cx.) 6 Li The excitations and widths of states in 6 Li found in the 7 3 6 reaction Li( He, a.) Li by Allen et al. (1960), by Linck et al. (1963) and in the present work are shown. All energies are in MeV. The widths are expressed in terms of energy in the 6 Li system. See pages 81, 82 and 85. 106 Table VIII 6 7 3 Excitations and Widths of States in Li from Li( He, a.) 6 Li Allen et al. Linck et al. Present Excitation r Excitation r Excitation 0 0 0 0 0 2.187 :::;. .1 2.179 ± .008 :s_.04 2.17 ± .02 3.56 + 0.06 < .1 3.568 ± .008 :s_.04 3.55 ± .02 5.47 ± .04 5.34 ± .02 r 0 4.3 ± 0.2 5.35 ± 0.07 .1 5.6 ± 0. 2 2.0 6.63 ± 0.08 .2 7.40 ± 0.10 .6 8.37 ± 0.08 .2 (9.3 ± 0.2) .6 .600 .36 ± .04 107 Figure 1 A proton spectrum from the magnetic spectrometer taken 3 at E( He) = 10 MeV, ep = 90° is shown. The abscissa is the frequency of the nuclear magnetic resonance probe used to measure the magnetic field strength. The region between 33. 2 and 37. 0 MC /S was taken with a thinner target than was the remaining spectrum. Corrections for energy loss in the target by both beam and protons have not yet been made. Groups at 7.94 and 9.1 MeV are not in evidence. See page 12. PROTON ENERGY(MeV) 70 8.0 9.0 100 9.0 8.0 10.0 11.0 120 13.0 14.0 15.0 16.0 LO 00 170 EXCITATION IN 9 se (MeV) 70 6.0 5.0 40 30 20 7 Li( 3 He,pl 9 Be E 3He = 10.00 Me V 20 8LAB = 900 • (f) I- ~ 15 z ::> ~ ....... 0 co i 0 ...... .u °2~ >w ~ ....... I + I<l: ~xi I x4 x 14 N(0.0) _J 10 .w cc • i ''/\ 5 x • x 24.0 25.0 26.0 270 280 29.0 30.0 31.0 320 33.0 NMR FREQUENCY (MC/S) 34.0 35.0 36.0 370 380 109 Figure 2 A proton spectrum from the magnetic spectrometer 3 taken at E( He) = 8 MeV, 6 = 90° is shown. Corrections p for energy loss in the target by both the beam and protons have not yet been made. See page 12. PROTON ENERGY (MeV) 6.0 7.0 10.0 8.0 9.0 9.0 8.0 10.0 11.0 EXCITATION IN 9Be (MeV) 6.0 5.0 4.0 7.0 900 800 12.0 13.0 14.0 15.0 3.0 2.0 1.0 0.0 16.0 7u ( 3 He, p) 9 Be l E3He = 8.00 Me V BLAB= 900 700 14 N (2.31) ~ 600 z => "rj ...... u 500 w ~ 0> ~ co ~ t..:i g 400 + I I 300 ~ 200 ISF (1.0) 18 F(0.0) + + ff y \ ~ ~l 14 N (3.95) ~ t ···''·~ 14 N (0.0) + '- +' rt r I ' v · \+ 31.0 33.0 x t' A 100 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 32.0 NMR FREQUENCY (MC/S) L ri6 I 0 34.0 35.0 360 37.0 ........ ........ 0 111 Figure 3 A proton spectrum from the magnetic spectrometer taken at E(3 He) = 8 MeV, e = 15° is shown. The 4.6 MeV 9 state in Be stands out mor~ clearly in this spectrum than in any others taken. Double- peaked contaminants are from carbon buildup on both sides of the target. Corrections for energy loss in the target by both the beam and protons have not yet been made. ~ee page 12. PROTON ENERGY (MeV) 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 4.0 3.0 2.0 1.0 0 .0 EXC ITATION IN 9se (MeV) 10.0 9.0 9 ~ 8.0 7.0 6.0 5.0 14 N (2.31) 7u( 3He,p) 9 Be ~ f E3He = 8 .00 MeV ~ 8 BLAB' 15° 7 (/) 1- 6 ISF (0.0) t II 14 ! I : ~ .~. rl ~- 3 2 I N (0.0) i1 I • t 1 ~~ ~ ! t ~ \ 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0 35.0 36.0 NMR FREQUENCY (MC/S) I x~ /Ix I~ \. . J\ ix ., \ 37.0 ' 38.0 39.0 40.0 41.0 ~ 113 Figure 4 A proton spectrum from the magnetic spectrometer 3 0 taken at E( He) = 10 MeV, e p = 1. 7 , demonstrates the carbon contamination problem in the excitation region around 9 the 11.29 MeV and 11.81 MeV levels in Be. Points shown as triangles were taken immediately following evaporation of the lithium target. Points shown as solid dots were then taken, scanning toward higher frequencies beginning at 26.0 MC/S, in 15 µc runs. Points shown as x's were taken after the target had been bombarded by 1750 µc. The +'s show the 12 3 14 proton yield from the reaction c( He, p) N, for which a natural carbon target was used. The growth with bombardment of carbon on the lithium target is apparent. See pages 10-12. PROTON ENERGY (MeV) 7.5 8.0 8.5 9.0 9.5 10.0 10.5 EXCITATION IN 9 Be (MeV) 12.5 12.0 11.5 10.5 11.0 4Ki--~~~--'~~~~~--'~~~~~-'-~~~~~.1..-~~~~----'-~~~~-'! 7 Li( 3 He ,p) 9 Be E 3 He = 10.00 Me V •• BLAB= 1.70 3K r I CJ) ~ .,.... I- ~ 1-i ::l ct> PROTONS FROM FRESH 7Li TARGET • SCAN TOWARD HIGHER FREQUENCIES IN 15µC RUNS x AFTER 1,750µ.C BOMBARDMENT + PROTONS FROM CARBON FOIL 6 r~ x z 0 U 2K I I ........ ........ x ~ ~ •• IK 14 EX. IN N 6.14 (MeV) + ,~6.23 I 5.83 5.69 t 5.10 ; ; 4.91 t ~t.,. .11._L_.J...1~-- ...·'*~.Ji.M. . 26.0 27. 0 28.0 NMR FREQUENCY (MC/ S) +.l. 29.0 ~·- -t'.3~ n • _*_,,, ...... D 30.0 115 Figure 5 Excitation spectra, converted from magnetic analyzer 9 spectra in the region of the 11.81 and 11.29 MeV states in Be are shown for E(3 He) = 10 MeV, e = 1. 7° and for E(3 He) = 7 0 p 3 MeV, e P = 10 • The spectrum at E( He) = 10 MeV is a conversion of fig. 4. Corrections for energy losses in the targets have been made. Regions suspected of having large contributions from contaminant lines have been omitted. The ordinates on the two spectra are independently arbitrarily normalized. The solid lines have the form of two non-interfering Breit-Wigner resonance shapes superimposed on a linear background, as given by eq. (13,1). In each spectrum the parameters used in this equation were adjusted to yield the lowest value of chi- squared. The corresponding values of the resonance parameters found are shown in the two spectra. See pages 12 and 13. 116 40 E ( 5 He l• IO MeV 8p. 1.1• 30 E u ~ "O ltJ E Ai • 11 .30 MeV "O f 1 • .63 MeV 'b N "O EAz • ll .81 MeV 20 f 2 • .4 1 Me V ltJ ~ t<1 ....J ltJ 0:: 10 0 10.0 10.5 11 .0 11.5 12.0 12.5 14 12 E ( 5 Hel• 7 MeV E u ~ 8 p • 10• 10 "O ltJ EAi • 11.28 Me V ~ 'b f 1 • .62 MeV 8 N ltJ > ~ ....J ltJ • ER2 • 11.83 MeV "O f2 • . 40 MeV 6 • 4 0:: 2 0 10.0 10.5 11 .0 11.5 EXC ITATION ! IN 9 12 .0 B e (MeV) Figure 5 12.5 117 Figure 6 A proton spectrum from the magnetic spectrometer 3 0 . taken at E( He) = 9 MeV, e = 12 is shown. Proton groups 9 p from states in Be at 14.392 MeV and 13. 78 MeV are seen. The group at 23.6 MC/S represents protons elastically scattered by hydrogen in the target. The width of this group is due to its large change in energy over·the acceptance angle of the spectrometer. See pages 13 and 14. PROTON ENERGY (MeV) 2.7 2.8 . . i 16.75 2.9 16.70 3.0 EXCITATION IN 9 Be (MeV) 16.65 16.60 7u (3 He, pl 9 Be 1200 I 16.55 E ( 3 He) = 10.00 MeV I ep = 15° 1000 i (/) 800 ~~:::> ~ l I ~ ct> 0) ~ 0 u / ~ ''-.__++ t. 15.9 16.1 j j ••• ~~ co I 600 I + I I l I i 400 11 ! 200 ll i ! l ·l ·l 15.4 15.5 15.6 15.7 15.8 16.0 NMR FREQUENCY (MC/S) 16.2 16.3 119 Figure 7 A proton spectrum from the magnetic spectrometer taken at E(3 He ) = 10 MeV, e = 15 0 shows the 16.671 MeV 9 p state in Be. See pages 14 and 15. PROTON ENERGY (MeV) 4.5 5.0 7K 5.5 6.5 6 .0 EXCITATION IN 9 Be (MeV) 14.5 14.0 13.5 13.0 7 u (3 He, p) 9 Be 6K E 3tte =9.00 Me V BLAB =120 p(3He , p) 3 He 5K ~ "'rj ,.... ~ "1 CD ...J (J) I- • 4K z :J 0 • •• • ..... N 0 (.) 3K 2K • IK 20.0 21.0 2 2.0 NMR FREQUENCY ( MC/S) 23.0 24.0 121 Figure 8 The velocity diagram for the sequence 9 8 7 3 Li( He, p) Be(2. 43)(n) Be(g. s.) is shown for the conditions 8 used in the measurement of the Be(g. s.) decay from 9 Be(2. 43 MeV). All velocities are to scale. See pages 18 and 19. VELOCITY DIAGRAM 7 u (3 He,p) 9 Be (2.43) (n) 8 Be(g .s.) E ( 3 He)= 2.2 MeV 9L,p =150° .,,,,,...,,,,....,.,,.,,,,,-- 1-rj ..... ~ ~ ct> CX> 3He BEAM AXIS ....... !:'-' !:'-' 123 Figure 9 The solid curve represents the laboratory neutron time-of-flight spectrum which would result from the sequence 9 7 3 5 4 Li( He, p) Be(2. 43 MeV)(ct) He(g. s. )(n) He, for values of 9 the parameters given, if the decays of both Be(2. 43 MeV) 5 and He(g. s.) are isotropic in their respective centers-of9 mass. The a.-particle has been taken to leave the Be with and orbital angular momentum -e, = 2. A detailed description of the calculation is given in appendix B, pages 66-69 • The expected location of neutrons from the sequence 9 8 7 3 Li( He, p) Be(2. 43 MeV)(n) Be(g. s.) is indicated by an arrow. See page 19. CALCULATED 7 NEUTRON TIME SPECTRUM FROM Li ( He,p) 9 Be(2.43 MeV) (a} ~ He(g.s.)(n) 4 He 3 3 E( He) •2.2 MeV _J ~15 0:: w ....z 8L,p • 150° BL,n • - 15.7° d • IOOcm w ~ j:: ~ ~· 0:: ~ ~ ~10 (t) 0 co !:'-' """" ~ _J w .· ): w ~ ~ _J w 5 0:: eBe(g.s.) I OL-~~~~~...L..-.-tC.~~~~.....L-~~~~~---'-~~~~~---'~~~~~~....._~~~~----' 40 50 60 70 NEUTRON FLIGHT 80 TIME (ns) 90 100 125 Figure 10 The target chamber used for the branching ratio measurements is shown. The target transfer system is shown schematically in the side view. The target rod may be withdrawn into its sleeve, maintaining a vacuum between the 0- rings on the rod. The entire sleeve may then be transferred to another vacuum system without exposing the target to the atmosphere. See pages 20, 29 and 30. 126 ; ' /, BRASS // NEUTRONS / 3 He f-- BEAM COLLIMATOR- - - - SURFACE B.ARRIER DETECTOR . . 5cm TOP VIEW LUCITE SURFACE BARRIER DETECTOR TARGET BEAM AXIS ------------ SIDE VIEW Figure 10 , 127 Figure 11 A sample spectrum from the surface barrier detector used in the measurement of neutron decay from the 2. 43 and 9 3. 03 MeV states in Be is shown. The counter was covered with a O. 023 cm. aluminum foil. The solid line shapes drawn below the proton groups from the 3. 03 and 1. 70 MeV states 9 in Be have the form of the appropriate "generalized density of states" functions (Barker and Treacy, 1962), folded into the experimental resolution. See pages 21 and 22. 128 7 LI ( 3 He,p) tee E ( 3He)• 2.20 MeV 7000 BP • 150• 9 01(2.43) 6000 5000 ~ 4000 z ::> 0 u 3000 9e. <11.1.> 2000 1000 0 60 80 100 120 140 160 CHANNEL 180 zoo NUMBER Figure 11 220 240 260 129 Figure 12 A block diagram of the electronics used in measuring 9 the neutron decay from the 2. 43 and 3. 03 MeV states of Be is shown. See pages 21-23. CHARGE SENSITIVE r-PREAMP TIME PICKOFF i--- r--- ....----- p n .......___ ......_ AMPLIFIER l-%j ,.... START - ~ 11 ...... N SLOW COINCIDENCE I ~GATE SCALER IN _ AMPLIFIER FAST ' SINGLE CHANNEL ANALYZER STOP Tl ME-TO-PULSE-HEIGHT CONVERTER (!) - -• -------- ZERO CROSSOVER PICKOFF to-------SINGLE CHANNEL ANALYZER SLOW MULTI -CHANNEL ANALYZER ...... ~ 0 131 Figure 13 Measurements of the relative efficiency of the neutron detector as a function of neutron energy, using the 3 reaction 3T(p, n) He, are shown as open circles. The solid line is a theoretical curve, calculated ignoring scattering of the neutrons by carbon atoms in the scintillator, and taking the bias cutoff to occur at a neutron energy of 450 keV. The relative data points are normalized to lie on this curve at a neutron energy of 6 MeV. The point shown as a triangle represents an absolute efficiency measurement 3 done with the reaction D(d, n) He, using a gaseous deuterium target. See pages 23 and 24. .71 EFFICIENCY .6 ~ t >0 ~ .5 0 t ~ ~ ~ .4 ..... w 11 CD 0 ~ 0 ...... - l/ ~ ~ ~ OF NEUTRON DETECTOR 0 RELATIVE POINTS FROM 3 T{p, n) 3 He A ABSOLUTE POINT FROM d(d ,n) 3 He E -8 -"-(1-e-crHNHL) En I~ ----------- w t;j .3 0 .2 .I 0 2 3 NEUTRON 4 ENERGY (MeV) 5 6 7 133 Figure 14 This neutron time-of-flight spectrum was recorded with the proton detector window accepting protons corre9 sponding to the excitation region in Be between 2.2 and 3.9 MeV. Groups marked 3.03 and 2.43 represent neutrons 8 from the Be(g. s.) decay of the 3.03 and 2.43 MeV levels in 8 9 Be. The neutron flight time corresponding to a Be(g. s.) 9 decay from an excitation of 3.9 MeV in Be is marked "pwindow". The broad neutron group peaking near channel 305 represents neutrons from the decay of the 2.43 MeV 9 state in Be via modes (2) and (3) (see text, page 18 ). The dashed line indicates the random time coincidence background. See pages 24 and 25. 40 30 70 50 60 FLIGHT TIME (n sec.) 180 t- NEUTRON TIME SPECTRUM 7Ll(3He,p) 9 Be(n) 8 Be 160 1- Bp • 150• Bn •-15.7° 80 E (3He) • 2.20 MeV d • 100 cm 140 .J ILi ~ 120 ":tj ~· (Jq u a:: ILi 100 ..... (/) ~ ' I ~ (D 2.43 <t • ~ 3.03 i I- z :::> 80 0 • ..... c,o) ~ p·WINDOW l u • 60 • '40 •• . .. 20~ - • • • • •• 0 200 • 220 240 260 280 CHANNEL NUMBER 300 320 340 135 Figure 15 The time-of-flight spectrum of fig. 14 has been converted to counts per neutron energy interval versus neutron energy. Each point below E = 2...2 MeV represents 11 an average over approximately a 50 keV interval of the corresponding points in the time spectrum, while each point above E = 2.2 MeV is an average of two points in n the time spectrum. The upper scale refers to excitation 9 8 energies in Be if the neutron decay goes to Be(g. s. ). See pages 24 and 25. 1.8 2.0 2.2 2.4 2.6 2.8 EXCITATION 3.0 IN 9se 3.2 3.4 3.6 3.8 4.0 (MeV) NEUTRON ENERGY SPECTRUM 7u (3He,pl 9 se (nl 8 Be E ( 3He) • 2 .2 MeV BP• 150° Bn • -15.7° d • 100 cm 300 _J ~ er w I- z >(,!) er w z w 1-tj ,.... w Q_ <t> I- ~"'i ..... C11 2.43 ~ er 200 ....... c:.:> (/) 0) z :::> 0 3.03 ~ (.) w > ~ G:1 '00 a:: p-WINDOW CUTOFF ~ ------------------------------- 0 0 1.0 2.0 NEUTRON 3.0 ENERGY ( M eV) 4.0 i+-__! 5.0 137 Figure 16 These neutron time-of-flight spectra were recorded with narrow proton windows. The scale above spectrum B 8 shows corresponding excitations for Be(g. s. ) neutron decay and refers to both spectra. Each region indicated by "pwindow" shows, when read on the upper scale, the region of 9 excitation in Be accepted by the proton window. A) The 9 Be(2.9 - 3.5 MeV) excitation region is seen to decay 8 9 predominantly to Be(g. s. ). B) The Be(2.17 - 2.65 MeV) excitation region decays mainly via modes (2) and (3) (see 8 9 text, page 18 ). Be(g. s.) decays from the Be(2.43 MeV) 9 state and from the tail of the Be(3.03 MeV) state are indicated by arrows. See pages 25 and 26. 138 3 .5 3.0 2.5 2.0 I~ NEUTRON 200 3.8 3.4 3.0 2 .6 2.4 2.2 ID ENERGY ( MeV) 2.0 .5 7 1.8 EXCITATION IN 9s. • • • • 150 ( MeV) NEUTRON TIME SPECTRUM 7Li (3He,p) 9 se (n) 8 Be E C3 Hel • 2 .2 MeV • (}p • 150• Bn • -30.1• d • 62.5 cm p -WINDOW .....J • w z z <t • 2.43 ~ 100 t a:: w a.. en 1- z :::> 0 u z 0 a:: I- ::> w z 50 .••..• • . -----·________________ ...__ ... ·•· .. B ,-~..,,...., ~y~• A p-WINOOW t • 3 .03 • 150 160 170 . 180 190 CHANNEL 200 NU.MBER Figure 16 210 220 230 139 Figure 17 The angular distribution of neutrons from the decay 9 8 of Be(2.9 - 3.5 MeV) excitation region to Be(g. s.) in the 9 Be(3.03 MeV) center-of-mass system is shown. The vertical 3 scale is the number of neutrons per steradian per 10 protons in the proton window. See pages 26 and 27. 140 . 110 ANGULAR DISTRIBUTION OF NEUTRONS IN 9 Be SYSTEM 7u (3He. p) 9se (3.03) (n) See (9.1. ) E ( 3 He) • 2.20 MeV 100 CJ) z 8p. 150° 90 ·o lo a:: 80 a.. I() 0 a:: w a.. 70 ·zso <l 0 <l 5I- 50 C/) a:: W40 a.. CJ) z ~30 I- '.:) w 2 20 10 -ao -60 -40 -20 80 (C.M.) (DEGREES) Figure 17 0 141 Figure 18 of the 9 The angular distribution of neutrons from the decay 8 9 Be(2.43 MeV) state to Be(g. s.) in the Be(2.43 MeV) center-of-mass system is shown. The vertical scale is the 3 number of neutrons per steradian per 10 protons leaving the 9 Be in its 2.43 MeV state. See page 27. 142 18 ANGULAR DISTRIBUTION OF NEUTRONS IN 9 Be SYSTEM 7 u {3He,p) 9Be{2.43) {n) 8ee{Q.s.) 16 E {3He)=2.20MeV Bp = 150° (f) z 14 0 l- o 0:: a.. 12 0:: ~ 10 z <l: 0 <l: 0:: 8 w 1(f) 0:: 6 w a.. (f) z 0 0:: I- 4 ::> w z 2 -80 -60 -40 -20 0 20 Bn (C.M.) (DEGREES) Figure 18 40 60 80 143 Figure 19 7 Calculated kinematic lines for the sequence 9 8 Li( He, p) Be(n) Be are presented in a proton energy 3 versus neutron flight-time representation for cases in 8 which the Be is left in its ground state and in its first 9 excited state. Excitation energies in Be are included for convenience. Regions which are populated by the 9 decay of levels in Be at 2.43, 3.03, 4.65 and 6. 76 MeV 9 are denoted by their respective excitations in Be. The regions are indicated to facilitate the discussion of the data shown in fig. 20. See pages 30, 31 for a discussion of the kinematics. 9.0 80 . 8.0 20 30 40 NEUTRON FLIGHT TIME 50 (ns/m) 60 9.0 145 Figure 20 A sample two-dimensional coincidence spectrum 0 0 3 taken at eL = 90 , eL = -30 , E( He)= 10.0 MeV 'P 'n and d = 98 cm is shown. The number of counts in each channel is proportional to the intensity of the spot in that 9 channel. The decay of levels in Be at 4.65 and 3.03 MeV 8 to Be(g. s.) appear at (31 ns, 11.8 MeV) and (40 ns, 13.4 9 MeV) respectively. The decay of the 6. 76 MeV state in Be is seen in the vicinity of (38 ns, 9.8 MeV). The decay of 9 8 the 2.43 MeV state in Be through the tail of Be(2+) and 5 through the ground state of He produces a band of neutron energies at approximately (50 - 65 ns, 13.9 MeV). The corresponding regions are indicated in· fig. 19. See page 32. 146 •. EXCITATION IN N 0 U) t. j .; \. -.~ ; l- .; t- 0 ..:j• :·.~ ·1 i ···s.I t.\ ( ~ 'jI t ,, 0 !"ii I ·' I ! ·'l J .- 0 •.i N .~ }. ··i \ I ··•. }. ' iL s 0 N NO lO ~d Fi~-ure 20 co ~., c: !- ··: i - 147 Figure 21 A sample Qharged particle singles spectrum, typical of those obtained during measurements of the branching ratio 8 9 to Be(g. s.) from the 4.65 MeV state in Be. The particles must pass through the 0.051 mm tantalum target backing and a 0.025 mm aluminum foil en route to the 1000 µ counter. 9 Protons populating the ground state of Be are not stopped . 8 7 in the counter. Deuterons from Li(3 He, d) Be(2+) completely obscure the proton spectrum in the vicinity of 9 Be(4.65 MeV), requiring that a singles spectrum be taken with the magnetic spectrometer (fig. 22). See page 33. ., PARTICLE 6.0 8.0 PARTICLE ENERGY 10.0 SPECTRUM FROM (Me V) 12 .0 7 14.0 16.0 L i + 3 He E ( 3 He) = 5 .0 Me V 7K BL • 00 6K 7 7 3 8 Li( He, d) Be(2+) 5K l'rj ..... ~ 11 CD : .... ~ 3 Li( He,p) 9 Be(2.43 MeV) t t ~ I/) ~ I- °' z 4K ::> 0 u 7 3KL 12 U( 3 14 C( He,p) N(g.s.) 3 He,d) 8 Be(g.s.) t 2K IK 0 60 70 80 90 100 110 CHANNEL 120 NUMBER 130 140 150 160 149 Figure 22 This proton spectrum from the magnetic spectrometer was taken at the same bombarding angle and energy as was that shown in fig. 21. The number of times the 4.65 MeV 9 state in Be was populated was derived from this spectrum. 9 The proton yield from the 2.43 MeV state in Be was used to normalize this spectrum to that of fig. 21. The solid line 9 beneath the proton group from the 4.65 MeV level in Be represents the background necessary to leave the width and excitation of this group as 900 keV and 4.65 MeV respectively, if a Breit-Wigner line shape (eq. 34, 1 ) is assumed for the level. This background was used in determining the proton yield from the state. See pages 33 and 34. 7 u (3He , p) 9 se Bp :QO ErHe) = 5 .0 MeV 15 (/) .... z I jl"'x2 :> 0 0 z 14 0 t-10 0 0:: lo:J:j ..... Q. ~ IA.I CJ'CI Ii (t) t-.:1 t-.:1 ~ .!,................... • ....... • t.._• I• ~ ~ _J N(0.0) • I 9 ,. ,,.'4". ' ,,~ ~•.!.._....,. IA.I 0:: 5 ee (4.65) ' • \ 1\I . ;I • I \. • • \. l '. \ ' l ~~ • .\he ~·' ,Ll O '---2-L6--l2""-7--2....1..8_ _2L-9--3.....1..0_ _3.J.....I---'32--3-'-3----13-4--3-'-5NMR FREQ (Meis) 36 37 38 ~ CJ1 0 151 Figure 23. The time spectrum corresponding to neutron decay 9 from an excitation region at 4. 75 MeV in Be is shown. This spectrum is taken from a two-dimensional coincidence spectrum, and corresponds to a single proton channel. The 8 peak in channel 22 represents neutron decay to Be(g. s. ). 8 The sum along the Be(g. s.) line was made by measuring the number of counts in this peak as a function of proton channel. See pages 33 and 34. FLIGHT TI ME 10 0 ( n sec) . 30 20 40 u (3 He, p) 9 Be (4.75 MeVHn) 7 E (3 He) =5 .0 Me V 140 120 8L,p. =0° E(p)= 11.422 8L,n =60° d =23.9 cm _J w 100 z z <l 1-%:1 :r: ...... 0 ~ '1 (!) ti:> 0:: ao .f \ Ttl1 1\ r I , W . a.. (,) Cf) t- z 60 :J 0 0 40 20 OL-__1~--1.~_L~___J_~-L~__._-,--~~...l-~.L.-~L----'~__..~_._~ 0 10 20 30 CHANNEL 40 NUMBER 50 60 1-4 OI ti:> 153 Figure 24 An example of the spectra obtained by summing along 8 the Be(g. s.) kinematic line is shown. The number of counts 8 per proton channel in the Be (g. s. ) peak is plotted as a function 8 of proton channel number. Neutron decay to Be(g. s.) from 9 states in Be at 3.03 MeV and 4.65 MeV produces resonant 8 groups along the Be(g. s.) kinematic line. The solid curve 9 through the data points in the vicinity of the Be(4.65 MeV) group has a Breit-Wigner shape (eq. 34, 1 ) with width and 9 excitation in Be of 900 keV and 4.65 MeV respectively. · The solid curve below the data points indicates the assumed back9 ground. The total 8Be(g. s.) neutron yield from Be(4~65 MeV) at eL ,n = 60 was determined by measuring the number of counts in this peak. See pages 33 and 34. 154 8 Be(i;i.s.) YIELD FROM 7 Li fHe, p) 9 ee (n) 8 ee (i;i.s.) 8L,p = 0° 8L,n •GO• 400 E(3 He)•5.0 MeV 300 I l CJ) 1- z => ~x.l 2 0 (.) 200 l oo~~~'--~---;:-~__J~~-:1-:--~---1~~-L~~__J 10 20 30 PROTON CHANNEL Figure 24 ; ' 155 Figure 25 7 3 For the sequence Li+ He __. p + n + 8 Be(g. s. ), a measurement of the outgoing neutron and proton angles leaves the determination of only one remaining independent variable necessary to provide enough information to calculate the final vector velocities of all three particles. If this variable is 9 taken to be the excitation in Be, the corresponding excitation 9 in B can be calculated. The resulting plots of excitation in 9 9 B as a function of excitation in Be are shown as light solid lines for several values of the neutron angle for the kinematic conditions used in the measurement of neutron decay from 9 Be(4.65 MeV). The solid points show the experimental 9 8 locations of the Be(4.65 MeV) group on the Be(g. s.) kinematic line for several neutron angles, with associated experimental errors. The apparent excitation of this group remains sufficiently constant for e L n ~ 90° to lend confidence to the ' coming from a single level in interpretation of the group as 9 Be. For 8 L n > 90°, the apparent excitation falls, giving ' . rise to the suspicion that the group may be receiving contri9 butions from a level in B in the vicinity of 9.5 MeV. Points in the backward hemisphere were accordingly excluded in calculating the branching ratio• . See pages 34 and 35. 156 9 LOCATION OF FROM 11.5 7 Li + 3 Be (4.65 MeV) GROUP p +n + He - 8 Be (g.s.) 3 E( He)= 5 .0 MeV 8L,p • 0° 11.0 >., ~ m en 10.5 8L," •30° z z 0 ~ I- u x w 10.0 BL.• •60° 9.5 3.5 4.0 4.5 EXCITATION IN 5..0 9 · Figure 25 . Be (MeV) 157 Figure 26 The angular distribution of neutrons from the decay 9 8 9 of the Be(4.65 MeV) state to Be(g. s.) in the Be(4.65 MeV) center-of-mass system is shown. The vertical scale is the 3 number of neutrons per steradian per 10 protons leaving 9 the Be in its 4.65 MeV state. See page 35. . 158 ANGULAR DISTRIBUTION OF NEUTRONS IN 9 Be SYSTEM 9 7 3 8 u( He, p) Be(4.6)(n) Be(g. s.) 20 E (~He ) =5 .0 MeV 9L,p =0° U) z 0 f- 0 a: 0... ,., 15 0 a: w 0... z <l: 0 <l: a: I 0 w f- U) a: w 0... U) z 0 a: ~ 5 w z 0 0 20 40 9C,n (DEGREES) Figure 26 60 80 159 Figure 27 A sample surface barrie:c counter spectrum, typical of those obtained in the measurement of neutron decay from 9 the 11.29 and 11.81 MeV states in Be, is shown. The particles must pass through the 0~076 mm tantalum target backing and a 0.025 mm aluminum foil before entering the counter. Proton groups are seen from the target con1 12 taminants H (channel 65), c (channel 136), and 160 (channel 125). The solid curve drawn through the data points has the form of two non-interfering Breit-Wigner resonance forms superimposed on a constant background of 400 counts per channel. The background is due to continuum protons and deuterons and of protons passing through the counter. Values of the resonance parameters used in calculating the smooth curve are compared with . those obtained from a magnetic spectrometer spectrum at the same bombarding energy and angle in table IL Regions denoted I-IV are discussed on page 37 • See pages 36 and 37. 2500 PARTICLE SPECTRUM FROM 7u (3 He,p) 9 Be 8L,p =0° E(3He)= 10.0 MeV 2000 •• 9 Be(ll.29) ~ • 1500 ":i:J ~· ~ ~ CD [).:> -J Cf) ~ z 3 3 H ( He, p) He ,o / ::> u ., 1000 I ..... . C1'l 0 \ ., 18F(l.7) ~ .\. '• ~ . ' 14 ' ....... ·~····. • ••••• ::::::::-...::: 500 I 70 m II 80 90 100 N(3.945) ............... N' 110 CHANNEL 120 130 140 150 161 Figure 28 The raw data from a coincidence spectrum taken at 3 0 0 E( He)= 10.0 MeV, eL, P = O , eL,n = 15 and d = 102 cm 8 is shown. Kinematic lines corresponding to Be(g. s.) and 8 Be(2+) decay are indicated. Random time coincidences have been subtracted. Regions I-IV correspond to excitation in 9 Be centered at approximately 12.5, 11.81, 11.25 and 10.5 MeV respectively, as indicated on the corresponding singles spectrum of fig. 27. Time spectra in these. regions were · added together, and the sums are shown in fig• .29. See pages 36 and 37. ~ ~ ..J .. -· + Q) C\.I en Ct 162 ~~P~-~~-••NN Q) (D Q) CD Q) -o-oooooooooooonoo--N~ no oo --oo-on-ooooo ooo~ ~N- ~ ____ o_oN-on-••-ONN - - N-o-NN ooo-ooooooooooonoo-o•••-~":•~•NN~-•-N---N•~-~-•o-o--NN-o-NNO--N- -000--0-000000--0-•o~~-~~2··~~-~--····~·~·-·--·~-·N·-- N --•ooNN-N I I I I I I I I •• I I __ O _ _ _ # I I I ) I I I _ _ _ _ _ _ _ _ N_N (INCREASING NEUTRON FLIGHT TIME - 4#N~NO##OOO-~-·-N_N_N_O 0---00-00--0000-0 00 -N•~~~=~· ~ --·--~·······--··-N- • ----·~·NO--~oo I ~0--0--0--0-0---·· :o-o-ooo~N OOOOOO -• 0 TIME CHANNEL Figure 28 z 0 ffi a: z ~ 0 ffi a: z i3 0 ~ z H 0 i3 ~ t z a: zw <.:> ..J >W GW ctz z zo Ott-0 0 a:: IL a: a.. 163 Figure 29 The summed time spectra from the regions indicated 8 in fig. 28 are given. Neutron decays to Be(g. s.) and 8 Be(2+) are denoted in region L The dashed curves represent the shapes of neutron time spectra from the sequence 7 3 9 5 5 Li( He, p) Be(a ) He(g. s. ) He, assuming isotopic breakup 9 5 of Be and He(g. s. ). Corrections for the change in detector efficiency with neutron energy were made in calculating the curves. These background shapes were used in extracting 8 the Be(2+) yields from each of the four regions. See page. 38 • . : 164 TIME SPECTRA FROM 7Li( 3He, p) 9 Be(n) 8 =0° E ( 3He)" 10.0 .83 ns/ch L,p 8 L,n =15° d= 102cm 1!50 REGION I 100 50 REGION II 150 100 50 150 REGION ~ 100 + +• •- ......-.-¥ ........ -.1...._._.... 0 _ .................. \)'J~+-.-r+-~-+--- - } I 50 m ,.:.....1__.:;_ ... _ __J.___ _....J ___._ _ __ . __ ____._ _ __ . __ _ REGION Ill 150 100 ¥~ 50 0 1-+..i • \.___ } + -- ---.....-.-.-+-+-.-.J • •_._.i...._._._._ • T-• -10 20 30 40 TIME CHANNEL 50 •-.. 60 ' Figure 29 70 165 Figure 30 A sample time spectrum representative of neutron 9 decay from Be(ll.29 MeV) (Region ID) is given. The heavy solid curve represents the expected neutron time spectrum 7 9 from the sequence Li(3 He, p) Be(ll.29 MeV)(a.) 5 He(g. s.) n 9 for isotropic decays of the Be(ll.29 MeV) state and the 5 9 He(g. s. ), assuming an .e, = 2 decay by Be(lL29 MeV). The dashed curve is the spectrum expected from 7 3 9 8 Li( He, p) Be(ll.29 MeV)(~) Be(4+}, assuming p-wave neutron emission. Corrections for the change in detector efficiency with neutron energy were made in calculating the curves. The shape of the solid curve was used in the 8 extraction of Be(2+} yields. See page ·38. NEUTRON TIME (ns) FLIGHT 30 20 40 7 8 u (3 He,p) 9 Be (ll.29MeV)n E ( 3 He) • 10.0 MeV ee (2+ l 8L,p • 0° • 300 50 8L,n • 30° d•84cm l>rj ..... ~ "'$ I/) ~ ~ 0) 0) z :> 200 CD 0 t,.:) (.) 0 Bee(g.s.) • 100 __fj - + -+_.-~ O"-~~~~--i.~~~~~---'-~~~~~_._~~~~~....L....~~~~~-'-~~~~---' 0 10 20 30 TIME CHANNEL 40 50 60 167 Figure 31 i The angular distribution of neutrons from the decay 9 8 9 of the Be(ll.29 MeV) state to Be(2+) in the Be(ll.29 MeV) center-of-mass system is shown. The vertical scale is the 3 number of neutrons per steradian per 10 protons leaving 9 the Be in its 11.29 MeV state. See pages 38 and 39. 168 ANGULAR DISTRIBUTION OF NEUTRONS IN 9 Be SYSTEM 7 Li( 3 He,p) 9 Be(ll.29 MeV)(n) 8 Be(2+) (J = L,p oo 40 (f) • 0 0 o z I- a:: a.. IO 0 30 E ( 3 He )= 10.0 Me V E( 3 He)= 9.0 MeV ~ a:: w a.. z <l 0 <l a:: 20 w I- (f) a:: w a.. (f) z 0 a:: I- 10 :::> w z 0 .0 20 40 Be, n (DEGREES) Figure 31 60 80 169 Figure 32 The angular distribution of neutrons from the decay of 8 9 the Be(ll.81 MeV) state to Be(2+) in the Be(11.81 MeV) 9 center-of-mass system is shown. The vertical scale is the 3 number of neutrons per steradian per 10 protons leaving 9 the Be in its 11.81 MeV state. See pages 38 and 39. 170 ANGULAR DISTRIBUTION OF NEUTRONS IN 9Be SYSTEM 7 3 9 u( He, p) Be (11.82 MeV)(n) 8 Be(2+) 40 8 L,p. =0° CJ) z 0 • o o l- a:: E ( 3 He) = 10.0 MeV E ( 3 He) = 9.0 MeV a.. 'b 30 a:: w a.. z <t i5 <t 5 20 1- CJ) a:: w a.. CJ) z 0 g: 10 ::> w z 0 0 I 20 40 Bc,n (DEGREES) Figure 32 60 80 171 Figure 33 The coincidence spectrum of fig. 20 has been projected onto the proton energy axis in two pieces. Figure A 8 represents all events falling outside the Be(g. s.) line. Random time coincidences have been subtracted. The large group in fig. 9 A corresponds to neutron decay from Be(6. 76 MeV). The solid curve through the data points has the form of a B-W. resonance (eq. ( 3.4 , 1)) of width 2.3 MeV, superimposed on an assumed background shown by the dashed line. Figure B shows 8 Be(g. s.) decay from 9Be(4.65 MeV) and 9 Be(3.03 MeV) groups, 9 but no resonant behavior at Be(6. 76 MeV). See pages 40 and 42. 172 9 EXCITATION IN 9 .0 8.0 7.0 8e(MeV) 6.0 7 5 .0 3 Li ( He, p) 4 .0 9 3.0 Be(n} 3 E ( He) • 10.0 MeV 8L,p 90• I 1500 8 L,n • -30• A SUM EXCLUDING 8 Be (Q.S.) LINE 1000 500 V) ..... z => 0 0 -! . 40 60 50 70 B SUM ALONG 8 Be (Q.s.) LINE 500 400 300 200 \ 100 40 50 60 PROTON · CHANNEL !i Figure 33 I 70 80 173 Figure 34 A neutron energy time spectrum corresponding to an 9 excitation in Be centered at 6.8 MeV is taken to represent 9 neutron decay from the Be(6. 76 MeV) state. Figure A displays a portion of the data of fig. 20, converted to an energy spectrum 8 in the Be center-of-mass system; figure B displays a similar spectrum taken at a different neutron angle. The data points have been corrected for the variation of detector efficiency with neutron energy. For neutrons proceeding via 9 8 7 3 Li( He, p) Be(6.8 MeV)(n) Be(2.9 MeV), figures A and B represent neutron center-of-mass angles of o0 and 79° with 9 respect to the Be recoil direction. The heavy solid curves in both spectra represent shapes expected from neutron decay 8 through Be(2+), folded into the experimental resolution. The dashed line in fig. A represents the expected shape from .t he 5 5 process 7Li(3 He, p) 9Be(6.8 MeV)(a.) He(g. s. )(n) He, assuming 9 5 isotropic decays of both Be(6.8 MeV) and He(g. s. ). The 5 dash-dotted curves represent expected shapes if the He(g. s.) 2 angular distribution is given by W(e ) = 1 + cos a • c,n c,n See ·pages 40 and 41. 174 NEUTRON ENERGY SPECTRUM IN 9 Be SYSTEM 3 7 3 BL,n = -30° d•98cm Bc,n •Oo 9 Li( He,p) Be(6.8 MeV)(n) E( 3 He) z 10.0 MeV BL,p. 90° z !t <t 0 <X 2 a: w ! I(/') A a: w /.r~·1·,t 1 ........''\. --- a.. ...J <X > a: w I- z z /,l~I 0 I<X !:: 0 • -1.0 u 0 .0 1.0 2.0 3.0 4.0 5.0 x 7 w a: w a.. 6 /\ (/') I- z ::::> 0 5 u w ~ I<X BL,n • 250 d • 50cm Bc,n • 790 4 ...J 8 w a: 3 I I 2 0 \ • j-----i//// ·./ -1.0 1.0 0 .0 EXCITATION 2.0 IN a-a : Figure 34 3.0 4.0 SYSTEM (MeV) 5.0 175 Figure 35 An isobar diagram of the mass 9 system is shown. The entire diagram is taken from the recent compilations of Ajzenberg-Selove and Lauritsen (1966), with the exception 9 of the excitations of levels in Be for which the values found in the present work are given. See page 15. 23.9 ,-,-/,., ,. , , , ,. , . / .,..., (+ 2?,.~......,.,,.,,,,.../ 7.~83 He'+ l 2 ~·~H/HH 20.907 Be1 +I ~~,,..,.,...,..,,..,, 917.63 17.I 18 . ~76 16.02 ·14.56 ...1312r;312 , ....~,, c312r;312I ____ 114.67 Li~ "rj ~· 16.601 Li 1 +He 1[14.0I] 7 4 .0L .... ,,, Cg I e• + P T•3/2 11.81 11.29. ....... -l 11 O') (t) CTI 1.22 r•3j _ _ _ _ ~ ~ ~ Bt' +Ht' B + n l;~,4.,...,,.,..,,,.,,,... ~.. ,76,.,·' .,.,,,712~ ~ _, v"' " " ,_ •' ~ - · · - "">/».?.: . ------~ ·"'"' ~" ,,. --- 1.665 - 1 Bt +n J=3/2- Beg - - - > I.~-~~~ l.685 Ll'+a 177 Figure 36 9 9 The positions of energy levels of Be and B and with respect to two-particle decay channels are shown. The 9 9 ground states of Be and B have been aligned. See pages 17 and 18. \ 14.67 14.01 14.39 13.78 8 Be(4+) + n 11.81 11.29 9.7 ----- ~ J.94_ ____ ~ 6.76 ~· '1 8 Be(4+)+p 7.----1 112- ...... CD c.:> -:J co en 4 .9 --- - 4.05 4 .65 3/2+ 512+ 5 He (312-) +a' I 1.665 I 3.03 2.43 1.67 8 Be(O•) + n (512)+ 512- Be i= · 't~ ..,, ... ·-- B9e(2+)+p 112+ 312- 9 -- - 1 >112-1 98 1-.185 8 Be (O+) + P I 179 Figure 37 A comparison of theoretical and experimental level 9 schemes for excitations below 14 MeV for Be is shown. For the negative parity states, the intermediate coupling level scheme of Barker (1966) is giveno Each state is labelled with the spectroscopic notation of the major LScomponent in its wave function. See pages 46, 47 in the 8 text for details. The level scheme predicted from a ( Be + n) model (Barker, 1961) is shown. See pages 48, 49 for further discussion. 46, 47 and 180 14 24 13 24 24 14 13 112+ 24 12 112+ 22 II 22 G 512+ 912- 10 312+ 12 II 10 7r~+ 9 > Q) 9 8 8 ~ Q) l'.D 312+ 7 --- --- Cl> z 6 z 5 0 ~ <l: I(3 312+ 4 5 4 3 2 0 7 6 --- x w 112+ 9 12+ ·512+r- 22 p 312- -----~-- [4, Q 3.0 2.43 512- 1.67 112+ /2 + 512+ 112+ 312- - - - - - - -- ------9 INTERMEDIATE COUPLING SHELL MODEL A" 9 Figure 37 2 0 Be EXPERIMENTAL 3 POSITIVE PARITY STATES MODEL 181 Figure 38 A sample energy spectrum of alpha particles from 7 3 the bombardment of Li with a 3. 78 MeV He beam is shown. The data were taken with a magnetic spectrometer and subsequently converted to an energy representation. The excitation scale has been corrected for target thickness. Groups were reported by Allen et al. at all of the indicated excitations. See page 82. 10 7Li( 3He, a) 6 Li _J E ( He)= 3.78 MeV ~ 9 0:: w ea -- 30° I- £ 8 >(.!) 0:: lJ..) z 7 • • 9.3 8.37 7.40 6 .63 • ": -. '• &'..... 150 (O.O) ~ 6 ~ _J .... w ~ 0:: 5 ..... ~ 3.56 ,.\ • ·..,_~ •.·.. w ~ 5.35 . I ·' l .,, 2.18 0.0 n ni II 11 EXCITATION 6 IN Li (MeV) TI ~ co 0:: w CD 0.. c,.., U'> • 4 co I- 2 ~ 0 t..:> ' 3 \ u w > 2 • ~ l_ I I 1- <l _J w 0:: 6 7 8 9 ALPHA 10 I ·~ 'l/ . \..__Lu - ENERGY (MeV) II 12 13 1 I 14 I 183 Figure 39 An alpha-particle spectrum taken with the magnetic spectrometer at a bombarding energy of 9.8 MeV is shown. The excitation scale has been corrected for target thickness. The kinematic limits of the alpha-particle energies from the 7 . 3 8 4 processes L1( He, d) Be(16.62 MeV)(a.) He and 4 8 7 3 Li( He, d) Be (g. s. ) (a ) He are denoted by windows labelled 8 8 " Be(l6.62 MeV) 11 and 11 Be(g. s.) " respectively. The shaded group for 8 . Be(16.62 MeV) represents the alpha-particle spectrum calculated from the measured angular distribution of the populating deuterons. . See ·pages 82- 84. 4 5000 6- ALPHA ENERGY (MeV) 10 8 14 12 16 18 20 7Li(3He,a) 6 Li E(3 He)=9.8 MeV 88e(g.s.) ' 4000 Ba= 20° ' 3000 (/) ..... z ::> 0 u l-%j ~· I 2000 t- -.- EXCITATION IN 18 6 Li(MeV) 17 16 15 14 13 12 II 10 9 8 7 6 k 4 3 Jk I ct I ~ 11 CD c,., co 1000. oI sse(l6.62) 1 I 15 1 ' 1 1 I 20 1 1 1 I 1 , , , I , 25 30 NMR FREQUENCY ( MC/S) ' fv/V/i22I?zvze z e z e z ~ 1J i I 35 40 ........ O:> ~ 185 Figure 40 A spectrometer deuteron spectrum from the reaction 8 Li( He, d) Be in the region of the 16.62 and 16.92 MeV levels 8 in Be is shown in fig. A. Fig. B shows the center-of-mass 7 3 angular distribution measured for the deuterons to the 16.62 8 MeV level in Be. The solid line in fig. Bis the shape used in calculating the alpha-particle energy spectrum from the decay of this state. See pages 83 and 84. 186 8 Be(16.s2) 2000 Cf) ~ A 1600 z 3 Li( He,d) 8 Be 3 E ( He) = 10 MeV ed (cm)= 31 .6° .'\ 1-- 7 6 1200 (.) 800 ---- _....;--"'· 400 0 • " ....... ._____.___________- - I _ ___._____._____._____ ~-----~---..._ 23 24 25 26 27 29 28 NMR FREQUENCY(MC/S) ANGULAR DISTRIBUTION 5 OF E u ~ 4 b "O 7u (3He,d) a Be( 16.62MeV) B "O ......... DEUTERONS FROM E( 3 He )= 10 MeV 3 w > 2 I<l _J w a:: 0 30 60 90 120 CENTER-OF- MASS 150 180 ANGLE (DEGREES) Figure 40 187 Figure 41 A series of alpha-particle spectra taken at different bombarding energies are shown. The calculated kinematic 1imits on the alpha-particle energies from the sequence 8 7 3 4 Li( He, d) Be(16.62 MeV)(a) He are indicated by windows labelled 118 Be(16.62)". The low energy edge of the observed group follows nicely the kinematics for this process. The 7 6 expected kinematic behavior of a group from Li(3 He,a) Li (9. 3 Me V) is indicated for comparison. Threshold for the 8 7 3 Li( He, d) Be(16.62 MeV) is at E(3 He)= 6.94 MeV. See page 84. 188 ALPHA ENERGY (MeV) 10 12 II 13 14 16 15 17 18K 7 16K Li ( 3 He,a) Ba= 20° 11 C(O.o> ~ 8 Be( 16.62) 14K 12K 6 Li(5.35) IOK l BK 8 Be{l6.62 5K <f) t- z ) 0 0(0.0) 6 Li{5.35) l EC 3 He)=8.88 6 Li {9.3) 4K MeV l :::> <.) 5 • 3K 2K 8 seCl6.62) • 4K 3K 2K 6 u (9.3) 4K I f 8 Be c16.62) 150(0.0 ) + . - - - 6 . . . - - - - - • Li ~5.35) 3K 3 E( He)=7.86 MeV 2K IK 0 '--~~--"~--'-~__._~_._~--~--~--~..._~--29 30 31 32 33 34 35 36 37 38 39 NMR FREQUENCY(MC/S) "Figure 41 189 Figure 42 This magnetic spectrometer alpha-particle spectrum from 7 Li(3 He,~) 6 Li was taken at the same bombarding energy and angle as was that of Allen et al. The abscissa fluxmeter reading is inversely proportional to the alpha particle momentum. The excitation scale has not been corrected for 6 target thickness. Alpha particles to the ground state of Li were too energetic to be detected by the spectrometer. Groups were seen by Allen et al. at all of the excitations indicated on the scale. See page 85. E 0 (MeV) 3.0 2 .0 4.0 5.0 7.0 6 .0 3 6 Li( He,a} Li E (3 He) =.90MeV 1 3000 Ba =90° EXCITATION IN 9.3 8.37 7.4 6.63 5 .35 6 Li (MeV} :2 (/) 4.4 3.56 2.18 ,., 2000 ~ ~ 11 (t) ~ N> ::> 0 ....... co u 0 1000 .. • • •• •••••• •-1· ··~........•, ••••• ...... .. .... . . • • 6 • • Li RECOILS : .450 • • .. •• 6L . '2 .. ,-, - . • .. !"II • ....,. .., ...I. I .A!. . . -. .\ 'o r, . ,. .350 FLUX METER READING (VOLTS) 1\ n , .."-'/.\ ., I 6L. ~ .400 l., .. ..N..J .300 .250 191 Figure 43 The spectrum of fig. 42 is shown in an alpha-particle energy represen.tation. The excitation scale has not been corrected for target thickness. See page 85. I I I I I 7 • _J • .~~ ~ a: ....;. . . ::..... .., . W2 .0 1- z >a: C> " z a: w Q_ 1.0 t - - 80 =90° ,. I. - , ..~............i .... :::> 6 Li( He, a) Li E ( He)= .90 MeV f. ......:·..., . i- 3 I 3 ~, .•••,., I w z w 1.5 t - I I ...... <O t'-' - (/) 1- z 5 u I I 9.3 8.37 • ____l L ____ LL I 7.40 6.63 5.35\ w > .5 t- I 2.18 3.56 : ft \ Ii\ EXCITATION IN 6Li (MeV) - i- <l _J w a: .••......J1\ Jorj I ~· ~ Ii (!) ~ (..:> 0 I I 2 3 l I 4 5 ALPHA ENERGY (MeV) I 6 !1 •. •••• 1t J 1 8