A may 0% mile: magma Mam mnaia Remains Thesis for the fifigree cf PH. D. MECRGAN STATE ENI‘JERSHY ' EVAN Ema-m PROCTOR i972 LIBRARY M lCh lg; n Sta t9 University ""V "w This is to certify that the thesis entitled A STUDY OF 170 AND 17? THROUGH CHARGED PARTICLE REACTIONS presented by Ivan Dwight Proctor has been accepted towards fulfillment of the requirements for __Ph_~L degree in _Phx§_i9_s_ a {a fig 5: 1:! Major pxofessor ' i: -‘ Date September 152 1972 ABSTRACT A STUDY OF 170 AND 17F THROUGH CHARGED PARTICLE REACTIONS By Ivan Dwight Proctor 170 and 17F have been Six transfer reactions leading to states in studied. Spectra and angular distributions are presented for the fol- lowing reactions and beam energies: 16O(d,p)170 at 20.93 uev, 160(h,d)17F at 34.64 MeV, 16061,h)170 and 1600:,t)17F at 46.16 MeV, and 19F(p,h)170 and 19F(p,t)17F at 39.82 MeV. The triton and helion spectra from the alpha and proton induced reactions were recorded simultaneously to facilitate an accurate comparison of the yield from these two sets of mirror reactions. Distorted wave approximation calculations were performed for these reactions using the code DWUCK. Spectroscopic factors 8 were extracted for the single nucleon stripping reactions. The two nucleon (p,h) and (p,t) reactions were analyzed with a microsc0pic description of the two nucleon transfer process. Enhancement factors Gare extracted for these reactions. The spectroscopic factors 8+ for the ld5/2 and 281/2 single particle states obtained from the (h,d), G:,h) and G:,t) analyses were compared to those obtained from the (d,p) analysis. This comparison serves as a test of the distorted wave approximation description for the stripping process induced by particles more complex than the Ivan Dwight Proctor deuteron. Values for 8+ extracted from the analysis of the (h,d) reaction were found to agree with values obtained from the analysis of the (d,p) reaction. Values for 8+ obtained from the analysis of the Qx,h) and Gr,t) reactions were found to depend strongly on the Optical model description of the entrance and exit channels. Reliable values for absolute spectrosc0pic factors from the G1,h) and (x,t) reactions could not be obtained. The relative values S+¢x,t)/€x,h) were also found to be sensitive to details of the distorted wave approximation calculation. The enhancement factors 6+, extracted from the microscopic (p,h) and (p,t) analysis to the ground and first excited states in 17O and 17F respectively, were compared for different wavefunctions describing 19F. A shell model wavefunction for 19F was necessary to describe adequately the two nucleon stripping process. The addition of a Spin-orbit force to the description of the two nucleon stripping process was not necessary to account for the different (p,t) and (p,h) stripping processes. A STUDY OF 170 AND 17F THROUGH CHARGED PARTICLE REACTIONS By Ivan Dwight Proctor A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1972 Kfl (5)4 ACKNOWLEDGMENTS I would like to thank Dr. Walter Benenson for suggesting these experiments and for his help during the writing of the manuscript. I would also like to thank Dr. Robson Wildenthal and Dr. Duane Larson for the shell model wavefunctions and the two nucleon transfer spectrosc0pic amplitude calculations. Thanks also to Dr. Nick de Takacsy for many helpful discussions related to the DNA analysis of this data. Many thanks to the entire cyclotron staff for making these experiments possible. Most of all I would like to thank my wife Deanne for her patience and understanding during our years in graduate study, and for her careful typing of this thesis. ii II. III C IV. TABLE OF CONTENTS LIST OF TABLES O O I O O O O C O O O O O O O 0 LIST OF FIGURES . . . . . . . . . . . . . . . INTRODUCTION I O O O O O O O O O O O O O O O O NUCLMR THEORY I O O O O I O O O O I O O O O O The Distorted wave Method . . . . . . . . Non-Locality Corrections . . . . . . . . Finite—Range Corrections . . . . . . . Extraction of Spectrosc0pic Factors From Wavefunctions for Unbound States . . . . Comparison of (a,3He) and Gs,t) Reactions Comparison of (p.3He) and (p,t) Reactions THE EXPERIMENT . . . . . . . . . . . . . . . . l 2 3 4 5 a. b. C- Beam and Beam Transport . . . . . . . . . Scattering Chamber . . . . . . . . . . . Faraday Cup and Charge Collection . . . . Targets . . . . . . . . . . . . . . . . . Counter Telesc0pes and Electronics . . . Detector Telescopes . . . . . . . . . . Detectors . . . . . . . . . . . . . . . . Electronics . . . . . . . . . . . . . . . Data Acquisition . . . . . . . . . . . . Experiment Collection Efficiency for Tritons and Eelions Data Reduction . . . . . . . . . . . . . Extraction of Cross Section . . . . . . Normalization of CaFZ Foil Data . . . . . Experimental Uncertainties . . . . . . . Particle Spectra and Resolution . . . . . EXPERIMENTAL RESULTS . . . . . . . . . . . . . \OmNO‘UVJ-‘le-J Introduct on . . . . . . . . . . . . . . 16O(d,p)1 . . . . . . . . . . . . . . . 160(3H ,d)97F 150(a, He 170 . . . . . . . . . . . . . . 1506:,t)1 F . . . . . . . . . . . . . . . The Ratio (1,t)/(a,3‘fle). . . . . . . . . 19F(p,3He)170 . . . . . . . . . . . . . . 19F(p.t)171=‘ . . . . . . . . The Ratio (p,t)/(p,3He) . . . . . . . . . THEORETICMJ ANALYSIS C C C C C C C C C C C C C C C C C C C C C 54 1. Introduction . . . . . . . . . . . . . . . . . . . . . . 54 2. Bound State and Optical Model . . . . . . . . . . . . . . 56 3. 160(d, p)17o Analysis -. . . . . . . . . . . . . . . . . . 59 4. 160(h, d)17F Analysis . . . . . . . . . . . . . . . . . . 64 5. 160i: ,h)170 and 1600;, t)17F Analysis . . . . . . . . . . 69 a. Introduction . . . . . . . . . . . . . . . . . . . . 69 b. Optical Model Survey for a Induced Stripping . . . . 70 c. Analysis and Comparison for the 1d5/2 Ground States . . . 74 d. Calculations for the Remaining States . . . . . . . . . . 81 6. 19F(p, t)17F and 19F(p, h)170 Analysis . . . . . . . . . . 87 a. Introduction . . . . . . . . . . . . 87 b. Analysis for the Positive Parity 1/2+to (5/2+,1/2+) TraDSfers C C C C C C C C C C C C C C C C C C C 90 c. Analysis for the Negative Parity 1/2+ to (l/Z‘, 5/2') TranSfers C C C C' C C C C C C C C C C C C C C C C C C C C 99 SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . 102 BIBLIOGRAPHY C C C C C C C C C C C C C C C C C C C C C C C C 104 APPENDIX A. COMPILATION OF EXPERIMENTAL ANGULAR ANGULAR DISTRIBUTIONS . . . . . . . . . . . . . Al APPENDIX B. SHELL MODEL WAVEFUNCTIONS AND TWO NUCLEON TRANSFER SPECTROSCOPIC AMPLITUDES . . . . . . . Bl iv V.2. v.3. v.3. v.4. v.5. v.5. v.5. V.6. V.6. V.6. V.6. V.6. V.6. LIST OF TABLES Optical Model Parameters. . . . . . . . . . . . . Spectrosc0pic factors for the positive parity levels in 170 from the (d,p) reaction. . . . . . . . . . . . Spectrosc0pic factors for the negative parity levels in 170 from the (d,p) reaction. . . . . . . . . . . . Spectrosc0pic factors from the (h,d) reaction for the positive parity levels. . . . . . . . . . . . . . Extracted normalization N and comparison with previous results. . . . . . . . . . . . . . . . . . . Measured ratio of the yields Q:,h)/61,t). . . . . . . . . Extracted Spectrosc0pic factors in the LZR approximation for the negative parity levels. . . . . . . . . . . . . . Extracted enhancement factors E for incoherent L, S, J, T calculations . . . . . . . . . . . . . . . . . . Comparison of the extracted enhancement factors G for the 160 core (5M1) and 12C core (5M2) shell model wavefunctions . . . . . . . . . . . . . . . . . . . . Effect of the spin-orbit potential on the extracted enhancement factors 5'. . . . . . . . . . . . . . . . Effect of the sign and magnitude of the d5/20d3/2 term on the extracted enhancement factors 8.. . . . . Effect of the binding energy and order of coupling. . Extracted enhancement factors for the negative parity level-8 C C C C C C C C C C C C C C C C C C C C . 57 . 64 .100 III.l.a III.4.a III.5.a III.5.b III.lO.aI III.lO.b III.lO.c III.lO.d III.lO.c IV.1 IV.2 IV.3 IV.4 IV.5 IV.6 LIST OF FIGURES Layout of the Michigan State University Cyclotron experimental area C C C C C C C C C C C C C C C C C C Schematic diagram of the target twister used to rotate the gas cell target. . . . . . . . . . . . . . Schematic diagram for a single AE,E counter telescOpe using a summing resistor to obtain the energy signal. Schematic diagram of the time of flight setup . . . . Level structure of the mirror pair 170-17F from reference Aj 71.. . . . . . . . . . . . . . . . . . . Spectra of 170 from the (d,p) reaction and 17F from the (h ’ d) reaction C C C C C C C C C C C C C C C Spectra of 17O and 17F from the (1,h) and Q:,t) reaction C C C C C C C C C C C C C C C C C C C C C C C Spectra of 17O and 17F excited in the (p.3He) and (p ’ t) reactions C C C C C C C C C C C C C C C C C Spectra for the mirror reaction (p,3He) and (p,t) . . Simple shell model description of 16O and the low lying levels of 17o . . . . . . . . . . . . . . . . . EXperimental angular distributions obtained for the (d,p) reaCtion. o o o o o o o o o o o o o o o o o o 0 Experimental angular distributions obtained for the (3He’d) reactionC C C C C C C C C C C C C C C C C C C Experimental angular distributions obtained for the (a ,h) reaction. 0 o o o o o o o o o c o o o o o o o 0 Experimental angular distributions obtained for the (a ’ t) reactionC C C C C C C C C C C C C C C C C C C C Experimental ratios for the 01,t) and (1,33e) reactions . . . . . . . . ... . . . . . . . . . . . . vi 17 21 24 26 33 34 35 36 37 39 42 44 46 47 49 IV.7 IV.8 IV.9 V.3.l V.3.2 V.4.l V.4.2 V.5.l V.5.2 VC5C3 V.5.4 V.5.5 V.6.l V.6.2 V.6.3 V.6.4 Experimental angular distributions for the (p,3H8) reactions 0 o o o o o o o o o o o o o o o o o o o EXperimental angular distributions for the (p,t) reaction. . . . . . . . . . . . . . . . . . . . . . Experimental ratios extracted from the (p,t) and (p ,h) dataC C C C C C C C C C C C C C C C C C C C C Calculations for the ground, first excited 1/2+ and 1d3/2 single particle levels observed in the (d,p) reaction. . . . . . . . . . . . . . . . . . . . Calculations for the negative parity levels observed in the (d ’ p) reaCtion C C C C C C C C C C C C C C C C C C Calculated angular distributions for the ground and first excited state from the (h,d) reaction . . . . . . . Calculated angular distributions for the negative parity levels observed in the (h,d) reaction. . . . . . . Calculated angular distributions for the 5/2+ ground states from the (o,t) and «x,h) reactions. . . . . Unnormalized ratios calculated for the 0 induced reactions C C C C C C C C C C C C C C C C C C C C C C C C L - 0 calculations to the 1/2... first excited states forthe(a,t)and(a,h)reactions............ LZR Calculations for the negative parity levels observed in the G:,h) experiment . . . . . . . . . . . . . . . . . LZR Calculations for the negative parity levels observed in the (“,t) 138801311”! 0 o o o o o o o o o o o o o o o o 0 Calculated angular distributions for the 5/2+ ground states using the 160 core wavefunctions . . . . . . . . . Calculated angular distributions for the 1/2+ first excited states using the 160 core wavefunctions.. . . . . The (p,t) and (p,h) angular distributions to the 5/2+ ground states.. . . . . . . . . . . . . . . . . . . . . . Calculated angular distributions for the first 1/2 and 5/2 levels using the 120 core wavefunctions. . . . . vii 51 52 53 60 62 66 68 75 79 82 85 86 92 93 95 101 I. INTRODUCTION Transfer reactions are a powerful method for determining many important aspects of nuclear structure. Using the distorted wave approximation, it is now possible to analyze accurately transfer reactions involving protons, deuterons and neutrons. These reactions may be classified as "simple" reactions because the projectiles invol- ved can be considered as either elementary particles without structure, or as a simple, weakly bound combination of elementary particles. The reaction mechanism in this case is well understood and the nuclear structure information extracted from experiment is reliable. The problem with the simple one nucleon transfer reaction arises experimentally when neutrons are involved. The (n,d) reaction is almost impossible to study because neutron beams having sufficient quality to allow study of direct transfer reactions are difficult to produce. The (d,n) reaction has been studied on some nuclei, but the difficulty of detecting neutrons with sufficient efficiency and energy resolution makes this reaction unfeasible in many cases. To avoid the experi- mental difficulties associated with neutrons, one can go to complex reactions involving projectiles of mass three and four. For example, the extremely difficult (n,d) experiment can be replaced by a (d,3He) experiment and the (d,n) experiment can be replaced by a (3He,d) or a (o,t) experiment. ‘ The trouble with these complex reactions for studying nuclear structure is in the theoretical treatment of the reaction mechanism. The-complex projectiles are strongly absorbed at the nuclear surface which should give, in principle, some reduction in sensitivity to Optical model parameters (An 70). That this reduction in optical model sensitivity is not found for transfer reactions involving alphas, helions, or tritons, is attributed to the transition between a tightly bound projectile and a loosely bound, easily deformable one (Au 70). The optical model parameters are in turn less well known for the complex projectiles than for the simple ones. Second order effects, such as two step processes, may also be more important in the complex transfer reactions, since the cross sections are generally weaker for the complex projectiles. . Accurate studies of mirror nuclei by mirror pairs of reactions are greatly hindered by the neutron prdblem. In this case one is forced to use complex reactions for an accurate determination of the mirror state nuclear structure information. One can then check the reliability of the results by comparison to the simple reaction not involving the neutron problem. These considerations led to an investigation of six single and double nucleon transfer reactions, all of which populated one of two mirror final states, and an attempt to analyze these reactions in the framework of the distorted wave approximation (DNA). The mirror pair 170 and 27F were chosen for study because they are formed by adding a neutron or proton to the nominally closed 160 core. The 16O and 160- plus-nucleon systems have received a thorough theoretical treatment. The 160(d,p) reaction has been studied extensively at deuteron energies below 15 MeV, but only one study has been reported at a higher energy (Aj 71). Similarly the 16O(h,d)17F reaction has not been studied at the higher energies (Aj 71, Ec 66, Me 70). No previous studies including an analysis in the DNA framework have been reported for the 160€:,t)17P 3 3 3 16061, He)170, 19F(p,t)17F and 19F(p, He)170 reactions. The DWA analysis of these reactions is, in principle, quite straight— forward. If the reaction mechanism is adequately described, then the single nucleon stripping reactions yield spectroscopic information related to the shell model single particle wavefunctions of the target and residual nucleus. In the same simple picture, the two nucleon pick- up reactions describe a coherent two particle component of the shell model wavefunction. This analysis will attempt to investigate the adequacy of the straightforward DNA description for both the complex and simple transfer processes and the resulting extracted spectroscopic information. II. NUCLEAR THEORY II.l.a The Distorted Wave Method The Distorted Wave Method (DWM) for analysis of direct reaction processes has been extensively developed by Satchler (Sa 64a, Sa 66) and many other authors and has been reviewed by Austern (Au 70) and Freedom (Pr 71). A brief outline of the method applied to transfer reactions as presented by the above authors is given in the following sections. The abbreviations DW and DNA will be used for distorted wave and distorted wave approximation, respectively. The reaction is written as A(a,b)B, where A is the target nucleus, a is the incident particle, B is the residual nucleus, and b is the outgoing (detected) particle. For a transfer reaction a - b i x, where x is the transferred nucleon(s). The reaction is classified as direct if it proceeds in a time interval comparable to the time necessary for the incident particle to traverse the nucleus. The residual nucleus is further assumed to be similar to the target nucleus in that minimal nucleon rearrangement has occured during the formation process. The differential cross section in the DNA for an unpolarized projectile on an unpolarized target is given by (Sa 64a)‘ I2 usub kb 2 MapauhmblT 0(0)D a "' .___.____ (II.l.a) w 2 2 (Zfl‘fi ) ka (2JA+1)(283+1) , where u is a reduced mass, 1: is a relative manentum, J and S are total and spin angular momenta, and the sum on the absolute square of the transition amplitude T is over all allowed projections of the angular l. moments. The transition amplitude in the DWA.is given by 1' - J j d? fa? ')*(Ib? ) (BbIVIA a) (”(712 '1?) (11 1b) a bxb 'b 9 9 X8 8’ a g o . where J is the Jacobian of the transformation to the coordinates ?;,?5. These are the coordinates for the separation of the centers of mass of A,a and B,b. The matrix element may be expanded into terms corres- ponding to the transfer of a definite angular momentum j and isospin t to the nucleus. The transferred isospin and angular momentum are defined by + + + t-i'B-TA- ta- tb (II.l.c) and 3-33-3, gage-:1), 1.3.2:. In this expansion the matrix element is J x (2'98 anoma‘mb Ij ’MB-MA> ! -+ .+ isjm(rb’ra) (II.l.d) where m . MB - MA + mb - ma. All of the radial dependence is contained in Gisjm' Substitution of the expansion II.l.d into equation II.l.b defines the reduced transition amplitude st bm°(i£,t;) T . 9:. jar mu)" (JA,J,MA,MB-MAIJB,MB> airmafija) . (II.l.e) , . The six dimensional integral over d¥a and 4:5 is explicitly retained. The DH cross now appears in B and the isospin recoupling coefficient C T section in terms of B is p u (ZJ +1) °(9)Dw ' £1123 2 i B CTZ (anfi ) ka (NATO-DOSa +1) x 2 I X I3';"""b“'4't|2 , (II.l.f) jmmbma is , where CT2 is the isospin recoupling coefficient 2 2 2 CT - <—>Sb'“3 _ x I dire I ditb x1231; dzb’itb) stjm'ab’iz) xiii-115%.} The zero-range approximation is usually made to simplify the six dimensional integral appearing in 8:1 bm‘. The ZR approximation assumes that particle b is emitted at the point at which particle a is absorbed. Then ¥£ can be replaced by (A/B)r;, where A and B are the masses of the target and residual nucleus. This reduces the six dimensional integral to a three dimensional integral with a delta function at rb - (A/B)ra . The reduced transition amplitude for a stripping reaction is formed by assuming that the interaction causing the reaction is just the potential binding the stripped nucleon(s) to the emitted particle. Then V in equation II.l.b is interpreted as Vbx for a stripping reaction. The DU cross section for a given L,S transfer is then calculated from equation II.l.f. The cross section for a pickup reaction.is formed by evaluating the inverse stripping case, then using time reversal in- variance to obtain the pickup cross section. The DH computer code DWUCK (Ku 69) was used for all of the analysis presented in this thesis. DWUCK.was compared with the code JULIE (BA 62) for a few test cases. The agreement was very good at the forward maxima, deteriorating some- what in the vicinity of sharp minima and at back angles in some cases. The relationship between the DW cross section as calculated by DWUCK and the experimental cross section is given in section II.2.a. II.l.b Non-Locality Corrections The non-local Schrodinger equation may be written as [1:2 2 EA + a] M?) - f a! 1:5,?) ME?) . (11.2.» Optical model potentials used in the calculation are known to be non- local in character, so at least an approximation to the effect should be included in the calculation. In the local energy approximation (Pa 64, Bu 64), the result of a non-local potential is a damping term applied to the radial form factor. The damping term calculated by DWCK (Ru 69) is of the form B2m1 ]-k (II.2.b) Vi(r) . W1 (r) - C 1 - --- NL 2h2 8 where C is a normalization constant and B is the range of the non- locality. The mass and potential of the incoming, outgoing or bound state particle is given by m and Vi(r) respectively. The constant 1 C is unity for scattering in the entrance and exit channels and is determined from a normalization requirement of the wavefunction for a bound state. The values of 8 used in the calculations are those given in reference (Kn 69). II.l.c Finite-Range Corrections A zero-range approximation is normally used in the DW codes for evaluation of the reduced transition amplitude. This approximation tends to over estimate the contribution from the nuclear interior (Sa 66). In the local energy approximation (Fe 64, Bu 64) the finite- range effect is approximated by a damping term applied to the radial form factor. The DW code DWUCK (Ku 69) uses a finite range correction of this form. For a general one-nucleon stripping reaction A(a,b)B, the radial form factor appearing in the reduced transition amplitude is multiplied by a damping term 2 “b“x -1 WFR(r) :- 1 +£2- -;:— R2 (V8(r)-Vb (rA/B)-Vx(r)-Sbe) ] (II.3.a) R is the range in the LEA, V is the central part of the potential for 1 particle i and Sbe - Ea - Eb - Ex is the separation energy of particle x from particle a. The values of the finite-range parameter used in the single nucleon transfer calculations are those given in reference (x. 69). 9 Two nucleon transfer reactions have been treated in the zero- range approximation where the transfer process takes place at the c.m. of the transferred pair. This approach ignores the finite size of the two-nucleon wave function as well as the finite range of the inter- action responsible for the transfer process. Bayman and Kallio (Ba 66) have shown how to get the relative 8 state part of the wave function for two particles moving in a finite single-particle potential. Several authors (Be 66, Ch 70, Ro 71) have recently developed methods of approximating the finite-range effect for the two nucleon transfer process. The lecode DWUCK (Ku 69) was used to calculate the two-nucleon transfer cross sections. The separation energy was taken as one half the two-nucleon separation energy. A finite two—nucleon wave function (Ba 66) and the finite-range correction (Ro 71) were incorporated in DWUCK by Kunz. Parameter values for the two—nucleon transfer corrections are discussed in the experimental analysis. II.2.a Extraction of Spectroscopic Factors from Experiment The DH cross section (II.l.f) for a single nucleon transfer re- action is related to the experimental cross section by (Ku 69) '3 I2 2.8j 0(6) ___.1_23 4 ____.Dw (II.4.a) ZJAfl 1.0110 (2j+1) . 2J +1 0(e)£sj _ C 2 B In the zero-range (ZR) approximation 2 2 where Slsj is the spectroscopic factor and Do is the integral of the 10 bound particle wavefunction times the unbound potential, ¢ava for stripping. Various interactions and projectile wavefunctions have been used to evaluate |Do|2 for single-nucleon stripping (Sa 64b, Ru 69, Au 70). The values used here are those given in reference (Ku 69). The spectrosc0pic amplitude for the two-nucleon pickup reaction is not well defined (Ba 64, Cl 65, To 69). If the nucleons picked up come from different orbitals, then a coherent sum over the orbitals involved is required to calculate the DW cross sections. The ZR approximation necessary to evaluate IDOI2 for two-nucleon pickup is also somewhat questionable since a complete treatment with finite-range has not been performed (To 69, Ba 71). The single-nucleon transfer reaction spectrosc0pic factors for La‘O were obtained by matching the DW cross section to the experimental cross section at forward angles. For L - 0 the DW cross section was matched to the first observed maximum at approximately 30°. This far back in angle the reaction may not be entirely direct, thus the L - 0 amplitudes should be cautiously interpreted. II.2.b Wavefunctions for Unbound States The usual DW calculation for a stripping or pickup reaction pre- scribes that the transferred particle is bound in a Woods-Saxon well whose depth is adjusted to give the correct binding energy of the transferred particle. If a final state is slightly unbound to particle emission, in which case the usual DW prescription no longer applies, we may consider the particle to be quasi-bound by the Coulomb and centri- fugal barriers. This method was applied to the unbound states in 17F (Ex 2 0.6 Mew) and 170 (Ex 2 4.1 Mew). 11 The program EIGENFUNK (Yo 70b, Ko 71) was used to calculate the wave functions for particles unbound in a woods-Saxon well. The program varies the well depth to minimize the ratio of the exterior to interior amplitude of the wave function for a particle of J1' and binding energy -E The normalization of these unbound wave functions is discussed in B' reference (Yo 70b). II.3. Comparison of (a,3He) and (a,t) Reactions The "complex" single-nucleon stripping reactions (c.3He) and (a,t) have several interesting features (B1 64) and have recently received considerable study (Yo 70a, R0 70, He 70, Ga 69). As in all mirror reactions, these serve as a test of the charge independence of nuclear forces. In contrast to the "simple" deuteron stripping reactions to mirror nuclei, both of the outgoing particles are charged, which simplifies detection and consequently improves resolution and detection efficiency. Also, the use of a single telescope to detect both out- going particles during one bombardment eliminates some systematiczerrors which might be present in a measurement of the ratio of (d,p) to (d,n). For N a Z target nuclei these reactions populate isobaric mirror ground state nuclei and, unlike deuteron stripping, preferentially select high momentum transfers because of the large momentum mismatch in the incident and exit channels. However, the DW analysis of these complex stripping reactions is somewhat less precise than the deuteron simple stripping analysis (Yo 70a). The usual optical model description of the entrance and exit channels is somewhat questionable for low L—transfer,o-particle stripping. Elastic scattering in these channels is primarily a surface 12 phenomena and the small L transfers appear to have a large contribution from the nuclear interior (Yo 70a). The determination of a zero range normalization constant IDOI2 (equation II.4.b) is also difficult (Yo 70a, He 70). This determination requires an explicit treatment of the inter— action and relative motion between the outgoing three nucleon system and the stripped nucleon. A comparison of the (e,3He) reaction to the (a,t) reaction on 16O can serve as a test of some prOperties of the DW analysis of these complex stripping reactions. The ratio of the DW cross sections for (o,t) to (0,3He) using equation (11.4.8) is d°(a’t)lsj . kt Czt ”23:32 XIB(G ’t)| (II.5.a) do(o,33e)£sj k3H can: '32810|22|B(a,Hfle)l . where the sum 2 implies summation and averaging over all necessary variables and the momentum, isospin and spectroscopic amplitudes are explicitly retained. All of the DW approximations are included in the reduced amplitudes B. The lowest order approximation to this ratio is to consider the single particle structure of 17F and 170 identical and to assume an identical mechanism for the two reactions. The ratio (II.5.a) then reduces to (using equation II.l.g) do(o.t) k (0,;§,O,-1§|;§,-15>2 (15:15:;5!_;5l090>2 da k3 «3.0.1.1239 c.m.-4m o.o>2 k3He (II.5.b) 13 This simple approximation includes only the kinematic effect of the Coulomb force and the n-p mass difference. The effect on the reaction mechanism of the Coulomb force and the n-p mass difference may be investigated by modifying the bound state of the stripped nucleon. 11.4. Comparison of (p,3He) and (p,t) Reactions The basic theory of direct two-nucleon transfer reactions has been developed by a number of authors (G1 63, Bl 64, Ba 64, Cl 65). Towner and Hardy (To 69) have presented shell model expressions for the spectroscopic amplitudes and formulas for evaluating the two-particle coefficients of fractional parentage (cfp). Fleming, Cerny and Glendenning (Fl 68) have shown that the basic two-nucleon pickup theory does not explain the relative population of (p,t) and (p,3He) transitions to mirror nuclei. They suggest that a strong spin dependence in the nucleon-nucleon interaction or interference terms arising from either spin-orbit coupling in the optical potentials or core excitation may resolve the difference between the calculated and experimental ratios. The DW formalism of Towner and Hardy (To 69) for (p,t) and (p.3fle) with the interaction taken as a two-body potential which includes exchange of spin and isospin gives [1] [2] LST m 2 Z CSTGMSJTBMoaob (II.6.a) J ”aub kb 28b+1 0(a) . -- —— (2nh2)2 k8 28a+1 M0801) where the square bracket [1] represents the single-particle orbitals [nilijil’ The term BLJ contains the details of the reaction Monoa mechanism and may be evaluated by a DW code. The term GMLSJT contains the nuclear structure information and is defined by 14 21 22 L ‘2 . GMLSJT -,CAB([1][2],JT) 3: is s (II.6.b) .11 12 J . where 7:23 is a spectroscopic amplitude and the bracketed term is a LS-jj transformation (To 69). The term CS is defined by T CST = bST (TB’t’MTB’mtITA A) D(S,T) , (II.6.c) where the Clebsch-Gordon coefficient couples the isospin of the final state TB to the initial state TA through the isospin transfer t. The factor bST is a spectroscopic factor for the light particles. It has the values -6SOGT0 for (p,t) and - 7é-(6806T1-6816T0) for (p,3He). D(S,T) is a measure of the spin-isospin exchange in the interaction (To 69). It has a value of unity for (p,t) (S-O, T-l only) and a value less than unity for (p,3He). Experimental values for the magnitude of the spin triplet to singlet exchange defined by R - ID(1,0)/D(0,1)I2 are given in reference (Ha 67, F1 71) as R - 0.38, 0.28 respectively. The coherent sums in the cross section (equation (II.6.a)) are over the single particle configurations [nlj], and if spin-orbit coupling is included in the Optical potentials, the sums over L,S,J and T. Assuming that the optical model spin-orbit coupling can be neglected, the cross section is prOportional to the incoherent sum over (L,S,J,T) Bad I 2 0(a) .. Z Gmsn C IC Cd MLSJT (I 6 ) l lell2] The sums over the single particle configurations [nlj] appearing in GMLSJT are still coherent and can have large effects on the calculated cross sections when contributions from different orbitals are considered 15 (Cl 65). This coherence of the configuration sum gives a sensitive test of a shell-model wavefunction, since both the sign and magnitude of the configuration contribute to the result. Taking the case where no spinrorbit coupling is included, the relation between experimental and DNA cross sections as calculated by DWUCK is given by (Ku 72, Ba 72) LSJT _ 2 0(6) 0(6)exp - N E ZLSJT (23+l) CST 2J+1 . (II.6.e) In this equation, N is an overall normalization factor, Eis an en- hancement factor which will be unity if the reaction is described correctly, and 0(6) is the DWUCK cross section calculated by the prescription of equation II.6.d with an incoherent sum over the allowed values of LSJT transferred in the reaction. Using equation II.6.e, the predicted DNA cross section ratio X - 0(p,t)/0(p,3He) is given by 2 LOJl C01 0(6) X = (II.6.f) 2 LOJl 2 LlJO C01 0(0) + 3 C10 0(6) 9 where the normalization and enhancement factors are taken to be the same for the (p,t) and (p,3He) reactions and a summation over the allowed L and J values is implied. III. THE EXPERIMENT III.1. Beam and Beam Transport The proton, deuteron, helion(3He) and alpha(4He) beams used for these experiments were produced by the Michigan State University sector-focused cyclotron (Bl 66). Figure III.l.a shows a schematic diagram of the tranSport system and experimental area. The momentum analysis system includes the elements up to Box 5 (Ma67, Be 68). It is basically an object slit, two 450 dispersion magnets and momentum defining slit at Box 5. Beam energy was determined by measuring the magnetic fields of M and M with N.M.R. probes (Sn 67, Tr 70). After 3 4 analysis the beam was bent through 22.50 by M and centered on Box 10. 5 A small steering magnet placed immediately behind Box 10 was used to place the beam over the center of the scattering chamber. A remote television monitor was used to view the beam on quartz scintillators at Boxes 3 and 5 and in the scattering chamber. The quadrupoles were adjusted to give a beam spot on target approximately 0.050 inches wide by 0.075 inches high. III.2. Scattering Chamber The zero angle and beam position were determined by optically aligning Box 10, the center of rotation of the scattering chamber and a pair of current reading jaws placed near the center of the scattering chamber. The jaws were spaced approximately 0.250 inches apart, so they normally intercepted no beam. Current in the small steering magnet behind Box 10 was adjusted to intercept half of the beam on one side of the jaws in the scattering chamber then the other, and the average of these current values was used as the central position. 16‘ l7 DOOR 0 5 \\\\\\ // \\\€ NNV \\\\\\\\ ///////fl!// //i°i°“}/////LZ /////, 1 ////////// 4 (”OR W// Figure III.l.a Layout of the Michigan State University Cyclotron experimental area. 18 Alignment was further checked by viewing a small vertical wire placed over the quartz scintillator in the target holder. Angular readout of the moveable arm was done remotely by an electrical system. The calibration of this system was checked against a scribed aluminum protractor. Agreement between the electrical system and the protractor was within 0.150 over the range 00 to 160°. Two AE,E counter telescopes mounted 10o apart were used to take most of the data. The angularposition of these telescopes on the mount was determined optically by establishing the zero degree line then rotating the arm until the detector collimators were aligned with the telescOpe. On three different runs, particles were then detected at a forward angle on both sides of zero degrees to establish that the Optical zero degree line agrees with the beam axis. When the beam was carefully aligned as previously described, the beam zero degree line was within 0.30 of the Optical zero degree line. III.3. Faraday Cup and Charge Collection A long (3 to 6 foot) piece of aluminum beam pipe, electrically insulated from the scattering chamber by a three inch piece of Delrin* beam pipe, was used as a Faraday cup. A 3 kilogauss permanent magnet was attached to the Faraday cup to act as a trap for secondary electrons. For most of the runs, the Faraday cup was placed inside, and insulated from, a 50 gallon drum filled with water to reduce neutron flux at the detectors. The beam current was monitored and the charge collected with an Elcor model A310 B current integrator. The calibration Of the current *Cadillac Plastic and Chemical CO., Detroit, Michigan. l9 integrator was frequently checked against the internal calibration source. It was found to be within approximately 12 on the current ranges used (10 na - 1 pa full scale). In addition to monitoring the current in the Faraday cup at the console, the output of the current integrator was used with a voltage-to—frequency converter as a dead time monitor when this was required. III.4. Targets All of the data taken with 16O as the target used gas cells filled 3 with natural oxygen gas (99.762 abundance of 160). The 19F(p, fie) data weretakennwith foil targets (CaF evaporated on 50 ug/cm2 carbon foils), 2 then normalized to the ground states of data taken with a gas cell filled with CF4 (freon 14 obtained from Matheson Gas Products). The normalization is described in section III.8.b. The gas cells used were made of brass with 0.5 mil Kapton* windows epoxied to the metal (Pi 70). At forward angles three inch diameter cells were necessary to exclude the beam entrance and exit points from the region Of space that the detector collimator accepts. When data was taken at back angles, cells of one or two inch diameter were used to reduce energy straggling in the gas. The gas pressure was reduced to 3 - 5 inches Of mercury at forward angles to compensate for the increase in target thickness due to the longer effective target viewed by the collimator. The pressure was monitored by either a mercury manometer or a wallace and Tiernan type FA-145 pressure gauge viewed by a television monitor. The Wallace and Tiernan gauge has a guaranteed accuracy of 10.03 inches * E. I. DuPont de Nemours, Wilmington, Delaware. 20 of mercury (absolute). In the pressure range used (three to twenty inches of mercury), this gauge agreed with the mercury manometer to the accuracy with which the manometer could be read (approximately :0.1 inches of mercury). The gas in the cell was assumed to remain at room temperature (Pi 70). The Kapton cell windows deteriorated rapidly at the beam entrance and exit points when filled with oxygen gas and bombarded with either alphas or helions, both of which had a differential energy loss of approximately 140 kev cm2/mg. The cells usually began leaking after 1 to 2 hours of exposure to 75 - 100 n amps of beam. When the deuteron beam was used (dE/dx . 40 kev cm2/mg), the cells filled with oxygen gas would withstand 3 to 6 hours of bombardment at approximately the same beam current. The time of failure for the cells when bombarded with 21 New deuterons was extended when nitrogen was used as the target (Pi 70). A "target twister" (Figure III.4.a) was constructed to use with the gas cells to extend the window life by moving the beam spot over a large area. It used the existing scattering chamber target angle drive and analOg readout. The positive analog signal from the target angle readout is fed into an inverter. The output of the inverter is then added to a positive comparison signal. The amplitude of the comparison signal determines a zero angle about which the gas cell oscillates. The null signal obtained is fed into a variable sen- sitivity flip-flop which turns on a relay driver when the flip-flop is in the (+) mode. The gas cell in then rotating c.w. for a (-) mode Of the flip-flop and c.c.w. for a (+) mode. The cells were rotated at two R.P.M. through approximately $150. 21 .muwmumu Hams mom was Oumuou On some “wooden uowumu one mo smummao owumsosom c.c.HHH musmfim mmmosh an an n+n7 "V Y'VY __——-——— Hwomflh ”’ c928. hoe x On ‘J“ :0. 22 This extended the failure time of the windows to approximately one beam day with the alpha and hellon beams as compared to the 1 to 2 hour lifetime when no rotation was used. III.5. Counter Telescopes and Electronics III.5.a Detector Telescopes The reactions studied have large kinematic broadening (from 90 to 190 kev/degree at 600 lab). The angular acceptance of the detec- tor telescope was normally chosen to give a 60 kev maximum energy spread from kinematics, 0.40 to 0.80 for most of the experi- ments. To reduce the counting time, two AE-E telescopes mounted ten degrees apart were used for most of the experiments. For a fixed solid angle and a gas cell of fixed diameter, the smallest lab angle at which the detector does not see the beam entrance and exits points is determined mainly by the distance to the front collimator. Two front collimators and side shields were constructed that could be placed 0.75 inches from the center of the cell when separated by ten degrees. Modular detector mounts,which were physically small and permitted easy access to detectors, collimators and cooling connectors,were constructed for the dual telescope. These mounts included a built-in summing resistor. III.5.b Detectors All of the data for these experiments was taken with commercial surface barrier or lithium drifted silicon detectors. The detectors were cooled by pumping alcohol at dry ice temperature (-78.5°C) through the detector mount. For the AE-E particle identification telescope, a totally depleted AE detector and an E detector thick 23 enough to stop the particles of interest was used. The AE detectors were chosen thick enough to give good identification of the particle(s) of interest. The l6O(d,p)170 experiment used an E*T time of flight particle identification system. Two 2mm totally depleted silicon surface barrier detectors were stacked for an E detector with the gold surface (minimal dead layer) facing each other to reduce energy spread due to straggling. The l60(3He,d)17F experiment used two AE-E detector telescopes. The detectors in the two telescOpes were 260 u + 5 mm and 500 u + 2 mm, reapectively. The experiments for simultaneous detection of t and 3He particles required changing the AE detectors between forward and back angle runs. A AE detector that was thick enough to give good particle identification at the forward angles would not pass the lower energy 3He particles at back angles. For the 19F(p,x) experiment, two 260 u + 2 mm telescopes were used at forward angles, and at back angles a pair with 200 u + 2 mm and 160 u + 2mm. For the 160(o,x) experiment at the forward angles, a pair with 260 u +22 mm and 170 u + 2 mm were used. These were replaced at the back angles by a pair with 170 u + 2 mm and 80 u +- 2 mm. III.5.c Electronics The block diagram of the electronics used for a single AE-E tele- scope is shown in Figure III.5.a. ORTEC 109A charge sensitive preamplifiers were used to amplify pulses from the cathodes of the AE and E detectors and Z, the sum of the AE and E, taken from the anodes of the detectors across a 200 KB resistor. Pulses from the preamplifiers 24 .mamnwwm 3.500 on”. mwmuno om Housman wofinanm m mafia: meoumoamu monsoon mums 0.35m w you Emuwmap sauna—050m m.n.HHH ouowam 200m 8.3 $6 ometKow T3132. D» C D... E A :51 a «om» . NW whom was _ “2.xmw. on: E ¢|J 92 .c. w d E ‘ : .3 d J «um» o .sawa m4 «323 allllllllmxtwtm L\H - uoa 0» 4{ fl 5 J//\\fi .ea T i 9. _ _ _ r _ _ _ _ mama m _ -D ./ T _ _ _ _ _ _ _ . _ 25 were sent to the data room where they were amplified by ORTEC 440 or 451 amplifiers. The prompt bipolar output Of the AE and E signals was sent to a timing single channel analyzer (TSCA). The TSCA outputs were fed into a slow coincidence module. The coincidence signal was used to gate the delayed unipolar pulses from the AE and X amplifiers and as a routing signal for the ADC's. The summing resistor makes matching the gains of the AE and E amplifiers unnecessary. This shortens the setup time, especially when identification of particles with large differences in specific ioni- zation is desired. The resolution of the summing resistor signal was compared to summing the AE and E signals at the data room, once with particles and a pulser and once with a pulser only. No difference in resolution was found. For the l60(d,p)170 experiment, a charged particle time of flight identification system was used. The block diagram of the electronics used is shown in Figure III.5.b. Two 2 mm thick silicon surface barrier detectors were stacked to stop the protons. The signal from the detectors is sent through an ORTEC 260 inductive time pickoff (TPO) to an ORTEC 109A preamplifier. The linear signal is then amplified and sent to a linear gate (LG). A timing single channel analyzer (TSCA) was used as a noise descriminator to furnish the gate signal. The gated signal was sent through a delay, then to the ADC's. Particle identification is performed by comparing the time of arrival of a particle at the detector (T) to the next time the RF Voltage passes through zero (I). The TPO signal is sent to a thres- hold discriminator in the TPO control which is set just above background nOise. The output Of this discriminator is sent to a fast discrimi- nator in the data room which triggers the start on an ORTEC 437A time 26 $33 233 no o5”. 9: mo sauna: oeugeom QCHHH one»; use :33 .>. 004 o... A _ o < a E m h. n .P _ zoom 0 .525 5.40 .>. 84 0» amazes ezmmtaom ...omhzoo cm... W b—-—-—__- - e g .. figs? LI> ---..4 27 to pulse height converter (TAC). The TAC stop pulse is obtained by feeding an attenuated signal from the cyclotron dee into an ORTEC zero crossing (ZC) discriminator. This is sent through a nanosecond delay to the fast discriminator which feeds the TPHC stop. The charged particle time of flight identification system has the advantage of working over a large energy range for a given particle type. However it will not discriminate between tritons and helions, so it could not be used for most of these experiments. III.6. Data Acquisition Data for these experiments was collected on a X.D.S. Sigma-7 computer. A Northern Scientific quad 4096 channel ADC was used to convert the linear signal to digital form. The ADC's and routing pulses were read by the data acquisition code TOOTSIE (Ba 69, Ba 70). TOOTSIE has two modes of operation, a setup mode for particle identification and a run mode in which the particles are stored as one dimensional spectra. For these experiments the setup mode stores AE (or T—r) pulses as the y axis, energy pulses as the x axis and number of events as the z axis Of a three dimensional array. Cuts through the x-y plane are then displayed on a CRT and particle identi- fication is performed by fitting polynomials on either side of a region of interest. In the run mode, x information from the regions selected in the x-y plane are stored as one dimensional arrays. The dead time was monitored using channel zero of the ADC's. When a monitor counter was used, the single channel analyzer output was scaled and fed into channel zero of the ADC's. When a monitor counter was not used, the output of the current integrator was sent through a 28 voltage to frequency converter whose output was then scaled and fed into channel zero. The beam current and/or gas pressure was adjusted to keep the dead time less than ten percent at the forward angles. At the end Of each run the data was punched out on cards and a line printer listing was obtained. At least one data point was repeated during each experiment as a consistency check. If the collimators or detectors were changed during an experiment, a data point was repeated as a geometry and efficiency check. III.7. Collection Efficiency for Tritons and Helions Since the triton and helions were detected simultaneously in the 16 3He 0(0, t ) experiments, any systematic error in the 19F(p.3ge) and geometry or charge collection cancels out in the ratio of the cross sections. The only other uncertainties in their relative cross sections are statistical errors and detection efficiency differences for the two particles. The detection efficiency of Si detectors is essentially unity for particles that deposit more energy in the sensitive region of the detector than the inherent noise of the detection system. However, because the detectors are of finite size and the AE and E crystals are mounted separately, it is possible that some particles will be lost through scattering. To reduce this effect, the height of the detector collimator was always less than 53 mm, as compared to the diameter of the detector crystal, which was 80 mm, and the AE detector was placed with the gold coated side facing the E detector, which reduces the crystal separation from 7 mm to 4 mm. The detection loss for the AE-E system was calculated for helions and tritons assuming that particles were lost in the E detector due to 29 single Rutherford scattering in the AE detector (Ja 62). The cal- culated loss for particles incident at the tOp and center Of the collimator was less than 20 events per million for both helions and tritOns. The loss of particles due to reactions in the crystal should be approximately equal for tritons and helions and of the order of 2%. Thus the relative detection efficiency for tritons and helions is approximately 98%. 111.8. Data Reduction III.8.a Extraction of Cross Sections The one dimensional particle spectra from TOOTSIE were reduced on the Sigma-7 computer. The area, statistical error and centroid for each peak were obtained. The statistical error is calculated as [(N + B) + B)%/ N, where N is the net number of counts and B is the background. A code using card input (PEAKSTRIP written by R. A. Paddock) was used to reduce part of the data. The remaining data was reduced with MOD7 (written by D. Bayer) using a flying cross on a storage scope for input. The reduced data, the geometry Of the experiment, target charac- teristics, and the individual run data were input to a computer program to extract the lab and CM cross sections. For the data taken on Can, the program FOILTAR (Pa 69) was used. The program GASCELL (Pa 69) was used for the remaining data. These programs calculate the cross sections, the CM angle of the detected particle, the statistical and total errors per point. These errors were formed by adding in quadrature the statistical and eXperimental errors. When cross sections had been Obtained for all of the data for a given reaction, the cross sections for repeated points were added by weighting a point 30 X as (wi/Zw i )X where w is the square of the error for the point xk. 11' k III.8.b Normalization of Ca F2 Foil Data The 19F(p’3He) foil target data was normalized to data taken 1: with a gas cell. This was necessary because a reliable measure of the thickness of 19F as Can was impossible to obtain. The NaI monitor counter used did not resolve the elastic peaks of 160 and 19F and the possible presence of calcium as CaO or CaO2 made normalization to the calcium elastic scattering unreliable. Very small pieces of the Can were observed to flake off the backing, making a single normalization for all the data unreliable also. The ground states of the Can data were normalized to the CF4 data, point by point, then these normalization constants were applied to the remaining data. A polynomial least squares fitting routine was used to extrapolate over any small angular difference between the two sets of data. The statistical and total errors for the ground state CF4 data were retained for the ground state cross section errors. The normalization error was taken as the statistical errors for both sets of ground state data added in quadrature. This was then added in quadrature with the total error for each of the other states in the CaF data to get the total cross section error for the 2 remaining states. III.9. Experimental Uncertainties The beam energy was determined by measuring the magnetic fields of the analyzing magnets with NMR probes. A beam transport calibration was performed with protons between 23 and 41 Mev by the spectrograph 31 crossover technique (Tr 70). The NMR measurements agreed with the determined beam energies to less than 75 kev. No corrections were made to the beam energy as measured by the NMR probes. The total uncertainty in the lab angle measurement is estimated as $0.30 with contributions from the electrical readout and beam align- ment. No corrections to the angluar distributions were included for the angular acceptance Of the collimators (0.40 to 0.80). The geometry error, including solid angle and gas target thickness, is angular dependent. These errors were calculated by the program GASCELL (Pa 69) assuming an error in the solid angle of approximately 0.42. a gas pressure error of 0.05 inches of mercury and a temperature error of 1.50C. A 12 error was assigned to the charge integration (Pi 70). This is probably somewhat Optimistic for an absolute error, but is quite reasonable for a relative error between experiments. ' The statistical error including background subtraction is discussed in section III.8.a. Except for the ground state transitions, this is normally the dominant source of error. The compiled experimental cross sections include a measurement error, a statistical error and a total error. The measurement error is calculated in the data reduction programs (Pa 69) by adding in quadrature all of the errors except the statistical error. The total error is then obtained by adding the measurement and statistical errors in quadrature. All Of the errors are to be interpreted as one standard deviation. 32 111.10. Particle Spectra and Resolution The experimental energy resolution (Figures III.lO.b-e) varied with the incident particle, the target used and the particle detected. The electronic noise, as determined by a pulser, was typically 30 to 45 kev FWHM. The energy spread Of the beam was less than 25 kev for deuterons, 40 kev for protons and helions and 50 kev for alphas. The remaining contributions to the energy resolution are due to kinematic spread, the difference in target energy loss per unit length for the incoming and outgoing particles, and energy straggling. The energy level diagrams of 170 and 17F are shown in Figure III. 10.a. With the exception of the state in 17F at 5.215 Mev, which had not previously been observed, the energy, spin and parity assignments are taken from Ajzenberg - Selove (Aj 71). The energy assignment of 5.215:0.012 Mev for the state in 17F is a weighted average obtained from 160(3 He,d)17F(S.204iU.013 nev), 160(4ae,t)17v (5.227i0.010Mev) and 19F(p,t)l7F (5.217i0.014'Mev). The error of this weighted average is then added in quadrature with a 10 kev uncertainty due to energy extrapo- lation in all of the above determinations. Representative particle spectra are shown in Figures III.lOb—e. The experimental resolution shown is the FWHM of the ground state. Many of the states above approximately 5.5 Mev are unresolved (Aj 71). Triton and helion spectra from 19F + p are shown for both the CF4 and CaF2 targets (Figures III.lO.d and III.lO.e respectively). At approximately 40 degrees in the lab, the 13C(p,t)11C ground state would not be resolved from the state in 17F at 5.215 Mev. However, the 110 ground state was not Observed in the spectra from either target at angles where it would have been resolved. 33 20. «20. r- ra 7/2'fl (7.53 7/2: _7,.5‘48 O1 5 arms! 7.373 353°” 7335?: -—— 3’2.4+++ 7.290 > 50' 7.153 | __ < I s 970 3/2- 7.027 -————————— § 8.859 / . —— + 3/3- 8:333 I l/Z'W 8.558 I _— ' l/Z‘W 8.358 7"— ‘ .5, ——__:—_ I Hz: 5935 ”2- 6'038 45, ____ 3/2 m 5.887 3/2‘4-H-44 5.817 | ___— 7/2--———-_.___ 5.698 7/2-m 5.972 *— I 3/2' 5.521 ___— —-——— 3/2' 5.377 _ ___.._.- 7/2' ”/2" 5.217 (XX) 5.215 I ——————_"" 1 ______' 3/2' 5.083 3/2°+.++,,_ 5.103 ———--—-—— .. = —_ 4 .x =—-—__ 3’2-+f4+ 9.898 = :1 ——_ I 3/2' “.559 I ___— I: _--—— __— > __- h 4 (D ___— a: a = ti: = I ___- U'O” :— E: "o- g I 5/2' 3.891 5/2' 3-35 ___.._ a . : — __— s » _— |———— . If. ___———‘ _— ». _———— _ =_—— .. m H‘— — “-I—+-—I-—I—- -H—4—#—o— “ fl * _ 2 m 5.’ ‘5. H—H l/2° .8708 l/2' .9953 Q. ._.—_ 5/2° .0000 5/2° .0000 ___.— JO. 170 17,: 17 17 Figure III.lO.a Level structure of the mirror pair 0- F from reference Aj 71. The first 7.5 MeV of excitation is shown expanded. 34 .coauomou Ap.ev one Bonn m use coauomou Am.ov mam Scum 02 mo ouuoomm n.0H.HHH muowwm NH .z:z nmzzcxu 0mm. omow . omw q omm omau in x . .. f is 2 A . m... t. .91 .9 6 r... 3 Mw m“ aw mmmm ‘1 9.Mw.a mw MW 1 Wm a l W W i N 9 as f . I. . H“ t a.%. .6 mm _v .1 mums .nu «3 .L i w nemw Nb 9 i N C 9 m w ..IIO m9! .1“ _.l A... l. 0 v .9 .0 07v A s a .c. .38 OS; mam u o i L c. m .35 gm .3: sure a new 3.. 2 58:35... 1.: Sdzmeofi 2: 22. Nye“ Name m:m_ . Nsxm .. mam .. Nye , Nrm wrmu ... . x 8 .9 V ..l 3 .. mm m .. m m W 8 i N .. t x... is m a . u t L m 0 3 _J o m 0 w .1 _n u .._ ... . N _ 4% .O W 8 Wu H in a w. . o .r _ 8 c. . u a m :2 2. 5.3.0.0 c. r. 38 2.8: mmm - o a an: 8 a. .... 2.2.13.1 1 «a .85 .92. .3: 8.8 u an OVN. 0... NB 0... saw Oh Om; _m.o. ow. m_N 23m 35 .mmowuomou Au. .0 mam A333 0.3 Bouw .m new 0 mo mmuommm 0.0H.HHH 0.”:me .rjz dzzcxu S 2 8m 8 8m 8m 09 , . . _ ..i 1 . . . . . 0 . a . u. _ . 0 m 9 0 W e. 9% i .1. 9 MW 3 9 O W 9 m B c. c. u . H % 7v .. .9 . 8 N m u b . W 8 8 3 H y i U w . __ a 3 3 o q . M... . _ s 158 emu? mmm u a I i a. .... on. . is... .80 mm.mm .3: 9.9. u aim 1% 8» o» 05 Emma s9 9:: 23m 8: 80 com com oomo , . 1.}-.3... . . x C. m C I. , . E .96 A“ 7 n 8. so A , .o m m m “we. n o m M w. .1. .i L mm c. 9 G c. 9 . O L I. q. 8 in mm o s 2 .9 m / i u .... a m .H. u. w. . w I N J a .... O“ A m .58 same: mmm u a , ..x 2. 29550 .80 mm.mm .8: 2.9. n of e 2o 0» m 8.. on. .35... sh Exmdri s2 mmS 23m 36 .mdoauummu Au.av wan Aumm.uv onu ca vmufioxm m vcm o «0 muuoomm v.0H.HHH wuzwum NH ha .232 4mzz¢1u om. . omw we 1 .86 . 9%... I m. an n. = .I .9 19 O my 9 fiw. b I D . w .9 a . m w. m m 9 fl fi+ .2 W .J g m: .I u H 9 . 9 . x m a J.— . m m sfi m . § . I w m 9 8... o» .58 SEE oym - o . u . .owo c.mm .>w: mm.mm u .m . 8o 2. So... 8 3.8.3.3.. E 3.“: .2 mm 22. - omu 41 0mm - 0mm}- . 020 g. . A” _ _ I .c. 13% L A _ M c.% 99 ? .C. W .0 . . I .S nu 8 mw nu 9 a: w r 9 V § 03+ 0 Z . mm mm . ... T 9 0 mo ...l r W 9 S W % A J- .. u I . o. w. a .w. .m .9 m . s .58 SEE 03m . c Q 3: z 295.90 .89 c.mm .3: 3.3 - .J . 8w 0» . h. :3: is. 0.: LIT“: .3. mm 22 13NNUH3/SLN003 WBNNUHJ/SLNHOJ '37 .Au.av wan Ammm.nv maowuumou Hounds onu pom muuomnm o.oa.HHH muswwm .zDz ...wzzcxu 8mm 8;, . . I I8Imw . .88 . . .82 I . .83 . . .820 .13 4 q , mun.uL AVGnKu I v. c. t...» %W% 8 .8 W m a 9 Be. .m m n . c. 9 92 7.. . N a t 8 9 Am I... . mu? .8.” S o .9 I. K. .9 m 2 0 MW n W . mw MW 0 3.. t z Hy . C. 9 4 N m w 4 a 4 am m. f I 1 u .m .mm 1. .... u n .9 r. 0 f .m. I m. it w L . «.3 w .08 m8: .5: 8.8 n J mhn OP >3 05.213..— . “K... R.P.n: mm" 7; 23m ommfi - pwnfi . ommm . ommw --. omfim . omm . ombu J :7 4+ w .. ...m s T .9 0 M9» my a 1 0 m .7 % Sn m um M a m . x 4 a Na. ...» x h ... nammu.s~m.a mm .0 .0 c. .c. . W .... .... .... .. I a r L II 4C.— fil +d nu . u 4 :0 .6 ..Sou omu_z mZL u o g . 9 a z. zofifiaxm .35 m6: .3: mm.mm n .m men o»... s .9. co. .33.. on“ .wIm.n: mm~ .1sz IV. EXPERIMENTAL RESULTS; IV.1. Introduction The measured angular distributions and ratios of cross sections are presented in this chapter. The error bars shown on the angular distributions represent the total experimental error and indicate plus and minus one standard deviation from the measured value. The error .bars shown on the cross section ratios (a,t)/(a,3He) and (p,t)/(p,3He), represent only the relative statistical error. The relative measurement errors for tritons and helions are discussed in Sections 111.9. and 111.7., respectively. A simple shell model picture of 170 and 17F will help the inter- pretation of the experimental results. Figure IV.1. gives the shell model single particle energies (from reference Ir 70) and some of the basic shell model configurations for 170. The corresponding conr figurations for 17F are the same, with all neutrons (v) and protons (n) interchanged. If one considers 16O as a closed core, then theaddition of a single particle in the 231d shell gives only positive parity levels. This would give a 5/2+ G. 8., a 1/2+ state at approximately 0.8 Mev, a 3/2+ state at approximately 5.1 Mev and no others. These states should be strongly populated in a single particle stripping reaction. Core polarization with n particles in the 281d shells and (n91) holes in the p shells account for the negative parity states. Cone sidering only Zp-lh excitations (although higher excitations are certainly important), one can easily imagine configurations which could give all the low lying negative parity states. For example, the 1/2- State at approximately 3.1 Mev could have the configuration 38 39 NLJ (Mew 1r v I d 3/2 +5.I 2 s I/2 . +0.8 I d 5/2 ...... - ...._..~_.... 0 o I p we 0 0 0 0 -II.4 I p 3/2 00 00 OO 00 425 Isl/2 00 00-45. "o (6.8.) + 2th + 4p4h +~- o . o A. :: .29 - W __:: ‘2:.- "o (6.3.) "o (I/2’) '70 (3/2“) + 3p2h + 5p4h +--- I o o O O O O o O 2."- z»- -- a: + M...— + - 1:.- 2:.» x + x x x "o II/2'-— mm") + higher 2plh + 4p3h +--- Figure IV.l Simple shell model description of 160 and the low lying levels of 170. Core excitations are possible. 40 t T-l/2 (“IMP") 5/2 _ 1/2 . . 31 ° 12 1’2 J-l/2 The isospin coupling that would lead to the lowest l/2-state with this jl 32 configuration is not well understood (W1 71). According to the prescription of Zamick (23 65), the t -1 configuration would lie lower 1 than the tl-O. The pairing energy of the d5/2 configuration reduces the (d5/2 - p1/2) difference from 11.4 Mev to the observed 3.1 Mev. 16 The 0 core is known to be deformed by p-h excitations without the addition of the extra nucleon (Mb 56, En 65, Br 66). The addition of 3p-2h and 5p-4h excitations are necessary to account for the four extra 3/2+ states in the region of 5 to 8 Mev (Bi 68). The low lying negative parity levels in 17O and 17F are thought to have an appreciable 4P—3h component (Go 67, El 70). 1V.2. 16O(d,p)170 This reaction has been studied extensively in the energy range 0.3 to 150 Mev (Aj 71). The only previously published results above 15 Mev are for the ground and first excited states. These are at 19 Mev (Fr 53) and 26.3 Mev (Ma 62, Te 64). A spectrum for the 160(d,p)170 reaction at 20.93 Mev is shown in Figure III.lO.c. The first three strong states in the spectrum have previously been assigned as single particle states (Co 63). These are the ground state (1d5/2), 0.871 Mev (281/2) and 5.083 Mev (ld3/2). On the basis of the strength and shape of the state in the (d,p) reaction, Hosono (Ho 68) assigned the known 7/2- state at 5.696 Mev 41 as a lf7/2 single particle level. This is somewhat questionable since the ld5/2 - 1f7/2 spacing is typically 14 Mev in the heavier nuclei (Co 63). If this state were the lf7/2 single particle state, it should be strongly excited in an (6,38e) reaction (Section IV.4). Since this was not observed, it is concluded that the 5.696 (7/2-) level does not contain a large amount of lf7/2 strength. The remaining states below approximately 7 Mev are not strongly populated as expected from their np - (nrl)h interpretation. No attempt was made to extract thewweak 5.217 Mev state from the tail of the strong 95 kev wide state at 5.083 Mev. The extracted angular destributions are shown in Figure IV.2. These were compared to the results of Hosono at 14.3?Mev (Ho 68), Keller at 15. Mev (Ke 61), Freemantle et al. (Fr 53) at 19. Mev, and Mayo and Testoni (Ma 62) at 26.3 Mev. All of the results of Hosono are approximately 752 higher than the present data and the three other sets of data. For the first two negative parity levels, these data are a few per cent lower than that of Keller. The other levels of Keller are quite similar in shape and magnitude. Freemantle et al. and Mayo and Testoni only extracted cross sections for the ground and first excited states. The results of Keller and this data agree within the errors. The data of Mayo and Testoni are a few percent higher than these data at the extreme forward angles. At the other angles their data are very close to these results. 42 603.com» 3.3 och you voawmuno osofiunfiuumdo Madam—um Housmaauog «.3 95w; Aem\nEV 3U\bn ) r ( q q 4 —~qqq1_fi —qduq— q — ____—d4 q 4 —-q__¢d~— # —q—q—d+d — ———_uq4 d _ ___qfi_ ( 1 I O - . 0 0 I.“ 4 2 fl ...: .2 V .2 +2 . 5 s v 0V .0. 9 V - v o O .. «I i ‘ M. m. s ”r O m..- m .0. a 0 l 0 0 3 3 u" . I U ‘I ‘l . A lo 0 I - O o “- s s 0 9 O s . A 1 o o O 0 O o T 0 O ‘I - . O l v s O O o .9. .7 A r e s s v - O s s V V . all 0 o O 0 o n Y O . o . O 0 mm 1m # O D o 0 O I “w n v 1 I?» b b hppbph b b ).hb.b> b b bhppbp > FL) hbhb-r» b). —._—_r» p b —-bhpb - b p _hL-bpt Io . . . cl 1 w w w o .o (c.m.) 9 43 IV.3. 160811.351) 17F A spectrum for the 160(311e,d)17F reaction at E3He- 34.64 Mev is shown in Figure III.lO.c. The very broad group appearing at large excitation energy is due to deuterons which passed through the rear defining aperature. The state at 5.215 *0.012 Mev has not been reported previously (Aj 71). From the energy and angular distribution of the state, it is assigned as the analog of the 5.217 Mev (7/2 11/2)- state in 170. As in the 160(d,p)170 reaction, the strong transitions are to the single particle states. The 1d3/zstate at 5.103 Mev is 1.5 Mev wide and was not extracted from the data. The extracted angular distributions are shown in Figure IV.3. In general they are more forward peaked than the 160(d,p)170 angular dis- tributions. The second minimum in the 1/2+ distribution at approximately 300 c.m. is less pronounced than in the (d,p) reaction. The distribution to the 5.215 Mev state shows very little structure indicating a possible two step formation process. IV.4. 16O(a,3He)170 Because of the large Q values involved, reactions of the type (a,3He) and (a,t) are expected to populate states involving large angular momentum transfers (St 67). For these reactions on 16O at Ea - 46.16 Mev, the momentum matching condition IKI - KOI R.~'L suggests that states of angular momentum transfer L - 2, 3, 4 would be preferentially populated over states with L - 0, l. A spectrum for the 160(a,3He)170 reaction is shown in Figure 111. 10.b. The extracted cross sections are shown in Figure IV.4. As 'expected from the momentum matching condition, the 231/2 state at 44 .aowuommu 26.0va map you vmawmuno maowuanfiuumav umfiawam Hmunmsuumxm m.>H mun—wan [4'1 4 d. c—dq4d d d .1 —qfidd d 4 d dddd‘ ‘4d4d1 q d d —dd- d d d d 1‘ dd‘dd d 4 1‘ l I 1" .2 +2 III III *I + + . .2 8 2 2 / V v v v 7 v . i U i It U m U m m m m F a 2 fl ... n m H. .IOI' W '0' I. I‘l u IOI. v i .... - I I II I. I 1 ‘H‘ 0. IOI I... It I‘ll O . * . It it In ‘I It . It - n‘l I'll L - i O i i - , 1 i L - - * * i i l .0- . IOI ..- .IOI.I 1 LP P h h P _PPFP P P _Pbb 8 b _Ptb b P b b —bbFL-Ib .P b P )8 IF b I—bbFFP h b l? I—tbbr? 8 . . II II 0 0 0 U .0 1 x 1 l I l 100 ‘00 80 9 (c.m.) 5“ 45 0.871 Mev is weakly papulated. The 3.814 Mev 5/2- state is also weakly papulated; Thus this state is interpreted as having a (n+l)p - nh configuration that corresponds to a small component of the up - nh 160 ground state wavefunction (Br 66). From a comparison with the (o,t) reaction (Section IV.S) and from the angular distribution (Figure IV.4), the 5.1 Mev doublet is primarily the 5.217 Mev state. The angular distribution of the 5.7‘Mev doublet indicate that it is largely the 5.696 Mev 7/2- level. From the strength of the transition and the slow fall off with angle, it 1.; concluded that this state is not the lf7/2 single particle level as assigned by Hosono (Ho 68). The ground and first two excited states exhibit the characteristic (o,3He) angular distributions for reactions that are considered as direct (St 67). The large momentum mismatch results in a forward peaking for all L values, a rapid fall off and not very much struCture. This makes the complex stripping reaction a rather poor tool for spinpparity assignments. IV.5. 160(a,t)17F 16 17 A spectrum for the O(o,t) F reaction is shown in Figure III.lO.b. This spectrum was obtained at the same time as the (0,3He) spectrum shown in the same figure. The extracted angular distributions are shown in Figure IV.5. The general features of the (o,t) reaction are interpreted in the same manner as the preceding (c.3He) reaction. The previously unobserved state at 5.215 Mev is strongly populated in this reaction. 46 .oonuwmu 3.3 us... you @0533 «coausfifiumwv spa—swam Hmong—:35 «SH one—mum. b b). { 5! > I 11 q‘ddddd d. d ~4ddd4d - - . d1 Ifi ddfiddlidu d d I‘d .- fi--- 1 d —Id»» » p b g —»-.>> » p - )\/— _b-p-b - .lc— )rr - wt b h _-P.~» b DSLO ..o mu .m. . ....u , mu ...0 ‘I I] 0‘ 1 cl. 1 9 (c.m.) ’57 #830me 3.8 93 now woodman—no mfioauaflfiumav H3993 Hmunoguonxm m.>H muswfim > 444 d u —««««4: d 41 d‘d4qdd 4 J —ddqdqd d d jaduu q u 14“} 114 ddddqdd . V i ‘ l 0 n..- 0 v IOI .u n O .0: v 0 L I, 0 O . I'I - / . + o . v v a a a 7 h v v v . ‘I r ‘- 11 A a o m o * - o o A r F M u. M 5 3 7 o m 3 . 0 fit I . .o. .9. 46 fi ' \I 0 - 0 t I O. 1 l l 0 a . o o . o r l\ w .. 0 - I 0 . o o 0 1w 5 3 w ‘I .0 .0- 1 | O .0- Qw . 3 L s r a 0 O o - - 0 f. . I . - - O O . LHV v 0 - .0. O. .9 0 v. I'l It 1'. IOI ‘ r up» P r p b —>»»» b t p p bppPP » p P >

H muswfim 100 80 60 '10 80 b D ) J) ) «#44144 d —dd41+1 d — ‘dqddd d‘ d d —>>>p b hp» (a r? * bat-P » b vb b n r —»bbbh - L I- J vslirr b beh FLI“<[ L—VFPPF b b b b a Ind . c l . x 1 w w w m 9 (c.m.) do/dw '9F(p,3He )‘70 / d0/dw'9F(p,t)l7F Figure data. $0 3.0 2.0 1.0 5.0 9.0 3.0 2.0 llo 3.0 2.0 1.0 3.0 2.0 1.0 53 ...1 [S/2+l / (5/2+) J § in me - 1.6 ‘1 . ’ '3 O ... O O .. . s . . . O s O . 0 . _j .1 u/a”) / u/efl 3 . 1 HT RUE . 1.6 j r + _j L . O . * * L " i .2 O .4 ‘ '2 O .. 0 . o ' o . ‘j 5. u/a') / u/a") + UT RUE 3 1.5 i + } + o * 1 o l + 1 l §§ r (5/2'1 / ['5er 1 E m sue . 1.5 : 2. * i I J - 1 _— + i l l l -+ _. § * * L L * 0* 1* .: .- 4 Ji_1 1 l l L J L l L l 1 J 41 1 J l 1 20 '40 60 80 100 9 (c. m.) IV.9 Experimental ratios extracted from the (p,t) and (p,h) The weighted average is taken over all angles with no sin 6. V. THEORETICAL ANALYSIS v.1. Introduction The results of a DNA analysis of the six transfer reactions studied are presented in this chapter. The analysis of the 160(d,p)170 and 16O(h,d)l7F reactions consists of a more or less straightforward determ— ination of Spectroscopic information.' The 160(a,h)170 and 16O(a,t)l7F reactions are investigated as Spectroscopic tools and the DWA predictions are related to an experimental comparison of these reactions. The DWA analysis of the 19F(p,h)170 and 19F(p,t)17F reactions is based on a shell model description of the two nucleon transfer process. The first three positive parity levels in 17O and 17F may be adequately described as a single particle coupled to a correlated (np-nh where n is even) 160 core (Section IV.1.). Thus these states behave like a closed core to single nucleon stripping and the DNA should adequately describe this process. Stripping into the negative parity levels is much less clear in a DNA description. Zucker, Buck and McGrory (Zu 68, Zn 69) suggest that the first four negative parity levels in 170 (1/2, 5/2, 3/2, 7/2)- may be adequately described by five particles in the lp1/2, ld5/2 and 231/2 orbitals coupled to an inert 12C core. In this limited basis set the direct DWA only allows population of the 1/2- level. The remaining levels require lp3/2 correlated holes or 2p3/2, lf5/2 and lf7/2 particle orbitals for their description in the direct DNA. These configurations seem unlikely, if only from the usual single particle level spacings in this region (Figure IV.1.). The simple shell model basis of lpl/z, ld5/2 and 281/2 particles to describe the first four negative parity levels may be retained if two step processes are included in the description of the reaction 54 55 mechanism. The conceptually simple two step process involved in the formation of these levels requires an excitation of the correlated 160 core followed by stripping or the inverse. Penny and Satchler (Fe 64) developed the DNA formalism of this two step stripping process for the (d,p) reaction by including the generalized distorted waves for the inelastic, as well as elastic, channels in the (d,p) stripping amplitude. Unfortunately the resulting set of coupled equations are very difficult to evaluate numerically, even in the zero range approximation (deT 72, As 69). Iano and Austern (la 66) considered an approximate treatment of the method of Penny and Satchler in which inelastic channels describable by a collective rotation are present to compete with the allowed direct reaction. In their treatment of the (d,p) reaction, they find that, compared to the one step DNA, the direct plus two step cross sections are: 1) not affected seriously at forward angles, 2) smoothed and increased at back angles, and 3) for a given L-transfer, the two possible J-transfers, J - L i 1/2, may be selectively enhanced or retarded. Ascuitto and Glendenning (As 69) treat the two step transfer process in a coupled channels formalism which describes inelastic scattering. The transfer process is added as a source term in the residual system. With their treatment applied to the (p,t) reaction in which strong inelastic rotational states are present (AS 71), they find that the two step process can contribute significantly to the shape of the angular distribution at forward angles. In fact the two step process in one case is as strong as the allowed direct transfer. 56 v.2. Bound State and thiCal Model The DNA analysis of a transfer reaction is characterized by the wavefunction for the transferred particle (particles) and by the description of the incoming and outgoing elastic scattering. The wave- function of the transferred particle is obtained from a Woods-Saxon well. The elastic scattering is represented by an optical model (0M) potential. The bound state for the transferred particle is taken as a Woods- Saxon potential with the depth adjusted to give the correct separation energy (SE). The single nucleon SE for the (p,t) and (p,h) calculations is taken as one half the SE of the deuteron or di-neutron pair. Unless specified otherwise, all orbitals used were assumed to have zero binding energy relative to the SE of the d5/2 ground state, and all unbound levels were assumed to be bound by 0.1 Mev. For the stripping reactions on 160, the normal orbital for the bound state of the captured particle is given by jfl of the final state. The bound state geometry was taken as ro - r0c - 1.25f, ao - 0.65f. The nonrlocality (NL) correction suggested by Kunz (Ku 69) was applied to the bound particle as well as the scattering channels in the NL DWA calculations. The form of the optical model potential used for the analysis is UOM(r) = Vc(r) + Vof(XR) + Wof(XI) d (V.2.a) 1 d d + 4WD ——de f()&) + v30 '1: a; aisofOC ++ so) L S , 1 where f(Xi) - l/(l+exp(X1)), X - (r-r01A /3)/ai. The term Vc(r) is the 0 1 3 Coulomb potential of a uniformly charged sphere of radius rocA I . The GM potentials given in Table V.2.a., with the exception of the sets YF and Re, are taken from a literature search. The sets YF and Re 57 «ewe on .1. .1. .1. .1. an a» .1. .1. .1. .1. .33 an I. .I 11 1| me an .1. .1. .1. .1. he... em .1 ... .l I. me am ae.o eH.H ow.e o.ee as ea .1. .1. .1. .11 he em .1. .1. .1. .1. hue he Ne.o mH.H o.o~ c.me ewe ea me.o mN.H o.- o.on as we we.o mm.o o.eH ee.m on he ae.o we.o ~.eH e.aa me he Hmo.H nou.a e.- m.m~ me e> mwm.o eHH.H e.eH e~.m~ we em ome.o ONH.H c.mN «on.ea as we mma.o eeo.a ~.eu ~.ea me a» mwm.o eHH.H m.e~ e_e.om . lee lee Ame shes lease toe om. om. ewe- nee k Nmo.o mo.o mmn.o wn.o NNw.o mm.o 0H.H 0N¢.o mHo.o «n.o em.o mw.o mam.o who.o om¢.o omo.o one.o Amy Hm ncN.H moN.H oq.H mm.H woN.H Amy Hu .moooouomou wmmnu mo muse ago you voowmupo snap «a oo.~ oo.m m~.~ $26 03! QMQfi HHHH \TMQM HHHI-I NH ONMM HHI-II-l oH.H m~.H nH.H n~.H m~.H e: on moo.o mo.o Nmn.o mn.o «mm.o hm.o no.0 m~o.o mqe.o can.o omo.o nh.o oN~.o Amv mm CH.H N¢H.H ONH.H o~.# N¢H.H Amv Mu N.oaH .nwa w.co~ c.cmH .ooH H.5NH .mma .oaa c.cHH m.em mm.~n o.em wo.mm mN.~¢ c.ce nm.~¢ mm.o¢ 905 O>I He me.o u as e .cm .oe .Ne .ae .oe .om o.o~ .ou .ON .ON m.om m.cN H.- e.m~ e.wm .oe a.em A>ezv hmuoom muouoEMHmm ammo: Hwowumo 6566 u.o¢m U a U“ 3.11.: ("MM 99:90-0- 'U'U'U'U mama 0% MM son an 01¢ am e: N-em he: on «-sm m-ee MN m> um um awn uom .m.~.> wanna 58 were determined from an analysis of thecx elastic scattering data of Yavin and Farwell (YF 59) and Reed (Re 68) using the OM search code GIBELUMP. The energy listed with each set of parameters is the beam energy used to obtain that set. The incoming or outgoing energy dependence of the OM potential was approximated by the prescription VO(E) - V(EO) + 0.33 (EC-E) , where V0 is the real volume potential, E0 is the laboratory energy used to obtain that potential and E is the actual laboratory energy of the particle (Be 71, Pr 72a). In all cases the energy extrapolation necessary to match the beam energy used in these experiments was small. The CM parameters listed were selected, by visual inspection, to be the ones which give reasonable fits to the ground and first excited state of the reaction considered. Proton parameters were selected for trial if they gave satisfactory fits to elastic scattering from several light nuclei. The parameters for the other particles were selected from the limited number available on light target nuclei. Since triton parameters of the energy required were not available for light nuclei, they were normally taken to be the same as the available helion sets. The effect of the small sym- metry term difference for tritons and helions was investigated in the comparison reactions. The proton parameters of Cameron and van Oers (Ca 69) have a Gaussian shape for the surface imaginary potential instead of the derivative WOods-Saxon shape used in DWUCK. The Gaussian potentials were converted to the Woods-Saxon form by keeping the strength and WS .0'698G' Also, the spin-orbit potential in DWUCK is given in Mev-F2 width at half maximum the same (An 71) which gives W - G aWS - ’ and in terms of i-g, as opposed to JULIE, which used'MeV and Z53. For 59 spin 1/2 particles the conversion is VSO(DWUCK) - 4 * VSO(JULIE). v.3. 16O(d,p)170 Analysis The 160(d,p)170 reaction has been studied previously (Aj 71). Data to the ground and first excited states for this reaction and the (d,n) reaction has been analyzed by Davison et.al. (Da 70) at Ed - 4 to 6 MeV and by Oliver et.al. at Ed - 8 to 12 MeV (01 69, Na 68). DNA analysis of (d,p) data to some of the higher lying states has been reported by Davison et.al. (Da 70) and a PWA by Hosono (Ho 68) to negative parity levels below 7 MeV. The present DNA analysis of the 160(d,p)170 reaction at 20.93 MeV is the highest beam energy reported. The results of the DNA calculations for the first three positive parity levels are shown in Figure V.3.l. Calculations in the LZR approximation for the ground state are shown with four sets of OM para- meters from Table V.2.a. The set of parameters (Ro, Va) give the best fit to both the L - 2 and L - 0 data. In general the adiabatic deuteron parameters R0 and Mps (Jo 70) gave better fits than the standard parameters Pi-A and Pi-F. The FRNL correction slightly improves the L - 0 fit but reduces the forward angles too much for the L - 2 data. The ld3/2 calculation to the unbound state at 5.083 Mev is shown with the binding energy taken as 0.1 Mev and with an unbound wave function calculated by the method of Youngblood(YO>70b) as described in Section II.2.b. The FRNL calculation with an unbound wave function changes the shape and amplitude of the predicted cross section drastically. Even when the neutron is taken to be bound by 0.1 MeV, the effect of the FRNL correction for the d3/2 state is significant. The extracted spectroscopic factors (8) for the positive parity levels are given in Table V.3.a. S(1d5/2) and 8(231/2) are in general 60 .02 r 50111...) "b POSITIVE man 3 E 21/2+ as 1 x1— (Rows) LZR (05/2) 4 x112 —-— (sown) m . .. —— ‘ xm -H- (ups.1\/<{:>TT/i '3 r 2.3 I 1 ‘ I (Re. 80) § . x W) charge (a.I) : LL norm . 0.82 E E norm - 0.22 3 L5 )- 1: r j . l “\J///““”“ , .. ? ,3 / 4 .3 > o' . o . o ' . if t L 1 .WMe—e—w. .LWW. 2,3 . 1‘ u I- (Du.Hi) 1 ’ u 0 vque (a.I) norm - 0.79 1 "0"“ ' 2-05 emweq) ' ammo) Figure 17.5.2 Unnormalized ratios calculated for thee induced reactions. On the left are three calculations with different optical parameters. 0n the right from tap to bottom the effects of 1) the proton bound state, 2) the triton charge and 3) the triton Q-value are show. 80 to a ratio of 0.24 calculated by the above prescription. This large effect is caused by a shift in localization of the partial waves contributing to the reaction amplitude. The large Q value compared to the beam energy re- sults in a dramatic decrease in the forward angle calculated cross section as is shown in Figure V1.5.2 (labelled Q value (01 ,t)).. The effect of the Coulomb interaction in the exit channel is also large as shown in Figure V.5.2 (labelled charge (1 ,t)). For this calcu- lation the charge of the helion (+2) in the outgoing channel was changed to that of a triton (+1). The cross section was increased by a factor of 2.3 by this change. Thus the reduction of the Coulomb interaction of the triton compared to the helion has a big effect on the cross section. Table V.S.b gives the extracted experimental ratios for these data on 160 at E0 - 46 Mev and, for comparison, those of Gaillard et 81. (Ga 69) at 3‘1 - 56 Mev and Hauser et al. at E0 - 104 Mev. The ratio, (a ,h)/(x ,t), is extracted taking a weighted average of all the angles. The experimen- tal results show a simple dependence on 2 and beam energy. The ratio increases with increasing Z and decreases with increasing beam energy. Table V.5.b. Measured ratio of the yields (o,h)/(0I,t). 10B 12c 1t.N 160 328 40Ca 1.88:0.11‘) b b 1.210.1b) 1.40:0.15b) 1.50:0.15b) 1.85:0.15 ) 2.0:0.2 ) 1.23:0.15c) 1.36:0.l7c) a) This experiment, Ea - 46 Mev b) Reference (Ga 69), Ba - 56 Mev c) Reference (Ba 72), En. - 104 Mev 81 v.5.d. Calculations for the Remaining States Figure v.5.3 shows the calculated angular distributions for the two 1/2+ first excited states using the Optical potential sets (Du, HiZ) and (Re, BC-8). Agreement between the shape of the calculated and experimental angular distributions at forward angles is poor, expecially when one considers that these two parameter combinations, of the 16 possible from Table V.2.a, represent the best agreement between calculated and experimental results. The sensitivity of the L - 0 calculated angular distributions to the parameterization used to des- cribe them is most vividly illustrated by comparing the LZR and ZRNL calculations‘with the Optical parameters (Re, BC—8). Damping the interior bound state wavefunction with the EL correction hardly affects the forward angle shape of the (a,t) angular distribution, but drastically alters the (e,h) shape. 0n the other hand, the same NL correction scarcely changes the shape of the calculated angular distribution using the optical model set (Du, 312). As previously discussed, this sen- sitivity is attributed to the momemtum mismatch condition between the entrance and exit channels. Taking the extracted normalization factors for each set of optical parameters as given in Table V.5.a spectroscopic factors were extracted for both 1/2+first excited states by matching the magnitude of the calculated maximum near 400 c.m. to the experimental cross section at 400 c.m. This prescription may give unreliable results due to the vagaries in the calculations and for the reasons given in Section II.2.a, but should indicate the approximate spectroscopic strength of these levels. Using the above prescription, spectroscOpic factors for both 1/2+ states of 0.14 were extracted for the LZR and 0.17 for the ZRNL 82 E “50(0). I)'7F J= l/2 3 L_ d I. XI (Du. Hi) LZR . L. XI/2 _._ (Du. Hi) ZRNL _4 . + XI/4 —.+— (Re. 80-8) LZR \ XI/8 —+-— (Re. 80-8) LFR 10‘ - .1 10'. Q _j : I I. -J b- — ’5 $ 3 r 3) E i :1 d _ 50(a.h)'70 J-l/Z . E I b O )- XI (Du. Ii) LZR 7 +. xvz —-— (Du. H) ZRNL 19' _ xv4 4+ (Re. 80-8) 128 1 E Xl/8 —.— (Re. BC-B) ZRM. : .4 )0" __. fi \_ o \ ‘6' E.- - 1 : \ : h- . _ )— -I 10'. L 1 A l L i l l L; 1 l i 1 L l 1 4 1 1 PL; 0 20 HO 80 80 100 120 amxdeg) + . Figure 15.3 L-O calculations to the l/2 first excited states for the (x ,t) and (1 ,h) reactions. 83 calculations. This small value is quite surprising. One expects the L - 0 levels to be weakly populated in.a induced stripping reactions due to the momentum mismatch condition, but one also expects the DNA to account for the expected small strength. This is interpreted as a further indication that the DNA (L-O) a stripping reaction mechanism requires more study. Figures V.5.4 and V.5.5 show the calculated angular distribuv tions for four higher lying states pOpulated in the (O,h) and (x,t) reactions respectively. These four states are either cleanly resolved, or from their shapes and a comparison.with the angular distribution to the mirror state, represent primarily population of a single level. The bound state orbitals for the calculations shown are taken as described in Section v.2. The calculated angular distribuions are matched to the experimental data at 110 c.m. SpectroscOpic factors are then extracted using the DNA normalization of Table V.5.a. These spectroscOpic factors are given in Table V.5.c. Table V.5.c. Extracted SpectroscOpic Factors in the LZR Approximation for the Negative Parity Levels. 0M Nucleus S(1/Z-) S(5/2-) S(5.2 MeV) S(7/2-) (Du,HiZ) 17o 0.5 .01 .005 .08 (Du,HiZ) 17p 1.0 .05 .02 .1 (Re,BC-8) 17o 0.9 .007 .003 .05 (Re,BC—8) 17F 1.2 .02 .01 .05 84 As discussed in Sections v.1. and V.3., interpretation of the extracted spectroscOpic amplitudes for these negative parity levels may require the inclusion of contributions from two step processes. The puzzling thing about the amplitudes extracted from.these<1 induced stripping reactions is the very large value obtained for the 1/2- level, especially when compared to the small values found for (d,p) and (h,d) stripping in Sections v.3. and v.4. respectively. This is in complete disagreement with the usual assumptions made in the direct DNA. One is then forced to conclude that the direct reaction mechanism assumption is false. The state at 5.217 Mev in 17O has been assigned a spinrparity of (7/2 + 11/2)- (Aj 71). The calculations shown for the (:,h) reaction to this state and the mirror state in the (a,t) reaction assume the normal odd L transfer to a state of j - 11/2-. The lack of structure in the angular distributions and unreliability of the DNA calculated shapes preclude a definite spin-parity assignment for these states, but do suggest that an L - 3 (7/2-) transfer is extremely unlikely. 85 '50 (ON '70 .uooefiuooxu An.ne emu :« oo>uumno OHO>OH moaned o>aumwoo one new meowumasoamu mug mws_ouowfim —“qaq d d A. dd<<441fl d 4 11.114 4 4 —4‘14<4 4 d —<-q» . t reppbb . P'lgpps b »\ r».>bL b FZFb.» » A M» —.--.h» b b .m mu. m ..r. Mu. W. W 388328 90 80 1 so 100 120 20 acflmkjeg) 86 '60 (0.1) "F .aoflomou 3.8 web a.“ omaomno mHo>oH moaned oZfimmoa one How mcguoanoamo MNA mgr madman o _<<._.d q A d d —~<»»»» » r:_y. 0 Au W 10“ thEv dgbn 10‘ 10' 90. m. (deg) 87 ' V. 6 . 19Mpg) 17F and ' 19l.='(1'1,'1‘1)]’70 'Analy81s - V.6.a. Introduction As pointed out by Fleming, et 81. (F1 71) and Vignon, et al. (Vi 71), a simultaneous analysis of (p,t) and (p,h) reactions to mirror levels offias a stringent test of the two nucleon transfer mechanism and of the shell model description of the levels involved. No previous comparison of the (p,t) and (p,h) reactions on 19F have been reported. Cole, et 81. (Co 67, Co 68) have reported a DNA analysis of 30 MeV 19F(p,h)170 data. Using a cluster transfer DNA formalism and only considering a single LSJ transfer, they find that the DNA is sensitive to the sign of the 19F wavefunction components but relatively insensitive to the amplitudes. This micrOSCOpic analysis of the two nucleon transfer process follows the formalism of Towner and Hardy (To 69) using the DNA code DNUCK (Ku 69). For spin 1/2 particles in the incident and exit channel, the reduced matrix element BLSJM calculated by DNUCK differs from the one used by Towner and Hardy by /2§:l (Kn 72), where S is the spin transfer. Following the notation used in equation II.6.e, but in terms of the reduced matrix element BLSJM calculated by DNUCK, the DNA micrOSCOpic two nucleon cross section is prOportional to J 2 “MW .. |[1][2] /2s+1 CST 6111.331: BLSJMI ’ (“6.1) where summation is implied over the single particle configurations [l], [2] and over the allowed values of M,L,S and T. This expression as written is coherent in M, L, S and T, but incoherent in J. DNUCK evaluates the quantity 8 LSJM [1], [2] whose amplitude is V28+l CST QMLSJT' The amplitude D(S,T) for a given two particle configuration 88 appearing in the term CST’ as defined in equation II.6.c, has been measured experimentally. Experimental determinations of R 271-" ID(l,0)/D(0,l)l2 range from 0.2 to 0.4 (Ha~67, Fl 71). The remaining term in equation V.6.1, the spectrosCOpic amplitude GMLSJT, may be evaluated for a shell model wavefunction. If no spin—orbit force is included in the optical potentials, equation V.6.l may be evaluated as an incoherent sum over L, S, and T as well as J. A computer code written by Duane Larson was used to evaluate the spectrOSCOpic amplitude GMLSJT for shell model wavefunctions provided by HObson Nildenthal. Two sets of wavefunctions for 19F were used, 8M1 with three particles outside a 160 core distributed among the dS/Z, 81/2, and d3/2 orbitals and 8M2 with seven particles outside a 12C core with active d5/2, 31/2, and p1/2 orbitals. The wavefunctions used and the calculated spectroscOpic amplitudes are tabulated in Appendix A. The spectroscOpic amplitudes GMLSJTare obtained in 8 JT coupling representation for the two single particle configurations (n1,11,j1) and (n2,12,j2) (To 69). The selection rules for J are Obtained by coupling the initial and final spins 3 -‘31 - 3f, where 3 e f.+ S. The restriction on S and T is that only (S - 0, T - 1) or (S - 1, T - 0) transfers are allowed. Thus for a normal (+) parity transition, L + S + T is even and for 8 (~) parity transition L-+ S + T is odd. It should be noted that the phase convention used in Duane Larson's code for evaluating these spectrosCOpic amplitudes is different from that used in DNUCK. If a coupling is between two major quantum shells, 231/2 0 1d5/2 for example, then the sign of the spectrosCOpic amplitude obtained from the code has to be changed to agree with DNUCK. This 89 comes from the usual DNA convention that bound state orbitals approach zero from the positive side at infinity as Opposed to the shell model convention that starts the radial wavefunctions positive from the origin. Taking the case where no spin-orbit force is included, equation II.6.e relates the experimental to DNA cross sections. The normaliza- tion N appearing in this equation is evaluated up to the usual cluster transfer normalization D02 in reference Ba 72. The remaining factors in the normalization come from the Gaussian range parameter and RMS radius used to describe the triton or helion. For these calculations a range parameter of 1.6 f and a triton RMS radius of 1.7 f were used, which gives a normalization of 3.93 D02 (Ba 72). The normalization Do2 was then fixed at 56.6 to give an enhancement factor near unity for the shell model (p,t) ground state calculation. To relate the experi— mental cross section in mb/sr to the DNA cross section in f2, the normalization N appearing in equation II.6.e has the value 2220. The factor E in this equation is then a measure of the agreement between experiment and the DNA normalized to the ground state (p,t) transition, as evaluated with shell model spectroscopic amplitudes.- The Optical parameters for these calculations were taken from Table V.2.a. The proton parameters Cam and Sn were modified for (Z,A) dependence using the prescription of Becchetti and Greenlees (Be 69) + 0.4 Z/A13 + 24. (N-Z)/A and NSF(Z,A) - N given by V(Z,A) - V F + 0 S 12.0 (N—Z)/A. This prescription resulted in somewhat better agreement between calculated and experimental angular distribution shapes than was obtained for the unmodified proton parameters. The helion and triton parameters used were the set (BC-8) defined in Section v.5 90 and the set Hiz from Table V.2.a. For the calculations including a non- locality correction labelled NL, the nonelocality correction was only applied to the optical channels and not to the bound state. The finite range (FR) correction was found to significantly alter the shapes of the calculated angular distributions (Ro 71). A large improvement in agreement between experiment and calculation was found for 8 FR parameter of 0.60. The value of 0.69 suggested by Kunz (Ku 72, R0 71) resulted in a drastically worse calculated shape. The value of the two nucleon FR parameter necessary is related to the binding energy of the single particle configuration, and for these relatively weakly bound particles (W7 MeV for (p,h)), the value of 0.60 vas adequate (Ku 72). V.6.b. Analysis for the Positive Parity 1/2... to (5/2+, l/2+) Transfers The results of calculations to the 5/2+ ground state and 1/2+ first excited state are presented in this section. The normalization of the calculations is chosen such that the enhancement factor 6 is unity for the (p,t) calculation to the 5/2+ ground state using the shell model wavefunction for 160 + three particles. No other normalization is included. Thus the "relative goodness" for a set of calculations is indicated by their deviation from this normalization. In particular the (p,t) to l/2+and (p,h) to (5/2+,l/2+) calculations should give the same enhancement factor E'as the (p,t) to 5/2+ calculation since all four levels are assumed to be nearly pure single particle states with unit amplitude. Calculations for the ground state transitions are set equal to the data at 18° c. m. to extract E. For the first excited state angular distributions, E is obtained by matching the calculated maximum near 300 c. m. to the experimental maximum valuetnear-30o c. m. 91 Calculations are shown in Figures V.6.l and V.6.2 for the ground state and first excited state angular distributions, where for both, the summation over L, S, T is incoherent. These calculations were performed using the shell model wavefunction for 160 + three particles with three sets of Optical model parameters and no spin-orbit force. The calculation using parameter set (Cam, BC) is shown in the local zero range (LZR) and finite range non-local (FRNL) approximations. Agreement between calculation and experiment is considerably better for the FRNL calculation. The extracted enhancement factors Efor these calculations are given in Table V.6.a. Also shown in this table are the enhancement factors obtained for a pure (d5/2)2 configuration. Agreement is much better for the shell model wavefunction than the pure configuration calculations. The shell model calculations did not significantly improve the shape of the calculated angular distributions however. Table V.6.a. Extracted enhancement factors E for incoherent L,S,J,T calculations. O.M. — B.S. E (1d5/2) 6(231/2) t h* h* t h* h* R90.3 RPO.2 RP0.3 RPO.2 (Cam,BC)—LZR~SM1 0.88 0.76 0.94 1.96 1.30 1.37 (Cam,BC)-FRNL-SM1 1.15 0.99 1.03 1.24 0.77 0.81 (Cam,BC)-—FRNL-(d5/2)2 7.67 6.79 8.27 2.35 1.72 1.91 (Cam,HiZ)-FRNL—SM1 1.64 1.27 1.55 2.13 1.10 1.16 (Sn,BC)-FRNL-SM1 1.02 0.81 0.99 1.36 0.97. 1.03 *R.mummeDV do/dn (mb/sr) 10° 92 '9F(p.t) "’F 0.0 Mev xn—(Cam“.Bc"‘) FRNL x1/2 ---(Com",Bc") LZR . Xl/4—(Com*,HiZ) FRNL . XV8--(Sn‘,Bc*) FRNL l I AmasaLl 10°C _ t \ : \—~—— : '9F(p.h)'7o 0.0 MeV XI — (Cami, Bc") FRNL > / ..... xn/2—-— Com ,sc") LZR . , xv — Com"E Hg) FRNL m. / xu/s --- (Sn‘. é. ) FRNL m" - '63: -1 : \‘ : i \ 2 . \_/"'"" . 16‘ . 1.1 n . J_ . 144_. . . . 0 20 ‘00 80 80 100 9cm. (deg) Figure V.6.1 Calculated angular distributions for the 5/2+ ground states using the 160 core wavefunctions. Calculations are shown for three sets of 0M parameters. da/dn (mb/sr) 93 E ”no.0”? 0.495 MW 3 ' ~+ ’ 4 :\ Xl—(Com; Bc:) FRNL ‘ ’ \ xv2 --- :Hsc )LZR < w. x174 — 1"}, FRNL , xvs --- (Sn éc ) FRNL 1 E\ i b \ /\ O ‘ 16'? 1 C J / . : A. . ‘ :J'F \\\ //’ E : /'\ o : - \ / . b 4 . \ \ . /—‘ . In" ‘ F \/ / ‘: JL. ‘ 10° ‘\ 4 ; \ '9F(p.h)'70 0.87! Mev 3 FRNL 3 $55? 3§°~=53° .. 3. as. * 1" xvs ---(Sn Sn“$9 .hc‘?) FRNL -. 16‘ 1 i / ‘ I / . IJ'_ ' _ ’ /"‘.s‘ 16‘ 1 i l I Id" .11...1...1mim1...m... 0 ‘00 m 120 6c.m.(deg) 16 Figure V.6.2 Calculated angular distributions for the 1/2+ first excited states using the 0 core wavefunctions. 94 Table V.6.b compares the extracted enhancement factors E for the shell model anefunction using a 160 core (8H1) to those obtained using a 120 core (8M2). All the calculations are performed with an incoherent sum over L,S,J,T. Agreement is considerably better for the 160 core wavefunction. The calculated shapes for the 1/2+ to 1/2+ transitions are also worse for the 120 core case. Thus the ld3/2 component of the 19F wavefunction has a larger effect on the two nucleon transfer process than the 1p1/2 component as one would expect. Table V.6.b Comparison of extracted enhancement factors E for the 160 core (8M1) and 12C core (8M2) shell model wavefunctions. R!0.3 is used for all the calculations. Calculation E(5/2t) C(5/2h) €(1/2t) £(l/2h) (Sn,BC) FRNL SMl 1.02 0.80 1.36 0.88 (Sn,BC) FRNL 5M2 1.63 0.94 0.75 0.83 (Cam,BC) FRNL 8M1 1.15 0.99 1.24 0.77 (Cam,BC) FRNL 5H2 1.57 1.17 0.64 0.72 Figure V.6.3 compares the calculated (p,t) and (p,h) angular distributions and shows the three largest calculated L,S,J transfers for R - 0.3, which are summed to form the incoherent (p,h) angular distribu- tion shown. The shapes of the different calculated (p,h) L,S,J transfers are nearly identical. The usual prescription for calculating (p,h) angular distributions, which ignores the S - 1 transfer part and includes an extra factor of two in the S - 0 part, would give the wrong enhancement factor in this case, however. This may be seen from Figure V.6.3 which is drawn to scale for the different L,S,J (Pyh)'transfers. do/dw ( mb/sr) 95 t" (can . BC) FRNL sm '5 t . 1 t ---x« [P.TlL-E 1 ~ '__‘ x 1 can) (ya . 5/21 >- ,/ - ' -' \R — - — (an) braid-65"! \ (m) L-Efid-‘ISIO 10 0 I . . u I . _ .. .. [P.H] Ltazdl‘lfi'l rTrrr] l Llell I lJlJll L 1 Y VYTTI'] l AJLILI W L lO-q44L1L14_141111111111[4L1 0 20 ‘10 60 80 100 120 0c.m.(d° 0.) + Figure V.6.3 The (p,t) and (p,h) angular distributions to the 5/2 ground states. The three largest L,J transfers and their sum are shown for the (p,h) angular distribution. 96 These calculations were perfOrmed assuming that the spinrorbit (80) force in the optical potentials could be ignored, which makes the sum in Equation V.6.l incoherent. To check the validity of this assump- tion, calculations were performed incoherently and coherently,,both with and without the SO proton potential of optical potential set Sn from Table V.2.a. The extracted enhancement factors 6 for these calculations are shown in Table V.6.c. The addition of a $0 potential slightly improved the agreement for the ground state enhancement factors, but at the expense of worsening the agreement between ground and first excited state enhancement factors. The calculated shapes were not improved by the addition of a $0 potential, in fact the calculated 1/2+ (p,t) angular distribution was worse with the 80 potential than without it. For these calculations at least, it is concluded that ignoring the spine orbit potential introduces no serious error. Table V.6.c Effect of the spin-orbit potential on A value of Potential the extracted enhancement factors E. RBO.3 is used for all the calculations. sets are (Sn,BC) with the FRNL correction included. The shell model wavefunction is 8M1, the 160 core set. €(5/2) Ell/2) (p,t) without so 1.02 1.36 (p,t) with so 0.912 0.674 (P.h) Without 80 0.795 0.880 inc°h°rent (p,h) with so 0.838 0.690 (p,h) without so 0793 0.887 where“ (p,h) with so 0.806 0.690 97 It may be noted that performing the coherent L,S,T (p,h) calculation with DWUCK, while retaining the incoherence in J, is somewhat easier than the incoherent calculation. No large differences were found between the two calculations in this case, no doubt because nearly all the strength comes from two terms of the same L but different J. If two large amplitudes involving different L transfers contribute to the calculated angular distribution, difference between the coherent and incoherent calculations could be very dramatic however. In this case the spin- orbit effects may also be more pronounced. The sensitivity of the extracted enhancement factor E to the sign and magnitude of a calculated shell model spectroscopic amplitude cMLSJT was tested for the term d5/20d3/2 occuring in the spectroscopic amplitudes calculated using the shell model wavefunction 8H1. This term was chosen as a test case because it is rather small and does not contribute to all the allowed L,S,J,T transfers. Calculations were performed with both an incoherent and a coherent L,S sum with the d5/2 0 d3/2 term multiplied by either -l.0 or +0.9. The resulting extracted enhancement factors are compared to the normal calculation in Table V.6.d. It is rather puzzling that in some cases the small change in amplitude resulted in as large a change in.E'as did a sign change. One must conclude that the calculation is sensitive to both the sign and magnitude of the shell model wavefunctions. As previously discussed, the calculated shapes were rather insensitive to the shell model wavefunctions, however. Table V.6.d Effect of the sign and magnitude of the dS/20d3/2 term on the extracted enhancement factors E. This term does not contribute to the l/2+(p,t). The calculation is for (Sn,BC) FRNL 5M1. 8(5/2) 8(1/2) normal 1.02 .1.36 (p,t) -1.0*term 1.13 -- ( h) normal 0.795 0.880 inc figrent -l.0*term 1.03 1.35 ° +0.9*term 0.805 0.901 ( h) normal 0.793 0.877 cohg;ent -1.0*term 1.03 1.37 +0.9*term 0.804 0.901 The shell model spectroscopic amplitude GMLSJT for a given coupling (n1,11,jl) (n2,12,jz) is independent of both the coupling order and interchange of particles in the (p,h) case. The usual prescription (Vi 71) for the microscopic two nucleon transfer calculation takes the binding energy per nucleon as one half the two nucleon separation energy. Using this prescription in DWUCK results in a calculated angular distribution for the (p,h) case which depends on both the order of coupling and ordering of particles when two different orbitals are involved. This is caused by the Coulomb repulsion present in the bound proton wavefunction. The different binding energy of a transferred S - 1 deuteron as compared to an unbound S - 0 neutron plus proton pair also affects the calculated angular distribution. Both of these effects were calculated for the most severzcase in this analysis, that is a pure 1d5/2 , 281/2 coupling. The results are given in Tahle V.6.e. The Prescription used for the.other calculations given in this.section was 99 to couple the neutron first, to take the binding energy as given for transfer of a deuteron, and to order the shell coupling as one would expect them to occur naturally, ie. ld5/2, 281/2, ld3/2. Table V.6.e Effect of binding energy and order of coupling. The enhancement factor E‘is given for the LZR calculation (p,h), LSJ - 202. A pure 1d5/2, 281/2 configuration is assumed. binding 1d5/20 2s1/2 2s1/2o 1d5/2 per nucleon ) n, PC) ’3 K. n ) P P)” -6.9053 1.97 1.91 - 1.91 1.97 -8.020b) 2.67 2.59 2.59 2.67 a) Correct for transfer of a S - l deuteron. b) Correct for transfer of an unbound S - 0 n + p pair. c) Used for these calculations. V.6.c. Analysis for the Negative Parity 1/2+ to (1/2-,5/2-) Transfers. Figure V.6.f shows the calculated angular distributions for the 1/2’ 3.1 MeV and 5.2‘ 3.8 hev levels using the 120 core shell model wavefunction. The agreement between experiment and the shape of the calculation leaves much to be desired, especially for the (p,t) 1/2- level. The rather flat angular distribution to this level suggests that it may not be direct. No attempt was made to improve the shapes of these calculated angular distributions. Table V.6.f gives the extracted enhancement factors for these levels with the calculation fit to eXperiment as indicated in Figure V.6.4. The very large enhancement factors for the (p,t) calculations suggest a much stronger 1p1/2 100 component is necessary in the shell model wavefunction. Table V.6.f Extracted enhancement factors for the negative parity levels. A value of R-0.3 was used and the FRNL cor— rection was made. Code 8(1/2t) 8(1/2h) EKS/Zt) £(5/2h) (Sn,BC) 11.3 0.485 12.7 ‘ 2.78 (Cam,BC) 11.2 0.660 13.9 3.44 101 . 25.325016: ouoo UNH 05 means mango." ...~\n and IQ." unuwm 05 you among—«sumac Hod—mam vouoaoodwo «.05 0.5th 180 .4. .4 . a a. 2 m n m .... m 1m m NR M RF F) )C m CB em. mm . w “_ o H- o a El?» 0 I w .w 0 2 .m 53.5 e286 9c.m.(deg) IV. SUMMARY AND CONCLUSIONS In this work it has been found that reliable absolute spectro- scOpic information can not be extracted from the usual DNA analysis of67 can. .xm >mr nmm.nm "mm amu\4ranufihsv.i..dfl mZOHFDmHmHmHQ MdADUZ< Aus «Km. nxm >mr 0mm.nm «am .haaflsovv.n\fi A3 noommmsedo onomm amused :mxmom mmmfisn mmlmammsn. om+mxfi¢oH. fi00mfim50Ho OOonm mmorsa NMflmofia MhmMoOH M....anfiOOHo mswfiimomo an+mamhmH. oo.m¢ mmms.a snmo.m ommn.m Hmamsonafi. on.MsHemfi. anommammfi. no.0: mmmm.a :nhn.m momfi.m “otmmonmfi. nw+mcswma. anowKnmflm. oo.mm cmwm.a msefl.n numm.n «nummmnma. oa+momsxfi. dn+momnmmo ooomm mmmmoa mamaom Hammon lemaaama. 0o+mwunmfi. no.mosssm. no.nm thos.fi Koms.m nome.m Ho-mmema. oe.naoaKm. 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