.. .4” . ‘~--.-q—~—..——m 14W511”)ATI:.‘9.8,3&GLAND 40.0 Mal? my THE STRENGTH or THE nausea FORCE g , m NUCLEAR mamas mesis for the Degree of .Ph. D. MICHIGAN STATE ‘UNWERSETY STANLEY HAIM FOX 1972 LIBRARY Micinv in State University This is to certify that the thesis entitled 1“N(p,p') AT 29.8. 36.6 AND no.0 rm AND THE STRENGTH OF THE TENSOR FORCE IN NUCLEAR REACTIONS presented by Stanley Haim Fox has been accepted towards fulfillment of the requirements for __Eh...D.._degree in M ””173? 4‘4} Date W 2 0-7639 ABSTRACT 1L‘N(P,P') AT 29.8, 36.6, AND “0.0 MEV AND THE STRENGTH OF THE TENSOR FORCE IN NUCLEAR REACTIONS By Stanley Haim Fox Measurements of the angular distribution of the 1L‘N(p,p°)1“1~1” (2.31 Mev), (1‘30) -- (0";1). reaction ‘were made at higher energies (29.8. 36.6, and no.0 MeV) and with better precision than before and information about the strength of the tensor force in nuclear reactions was extracted. Protons from the MSU Sector-Focused Cyclotron were scattered from gas and evaporated melamine th targets and detected either with lithium drifted silicon detectors in.a hO' scattering chamber or with position sensitive detectors in an Enge split-pole spectrograph. Angular «iistributions for elastic scattering and the excitation of Stanley H. Fox the 2.31 (0+31) and 3.94 (1+:0) MeV states were obtained at- all the energies. In addition, the angular distributions luN between for the excitation of the ten known states in 4.91 and 8.49 MeV were obtained for 29.8 MeV incident protons. ' Optical model fits to elastic data between 24.8 and 40.0 MeV were obtained using an average set of Optical model geometry parameters. Microsc0pic model DWBA calculations with exchange were made for the 2.31 MeV reaction including central, L-S, and (most importantly) tensor forces in the two body interaction. The interaction that best fit the shape of the inelastic scattering to the 2.31 MeV state at 24.8, 29.8, 36.6, and 40.0 MeV was a Serber central force plus the Hamada-Johnston spin-orbit potential and OPEP with a 25% increase in strength. Results for microscOpic model DWBA calculations with exchange are also reported for the reactions to the 3.94 (1*30) and 7.03 (2+;0) Mev states. 1“N(p,Pv> AT 29.8, 36.6, AND no.0 mav AND.THE STRENGTH OF THE TENSOR FORCE IN NUCLEAR REACTIONS By Stanley Haim Fox A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1972 Urlicht ,. 4/ a?” (Primal Light) from Das Knaben Wunderhorn as quoted by Gustav Mahler in Symphony #2 “Ressurrection' O Roachen roth " Der Mensch liegt in grosster Nothl Der Mensch liegt in grosster Peinl Lieger mocht' ich Himmel sein. Da kam ich auf einem breiten Wegs Da kam ein Engelein und wollt' mich abweisena Ach neinl Ich liess mich nicht abweisen. Ich bin von Gott und will wieder zu Gottl Der liebe Gott wird mir ein Lichtchen geben. Wird leuchten mir bis in das ewig selig Lebenl O Rosebud red Here man lies in greatest need! Here man lies in greatest woe! If only I could to heaven go. Then came I upon a broad fair way; There came an angel and he would reject me; Ah no, I would not be rejected. I am of God and will home, back to Godl Beloved God a candle light will lend me. And onward to eternal blissful life will send me! ii ACKNOWLEDGMENTS There are a number of peeple without whose help this work would never have been completed. First of all there is Dr. Sam M. Austin who formulated the problem and who always seemed to have useful suggestions. I would like to thank Dr. Duane Larson who helped me take the data and whose understanding of proton inelastic scattering was crucial. I am greatly in debt to all the staff members of the Cyclotron Laboratory. but especially to Norvel Mercer and his shOp staff and to Richard Au and the keepers of the 1E-7. Bob Matson was very helpful in preparing the many graphs in this work. I am also thankful for the good humor of my other friends in room 161, Dr. Lolo M. Panggabean and Dr. Helmut Laumer. The one to whom I am most indebted is my wife. Janet. LIST OF TABLES LIST OF FIGURES INTRODUCTION 1. 2. TABLE OF CONTENTS EXPERIMENTAL 2.1 General Discussion 2.1.1 2.1.2 2.1.3 2.1.h Experimental Layout Proton Beam Energy Beam Alignment Beam Current 2.2 Measurements Made with Gas Targets 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.2.8 2.2.9 2.2.10 2.2.11 Gas Target Construction Gas Cell Diameter and Scattering Angle Range Effective Target Thickness Gas Pressure Measurements Gas Temperature Measurements Scattered Particle Collimation Units Angular Measurements Beam Current Measurements EAAE Detector Telesc0pe BABE Signal Processing Monitor Detector iv viii xi ODGDNNNNH 10 10 10 13 1h 14 15 19 19 20 22 22 3. 2.3 DATA 3.1 3.2 v 2.2.12 Degrader-Detector Combination for 36.6 and 40.0 Absolute Normalization Measurements' Measurements Made with the Enge Split- Pole Spectrograph 2.3.1 The Spectrograph vs. the Scattering Chamber 2.3.2 Melamine Targets 2.3.3 Target spinner 2.3.4 Silicon. Surface Barrier. Position Sensitive Detector 2.3.5 Particle Identification 2.3.6 Signal Processing Electronics 2.3.? Computer Data Handling 2.3.8 Monitor Detector General Description of the Data Reduction of the Gas Target Data 3.2.1 2.31 MeV State Data; Gas Target Data 3.2.2 Inelastic Gas Target Data Other than the 2.31 MeV State Data 3.2.3 A Test of SAMPO 3.2.4 Reactions in the Detector and the 6.44 MeV State Angular Distribution 3.2.5 Normalization of the Gas Target Data 26 27 27 3O 32 3a 3a 35 35 36 no no 1+2 42 43 45 47 48 5. vi 3.3 Reduction of the Position-Sensitive Detector Data 3.3.1 Description of Difficulties 3.3.2 Background Subtraction 3.3.3 Point to Point Normalization 3.3.4 Absolute Normalization 3.4 Summary of Error Determination 3.4.1 29.8 MeV Gas Cell Data 3.4.2 Position-Sensitive Detector Data 3.5 Plots and Tables of the Angular Distributions OPTICAL MODEL ANALYSIS 4.1 Purpose 4.2 Elastic Scattering Data 4.3 Optical Model Searches 4.4 Spin-Orbit Form Factor 4.5 Variation of Well Strengths with Energy MICROSCOPIC MODEL CALCULATIONS 5.1 D.W.B.A 70A 5.2 Wave Functions 5.2.1 1? Shell Wave Functions 5.2.2 12C Core Plus sd Shell Wave Functions 5.3 Coupled Channels Calculations 5.4 Two-Step Processes 5.5 Nuclear Forces 5.5.1 Fitting Central Interactions to the 49 49 50 51 51 52 52 53 53 96 96 97 98 102 114 117 117 118 119 122 123 124 125 5.502 5-5-3 5050“ 5-5-5 5.5.6 5.5.8 5-5-9 5.5.10 RESULTS vii Yukawa Radial Form Serber Central Potential (S) Even State Ramada-Johnston Central Potential (HJ) Even State Ramada-Johnston Central Potential Plus 1P State Gaussian Potential (HJ-G) Blatt-Jackson Central Potential (BJ) Average Effective Central Potential (SMA) Spin-Orbit Potential “Complete” Ramada-Johnston Force Central Potential for Inelastic Scattering to States Other than the 2.31 MeV State 6.1 Results For Calculations of Inelastic Scattering to the 2.31 MeV State 6.2 Results for Calculations of Inelastic Scattering to States Other than the 2.31 MeV State CONCLUSION SUMMARY LIST OF’REFERENCES APPENDIX 1 APPENDIX 2 125 126 126 126 128 128 130 131 133 13a 1311 153 158 162 163 167 170 Table 9. 10. 11. 12. 13. LIST OF TABLES Collimation units' dimensions. forward angle limits. and G-factors. Dimensions of spectrograph apertures. 11"I\:(p,p)1b’l\’ elastic scattering. Ep 29.8 MeV. 1“Mp-13') 1“Mp-IV) 1”minim 1“N). E (“0910(0-80))9 E (5.11.(2'30)). E (5.69.(1'70)>. E (5-83.(3-:0)). E (6.2o.(1*;o)). E (6.uu.(3*;o)>. E (7.03.(2*:o)). E (7.970(2-30))0 E viii 29.8 29.8 29.8 29.8 29.8 29.8 29.8 29.8 29.8 29.8 MeV. Nev. MeV. QGVO MeV. MGV. MeV. MGVO MGVO MeV. Page 11 29 73 74 75 76 77 78 79 80 81 82 83 Table 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. ix 29. 8 MGVO 1“N(p.p'>1“n*<8.os.(1'.1>>. 8p II J luN(p.p')1uN*(8.49,(4-30)). E 29.8 MeV. P 1I‘iN(p.p)1L‘N elastic scattering for Ep = 3606 MBV 1"Ruhr)“‘N”(2.31.(0”;1». E 36.6 Mev. P 1“N(p.p'>1“N*(3.9u.<1*:0)). E 36.6 Mev. P 1LiN(p,p)1’+N elastic scattering for E 3 “0.0 MQVO p 1hN(p,p')1uN*(2.31,(0+;1)). E no.0 MeV. P LAO o O MBV. 1“N(p.p'>1“N*(3.9u.<1’.o>>. 8p 11+N(p.p')wN*(2.31 Nev) plotted against momentum transfer for EP = 24.8 MeV (Cr 70). 1I"N(p.p')1uN*(2.31 MeV) plotted against momentum transfer for Ep = 29.8 MeV. 1['"N(p.p')11+N* (2.31 MeV) plotted against momentum transfer for ED = 36.6 MeV. 1[‘N(p.p')1uN*(2.31 MeV) plotted against momentum transfer for Ep = 40.0 MeV. 1I“N(p.p)1LiN elastic scattering for Ep = 24.8 and 29.8 MeV with the errors used Page 84 85 86 87 88 89 9O 91 92 93 94 95 Table 27. 28. 29. 30- 31- 32. 33- 34- 35- 36- during Optical model searches. luN(p.p)1uN elastic scattering for Ep = 36.6 and 40.0 MeV with the errors used during optical model searches. th Optical model parameters found in this work 14 N Optical model parameters from Watson g1,a1. (Wa 69) 1MN Optical model results for free spin-orbit geometry parameters. 1“N wave functions. Central and tensor forces. Values of the spin-orbit force. Comparison of central forces. Calculation normalization factors Values of the tensor force. Page 99 100 103 109 112 120 127 132 138 152 159 Figure 2. 3. 9. 10. LIST OF FIGURES Layout of the cyclotron experimental area as of August. 1972 14 Energy levels of N up to 8.62 MeV. Definition of the line source target in a gas cell by the collimator's slits. A schematic drawing of one of the collimat- ing units. Two detector telescope summing circuit. Signal processing electronics. Two dimensional TOOTSIE display. A proton spectrum taken with the EAOE detector package and gas target. Kinematic compensation in the split- pole spectrograph. A schematic drawing of the target spinner. xi Page 12 17 21 23 24 25 31 33 Figure 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. xii Spectrum taken in the spectrograph. 40.0 MeV monitor spectrum from an evaporated melamine target. The detector angle is 150°. Pseudo spectra of the type used to test SAMPO. Arrows indicate centroids as assigned by SAMPO. 14N(p.p)1uN angular Ep 3 29.8 MBVO 1“N(p.p'>1“N* (2.31 distribution for Ep 1aN(P-P')1hN* (3-9” distribution for ED 1iL'I*I(p.1>')mN* (4.91 .distribution for Ep 11‘1“(1>-13')1“N* (5-11 distribution for Ep it 14N1“N (5.69 distribution for Ep 1L‘N(p.p')1“N* (5.83 distribution for Ep distribution for + MeV.(O 31)) angular = 29.8 MeV. nev,(i*.o)) angular = 29.8 MeV.‘ nev,(o'.o)) angular = 29.8 MeV. MeV. (2"; 0)) angular '= 29.8 MeV- MeV. (1-: 0)) angular = 2908 MeV. Nev-(3-10)) angular = 29.8 MeV. Page 37 38 54 55 56 5? 58 59 60 Figure 21 22. 23. 24. 25. 26. 27. 28. 29. 30- 31- xiii 1"N(p.p')“‘1\1” (6.20 distribution for Ep 1nN(P-P')1uN* (6.44 distribution for Ep ' It 1L‘I‘I(13-r>')1L‘N (7.02 distribution for E P l- 1“N(p.p')mN (7.97 distribution for Ep 1“r¢(;>.p')“”1~z* (8.06 distribution for Ep 1“N(p.p')1“N* (8.49 distribution for Ep 1"Mp-101411 angular Ep 8 36.6 MeV. 1“N(p.p->1“N* (2.31 distribution for Ep 1“N(13.1>')MI~I" (3.9u distribution for Ep MeV. (1*;0)) = 29.8 MeV. MeV. (3*:o)) = 2908 NieVo Mev. (2*.o>) = 29.8 MGVO MeV. (2';0)) = 29.8 MBVO MeV. (1':1)) = 29.8 MeV MeV. (4':O)) = 29.8 MeV. distribution MeV. (0+31)) = 36.6 MeV. Mev. <1*-o>> = 36.6 MeV. angular angular angular angular angular angular for angular angular 1l‘N(p.p')1u’N angular distribution for E 8 40.0 Nev. p 1 14N(p'p,)14N* distribution for Ep = 40.0 MeV. (2.31 MeV. (051)) angular Page 61 62 63 64 65 66 67 68 69 7O 71 Figure 32- 34- 35- 36- 37. 38- xiv Page 1! “MM-)1“). (3.91 Mev. (1".o)) angular distribution for Ep = 40.0 MeV. 72 The differential cross sections for the 14N(p.p')1uN* (2.31 MeV) reaction analyzed in this work plotted against momentum transfer. 72a Optical model fits to the 24.8 MeV and 29.8 MeV 1“N elastic scattering for the Optical model potential determined by this work with rSO = rR and aso = aR. 104 Optical model fits to the 36.6 and 40.0 MeV 1“N elastic scattering for the optical model of this work with rSO = rR Radial dependence of the Thomas form of the spin-orbit potential and of the Thomas form as modified by Watson gt‘gl. (Wa 69) for A = 14. 107 Optical model fits to the 24.8 and 29.8 MeV iuN elastic Scattering for the geometry and parameters from the work of Watson g3,al. (Wa 69). 110 Optical model fits to the 36.6 and 40.0 MeV 1“N elastic scattering for the geometry and parameters from the work of Watson £3,31. (Wa 69). 111 Figure 39- 40. 41. 42. “'3. an. 45. 46. Optical model fits to the 24.8 and 29.8 1eV th elastic scattering. The spin- orbit potential has the Thomas form with parameters varied to best fit the data. Variation of the strengths of the Optical model potential found in this work as a function of energy. 1L‘N(p.p')1uNfl (2.31 MeV) calculations with OPEP alone. 1"iN(p.p')11‘iN« (2.31 MeV) calculations with: OPEP and HJ-T alone at 40.0 MeV (A); V-F and C-K wave functions with S 9 OPEP at 29.8 MeV (B); and optical model parameters of Cr 70 and this work with S 9 OPEP at 29.8 MeV (C) and 40.0 MeV (D). 1I“N(p.p')wN* (2.31 MeV) calculations for HJ central plus HJ-T. 1L‘N(p.p')1“N* (2.31 MeV) calculations for HJ-G central plus HJ-T. 1I"N(p.p')1"‘N* (2.31 MeV) calculations for BJ central plus OPEP. 1uN(p.p')mN* (2.31 MeV) calculations for SMA central plus OPEP. ' Page 113 115 135 137 140 141 142 144 Figure 47. 48. 49. 50. 51- 52. 53. xvi * 1“N(p,p')1“N (2.31 MeV) calculations for S central plus OPEP and S central alone. 1! 1I"N(p.p')wN (2.31 MeV) calculations for S central plus HJ-LS and OPEP. 11‘N(p,p')wN* (2.31 MeV) calculations for the complete Ramada-Johnston potential as put into Yukawa from by Escudie £1.31. (Es 72). 1I"N(p.p')mN* (2.31 MeV) calculations for S central plus HJ-LS plus OPEP. Calculations are normalized to best fit the data at forward angles. 1“N(p,p')1uN% (2.31 MeV) calculations for S central plus HJ-LS and 1.25 X OPEP. Calculations are normalized to best fit the data at forward angles. 1hN(p.p')1uN* (2.31 MeV) calculations for S central plus HJ-LS and 1.4 X OPEP. Calculations are normalized to best fit the data at forward angles. 1l'iN(p.p')1uN* (2.31 MeV) calculations for S central plus HJ-LS and OPEP plotted as a function of momentum transfer. The symbols are for identification only. Page 105 146 148 149 150 151 154 Figure 54- A1. xvii 1l'iN(p.p')1L‘N* (3.94 MeV) calculations for S central and C-K wave functions normalized by the experimental to calculated E2 transition ratio. 1nN(p.p')1uN* (7.03 MeV) calculation for S central and C-K wave functions normalized by the experimental to calculated E2 transition ratio. Collimation slits defining the line source at 900 in the Lab. Page 156 157 169 1 . INTRODUCTION The inelastic scattering of protons from the 2.31 MeV first excited state in 1[‘N is germane to the study of the nucleonpnucleon interaction in inelastic scattering as well as to aspects of the reaction mechanism itself. Earlier studies of inelastic scattering at 24.9 MeV by Crawley 9;: 5;. (Cr 70) and at 17 Hall by Rogers (Re 71) and of the analogous reaction 14C (p.n) 14N (We 67, we 71) at proton energies between 6 and 14 MeV show that for microscopic model analysis, not including the knockout exchange amplitudes. a central interaction alone is not sufficient to explain the experimental data and that including a tensor component in the nuclear force results in greatly improved agreement. This outcome was not unexpected. In the distorted wave Born approximation (DWBA), neglecting exchange, the cross section for a reaction A (a, b) B is proportional to the square of the transition amplitude. Tba..fxb(-) < ‘1'; | veffl 57; > X8“) or, where )[a(+) and X:b(-) are the incoming and outgoing distorted waves and ‘1’,- and ‘t’; are the initial and final projectile- target states. In the microscopic approach to proton in- elastic scattering it is assumed thatV’eff can be written as the sum of the two-body interactions between the projectile 1 ”p" and the target nucleons "i '. Thus: veff " z"11> the sum being over the valence target nucleons. If only the central part of the nucleon-nucleon force is usedv1p can be expressed as: T1 'Tp ‘1’ v11(1.)(‘}i 05p) (‘?1 .713) where the subscripts on the VST are the spin and isospin transferred in the reaction. The selection rules for the direct (non-exchange) process are (Sa 66): 333; -:I[ Til-T; -T1 -r -7 —-r L s..s1 --.sr 11., 7r; .(-1) 1.3 -5 :where 3;‘§, ande are the total angular momentum, spin, and orbital angular momentum transferred in the reaction and T is the transferred isospin. For 1“N (p.p') * (2.31 aw) (Jinn- . Ti) are (l, +, 0) and (J; , ’rr¥ . T1!) are (0, +, 1) and for 1“c (p.n) th we have) (0, +. 1)'---% (l, +, 0). Both of these interactions select out the V11 part Of the central force and for both. only L = 9 and L a 2 are allowed in the direct process. For L a 0 and V - V11 (3 1 . 3p) ( :6.- .%p) the inelastic scattering matrix element has been shown (We 67) to be nearly proportional to that for the Gamowaell r beta decay of la . This decay is found to be strongly inhibited (Ba 66), and so the normally dominant L s 0 contribution to the cross sections for the inelastic scattering and charge exchange interactions are also supressed. The orbital angular momentum selection rules that apply when a tensor term. which is always an S - 1 term. is added to the central force in a direct calculation are: L :- 7\ or L . 7K 2. 2 where 1' is the orbital angular momentum transferred to the projectile and X the orbital angular momentum transferred to the target nucleon. Fbr central forces 7s:- L. The 7K - O and L . 0 amplitude for a tensor force is suppressed just as is the L :- 0 amplitude for a central force. but the 7K- - 2 amplitudes (L - 0 and L - 2) are not (We 71). Inclusion of a tensor force thus allows an L . 0 amplitude which turns out to dominate the L . 2 amplitude of the central force. When the microscopic DWBA formalism is modified to include the effect of exchange the selection rules change somewhatwiththeresultthattheunnaturalparityL-l transition is allowed for both a central or a central plus tensor effective interaction. For central forces the selection rules are the same as for the direct amplitudes with the exception that the angular momenta transferred need not satisfy the IT; “IT; . («1)L condition (LO 70). In all cases studied to date the amplitudes for these so-called unnatural parity L trans- fers are small (At 70) for small L transfers. For central forces that act only in even (Serber forces for example) or odd relative orbital angular'mementum states, the same com- ponents of the force contribute to the direct and exchange amplitudes. In the limit of zero range even state forces there is constructive interference between the direct and exchange terms. The selection rules that govern the tensor exchange amplitudes are found in reference 48. Here A TV need be neither {-1)L or (-l)} . and unnatural L transfers are also allowed. Calculations by Love ggflgl. (Lo 70a) (1hN(p.n)1u0.(gs) the analogue of 1l'iN(p.p')1LiN*-(2.31 MeV)), and Satchler (Lo 70b) (data of Crawley 33 2;.) and Escudie 232 2;. (Es 70) (MN [pqp'] MN" [2.31 MeV] at 2(- HeV) show that inclusion of exchange does not eliminate the need for inclusion of the tensor force. In summary, all calculations for the inelastic scattering to the 2.31 MeV state in MN with central forces produce an L - 2 shape. a rather‘broad shape, while the observed angular distributions are forward peaked. Direct calculations of or (0) at 24.9 MeV which include the tensor force, reproduce this forward peaking see (see Figure (47)). The major purpose of this project was to measure cross sectionsfor the 1[“N (p, p") 1411* (Ex - 2.31 MeV, 0 +, l) reaction.at higher energies (29.8, 36.6, and 40.0 HeV) and with better precision than before, and so to extract information about the tensor force in nuclear.reactions. The reason for going to higher energies is to avoid compound nuclear effects. Even at 24.9 MeV, there is evidence of compound nuclear effects. Extending the energy range at which this inelastic scattering has been measured also allows one to look for energy dependencies in the effective interaction. There are very few angular distributions available for MN inelastic scattering to the states above the 3.94 MeV state for proton energies above 15 MeV. For this reason, angular distributions to the first 12 excited states of MN were measured at 29.8 MeV, A1; 36.6 MeV and 40.0 MeV the 3.94 MeV angular distribution was measured. These angular distributions were compared with calculations using the microscopic NBA formalism and available wave functions. 2. ENERIMENTAL 2.1 General Discussion 2.1.1 Egerimental Layout Figure (1) is a schematic of the beam handling and analyzing system at the 14.8.0. Cyclotron Laboratroy where all of the experimental work for this thesis was done. Measure- ments with bombarding protons of 29.8, 36.6, and 40.0 MeV on melamine targets were made with the Enge split-pole spectrograph while the 29.8 MeV gas target date was taken in a 35 in. diameter scattering chamber located about where the 40 in. scattering chamber is now placed. Normalization measurements for the 36.6 and 40.0 MeV elastic cross sections were made with a gas target in the 40 in. diameter scattering chamber. 2.1.2 Proton Beam Energy The 11.8.0. beam handling and analyzing system has been described by G. H. McKenzie gt 9;. (Ma 67). In this experiment, the slits at boxes 3 and 5 were 0.10" wide. Thus the energy resolution of the beam was about 1 part in 6 .29 .an :93 .8 as a one acres 5583 coupon. use an» do 25 >3 4 measure 13 $1? \:\\\\\\\\fir\\\a 8 1500. The fields in the two 45° bending magnets. M3 and M4, were set using nuclear magnetic resonance probes. The beam energy calibration is accurate to 1 part in 103. In practice the bombarding energy was measured and when necessary reproduced to the nearest 0.1 MeV. 2.1.3 Beam Alignment The beam was centered on the target either visually, using a wire target on a quartz scintillator and remote T.V. monitor or by balancing the beam on pairs of vertical and horizontal slits placed Just before the spectrograph scattering chamber and just after the 40” scattering chamber. These slits were withdrawn after the beam was aligned. The beam spot was about 0.05" to 0.10" wide and about 0.1” high on gas targets and about 0.07" high on the solid melamine targets. 2.1.4 Beam Current The beam on the melamine target was kept below 300 nanoamps and on the gas targets. below 800 nanoamps to avoid target or gas cell window deterioration. FIGURE 2. . +s # .. -. LL 8.H9 8.63 "' " L11 737 8.06 .21LL 7.03 :33 “ 63" _. 6.20 -' "' 5.69 5.83 .. .BLLQ D... D . ”.91 5.11 Ail-9 3.94 _Q:.*.LL 2.31 ._Jk:i_jl__ 1J30 IHN 14 Energy levels of N up to 8.62 MeV. 10 2.2 Measurements Made with Gas Targets 2.2.1 Gas Target Construction At 29.8 MeV bombarding energy, the angular distri- butions for elastic scattering and for inelastic scattering leading to the first twelve excited states of “N were obtained with gas targets in the 35" and later 40" scattering Chubers. The gas targets used were machined of brass and the 0.5 mil. kapton windows were epoxied onto the sanded clean brass with a ten to one mixture by weight of Ciba Application of solvents to The gas Maldite 502 and 951 hardner. the brass after sanding seemed to weaken the bond. ”98811” was about 50 cm of Hg for the 1" cells and 30 cm of H3 for the 2" cells. These pressures represent a compromise betWeen the desire for higher count rates and sufficient ”11 lifetimes in the beam. At higher pressures, the cells tom1“! to develop slow leaks after on hour or so in the beam. 2.2.2 Gas Cell Diameter and Scatterigg Angle Rage Figure (3) shows how the front and back slits of the °°111mating system define the line source of scattered I I ticles observed by the detector at any given scattering ”181° 9. If G is smaller than some angle, 9min! or greater 1 some angle, am, the area of the Kapton window through 11 .mpnmaos wean swasmsmvoou pmcfiw>«:do on stomach mummaon “Ham msoapoe H00.qu 80.0.H no.0“ no.0 n-0a x mm.a no.0 ~.HH m.a~ 00H.0 cmH.0 mma.0 0.0a m.~H e0 m00.0H «00.0“ H.0H H.0u muoa x ~H.¢ ~H.0 m.eH .a.mn man.0 *HmH.0 e~H.0 0.0 n.0a no m00.0fl «00.0” H.0H a.0fl m-0H x as.~ 00.0 ~.eH m.0~ em~.0 tama.0 sNH.0 0.0 0.~H N0 m00.0u N00.Qu H.0H H.0u n-0H x 0s.a .50.0 .m.nH .s.m~ He~.0 eHeH.0 ema.0 0.0a m.¢s H0 Auenunav .a.n.>.u Haoo em Haeo =H Aesnonav Amenonav Amencnav Asenccav Anenensv a 0 m4 case. $30 $03 a n e n a accesses .mmovosu a one .mvasaa mamas tussouoh .msoamcosav .mwams coupesdaaoo .H mgm<9 12 V BEAM FIGURE 3. Definition of the line source target in a gas cell by the collimator's slits. 13 which the beam enters or leaves the gas cell becomes part of the target. This would complicate the calculation of the cross section and include unwanted background peaks in the spectra, for Kapton background peaks due to hydrogen and carbon would appear. It is shown in reference (Pi 70) that for small beam widths as used in this experiment, 9min can be calculated from the formula: t... 8.1.. . 2.3.921 where t (90°) is the length of the line source of the gas target for a lab scattering angle of 90° and D is the diameter of the gas cell. emax is (180-Ghih).- emin' emax’ and i t (90°) for different collimators and gas cells are tabulated in.Table (I ). In practice, the appearance of 12C peaks in the spectra was used to detect these limits. . 2.2.3 Effective Target Thickness The effective target thickness of a gas target is just the product of the gas density and the effective length of the line source defined by the collimators. neglecting corrections for the changing ,effectiveness of the penumbra, the effective target length at angle a is t(9o°)/sine. For the collimator system with the best angular resolution, a gas pressure of'é atmosphere; and temperature at 23°C, the effective target thickness at 90° was 268l4g/cm2. This amounts to an energy loss of 4 kev for 30 MeV protons. 14 2.2.4 Gas Pressure Measurements For the absolute measurement of the 1“1‘1 (p,p) angular distribution at 29.8 MeV a mercury manometer was used to continually monitor gas cell pressure. The error for this measurement was about‘i 1 mm. The cell pressure for the normalization points taken at 36.6 and 40.0 uev ‘were measured.with a Wallace and Tierman Type FA-l45 MM 17069 aneroid gauge. According to the manufacturer's specif- ications these measurements were good to‘: 0.8 mm or,¢ .1% of full scale. The gauge checked with the weather bureau to within 2 mm or 0.3%. 2.2.5 Gas Tegperature Measurement The gas temperature was measured by determining the temperature of the scattering chamber and assuming the gas cell and gas temperature to be the same. The temperature of the scattering chamber was observed not to vary more than :;0.5'C during a run. H. W. Laumer (La 71) and W. L. Pickles (Pi 70s) have both looked into the question of local heating of the target gas by the passing beam. Both Pickles and Laumer measured a particular cross section with different beam.intensities. Laumer found no significant change in 15 cross section for a fiveifold increase (100-500na) in cur- rent while Pickles found the same result for a ten-fold.in- crease (10-100na) inocurrent.. The statistical error in Laumer's investigation was 1.5% and in Pickles', 1%. 2.2.6 Scattered Particle Collimation Uhits For a gas cell target, two apertures are needed to define the solid angle and the radial acceptance angle. If only one aperture is used in front of the particle detec- tor, the entire length of the beam passing through the gas would be the line source of scattered particles. To restrict the length of the line source of scattered particles, a slit at some point between the target and back aperture must be used. In this experiment the height of the target was determined by the beam's vertical width and so the front slit functioned only in the horizontal direction. In Figure (3) we have a top view of the situation. The horizontal openings of the two apertures define two regions of the line source. For the center section, defined by the intercepts of the two dashed lines with the beam, each point along the beam.has access to the full solid angle of the back aperture. Points along the beam in the penumbra of the slit telescope have access to only part of the back aperture. The geometry dependent G factor that appears in Silverstein!s (Si 59) expression for the differential cross section below is the 16 integral of the solid angle from any point along the been over the length of beam that the slits define as the target, and includes corrections due to the first and second deriv- l atives of the differential cross section. N G-Go(l+X+-‘,-Z-'Y+ 2) fll Nb - the yield at lab angle 0 NT - the number of target nuclei percm3 NB . the number of incident particles X, Y, and Z are functions of the shapes of the beam cross section and of the slits o' and o " are the first and second angular deriv- atives of the differential cross section. The program 'G-FACTORF written by Dr. R. A. Paddock and based on Silversteins analysis was used to calculate the values of G needed. a 'lo- and a'lo- were nowhere large enough to require slope corrections to be included in,G calculations. Formulas useful for estimating Go and the kinematic broadening for certain slit telescopes are developed in Appendix A. . The collimating units used were designed and built by Dr. Bill Pickles and are described in his thesis (Pi 70b). Figure (4) is a schematic drawing of one of these units. An important feature of these units are the baffle slits. Their purpose is to eliminate particles slit scattered by the sides 7 1. 5m #20:... g gmzwhxw >0 owhuubcca 0 owhowhocm g E3 9808 >0 omcuhoxm (up? 5 g >0 abouhoca (g u 52¢ 91.0"... @9230 ”8 gig M N? 9.5m .15... .255 05902330 05 no one no 05380 03323 4. .2 E05 235.5... mo 33! "35.. / oasis: . , 20.5mm con 529;. .343 m8 .alllloltlIIIHHHIIIIII/I/t {1:115:11}. -\-1 el IIIII IHIIIP III |IIIIII| IIII|IIII|I||II\ O 8.5:: on uuunuvlrfl ........ . IIIIIIII I’ll Illllll II||||‘| . Ill ------- 1......1 0.00.5 50 505 a Ilia}! 023000 :6 ii! :05wa . 3&3 5E. .35» _ Sm um 3&5 98 _ mtg 22:54.50 9‘ [it .‘ (if if 551' 18 of the front slit. The front and rear geometry defining slits are themselves made up of two slits. The first de- fines the opening of the slit but is thick enough only to degrade particles passing through it so that they appear in the spectra below the region of interest. The second slit placed just behind the first is thick enough to stop the expected products of the reaction but has an opening slightly wider than the first slit. Thus only an area proportional to the thickness of the first slit is a source of slit scattering. A small permanent magnet was set in the collimator to trap electrons that might have been swept along by the scattered particles. Side walls of tantalum or brass protected the counters from stray particles. Four different geometries were used in taking data. They will be referred to as Cl, CZ, C3, and C4 and their dimensions and specifications with errors appear in Table (1). Cl had the best resolution and smallest G factor. It was used at forward angles where the background under the peaks of interest was highest and resolution a definite asset. C} is characterized by poorer angular resolution but larger solid 81181-0 and was used at backward angles. C2 represents a comm-lee. It was used at a number of middle and back 8118108 and for the measurement of the elastic scattering. C4 was used in absolute normalization runs. l I“. n '0. ‘l n. a 's e.. 19 2.2.7 Angus: W The apparatus used to measure the scattering angle in the 35” scattering chamber is completely described in Dr. Pickles' thesis (Pi 70c). The relative angle error for the system is quoted to be 0.10. Before each run a surveying transit was aligned along the beam line. The collimator was rotated to 0.000 on the readout and the beam line was seen to go through the middle of the slits to within a few mils. The wire target on the scintillator was then aligned with the beam. Thus the angular errors were much less than the 0.70 full angular acceptance of C1. 2-2-8 Beam mm Measurement The beam is dumped on an aluminum plug at the back of a 57” long section of 4" diameter beam pipe, insulated from the scattering chamber by a 1.5" plastic section of beam pipe. Horseshoe magnets were placed on the beam line to trap electrons streaming along with the beam. The current was integrated by an Elcor model A310B current indicator and integrator, tested with a 1.35 volt mercury battery in series with a 1% 4.5 meg. ohm resistor. Input was made at both the Fraday cup and at the current integrator and the calculated charge and integrated charge agreed within-1%. The overall integrating accur- 20 acy was 2%. 2.2.9 EZA E Dectector Telescope Charged particles of equal kinetic energy but differing in mass and charge will loose different amounts of energy in passing through a detector. Using a detector telescope this can be exploited to generate separate energy spectra for different detected particles. The front detector, the aE-detector, must be thin enough to transmit the least penetrating particle of interest, yet thick enough toproduce a useful signal for the most penetrating particle. The back detector or detectors must be thick enough to stop any par- ticles of interest after they pass through the A E detector. In this experiment, the AB detector was a 500 um surface barrier silicon detector and the back detector was a 5.0 mm lithiml drifted silicon detector. The detectors were cooled by circulating alcohol, cooled in a reservior in contact with dry ice. This alcohol was pumped through copper tubing attached to a brass cold finger in contact with the detectors. Figure (5) is a schematic of the detector package. Three signals are measured; a A E signal from the front detector, an EB from the back detector, and the total energy, Es . AE + EB from the connected cases of the two detectors. 21 SUMMING CIRCUIT AE —>A£ SIGNAL E —>E SIGNAL 2 —->2 SIGNAL éfimmm $- FIGURE 5. Two detector telescope summing circuit. 22 2.2.10 EZQE Sigggl Processng The electronic set up for handling the signals is shown in Figure (6). The A E/E option of program TOOTSIE (Ba 71) running in the M.S.U. Cyclotron Lab. SIGMA-7 computer was used 'to provide particle identification. The code first generates two dimensional AE, Es spectra which may be dis- played on a cathode ray screen (Figure [7]). The different particle bands are then defined by lines generated as poly- nomial fits to chosen points. The code uses these lines as gates on the AE and Es signals to generate separate Es spectra for each band. For the detectors used here only proton and deuteron bands were defined. Only the proton spectra were useful and one is reproduced in Figure (8). The f.w.h.m. for peaks of interest in this spectra was 80 Kev. For some spectra the f.w.h.m. was as high as 105 Kev. 2.2.11 Monitor Detector A cesium iodide crystal mounted on a photo tube "as used as a monitor counter with the gas targets. 1‘0 ”Wide dead time corrections, and for run to run normaliza- tion when necessary. The package used was designed and built by L-oLGarn of the Cyclotron Lab. except that an additional 8111’ was placed between the detector and gas cell. A single channel analyzer was set to accept the elastic proton peak. .moasouvooao mfimmoooua Hoe—Mam .w MEGS ES . <0» T 00. oz ~50 . . . .0.» z... I A . _ . sac. . - . ..0.. 43.2410 T NW 9H ciao». . ..0.. ..mzz$.0 . 00. oz In. T z... 3 2 004 h N 24 FIGURE 7. Two dimensional TOOTSIE display. 25 Aromas». new one ommxosm hopoopon .m<\m on». :33 some» Emuvomam £393.. < .w mm:on .oz szzmIo mmkd mmwd mum“ mmru mama mama . mu: Al _ t _ 1 — — 3 3 0 n _ N _ I. u be S me a n an _ e um. _ _ : mo m {ON an: _ 29 _ “No c an _ m s _ m n 9 mm _ 6 .l. 6 .l _ h .c. _ m 3 3595 n .9 .. S\H x w a _ I. 22 ..omnefie 0.: m. 0) min Eéza 26 The slow logic pulse output of the single channel analyzer was sent to a sealer and the channel zero input of the program TOOTSIE. 2.2-12 Eegradez.-'22122322,92mhinaiien.fezflléié and.flQiQ.Mel.Ahseluie.Hermalizaiien Measurements Absolute normalization of the 36.6 and 40.0 MeV spectrograph data was accomplished by measuring points of the elastic scattering angular distributions with a gas cell target in the 40" scattering chamber. The detector was a 5 mm Si(li) detector with a 0.114” thick aluminum absorber for 40.0 MeV bombarding protons and with a 0.064" thick alum- inum absorber for 36.6 Mev bombarding protons. The degraders were placed directly in front of the detectors so that losses due to elastic scattering at angles less than 45° could be neglected. The total reaction cross section for 29 MeV protons on 27Al is 775 t 37 mb (Ma 64) and for 34 MeV protons, 600 t 20 mb (Go 59). The total elastic cross section for 29 MeV protons by 27A1 at angles greater than 45° in the lab, is 90 mb (Ma 64). Thus proton react- ions with the aluminum absorbers could remove about 1% of the proton flux to the detector, and the resulting cross sections had to be corrected for this. 27 2.3 ifleasurements made with the Enge Split-Pole Spectrogggph 2.3.1 The Spectrogggph vs. the Scattering Chamber There are a number of problems associated'with doing this experiment in the scattering chamber as described so far. The excitation of 1.78 MeV state of 2351 by in- elastic scattering in the solid state detectors. of protons elastically scattered from the 14N gas target, produces a peak in the proton spectra close to the peak due to excitation of the 2.31 state in ”‘11. For 29.8 MeV incident protons and at 30° in the lab, the silicon reaction peak was 250 Kev f.w.h.m. and appeared 410 Kev above the 1"N 2.31 peak. The 2.31 state is weak and of primary interest. Thus one must resolve it and the peak due to the above excitation in the detector. For a light nucleus like “N where kinematic broadening is important this means a small solid angle. Even if the resolution is good enough at forward angles, this artifact peak will get closer to the 2.31 peak as you go back in.angle. As you go back in angle, the spectrum becomes compressed. For 36.6 nev incident protons, the difference in lab energy between elastically scattered protons and protonsfrom the 2.31 state in 1"N at 5° is 2.315 MeV, at 90° it is 2.152 nev, and at 120°, 2.071 MeV. The peak, due to the reaction in the detector, appears at the same energy down.from the elastic peak for all angles. In the scattering 28 chamber the tail of the elastic proton peak produces a high background at angles forward of 30° in the lab. Also, the high elastic count rate is a problem in itself at forward angles in the scattering chamber. These problems are all avoided by using the Enge Split-Pole spectrograph, since the elastic protons do not fall on the detector when the 2.31 state is being measured. This allowed measuring the cross section for the 2.31 state at angles as small as 10° in the lab, and reduced the resolution required so that thick targets and solid state position sensitive detectors could be used. The Enge Split-Pole double focusing magnetic spectro- graph also allows one to compensate for kinematic broadening by proper positioning of the spectrograph focal plane and so a large solid angle can be used without loss of resolution. The program SPECTKINE (Tr 70a) incorporates Enge's (En 67) linear approximation to the displacement of the focal plane from the first order focal plane due to kinematic broadening. For a given interaction, energy, and effective radius of curvature, SPECTKINE calculates the required magnetic field strength and focal plane position. Thus it was possible to use a slit 0.368” x 0.372" that subtended 1.202 millister— radians for the 36.6 nev runs and a slit that was (0.372") x (0.298") subtending 0.972 millisterradians for the 40.0 MeV runs. Table (2) contains the dimensions with errors of the slits used. In the spectrograph it was possible to measure the weakest points of the 2.31 angular distributions with 3% 29 TABLE 2. Dimensions of spectrograph apertures. Slit Height Width Solid Angle Error Due to (Millistereradians) Rounded Corners 1 0.372" 0.368" 1.202 .75% $9.001" $9.001" (2°) (2°) 2 0.372" 0.298" 0.972 1.0 % 39.001” $0.001" (2°) (1.7°) 30 statistical errors in about 30 minutes of running time. One disadvantage of doing this experiment in the spectrograph was the small area of the focal plane that we could cover with the one working solid state position sensi- tive detector available. Thus it was only practical to measure the elastic and first two excited states in 1“N. Another disadvantage is that the spectrograph scattering chamber and beam line has equipment incorporated to facili- tate high resolution spectroscopy. This equipment limited .the back angle to which we could measure the 2.31 cross section at 40.0 MeV to 6 £ 120°. Figure (9) shows the the basic geometry of the spectrograph. .2.3.2 Melamine Targets The th target used in the spectrograph experiments was melamine (C3 “6 N6) in.NH:C:NC(NH2):NC(NH2):N on 100 #B/sz carbon foil backings. There are several problems associated*with making evaporated melamine targets. Melamine is a fine white powder that sublimes at 354°C. If one evap- orates it in an open boat, the escaping vapor carries with it unevaporated clumps of the material. If one uses a boat with one or’more pinholes as a source, heat radiating from that source raises the temperature of the carbon foil and the melamine plates out on everything but the target. A heat shield with a small hole will trap almost all of the 31 AE/A'G = KINEHFITIC BROFIDENING FIGURE 9. Kinematic correction in the Bulge split-pole spectrograph. 32 vapor before it gets to the carbon foil and the hole will fill up before a useful target is made. A solution was found by covering an open boat with a fine stainless steel mesh that was heated along with the boat itself. The clumps would either be trapped or evaporated by the mesh which was of 0.0021" wire with 200 wires to the inch. Relatively clmnp free targets as thick as the 3.1 mg/cm2 target used for the 40.0 MeV measurements were made with this mesh covered boat. Melamine slurry targets were also used for some of the data at 36.6 MeV. One part polystyrene to three parts by weight of melamine were mixed in benzene. The mixture was sprayed onto a glass slide that had been covered with a thin layer of Tepol. The target was then peeled off the slide. . These targets were relatively grainy and non-uniform, worsening the resolution in the spectra taken with them. 2.3.3 Target Spinner If the melamine target were left stationary in the beam the beam would evaporate the melamine off the target spot. Thus the target was rotated about an axis parallel to the scattering plane but displaced about 3/8 of an inch above the beam. The target spinner is shown in Figure (10). - The driving torque is transmitted through a 1 an quartz vacuum window by means of a "magnetic clutch." The target was rotated at about 600 rpm and withstood beams of 300 nanoamps 33 mo m_x< hw01 7). << | I I I \\ 3002 :5 Nka<30 Es. _ is «.052 made 9 mthOSZ ZOthm 34 for 10 to 20 hours. There was discoloration of area exposed to the beam but little decrease in thickness as measured by the monitor counter and integrated current. 2.3.4 Silicon, Surface Barrier, Position Sensitive Detector The scattered particles were detected at the focal plane of the spectrograph by a Nuclear Diodes (Ba 69) silicon surface barrier position sensitive detector. This detector was 3 cm long and 1 cm high. Its thickness was Boo‘nm, but since the particles were incident at 45°, the effective thick- ness was 425 pm. Two signals are taken from the detector, an E signal proportional to the energy lost by a particle passing through the detector and an XE signal proportional to the product of the energy lost and the position along the segment of the focal plane covered by the detector. The XE signal is obtained by dividing a signal equal to the E signal between the two ends of the thin resistive back layer of the detector. 2.3.5 Particle Identification For particles of equal magnetic rigidity, Bg, but different masses and whose range in silicon is long compared to the detector thickness, the E signals are proportional to their’masses squared (Ba 69). This makes it possible to 35 separate events due to particles differing in mass. 2.3.6 Signal Processing Electronics The electronics setup used including that for the monitor counter is shown in Figure (6). The detector has a large area and so large capacitance. Noise in the XE signal is due to a relatively small resistance (~lOKn) in series with that capacitance. A short shaping time constant (~ .2 ,usec) will reduce the more serious resistive noise at the cost of reducing the size of the slow rising XE signal, and increasing its non-linearity. 40 MeV incident protons lose only about 900 Kev in 450 A of silicon so that one cannot afford too great a reduction of the KB signal. In this experiment, all the shaping times on the Ortec model #51 spectroscopy amplifier used for the XE signal were set at 2 nsec. Other settings did not improve the resolution. 2.3.7 Comter Data Handling The two signals E and XE were handled by the XE/E routine of the program TOOTSIE (Ba 71a) running in the Z 7 computer. In SETUP MODE the E and the quotient XE/E were analyzed into a 128 x 128 array. This array was displayed on a TEKTRONIX 611 stOrage scope with E the ordinate and XE/E the abcissa. The program allows for areas in the E, 36 XE/E space to be associated with particles of a particular mass. In RUN MODE, the windows set in SETUP MODE are used to separate the incoming data into position spectra for the particle masses defined. In this experiment proton and deuteron bands were defined and 512 channel position spectra ‘were obtained. One such spectrum is shown in Figure (11). The resolution in this spectra is 56 Kev f.wth.m. which corresponds to a position resolution of about 1.6 mm. f.w.h.m. Other data taken also at 40.0 mev but with a thinner target had a resolution of 35 Kev frw.h.m. or about 1.0 mm f.w.h.m. 2.3.8 Monitor Detector The monitor counter was very important in this experiment because it provided the only reliable point to point normalization of the data. The melamine target contains 12c as well as nitrogen and so resolution had to be good enough to separate the elastic peaks due to the two. For the 36.6 uev run a 5 mm Si (Li) detector was placed at 150° inside the spectrograph scattering chamber. A 10 mil copper absorber‘was used to insure that the particles would stop in the detector and the detector was not cooled. Background from the Faraday cup limited the beam current to about 250 nanoamps. One of the monitor spectra taken at 40.9 MeV is shown in Figure (12). For the 40.0 mev run, the monitor was again at 150° but now it was outside of the scattering chamber 37 103 - ‘Nem (2.31 I‘EUI Era-won use 9W7" 56 KEU V- PHI-l1 10 COUNTS PER CHRNNEL CHBNNEL NO. FIGURE 11. Spectrum taken in the spectrograph. 38 103 10a 10 COUNTS PER CHRNNEL 1 .4 ‘ I n . 1700 1800 1900 2000 m NO. FIGURE 112. 00.0 MeV monitor spectrum from an evaporated melamine target. The detector angle is 150°. 39 and cooled to the temperature of alcohol circulated around dry ice. The 10 mil absorber was still used. Due to the increased distance between the detector and Faraday cup and to improve shielding made possible by the improve geometry, current was not limited by background in the monitor. As one can see from the monitor electronics in Figure (6), that monitor spectra were recorded. A logic signal generated by a single channel analyzer on the E signal from the position sensitive detector was used to keep track of the monitor spectra dead times. 3. DATA 3.1 General Description of the Data For incident proton energies of 29.8, 36.6, and 40.0 uev angular distributions for elastic scattering from 14N and for the reaction 14N(p,pt) 14N* to the first two excited states at 2.31+ and 3.94 mev were obtained. In addition angular distributions for 29.8 mev incident protons of the reaction 1“11(p,p') 14"“ to the ten excited states between 4.91 and 8.h9 uev were obtained, These 29.8 MeV ang- ular distributions were taken with gas targets. The resolup tion obtained for these angular distributions was as good as 80 Kev at 30° and as poor as 105 Kev at about 85° where kinematic broadening is greatest. This resolution was such that all but the 7.97 and 8.06 MeV state and the 8.62 and 8.A9 uev states were resolved. Where the 5.69 uev state was not resolved to its half maximum point from the 5.83 MeV state, the code SAMPO (R0 69) was used to reduce the data. 4. . IAN energy levels are taken from the F. Ajzenberg- Selene compilation of energy levels for.A a 13, lb, and 15 :nuclei. F. Ajzenberg-Selone, Nucl. Phys. A122 (1970) l-221. #0 1+1 SAMPO can be used to fit a Gaussian shape with exponential tails to isolated peaks in the spectra. The three shape parameters involved are stored as a function of channel number of the peaks fit. The program does a linear interpolation to assign shape parameters to other peaks in the spectrum. To fit a doublet the program varies the heights and centroids of the two appropriate shapes until the overall envelope is fit. An attempt was also made to separate the states at 7.97 and 8.06 MeV with SAMPO, but here the results were not as reliable. At forward angles reactions in the detector and contaminants in the target complicated the extraction of the angular distributions for the 6.1-I’ll and 7.03 MeV states. The angular distributions at 36.6 and 40.0 MeV were taken in the 14.3.0. Enge Split-Pole spectrograph. Non- uniformities in the target used for the initial 36.6 MeV run spread the peaks out and made it necessary to make some correction for non-linearities in the silicon surface barrier position sensitive detector. The #0.0 MeV data as well as check points for the 29.8 and 36.6 MeV angular distributions of the 2.31 state were taken with improved evaporated targets. Here the peaks were narrow enough that background and non- linearity corrections were not serious problems. The relative uncertainty of this data was less than 5% and the check points agreed with the earlier data at 29.8 and 36.6 MeV. 42 3.2 Reduction of Gas Target Data 3.2.1 va The peak to valley ratio at 30° in the lab was 1.5 to 1 for the 2.31 mev peak and so background subtraction for O 5. 60° was the main source of error. The background was subtracted using the code MOD-7 (Au 70) which fits a poly- nomial to sections of the background on either side of the peaks of interest and then Continues this background under the channels containing the peaks. Backgrounds representing upper and lower limits were drawn and the average taken. The error assigned to choosing the background was L/3 of the difference between the net number of counts in the peak ‘with either extreme background. Where the 1.78 hev silicon state was clearly separated from the 2.31 nev peak it too was reduced and its strength relative to the elastic peak calculated. The ratio of 1.78 2881 to elastic 1“N was found to average 20‘: 2 x 10’“. Where the 1.78'MeV silicon peak and the 2.31 uev peak were not separated SAMPO was used to strip the 2.31 MeV peak. MOD-7 was used to find the total number of counts in the combination from which an estimate of the 1.78 uev silicon peak based on its ratio to the elastic peak was subtracted. The final result was the average of the two values with an error due to separation of 1/3 the dif- ference between the two values. 1l‘l‘l(p,pi') spectra taken at “3 24.8 MeV incident proton energy by Crawley e_t_ _a_1._. (Cr 70) were reanalyzed in this way, and no disagreement with the published cross section was found. 3.2.2 Inelastic Gas Target Data other than the 2.31 MeV State Data The rest of the gas cell data was stripped using both ammo and non-7. MOD-7 was sufficient for all but the 5.69 and 5.83 MeV state combination and the 7.97 and 8.06 MeV state combination. The backgrounds most easily drawn with MOD—7 seemed a little low to the eye and since the background of SAMPO seemed to be high to the eye, thus all the data was stripped with both SAMPO and MOD-7. The isolated peaks were used as a test of SAMPO's ability to reproduce the peak shapes and areas. For the elastic, 3.94, 6.20, 6.44, and 7.03 MeV states the results of SAMPO and MOD-7 were averaged and 2/3 of the difference between the average and either of the results taken as the error due to background subtraction. The 4.91 and 5.11 MeV peak combination and the 5.69 and 5.83 MeV peak combination were first stripped with SAMPO and the results taken as the lower limit. Then MOD-7 was used on the combined peaks and the sum for each combina- tion taken as the upper limit. The SAMPO results scaled up to that seem to provide upper limits for the peaks. The average was then taken. The 7.97 and 8.06 mev states appeared 44 as a doublet and SAMPO was the only hope of obtaining separate angular distributions. The results of separating these two peaks using SAMPO indicates that the 7.97 MeV state is from 5 to 10 times stronger than the 8.06 MeV state. A test of SAMPO on a series of manufactured doublets described below leads to an estimate of the error in separating out the 7.97 uev state of 5% and of 20% for the 8.06 MeV state. SAMPO was also tried on the 8.49-8.62 MeV state combination, but it could not locate the 8.62 state. The assumed controid locations for the two peaks were input to SAMPO. The code rejected the 8.62 mev state and fit the combination as a singlet. The resultant fit was as good as that to known singlets. Thus the excitation cross section for the 8.62 MeV state must be less than 30 Ab/sr at 30° in the lab. The test of SAMPO described below indicates that the peak would not have been rejected if it were 10% as strong as the 8.49 Merpeak. ’ The quantum numbers (0‘+ 1) of 8.62 mev level were established in the early 1950's, through the study of the 130 (P¢.)‘) 14N* reaction and resonances in the cross section of the reaction 13(3 (p,p) 13c: (Se 52, W0 53, M1 54). The state has been seen in the reactions 120 (3H3, p) 14N'with a cross section of about 0.3 mb/sr at 15° in the lab for 20.1 MeV incident 3He (Ma 68), and in the reaction 151v (p,d) 1"N with a cross section of 0.02 :,0.01 mb/sr at 21° :_2° in the lab for 39.8 Mav incident protons (Ma 68). “5 3.2.3 A Test of SAMPO To see how'well SAMPO could be expected to do on the present data a set of spectra were manufactured. A section of a typical spectrum containing an isolated peak was selected. It was then added to itself after being shifted some number of channels and multiplied by a scale factor. Thus the areas and separation of the peaks making up the resultant doublets were known. The scale factors used were 1, 0.75, 0.5, and 0.1, and the centroid separations ranged from 1 channel to 8 channels. The frwzh.m. of the original peak was about 6 channels, and the shape parameters were taken from other peaks in the original spectrum. For the spectra with scale factors 1.0, 0.75, and 0.50, SAMPO separated the doublet into two peaks with the correct area within 2% when the separation between the two was 5 channels or more. For the spectra with a .10 scale factor, the larger peak was reproduced quickly but the smaller one was about 15% too large at a separation of 5 channels. At a separation of 8 channels the error was about 7%. It should be pointed out that 5 channels of separation were less than the ftwth.m. of the peaks and the doublet looked unresolved to the eye. See Figure (13). Itwas found that changing the initial estimate of the centroid locations for the peaks in a doublet did not effect the final results. If the fitting process converged, it always converged to the same result. as fl'tflXIJ ”3981.0 4 SHIFTED 12 ms LEFT 4 SHIFTED 5 ms LEFT . "Q I " J“: r“ t rm ' eescm a run P J 1 l l i 1 1 7 I 1 l I 1 1 I n l ' m 150 ' IN 150 mm. MM). ”'3’!“ ”3880.1 : SHIFTEDSWLSLEFT .’ SHIFTEDSWLSLEFT l macaw CMTSPEBCIML FIGURE 13. Pseudo spectra of the type used to test SAMPO. Arrows indicate centroids as assigned by SAMPO. a? The effect of changing the f;wzh.m. fitting parameter by 5% was explored. For the test spectra with a 1.0 scale factor, the doublet was not separated to 1% until the centroids separation reached 6 channels. For the spectra with 0.1 scale factor, the smaller’peak was underestimated by 20% for a centroid separation of 6 channels. Changing the tail shape paramenters by 20%ihad little effect. Since the centroids of the 7.97 mev and the 8.06 MeV states should have been separated by about 6 channels, these results were used to assign errors to their intensities. 3.2.4 Reactions in the Detector and the 6.44 MeV State Angular Distribution The 6.44 hev state is as weak as the 2.31 uev state and its peak is over a peak due to inelastic scattering to the 6.27 mev 2881 state in the detector at forward angles. Unlike the 2.31 mev case, the detector reaction peak and the peak of interest are not separated at forward angles. K. M. Thomson .e_t_ 9;. (Th 67 ) measured the strength of the reactions induced in silicon detectors for 25 MeV inCident protons. These results were used to subtract the counts due to reactions in the detector from the 6.44 MeV peak. The large errors assigned to the forward.points of the 6.44 uev angular dis- tribution reflect the uncertainty involved in this subtrac- tion. At 30° in the lab, for example, the sum was about 2400 48 counts, while the Thomson‘gtugl. result led to an estimate of about 1700 counts for the 6.27 mev reaction in the detector.‘ The energy of the protons reacting with the detector is 29.2 nev in this experiment and the peak due to the 1.78 mev reaction in the detector is 30% less in this experiment than in the work of Thomson at 21. 3.2.5 Normalization of the Gas Target Data The gas cell data required long counting periods and were taken in a number of separate runs. It was decided to normalize it to the elastic scattering and take a separate elastic angular distribution measurement. This procedure introduces an additional normalization error, mainly due to uncertainty in reproducing scattering angles. This is most critical at forward angles, but the forward angle data 'were taken during the same run as the normalization data. Thus the reproducibility of these angles was good to .1°. For most other angles except those around 80° this was a less critical factor, and the uncertainty in reproducing angles was taken as :_O.3°. This lead to an uncertainty in the cross sections which was at most 2.8% and which was added in quadrature to the other uncertainties. The absolute level of the 29.8 mev data.was also checked.using the same setup used to obtain an absolute normalization for the 36.6 and 40.0 mev data (see section 3.3.4). 49 3.3 Reduction of the Position-Sensitive Detector Data 3.3.1 Description of Difficulties The solid state position sensitive detector data were taken relative to a Si (Li) solid state monitor detector for point to point normalization and absolute normalization was by gas target runs (see section 3.3.4). There were a number of problems in stripping the data. The position sensitive detector was not linear over its entire length and there were regions where its efficiency dropped. Thus in taking data, one not only had to make certain that the detector was at the right height in the focal plane but one also had to map out the areas of constant efficiency and reasonable linearity. The efficiency was mapped by varying the spectro- graph field to move a peak along the detector and noting the ratio of counts in the peak to monitor counts at each stop. Thus areas of poor efficiency were noted and avoided. The linearity of the detector‘was measured well enough to make a first order correction to the background by looking at slit scattering which was assumed to be constant across the face of the detector. The best data taken was the evaporated melamine target data. The errors on the points in the relative angular distributions of these data are less than 5%. The peaks were narrow and easily kept on the "good" part of the detector, 50 ‘background subtraction uncertainties were minimal, and the monitor spectra of high quality. A number of the points were retaken during the run and data at 30° was taken several times as a safety measure. Data of this high quality was taken at 29.8 and 36.6 mev to check the data taken earlier. In each case the agreement was within the errors assigned. The peak to valley ratio at 30° in the lab for the 36.6 uev incident proton, 2.31 nev state data was 12 to l 'with the slurry target and 40 to l with the evaporated melamine target. This compares to 1.5 to l for the gas target data at 30° in the lab and 29.8 mev incident protons. 3.3.2 Backggound Subtraction Only the 36.6 MeV slurry target data presented any background subtraction problem. Since the slurry target had many large grains it had many spots that were quite thick and the peaks in these data are spread out. Backgrounds were drawn for the spectra as taken and after the background on each side of the peak were corrected for the non-linearity of the detector. The results were averaged and the difference included in the error. For the data taken with the evaporated melamine targets the peaks were narrower and the background could be subtracted directly. ‘ 51 3.3.3 Point to Point Normalization Point to point normalization was by a 5 mm Si (L1) detector used in conjunction with hardware and electronics described earlier (see section 252.9 ). For the 36.6 mev slurry target data the monitor spectra began to deteriorate toward the end of the run. The monitor detector had been damaged by v-rays and neutrons from the Faraday cup and there was no replacement available. The channel "0" scalar, the stripped monitor spectra, and beam on target corrected for changes in target angle were all compared. The percent difference between the channel "0" scalar and the stripped monitor counter spectra, which was as high as 5%, were included in the uncertainties reported. For all the later data an improved monitor detector holder‘was used and the channel "0' and the stored monitor spectra agreed to within 2%. 3.3.4 Absolute Normalization Absolute normalization of the spectrograph data was done by measuring the 14N elastic mass section at certain points using a gas target and collimator system described earlier (see sections 2.2.1 to 2.2.8). Use was made of the fact that the elastic angular distribution was least dependent on angle at about 55° in the lab. The measurement error in the absolute cross section due to local heating in the gas caused by the beam 1%;- 52 due to pressure measurements was 0.3%; due to temperature measurements, 0.2%; due to beam current integration, 2%; and due to collimator dimension measurements, 2%. Corrections for reactions in the absorber of + 0.8%,; 0.3% at 36.6 MeV and 1.3 i 0.3% at 40.0 MeV were made. A 1.7 3; 0.3% correction ‘was added for counts lost due to nuclear reactions in the silicon detector (Ca 70). The error in the absolute level of the angular distributions should be less than 4% for the 36.6 and 40.0 mev data. 3.4 Summary of Error Determination 3.4.1 29.8 MeV Gas Cell Data In assigning errors to the points of the relative angular distributions taken with a gas target at 29.8 nev, the following sources of errOr were considered; statistical uncertainty in the number of counts in a peak (m where N is the net number of counts in the peak and B is the number of background counts under the peak), statistical uncertainty in the number of counts in the elastic peak in the spectrum, statistical uncertainty in the number of counts in the elastic peak of the normalization run, the error due to angle non-reproducibility in the normalization run, uncertainty in determining the background, the error involved in separating peaks not completely resolved and in subtracting 53 contaminant peaks, and the error involved in subtracting peaks due to reactions in the silicon detector. All the above errors were added in quadrature. 3.4.2 Position Sensitive Detector Data For the position sensitive detector data the errors included were statistical uncertainty in the number of counts in a peak, the uncertainty in determining the background, and the uncertainty in the number of counts in the monitor. The errors in the absolute normalization are the same here as in the gas cell data only an error in the correction for reactions in the aluminum degraders in front of the detectors must be included. This uncertainty was about 0.3%. The overall normalization error is about 4%. 3.5 Plots and Tables of the Angular Distributions. Plots of all the angular distributions measured for this work are found in Figures(l4-32). The data are also tabulated in Tables(3-zll The 2.31 angular distributions plotted as a function of momentum transfer are found in Figure(33)and in Tables(22-25L Where not shown explicitly, the relative errors are smaller than the points. 54 2 . “mnpll‘m E..=29.s nsu . 53:0.0 "EU (1’30) 7% 5 I 3 3 a 5 2 . a z 102 .9. a 5 5 3,’ 3 I U) 2 "—I 8 I 5 10 I a 2% 5 - '- 3 g a t 1 *4 a 5 e 3 . O 30 80 90 120 150 180 C-fl ENGLE - (DEGREES) FIGURE 14. 1l‘N(p,p)1u’N angular distribution for Ep I 29.8 MeV. (Where not shown explicitly, the relative errors are smaller than the points.) 55 3 " “swarm Ep=29.8 nsu 2+- ' ! 5,-2.3: nsu , (0’31) '5‘? . E5: 1cfi3h_ II P- . _ II 5 1' :2 5~ ' OD 53" é a. E. ' F4 5 32 10h-- . II ii Lu UL LL f4 (3 3a so So so 120 150 180 c-n Busts - [DEGREES] FIGURE 15. 1“N(p.p-)1“N* (2.31 Mev,(o*,1)) angular distribution for ED = 29.8 MeV. (See caption of Figure 14). 3r “NIPMWN Ep=29.e nsu a » 53:33.94 "EU (1‘30) é '- 3. 5‘- '- , K a . t s 3 - s F'- 5" I 8 H L- I 00 II 3L s g a . II (.1 22b 'I II 'fIIII E5 . II II '1. E 10"1 '. .' u. ' as. he F1 ° 5 I. 1 1 l 1 1 l 1 1 l 1 1 l 1 1 1, 1 1 I 0 so so so ‘120 150 180 c-n HNGLE - (DEGREES) _._—_ FIGURE 16. 1“N(p.p')1“N* (3.94 Mev.(1"'.o)) angular distribution for Ep 8 29.8 MeV. (See caption of Figure 14.) 57 103E I‘INIP.P‘]1“N EP=29.8 "EU 9 ~ Exam: 1150 (o to) ' a 5. 3 ~- 3.- 3}. i i ' i I I 5 eh i... ..H. a U I a” 02 .- 1 h— a) ll 8 9t 'i- 5 ~ '- 3 5_. ".-I. {'1 '-l- '- 5 5 3" t 5' 2" lOJLllJllllllllllLlJ a so so so 120 150 180 c-n HNGLE - (DEGREES) FIGURE 17. 1nN(p,p')1uN* (4.91 Mev,(o'.o)) angular distribution for ED = 29.8 MeV. (See caption of Figure 14.) 58 ‘i r' 1"N(P.P')1'*N Ep=29.8 neu _ i 3 5,5541 nsu (2'30) E3- .1:- ‘5h— IIII ". fig . _ ll 55" II '1 " a 3 - a OIF F ERENTIHL CROSS SECTION - 018/ SR] 8 JL I Q” 1 1 l 1 1 .1 1 1. l 1 1 I 1 I 1 1 J 1 l 0 so so so 120 150 180 c-n ENGLE - (DEGREES) 43 FIGURE 18. 1hN(p.p')1uN* (5.11 MeV,(2-:O)) angular distribution for ED = 29.8 MeV. (See caption of Figure 14.) 59 1037 “*NtPF'P‘m Ep=as.s nEu Z Ex=5.69 nsu (no) Se- ‘1 - a is h... s- I. I 2+ .- .I I I 'I- lo8 DIFFERENTIRL cnoss SECTION 4- 0.9/39) 4: (n C) l 31‘ r I er1T 41' 1‘) 1 1 I 1 1 l 1 1 l #1 1 l 1 1 l 1 1 I] 0 30 SO 90 120 150 180 c-n’ aNsLE - (DEGREES) FIGURE 19. 1"N(I>.1=')“‘N” (5.69 Mev.(1'.o)) angular distribution for Ep 8 29.8 MeV. (See caption of Figure 14.) 6O s- “NIPF'JI‘M Ep=ase rlEU . L. . 3 bx £385.83 "EU (3'30) 5 \ a» g g...- 1 I ' I I 5 1 _ I H 9H: 5 . ' g 5 b I s "' ' J 3 t .I- a: I- E a b .- .- m I 31 fl: .1 E3 IUO‘DL- a: 1 1 AI 1 1 l 1 1 I 1. 1 I .1 1 l 1 1. J v, 0 30 60 90 180 150 180 C-l‘l HNGLE - (DEGREES) FIGURE 20.» 1“’N(p.p')1"N* (5.83 Mev.(3‘.o)) angular distribution for Ep 8 29.8 MeV. (See caption ofFigure 14.) 61 3" 1“N(P.P'11“N Ep=29.8 neu Egzseo rlEU (1°30) 25 On 1T1ri I s .s I xi .3 11;} f 1! I iii; a - J. i Eh; (I) 1 OIFFERENTIRL CROSS SECTION - (119/ SR) 0| 1 T T I =11I11I11.I11l11111l v 0 30 80 90 120 150 180 C-l‘l RNGLE - [DEGREES] ' *—— FIGURE 21. . 1"N(p,p')1“1~z“ (6.20 MeV, (1*.o)) angular distribution for ED = 29.8 MeV. (See caption of Figure 14.) 62 5' “'N(P.P')"'N Ep=29.8 men I. Exes.“ HEU [3‘30] “ O N r TWTI'I r i 3? w k hiifiii'fi . g .C DIF F ERENTIRL CROSS SECTION - 018/ SR] (n o ‘ so so so 120 150 180 c-n ENGLE - (DEGREES) FIGURE 22. iun(p.p')1“N' (6.44 MeV, (3*.o)) angular distribution for Ep =- 29.8 MeV. (See caption of Figure 14.) 63 g: 1"N(F.P')1‘*N Ep=as.e nsu Ht Ex=7_.03 nsu (2‘50) 3- ‘ at ' II II 1L—. '21 S, II II DIFFERENTIRL caoss SECTION - Ins/SR) a so so so 120 150 180 c-n HNGLE - (DEGREES) FIGURE 23. 1"r1(p.p')1"a" (7.03 MeV. (2+:0)) angular distribution for Ep 2 29.8 MeV. (See caption of Figure 14.) 64 l"N(I=>.P')1“N Ep=es.e mu 4: (fl Ex=7.97 NEU (2":01 7"“ s .l: T DIFFERENTIRL CROSS SECTION - W88) (n 08 I '1 1 I 1 1 I 1 1 I 1 1 I 1 1 1 1 I 1 O 30 SO 90 120 150 180 0"" RNGLE " [DEGREES] FIGURE 24. 1“N(p.p')1”N' (7.97 MeV. (2':o)) angular distribution for Ep - 29.8 MeV. (See caption of Figure 14.) OIEEERENTIRL CROSS SECTION - [pa/SR) 8 ~ I 65 3' “N(P.P')1‘*N ’ Ep=as.e NEU 2- Exams NEU (m) 3 On I-I-I 00 00 .1: (n T (fl 1 1 I 1 1 I 1 1 I 1 1 1 1 CI 1 1 I I 0 so so so 120 150 180 cm RNGLE - (DEGREES) OD -:? FIGURE 25. 1l‘I~:(p,p')1“N" (8.06 MeV, (l‘.l)) angular distribution for E1) = 29.8 MeV. (See caption of Figure 14.) 66 8 I‘thpf'jl'IN EP=39.8 I‘IEU 5‘: Ex=8.‘19 flEU (W10) lfb O _ i I 3_ if I I g I I 2% s r 3.!“ 10’- ' fipfi DIF F ERENTIRL CROSS SECTION - [pB/SR) 0 V0 11111 111 I I 1 1 l a so so so 120 150 , 180 C-I‘l RNGLE - (DEGREES) I 1 FIGURE 26. 1hN(P.P')14N* (8.49 MeV, (4'.o)) angular distribution for. E1) = 29.8 MeV. (See caption of Figure 14.) 67 3 ‘ “N(P.P)“*N Ep=ss.s r1EU Ex=0.0 HEU (use) NO 00 (I 10 . no 40 CR 10 . OIFFERENTIRL CROSS SECTION " [PE/SR) 00' .' I C” II I”. II RD 00 0 so so so 120 150 180 cm RNGLE - (DEGREES) FIGURE 27. 1“'I‘J(p,p)1'"N angular distribution for Ep = 36.6 MeV. (See caption of Figure 14.) 68 3F 1‘*N(P.P')1"N Ep=ss.s rlEU s-s O N .1: a! I he 00 U M DIFFERENTIRL CROSS SECTION - (pH/SR) n) I I C 6‘." 3W 0 30 80 90 120 150 180 C-fl RNGLE " (DEGREES) FIGURE 28. 1l‘N(p.p')ll‘N* (2.31 Mev, (0+.1)) angular distribution for ED = 36.6 MeV. (See caption of Figure 14.) 69 3r 1"NtF.F")1'*N EP=36.6 NEU I - Ex=3.9'~l HEU (1,“:o) .—. I m 1 W of: .- “. ' II 3:» P I. I 51— z u L. 3 1 5 3* g I I to 3" I I. I ag 10"+- I H 9 E I 111 u. u. H a 0 30 80 90 120 150 180 C-fl RNOLE " (DEGREES) FIGURE 29. 1I“N(p,p')ll’N* (3.94 MeV, (1+;O)) angular distribution for Ep 8 36.6 MeV. (See caption of Figure 14.) 70 2 “N(P.P)“N Ep='+0.0 r1Eu 3 . 1° 0. Ex=0.0 nEu (1*;0) . I c: 5 a: I E s I 103 g s 5 5 I S 3 ' a) 3 I... g 10 I I c: 2 I . IT; 1 .'I. H a 5 I 3 . I E?— 1, 1 I 1 11 I 1 1 I 1 .1 111__1__1__1__J _ O 30 SO 90 120 150 180 C-I‘I RNGLE - (DEGREES) FIGURE 30. 1l‘N(p,p)mN angular distribution for ED I 40.0 MeV. (See caption of Figure 14.) DIf-‘FERENTIHL cnoss SECTION - (pH/SR) 8 . 71 8r “'N(P.P')1‘*N EP=HO.O neu E3=2.31 flEU (0’31) ’6 ON I l mw£01 (~3/3e) (353.) (“B/S?) ER??? 1:'/3 2-7365-31 3.30 2.341E-31 8-2 “.3 ?:-~~ 1-372E-31 20-30 1.568E-31 1-8 “-3 21-5; 1-9672-31 20.10 2.145E-31 6-6 “-1 ?6°/’ 1-?7#E-31 25-36 l-ERZE-Ol 1'7 “-3 39°11 30157i-32 33030 902235'32 1‘1 “OD 37-«2 b-usca-gg 35-30 6.157E-32 3-3 “-3 eg-V; 3-733L-:2 40.30 4.228E-32 2-2 “-3 e7-98 p-«Sez-gg 43-30 2-755E-02 3-1 “-3 33-53 1-C23Z-32 53-30 2-106E-32 2-3 “-3 C&--E 1-4365-3? 55.30 1.774E-ca 3.1 a.) ‘3-55 1-=e9£-:2 63-30 1-561E-32 2-7 “-3 ea-:: 1-4152-3, 55.30 1-714E-32 3-# “-3 73.96 1.3333-32 790:3 EOQQSE'CE 2'3 “'3 7”02H 2.144;-3' 75-3 209245.32 g0? 40” = -15 2-2323-3. 53-33 2.259E-32 2-7 #-, r,:‘7 2,;‘795.C_ 55.4.3 2.333E'CZ 3'3 1*.“ da-al 2-2537-3 33-33 3°?5“E‘OE 3'“ “’7 75-57 E'QEEi-fl? 95039 203195'32 805 “'2 z'u-éa 2°?832-Cr 133-30 2.215E-02 6-7 “-3 1 m-ee 1-2162-2 135-3: 1-8395-32 '2- 4-3 :.u-12 1-9122-3; 113-33 1.713E-32 7-2 “-3 112-97 1-‘835-2 115-30 1-759E-32 6-# 4-3 ::x-:; 1-‘135-3 123-33 1-4855'32 3'3 “'3 123-:2 1.~:1£-3 125-33 1.278E-32 7-9 “on ICE-55 907ééi'33 13303: 5I8125‘33 5'3 #0) ZFE-l; r-Faéi-c. 135-*3 5.533E-33 7-1 #-3 j§?-:E 3-“;6Z-:3 1430,: 50227E'C3 1107 “-1 ;e7.3; 5-F7EZ-”3 iufi-ZC 5-7695-33 3'3 “-1 ;‘3-13 E-Fiea-g3 :53-:: 8-293E-:3 7'2 “-3 1‘6'75 1-‘17E-'2 155-“? 1.433E-32 5-8 “-3 ‘§;°73 297:9:-:9 351.33 ZIQCCE'G 7'8 “I3 z--s-.3 3o~ee;-: 155-3: 8-629E-32 4'3 “-7 75 A ’ = .8 MeV. TABLE 5. 1“N(p.p')1“N* (3.9u.(1 :0)). Ep 29 r“- ~ 5‘4?“ \ :P: 3"? A;- K; ATIVL \" P . :1;::Q’xTIA; A30 ”I’ZZQZ-lI 9E: :EVT ERQE ‘." - ,.- -r 75\ ‘ L: :QSDS DL'Tlg‘ .' , ’QCNQ Q- T“. \VJ __ rQSQ A db; - ~-~ 9"“ -n ) (“B /S?) 5* ( _J,) (WE/31) < 0° an 6 “0; - "fi .662E+‘_’U 2. ;1.35 104“1;+3C 29.:J 10472E*QO 309 “'3 :5-92 1-2fi2?*33 53'3“ 1.979£+¢; 2-3 “'3 fip-é7 1°1$31+33 590:; 1o; ~45+3.3 505 “'7 7)0fi: 90?16E'31 33.x: c. 34Eonl 209 “'3 93.7; a-zali-Cl “:°*: ; :135-11 u.s --1 ,;.,1 609331'31 “3'3: '::«E.;. 1.7 “-2 - c.9:47‘-"‘| 5:4va 6' “‘3 ,, Q0”: z-I‘th _. - :- g; up nfi S. 22 5E.q1 L02 .. ,, ‘- '1 ..f. ‘35. U ’30]: 4.7.12- qJ ' :A haQ3E-31 l.“ “.3 LW-“E 3'§*11'51 6Z.‘: 3 769E-41 3-2 “'3 .n.=- co~752-:1 53'3“ 3"5§5-:1 1-8 “-3 - *‘ “ . ~ , W A“ ‘9' V vu.5e a-’/6i'u1 7~':: 2 537E-~1 3-2 “'3 73.;8 80:4CZ’21 75.”: ..195E_:1 3.6 #03 ; a! “-443L'"1 RC'J“ 80 Va 404 “’3 f“. .4 C I '- \" ;P.-f‘ 1.812E-S‘ g~.5? 1o7€3;'01 “3 V: 1.5‘3E'“1 #01 4'3 ‘ A ;-\| r\_ ‘ \i 04-53 1'Flég‘u1 95.“; 1.28?Eufil 402 “'3 _. - ..'," :15 '\v 'c- \J , “3'31 103_4_’31 ‘J.um 1."31E'”1 3.7 “.3 --.-~s 1-Cfi3i‘31 139'12 9.259E-32 4'3 “'3 ~ -.37 9.4711-22 1J3’”: 7.5225-32 4-1 “-3 -~ A v ‘19075 7.?écr-ZP ilJ'J: 7 “C5E'CE 1.5 “03 ::”-’” 7‘é48T‘C? 113.9g . R z 701 403 .3; i: r 'f . A? q;)/\.:}3 7.7-c5E.‘T12 :" “ 7?3'75 5'“’1,"‘ :7; «n 8.619E-32 305 '3 ‘“i°71 90u761'72 $54.:J qin.n1 a.“ “.3 1C - 4 '\ n 1.5, '- V 923997 J'IQQL'AI 43:.”1 ‘91E’" 208 “'3 §~». ~ -.?29€-:1 133°J¢ 1'i 1 2.9 4-3 ‘(I' C... ‘ :-'- n QQ‘QOC 1.583E-‘J1 . a . :«2-71 1'“331'~1 ‘.i ~r 1 365E-“1 8'5 ‘3 , - :a~:-r~ Ewe-vw ' ‘ ~ 5 a-fi :g793: ‘..-4 :u. “l ‘”d .\f' 1.:1\85E.:\’1 C. _. ‘4’ g--;.~« 155°T9 l'J" ‘ ' ’ r.(. 1.. 9‘ ¥_. H‘ .3 4.", J ’1 ‘ ‘ an 1 P7EE' ¢ 4 . ' 7 ‘IHRAT"1 lél'uv .~ p a “ 40W .2- - . -- n 1.153;»..1 v3 v Qr-‘r‘017 1.332;.5;1 £53.51V . ‘ fl. 76 TABLE 6. 1"Mmpv)“‘N"(u.91.(o".o)). Ep 2 29.8 MeV. C. . DIFFgaaxrxA; LAB. DIFFERENTIA; RELATIVE NSRW. Lxsga CQBS9 SECTISV AVSLE 2:385 SECTISV PER CENT ERRSR (755.: (YB/S?) (353.) (*8/82) ERRSR ?1¢5& 2.5«15-31 20030 20941E'31 1204 403 96-96 2-5205-31 25.33 2-901E-31 7-3 “.3 32.31 2-353E-31 30.30 2.691E-31 4.7 “.3 37065 20537E'31 35030 209535‘81 707 403 “a-3 203565-01 43-30 2.687e-31 3-5 “-3 «5°27 293375-31 45-39 2.57QE'31 6'3 403 33-3“ 2.375i-31 53-30 2-6235-31 2-3 “-3 44-79 2.?25:-31 55.30 2.“31E-31 3-3 “-3 64-31 1.9975-31 53-33 2.1565-01 1'8 “-3 69°19 1-6723-31 65-30 1-7335'01 303 “-3 74.35 1-“335-31 73-30 1.5065-31 2-1 “.3 79.47 1.234;-31 75.33 1.253E-31 3.3 4.3 34-55 1-3728-31 83.30 1.0“9E-31 “-2 “-3 99-61 9-8685-32 85-30 9-662E-32 “-7 “-3 Gu-bE 1-0275-3 90000 100045‘01 3'9 “00 99-51 9-1445-32 95.30 8.985E-02 3°9 “-3 1:“-55 9-3165-32 133-30 9.3275-32 13-9 “-3 139-45 goesaz-se 135.33 5.2495-32 3.5 “.0 11Q-34 7.5165-32 113.33 7-C8SE-32 3-“ “-3 119.19 5.0975-32 115.33 b.509E-cz 3.4 “.3 12.-:3 5.853E-02 123-3O 5-377E-32 2-1 “-3 122-7% 5-6515-22 125.33 5.137E-32 3-8 “-3 133.54 5-1855-32 133.33 4.652E-32 2-9 “.9 1?8-36 5-::“E-32 135-33 “-8855-32 2-8 “-3 :«2-97 ~-~&sE-\? 143-33 “-6“9E-32 2-7 “-3 :47'55 5.132?.n2 135.33 405“5E'32 3'3 “'3 1:2-51 5-:;9E-32 153-33 “-763E-32 2-9 “-3 126-95 5-2335-33 155.33 “-“9“E-32 3-0 “-3 142-:; 4.558:-:? 151-33 3.897E-32 4.7 «.3 155-19 ..nalz-Ve 155.33 3-“785-32 “-1 “-3 TABLE 7. 1QN(P-P')1uN*(5o11.(2-80))- \U I} m- U' H'Wt‘ f7 “.2. . "I {Y thk‘fi)w’r\fluwrhz -3 l" "" \1!“ 4" (A? \J ‘13 I“ L FI>C’C (YE/s?) -’3“£+:3 '331i+33 '17“Z+30 vlé7i+33 02 M4E :3 '19OE+CC '11“Z+30 v629E-31 -9855-;1 é-u36E-31 u-7125-C1 3-729?- 3 £16:-31 \J \D t) F4 r4 +4 r» h‘ 3* r-Hr-H-JH-awmmm'xs O o... I ;)()(‘;(:'~'.‘f‘( filinira ' ()()() ..J p.‘ *4. 3... p—L H ..3 ..A 0 xx IA) ( ‘ ‘4 I .:~71: 295:? SZCTIS‘ 3») ..A ) b -..J :..A f) w o L) C) i.) (J (.3 (D L) U o (J (J () (‘ I?) t) () (A) (j C) (A) () (J (.3 C) C) C) C) o -‘-) (J C) (3) \l U‘. o "l’ . ( j a; I WC)UH; L)(‘. UN; 0 O O O (3) (3' L)(J¢.) l'.)L)()()(_)x')() ()(3 (r 'j‘ ‘J' l:' r “ I) ' ‘ UHJ O 77 DIFFEQZVT1A_ C?BSS SECT13\ PER CENT (Wa/s?) 1-193E*CC 1.1885+33 1.344E+03 1- 3“8E+QQ 1. 3S7E+33 1°393E+3C 10231E+OC 10353E*C0 5-515 '31 éogééE'Ol 40962E’31 3|375E’S1 30391E‘3 2.«59£-31 2-1945'31 2-3u7E'31 109755'31 10873E'31 10599E'31 10711E’31 10603E“Cl 10525E'21 1-5595'31 10533E'31 1-51“E'31 lOEQSE'Ql 1.732E~31 10554E'31 -275'31 105615.31 Ep 3 29.8 MeV. RELATIVE ERQSQ 3-5 “-3 2-3 5-3 2-8 u-s 105 109 1-2 2-7 1'5 2-9 U.) c _4 1 3 5 3 7 3 3 3-3 301 3-3 1-7 302 2'5 205 2'3 a.“ 90“ 2'3 307 2-9 VJQWO 5?Q9R 40d “03 403 “of 403 “9? “9’3, “IQ #- 4- “- “- Q- “o 4- Q. “o 9- 4- “a “- 40 4c “o 4.3 4.3 403 4.3 4.3 “03 L) L) 5.) L) L) ‘1.) L) I) L) U I.) k.) L) L) ._) Z.) TABLE r" ‘1 '1 0 U \n‘ U‘ ‘13 I“ )‘HU 9 O O O .J‘ 'A' (t I," P r’j) -\ . D [U J" LL) \J :U U" >“ o 1': \JUH: %HH ‘2' O 1 $.40 :m: d \i O \7 U' ..l \ r J O O h'rtffFU\V(T n:w a m;gaép\g C‘ ‘1)'.)") o o o o 0 '(1(J~l)(‘.l,'\u 4‘ I? o o '-\I (J. l (h TD 0‘ ‘4 h: o o '31.! mafia 8. \g? n»- w U) I‘J (’ uwu~clvvh F‘ 4' (A1 (\‘(‘ U-HI“ '\‘() I \ ‘ an (A) I" .,h (3 U ) a I" h C H H -1) I I ( 1:7 Vi“ I 5%? SiCTI ( 3/?Q) 3-9995-31 3-7743-31 3-9855-31 3-7132-31 B-EQEE-cl 3-497E-31 3-“142-31 3°27QE-31 "' "1 '.L ,1 l 1 ‘1 N C u) H A m l 3 \ (). K ( I i 1.916i-31 1-7425-31 1-“353-31 1-P512-31 1-1355-33 1-2255-31 9-723t-32 A ~ .1- Lt" .0- 3C — 4 p... .4 p.) -h 9&- 9 1‘)()()()()" .4 ..5 FJ l \ I . I ‘ “ . , .’l‘ r~r \)/I u L)rlfl I“. waUWDLHQ{f() o. o. o o o o ‘ (3 (.J L) ()(1 L) L‘ 0090‘: ¢U)(~‘IU fl) ‘. ('3 O C) O L) {J (J (A) t) 115-:3 120-“3 125-33 133-33 135-33 143-33 145-33 133-33 151-32 165-33 78 1“N“‘N"(5.69.(130)). B NF: QSSS (% P 3/5?) 40381E'Ol 40354E'31 “oSéSE'Sl #oBZEE'Ql “OSEOE'CI 30938E'C1 30775E'Cl 30585E’31 30352E‘31 30107E‘31 2.6815’31 2-“135'31 20151E‘Ol 10337E'Ol 10735E'31 IOBBOE.31 1-8125’31 1-3845'31 90651E‘32 90333E’32 8.801E'Q? 90283E'32 905655'32 l-lSQE'Cl lilBlE’Cl 10225E.:1 10258E'31 1.185E.31 19317E'21 R’E\.*T1A_ = 29.8 MeV. RELATIV SECTISg PE? CEN ERQ3Q 9UU|wViU07w o o o o o o o o [PWHUJU‘LXIU‘U’J rack-Pg o o o \JUIV u) o H 305 4-3 307 4-3 303 3-5 3-7 F’w o o Wt» WPWIUWNIUW ..0..... HWJ‘QUIWIPLHU} } N r b - \f 2; Q; A) 'U 493 :.t4>r.csrr.pJrcr:.c:=c-r4r: I .-uuuvuu JQIJUQJUVJ .. .)I"-' s..- O Q 79 TABLE 9. 14N(p.p' ’14" (5. 83.(3' .o)).E = 29.8 MeV. :.“ 3IFCEQimTIA; gAB. DIFFEREVTIA; RELATIVE 35:4. ¢.S.F C3839 SECTISV AVELE CQBSS SECTISV PEQ :EVT ERQBQ ("53.) (WE/SR) (358.) (”B/S?) ERQSQ 91-b. 1-168£+3- 0.30 1.355E+33 4.2 #.3 gg.3? 1.?893+33 25.30 1.4885+QQ 500 #03 32-3: 1-‘13:+c3 30-33 1-731E+30 2-1 4.3 ?7-71 1-4981+3 35.30 1.7CSE*30 5-3 4.3 4?'33 1'588i+03 #0000 10793E+33 209 403 aE-54 1-617E+oo 45.00 1.808E+co u-S 4.3 53-62 1-F4EE+QQ 50.00 1.706E+33 1.7 #.0 33.57 1.37.5.03 55.00 1-504E-so 1.7 4.0 Eu-QE 1-159E+OO 60-00 1.25“E+30 1-1 “-3 69-28 1-3335+33 55-30 1-371E-30 3-1 “-3 74.43 7-6325-31 73.30 8.343E-31 1.3 4.3 79-5: 6-2345-01 75-30 6.asaE-o1 2-9 #.3 94-55 4-839E-c1 80-30 4.931E-01 3-3 4.0 59'7: 309255.01 85030 30865E’31 #03 403 °#°7E 302205-01 93030 30203E'01 306 493 ' 2'899E'C1 95000 20847E’01 3'8 “-0 206335.31 130030 20549E'01 3'0 “-0 2'“50E-01 135-GO 2.339E'01 3-3 4.) 2-093E-31 110.30 1.924E-Q1 3-2 “.3 2-171E-31 115.33 2.317E-c1 2.8 4.3 2-1523-31 123-33 1-928E-31 1-7 “-3 2 236'-Cl 125-30 2-325E'31 3-1 “-3 2- P335- 3 133- 33 1-973E-31 2-3 “-3 2 3275-31 135.33 2.114E-31 2.4 “.1 2-“h25-31 143-33 2.1“3E-31 2-7 “-3 E-“éli-Dl 1H5-33 2-135E'21 2.3 4.3 2-2135-31 155.93 1.895E-31 2.5 4.3 109785.31 ‘51033 10682E'31 308 “03 1-7475-31 165-38 1.481E'Cl 3-3 4.3 TABLE 0... 0.; “.30; .' \ - ( ..D’A ..I 4-1%Oi-32 4-3985-3? 4-174i-02 1-“915-02 3'7905-32 40084E-02 4'243E-02 3-4505-32 3-9785-02 2-8435-22 2.700;..n2 2'4332-32 2-127i-32 10943E'3 1.7575-02 P-CS9i-02 2'2005-02 201433:- 2-4H7E-32 8-6722-3? l 3 39C251-32 %-299§-32 4-‘98E-02 4'9531-32 “-EbBE-"P 6-’7#i-12 Will- 115033 120030 125033 130-35 135-30 143-33 1#5OJG 153'33 155-3 :61-33 16500: 80 N (6. 20. (1" 30)).3 313FEQEVTIA; P 3 29.8 MeV. RELATIJE CEVT :Q3SS SECTI3\ PE? (*8/32) ERQSQ 5.5856-02 45.7 90333E'32 5503 503495'32 17'1 40755E'32 2#'3 20P49E'32 2107 40241E’32 2?.“ 40522E'32 509 40647E'32 9'5 3.733E'32 701 302895.02 1005 809985’32 805 EOBOSE'OB 13.1 +92E'02 3'1 EGISDE'OE 1109 10335E'32 8‘8 10735E'32 9'“ 10993E'02 807 20399E'32 703 2655-32 803 E73E‘32 503 20#48E'02 4'4 20435E'32 503 20394E'QE 404 207535-32 507 2.553E'CE 5'9 30383E'02 5‘1 30959E'32 304 ~-146E-32 3-2 405335.32 5'3 50548E'32 401 V3QWO :QRQ? “-3 Q. 4. 403 403 “.3 “.0 #03 403 #03 “03 “93 40W .1 403 «JEW' 403 81 TABLE 11. 1“lump-)“‘N"(6.tm.(3*.o)). Ep 2 29.8 MeV. C. - TI:VECL2TIAL 0A3. 313F5R3NTIA; 4ELATIVE \3Qw. ; 3_i $093: SLCTISn ANGLE CQBSS SECTISW pER :E\T 5*??? < ;:.) (VF/QR) (356.) (VS/SQ) ERQBQ ?2-:J E-n7lf-02 33-39 10331 '31 17-3 “-5 “7-74 6-7261-32 35.39 7.569E-CE #3-2 “.3 «3-3‘ 6-a49Z-;° ua-JC 7-516E-32 1P-5 “-3 ~?-35 u-7552-3 ab-QO 5.325E-32 18-3 «.3 ‘3-37 4-1333-02 53-30 4.531E'82 11-2 “-3 zn-fig 4-C595-A? 55.30 4.u58E-02 8-5 4.3 au-.a 2-9762-0? 50.3C 3-822E-02 R-S 4.3 43'5“ 1-‘452-3? 55033 3.895E'32 9'3 “-3 7w-3: 2-9523-3p 73-30 3.308E-32 8-3 h-fi 3-52 2-971—--? 75-30 3.391E-32 9-7 “-3 14.7. 3.304,.02 30-30 3.3?8E-32 6-3 “-3 P9-7é 3-331n-“2 35-30 3.573E-OE 7-3 “-3 :4-75 3-9755-32 93-33 3.2635-32 5-# “-3 39-75 3-3302-32 95.30 3-273E'CE 7-1 “-3 134-71 3-2395-32 133-:0 3.134E-32 6-6 “-0 139-52 e-RBOt-SE 135-DO 2.748E-02 6-3 “-3 ll‘tféfj 20751C-Q? ‘13.?“ 20588E'32 7'5 “93 119-33 2-757Z-32 115-QC 2.558E-32 u-i 4.3 139'14 2-519i-72 123-:3 2-307E-32 9°? “-3 1? 'h‘l 206373'3? 1250:}? EOBSBE'CE 508 403 1?3-55 2.5a3z-cg 133.": 2.543E-32 4-5 “-3 ;3=-:7 5.9213-32 ‘35.0: a.582€-:2 5-3 a.) :91. 7 20752;-:2 190033 EIQOSE.:2 6'5 “0" ;«7-/a 3.235;.39 135.0: 2.452E-32 '5.5 4.: 132-1? 2.645;-12 153- C 2.275E-32 5-2 4-: 1?7';2 2-0822-32 155.38 8.5u7E-32 4-7 “-3 1‘3'32 a-CBéZ-ce 151-33 2-4“9E'32 7-1 “-3 :95‘55 3044912-32 155013 20951E‘32 605 403 82 1hN(PuP')1u TABLE: 12. N’(7.03.(2’.o)). Ep = 29.8 MeV. 2.4. ClrrEQE\TIAL LABO DIFFEQENTIA; RELATIVE VflQW. A2353 c2338 SECT10\ AVSLE C?BSS SECT13\ PE? CEVT E443Q (353-) (VB/3:) (353.) (*8/85) ER??? 91-55 2.2335+33 23.3 2.566E+33 3.4 h.3 ?7'£5 1-698E+30 25-30 109675400 4'4 ’HC) 32-~2 1-392E+cc 33-33 1-602E+30 2-5 “-3 37-75 1-113E-30 35.30 1-271E+00 5-5 “-3 “3°12 9-1535-21 uo-so 1-0395+33 2-9 “-3 “R'g3 802635-13 (+5030 902655'01 1.05 4.3 53-71 7.152e-31 53.00 7.935E-31 1-9 u-3 58-27 e-ea-a-31 55-30 7-3“3E-31 1-9 “-3 6“°E: 5-4175-01 50-00 5-869E-31 1-9 #-3 69'39 503545-31 55000 50737E'31 3'3 “'0 79-56 4-5175-3 70-30 4-767E-01 1-3 4-3 79-55 4.159;.31 75.00 4.359E-31 3.2 4.3 2Q°77 3!“75E'31 83030 30566E'31 3'3 40:) 99°53 3-1283-31 85-00 3-163E-31 “-1 “-3 24,55 3.737E.31 93.00 2.727E-31 #00 4.3 59-83 2.3135-31 95-00 2.?735-31 #-2 4-3 3:“'77 201845-01 130030 201135.31 305 40:) 139-5: 2.3525-31 135.30 1.985E-31 3-6 4.3 114-55 1.9245-31 110-30 1.808E-31 3-8 #.3 119-39 2-3335-01 115-00 1.856E-01 3-1 4.3 13“°l§ 109645-31 120030 10796E'31 109 40f) 1?S'95 2.2535-01 125-30 1.863E-01 3-3 “-3 133-71 1.9973-31 133.30 1.7825-01 2-5 “.3 138-~2 2-1945-31 135-30 1.9355-31 2-8 “-3 153-11 2.?515-31 143.30 1.965E-31 2-8 4.0 *“7'77 2-u99a-31 145.33 2.162E-31 2-4 “-3 158-ka 2-7112-31 153-33 2.326E-01 2-5 ~-3 157-;« 2.9372-31 155-30 2.5335-31 2.5 4.3 162-57 3-3365-31 151.33 2.7396-31 3-8 4.3 1‘5'E5 3-P951-31 155-30 2-779E-31 2-8 “-3 83 TABLE 13. 1“N(p,p-)1“N*(7.97.(2“.o)) Ep = 29.8 MeV. :. . ‘I:?;¥;fi 1.- _A3. 31:?=?:\IIA- RE.AT v: \3?%. I 3-i :-”?r 8;:17" ‘\3_£ :QUSJ SE:YIQ\ pf? :ENT 5*??? {“ .) (~5/f£) (3&3.) (“3/S<) EQQ3? “?-1; 1-Eaa:-;1 25-33 1.79#E-31 1109 “-3 ~?-~' 1-9763-31 33.30 1.823E-31 5-5 ..3 =7-c~ 1-9972-31 35-30 1o~86E-31 1303 “on +?~;- 1oh13i-g1 43.30 1.5CIE-Cl 4.7 “-3 «i-f; 10337i-21 45-33 1.503E-Cl 801 4.3 :?~é; 1c%34:-31 53.33 1.939E-91 4.5 “.3 39-35 1.142;.31 55.33 1.4755-31 5.5 «.3 E~°I§ 101333.31 53033 102335'31 303 4.3 '9-~I 1°133i-31 55-30 1-182E-Cl 5-9 «.3 7a-éf 3.u182-"3 73.33 9.9516-32 3.4 4.3 79-7? 9-25:i-:? 75-33 9-4275-32 5-9 4.3 74“? 8"95:-29 93033 803C9E'22 303 #03 —9.;- 5.731;.»3 25.33 5.829E-GE 409 900 7407C 799243-;2 9303C 70893E'CE 401 403 ??-34 7-9383-32 95.33 7.788E-32 909 4.3 1“u-%? 7.5143-33 133.33 7.262E-32 3.8 4.3 1:9o7r 7c?853-:2 135-33 6.745E-32 403 4.3 :zaoea 508333-2? 113-:0 5.9255-32 7.5 4.3 :1?’“§ 7'?:3E'CB 115033 6056“E'32 4'3 “03 1?u-EZ 5-253i-g? 123-:3 5.711E-22 2-3 “.3 173-15 6-5?uE-22 125033 5.9#3E-32 503 «.3 ;?3°79 5-1772-32 133.33 5.4976-32 4.1 4.~ 1?%-é; éonhi-z? 135.3: 5.731E-CE 3-2 ~.~ 15f.13 fi.?26:-:2 143033 505385’32 3'9 40‘ 1.7.5. bou735-3; 1.5-3: 5.5836-32 3'3 4.: 1?E-~7 6-1552-32 153.33 5.264E-32 9.5 4.5 137-:3 5°729i-3? 155.30 4.864E-32 3-5 “-3 14?-51 5°?31E-32 151-30 4.469E-32 5'2 “-3 léfi'ib 4'?5“a'22 155033 30558E'32 803 403 8“ TABLE 1a. 1hN(p,p')1uN*(8.O6,(1-31)), Ep . 29.8 MeV. :.*. TI’CE*;‘TIA; _A3. 31:F£QEVTIA; RELATIVE V32“. 1 3-; Z=°S§ SECTI?\ nwsgs CQ3SS SECT13\ PE: :E\T E4459 (;§ .2 (‘E/SQ) cars.) (WB/S?) EQQSQ ?7'l; 1'937Z'31 ESOJC 10427E'31 1703 4.3 92-“: 9-2515-32 53-J3 1-368E-31 13-6 “-3 37.53 5.137;-32 35.33 5.952E'32 21'3 “'3 ~7-L? 3-454E-32 43-30 4-183E-32 15-2 «.3 “5.51 4.a19§-:2 45.33 4.968E'32 2301 “-3 33-2; 3-935L-32 33-:3 4-377E-CE 13'8 “'0 :a-;7 3-47uE-3? 55-30 3-8185-32 16-3 “-3 Ln-R; 3-5355-32 63-39 3.2955-32 13-u «.3 53.3; 2-312E-:2 55-33 2.475E-32 18-7 “-3 7.-e7 2.??az-32 73.;0 2.3aSE-32 12-4 4.3 74-5; l-Q7SE-CE 75-30 1-9Q7E-32 19-8 “-3 4~-:“ Q-QLEE-C3 83-33 1-317E'CE 24-3 “-3 9?-i: 1-1295-32 85.93 1-1“2E-CE 23-8 “-0 ra-sé 9-149i-33 33-33 9-113E-33 15-8 4.3 =9-34 2-7522-33 95-;3 5-6175-33 13-9 “-3 1;«-&3 9-7sfii-33 130-30 9.n08E-33 17-3 “-3 :r9-79 1-3242-32 135-30 1.2635-32 lh-D “-3 11.-55 1-5265-32 110-30 1-4326-32 25-3 “-3 119-~9 1-1aaz-32 115-30 1-338E-02 14-1 “-3 129-39 1'?3%E-22 123039 10125E'32 11.3 403 :3::..;5 1.1:QE-C2 125033 909““E.33 16.2 40;) 1p?.5: 9.3?9§.:3 123.33 8.3COE'33 1303 9'3 ;::-5; 7-255Z-33 133.3. 6.382E-03 13-7 “-3 1~?-15 5-83-i-g3 143-30 5.600E-33 lk-l “-3 1&7-59 5.7771-33 1.5-:3 S-SQEE'CB 13-3 “-3 1?£-~S 5-962i-23 153-33 5.952E-33 12-1 “-0 :a7-:e 1-3245-3? 155-03 8°5915'33 13'3 “'3 1*2-51 1-4372-32 151.33 1.211E-32 13-5 “-3 :ee-aé 1-63-2-32 155-33 1-3725'32 135'9 “'5 85 TABLE 15. 1hN(p.p')1l+lv”(8.l-9,(4'30”. Ep = 29.8 MeV. C. , DIFFEQi\TIA; LAB- DIFFEQEVTIAE RELATIVE \3QWO IND—L 2:389 SaCTI9\ AVSLE 8:535 SECTISR PE? CENT 5*?39 (353.) (VB/SQ) (353.) (“S/S?) E‘RSQ 21.7; 2.9423-31 23.33 3.u45E-51 13.6 u.3 ?7-12 3-d442-31 25.33 3.5“5E-31 6.6 4.3 32-51 3-“52E-31 33.30 3.993E-31 3-0 “-3 37-:: 3-286E-31 35-33 3.773E-31 6-8 “-3 43.23 3-P815-31 43.30 3-731E'31 3-5 “-3 .8-55 3-2935-31 45.30 3.733E-31 5-9 4.3 83-55 3.280E-31 53.30 3.552E-31 2.1 «.3 59'13 3'7575'31 55033 303645031 209 403 44-35 2-61“E-31 53-33 2-8“3E-31 2-3 “-3 ée-b: 2-337i-31 65-33 2.3275-31 5-2 “-3 79-55 1-65“i-c1 70-30 e-seae-al “-2 “-0 7--/E 1-9575-31 75-33 1-723E'31 ‘ 2-“ “-3 CQ'?E‘. 1-?5%£-;.1 330:: 10292E’C1 50“ 403 ?§-CC 1-359E-31 35-30 1.372E-31 5-3 “-3 QF-CE 9-5185-32 93-08 9.u83E-32 “-3 “-3' 1:?-:: 9-2105-32 95-30 9-333E-32 5-3 “-3 12“'3“ 9-“12E-C? 133-33 9-391E-02 3-6 4.3 13‘-?3 1-2685-31 135-3S l-CISE'SI 3'9 “-3 11~-71 1-T7SE-3 113-33 1-3085'31 4-3 “-3 119-55 1-1623-31 115-:0 1-37“E-e1 3-6 “-3 1-3-11 1-2375-91 120-30 l-OSSE-Dl 3-5 “-1 :P“-b“ 1-1575-31 125-33 1-395E-31 2-“ “-3 ,ii-xu 1-271E-31 133-:3 1.129E-31 3-2 “-3 172-3 '1-3395-31 135-3C 1-1“9E-:1 2-6 “-3 2-3-22 1-2295-31 143-30 1.113E-31 9-3 “-3 :«7-27 1-3212-31 145.30 1.137E-31 2-5 4.3 152-:: 1-381E-21 153-33 1.1735-31 2-9 “-3 157-12 1-«395-31 155.33 1-2195-31 3-3 4.5 1‘?°63 1-«745-31 161-30 1-E“3E-31 4-2 4.5 166-32 1-“325-31 155-32 1.233E-31 3-“ “-3 86 ) 1“N = 36.6 MeV. TABLE 16. 1“Mp4: elastic scattering for Ep 7. . 31?f:9 71;; A3. JIFFZQE\II£- REHATIW: \3QW- » 3.: $3239 SECTIBN A\3LZ $3533 SECTIS~ PE? CENT EQR3Q <:;,.) (Vs/AR) (353.) (“B/Si) ERQ3? 15°11 9-7585+:E 15-QV 1.123E+:3 -% “-3 :=-7a +-3€::-:2 17-5. 9-601E+:a 1'3 “-3 71.,5 5.9395+33 23.33 7.7F7E+72 .4 “.3 3“79 “'T“9§+32 25-33 4.6OEE+:E 1-3 4.3 39-:2 2-351i-32 33-30 2-323E+32 1-3 “-3 37-~3 9-9555-31 35-30 1-37“E+:? 1-3 “-3 “2,73 3.93:E+31 “3.33 4.328E+:1 2-3 “-3 '~-;; 2-1132-31 45-33 2-333E+31 1-5 “-3 :3-a: 1°7223+T1 53-32 1-395E+31 1'9 “'3 39°57 1°717i+31 550:3 10552E+31 1'2 490 43-e7 1-?33?-31 53-33 1-713€+31 1°“ “-3 (“-c- 1°°LLL+T1 eb-cf 1-379E+31 1-3 “-3 71-9; a-RBEZ-se 73-33 9- 05E+CO 1'5 “-3 77.39 5.3593+33 75-33 6.383E+33 1'9 “'3 =--;7 3-7a7;.gg 83-33 3-87“E+33 1-“ “-3 “9-32 2-375L+:C 85-39 2.399E+33 1-3 4.3 'u-:Q 1-427i+33 93.33 1.623E+33 10“ “-3 33-21 1-374£+33 35-33 1-854E+30 3'3 “-0 ::--:7 1-Cee;.3: 133-:3 l-OBSE-o; “-3 “-3 1759'J3‘ 8.233:-;1 135.3: 80375E'31 3'“ 4'3 113-2? 7--7ai-:1 113-3: 7-385E'21 “'3 “-3 112-*3 s-zce:—:1 115.33 5.717e-31 3.3 «.3 1?3-56 4-7485-21 123-33 “.39hE-Cl 3'3 “-0 :?%-“s ~-P;8C-;l 125-33 3.852E-31 3.4 4.3 :?7-‘9 “-QbOE-Dl 135-33 4.351E-31 “-0 “-3 87 ,)1#* TABLE 17. LN(p.p N (2. 31. (o .1)).E p a 36.6 MeV. c./. jxrrzagxrxA; _A3. DIFF—QEVTIA; RELATIVE NSQWO A‘3LE C95SS SLCTIB‘ AVSL: CQSSS SECTISN PE? CENT E4??? (35;.) (YB/SQ) (353.) (VB/SR) ERQSQ 13-/“ 1-3192-31 10-30 1-289E-Cl 2-9 “-3 IP-ft 1-9981-31 19-33 1-“12E-31 7-3 “-3 Ih-t“ 1-“36i-31 170:0 101835‘21 8'3 403 ?1°“5 8-789F-u2 23-“' 1-005E-31 201 “-3 95-73 7-625L-"2 35.33 8.678E-32 3.3 u.3 72-12 5-57eE-3 39.33 5.313E-32 1-8 #.3 21-«3 3-'12i -:2 35.33 3-385E-32 “-7 “-3 wz-/3 1- i43E-32 43.30 2.3555-32 2.1 4.3 «2.1; 5.9311-33 .5-33 9.8““E'23 2-9 “-3 53-25 7-368E-33 53.33 7.7445-33 2-8 “-3 98-“7 9-1125-33 55.33 9.88uE-33 «.2 a.3 ‘3-57 1-P80i-32 53-33 1-374E-32 2-8 “.3 ‘?-§« 1-799E-;2 55.30 1.909E-32 #04 “.3 73-98 1.9805-32 73.33 1.971E-32 3-8 “-3 79-39 2-“733-32 75-33 2-147E-OE 205 “-3 94-17 1-8172-32 23.33 1.559E-32 5-7 «.3 £9-ca 1- 6923-;? 55.33 1.7C9E-32 6-5 “-3 94'5“ 1035 45-3? 33033 IOBSCE’OE 205 403 33-32 1-37oa-32 95.33 1.353E-32 6-“ “-3 1'Q°l7 70?Q6E-;3 133030 70524E'33 704 4.0 11q-39 7-sza-33 135.33 6.9345-33 2-9 “-3 113':E 507751.33 113'33 50758E‘33 703 403 112-:3 e-Paai-c3 115-ac 5-8635-33 8-2 “-5 1?3-:& 6-TS9E-33 123.30 5.537E-33 3'6 “-7 198.96 “ORBQE'CB 125033 40424E'33 905 “03 1= -:9 3-292:-33 135-:3 2.953e-s3 17-2 “-3 88 TABLE 18. 1“1‘1(1‘),p)1‘"N(3.914, (1 .o)).E = 36.6 MeV. :. - 31::ERE\TIAL LAB. DIFFERENTIA; RELATIVE V324. Lgsgt 59395 S_CTI5\ A\3LE CQSSS SECTISN PER CENT EQQBQ (:a;.) (VB/$2) (DES (“B/SR) 1307b 10585Z+33 130:3 10824E+33 302 “03 32-58 1.539;.3312.30 1.735E+33 3-5 “.3 13'3“ 103E9E+CC 17000 10523E+CO 202 “00 ?s-79 1-119£.33 25.33 1.27uE+30 “-8 “-0 ?E-12 9-6433-31 33.00 1.091E+QO “-4 “-0 ?7-~3 B'EBBE-Ql 35-00 9.773E-31 1-9 “-0 “2°73 703685-31 #0030 80441E¢31 403 4.3 “90;: 60213E-C] #5030 605735'31 “'4 “to 333,047 30Q76i-21 5503:) 30771E.31 6.3 “.3 63-67 2.6915-31 53.30 2.888E-31 4-6 4.3 52-aa 2-2155-31 55-30 2.353E-31 “'2 “-3 73-98 1-9325-31 73.30 1.995E-31 4.3 “.3 79'L9 106355'31 7500 10694E'Ol 409 #00 84°17 103733-31 83'30 10‘955'31 “'5 “'0 29-22 1-3328-31 85-30 1-3“3E-31 3-8 “-3 ~4.54 7.937E-Cg 93.33 7.914E-32 4-0 “-3 ?9-82 5-8233-32 95-30 5.731E-32 7-1 “-3 134-.7 4-3325-32 133.33 “-183E-32 5-“ “-3 1:9.39 3.19-3-3? 135-3“ 3-Q55E'32 5'9 “'3 113-95 3-“502-32 113-30 3.273E-02 6-2 4.3 112-53 2-9995-32 .15-30 2-8375'02 5'5 “'0 1?3-éé 3.134;-32 123-30 2.873E-32 6o“ “-3 199-ue 5-993i-32 125.33 3.563E-32 7-7 4.3 l37'99 S'QElE-C? 13503: SOEEEE'CE 5'3 “'3 1“?~72 6-339i-32 143-2. 5.5395-32 5-8 4.3 89 TABLE 19. 1l"1*1(p,p)1l"N elastic scattering for Ep 3 40.0 MeV. :. . CIffEngTIAL LAB. DIFFEREVTIAL RELATIVE VBRu. p 3.3 £9688 SECTIS\ AvGLE 32888 SECTISV Pg? CENT ERQRR (323.) (“B/SR) (DEG.) (*8/52) aaaaa 16-13 9-“&RE+02 15.00 1.089E*03 01 “-3 19°38 8-67SE+31 17-50 9-263E+02 1'3 “-3 21.-e e-uaea-oa 23.33 7-3“8E+32 -2 “-3 25-5: 3-516£+32 25-30 3.003E+32 -9 “-3 32013 10917E+C2 30030 20347E+02 '5 493 37-~“ 7-5845-31 35-30 8.527E-01 1-4 “.3 “3'39 “-762§+C1 37-50 5-33“E+01 -8 “-3 “P-7“ 3-230£.31 43.33 3.604E.31 ' 2.9 4.3 95-37 2-1553+31 42.50 2.395E+31 1-“ 4.3 “g’il 1'95“E+01 45-30 2-051E+01 1-6 “-3 93035 105385+Ol 50-30 10795E+01 202 4.3 58'“5 10543E+Ci 55000 10674E+31 103 403 53-65 1-323£+31 53.30 1.417E+31 2.1 4.3 58-55 1-31#E+31 65-30 1.076E+01 1-1 4.0 7a-3C 6-939E+03 73-30 7.277E+33 1-2 4.3 79-11 4-364€+33 75-30 4.521E+33 1-3 4.3 ?u-19 2-567E.33 33.30 2.626E+33 1.5 4.3 59-23 1-725E+OO 85-00 1-74EE+OO 1'1 #00 94-25 1-331E.33 93.30 1.2975-33 1.5 4.3 99-23 1-398E+30 95-30 1-383E+30 1-“ “-3 zja-lé 9-“985-31 133.30 9.229E-31 1-8 4.3 113-59 b-“CSE-Gl 110-33 6.369E-31 1.2 4.3 1?3-é7 3-332E-31 123.30 3.3555-31 2-3 4.3 9O 1“N.E p TABLE 20. . . CIFF: Ra TIAL LAB. DIFFERENTIAL RELATIvE N32“. r 3-: 27558 SLC TI9\ AVSLE 22383 SECTISV PER CENT ERQ5R ( :3.) (VB/3:) 3E0.) (WE/S?) ERQSR .3-7- 1-1982-31 13-33 1- 3795-31 2-8 4-5 zfi-t“ 1-341E-31 17-30 1-19“E-312-7 “-3 91-43 1-3375-31 23-30 1.153E-31 2-7 4.3 2505: 7 63C:- '32 25-33 8-554E'32 204 “-3 39°13 5- #33L- -32 33.33 6.153E'02 1-8 4.3 77-u4 3-251E-32 35.33 3.555E-32 2.7 4.3 «q-lu 1-641L-3? 43.30 1.831E-02 3-0 “-3 “8':1 S'OQCE'C3 45033 8-8945'33 3'8 “-3 53°55 7'551E-33 50-: O 8-385E’33 3’2 “-1 33'“? 1'115::32 55-30 1-2135‘08 306 “.3 €3-Eh 1.475 _ 32 53.33 1.797E-32 2.9 3.3 (9.55 2.163E-52 65-30 20995E‘32 3'1 4'3 7#':Q 2'396E-32 73-00 2.513E-38 2'3 “-0 79-11 2-3445-32 75-30 2-489E-32 3-3 4.3 «4°19 2°881E-02 83-00 2.334E-3? 2-8 “-3 »9-23 1-726E-32 25-30 1-80“E-02 3-3 “-3 94-2: 1-“855-C2 93-30 1-481E-32 3-3 “-3 99-23 1-317:- 32 35.33 1.331E-32 3-7 “-3 Ida-18 7-531L-33 133.33 7.317E-33 u-o 4.3 113-33 .-6¢-E-:3 113-33 “-“19E-33 “-2 “-3 133'57 “-3255-33 123-CC 3-983E'C3 5-1 4.3 91 TABLE 21. 1“'1~z(p,p-)1l'1-J"(3.9l.,(1*.o)), Ep a no.0 MeV. C.*. 31FFEQ;»TIAL LAB. DIFFEQEMIIAL RELATIVE V3?“- iNSLE CQFSQ SECTIZ“i AVSLE CRBSS SECTISN PER CENT EQQQQ (35;.; (33/8?) (356.) (33/83) ERRBR 13.74 1-S#13+33 13.30 1.775E+QO 201 “-3 91.55 1.161£+QQ 20.30 1.328E+OC 2'6 “'3 32-13 1-020E+30 30-00 1-15“E+30 1-2 “-3 42-74 7°715E-Cl 43.30 8.638E-31 20“ “-3 33-25 4.351E-C1 50.30 4.7685-31 2-2 4.3 £3.68 20566E'01 50030 20754E'31 2'8 403 7“°33 1-7“6E-31 70-30 1.831E'01 2-1 4.3 ?“919 1-1185-31 80-00 1-1““E-01 2'“ “-3 04-25 5-9133-32 93-30 5-7935’02 3'9 “'3 r39-23 404625-32 95-30 “-3925'02 2-9 “-3 13a-18 3-5853-32 133.30 3.“83E-02 30“ “.3 113-99 2-4375-32 110-33 2-309E-02 3-“ “-3 1?3-57 2.5435-32 123-30 2-3535'02 3'3 “'3 92 TABLE 22. 1hN(p.p')1uN*(2.31'MeV) plotted against momentum Water for Ep 5 2&8 MeV (Cr 70). ‘ 3.340005'02 HSMENTuw DIFFEREVTIAL RELATIVE TRAVSFE? CRsss SECTISV - PER CENT <11?) (wa/sa) ERRaR .374 3.600005-01 “107 .392 2-1sooosa01 *16-3 .488 , 1-asoooa-o1 1308 .581 1-18000E-01 16~9 .656 .9oaooooe-oa 11-1 .747 7.799992-02. 15.4 .353 w#.aooooa-oa 803 .924 #ouooooa-oa 13°6- 1-02u Boasoooz-oa 10-5 10107 20250005-02 1303 1.262 eelooooe-oa 1u.3 1-392 2o4soooe-oa 11.3 1.52“ 2.73oooE-oa 11°7- 1o65~ EoBBOOOE-OZ 12oz 1-759 2-7ooooa-oa ‘,9-3 1.847 3.120005-02 6-4. 1.923 2088000E'02 7.5 , 1.985 2.200005i02 802 2-033 1 2.070002-02 8oz 20067 5'6 93 TABLE 23.‘ 1hN(p.p')j‘l'l’N‘WZJI MeV) plotted against momentum transfer for Ep 8 29.8 MeV. vSMEmTJ4 DIFraaavTIAL RELATIVE TQAVSFEQ C2838 532T13V PER CENT (ll?) (MB/32) ERRBR .218 20335803-01 2.2 o~27 1.371835-01 1-7 .533 1.374532-01 1-7 o633 80157205-02 1-1 o832 3.792735-02 202 .929 2.492402-32 3-1 1-323 1.922732-02 2.2 1-115 1-636305'02 3-1 1.204 '1o548733-02 2-6 1.293 1.515505-32 3.4 1.373 1-950305-02 2-3 1-635 2.279305-02 8.2 10833 20282705'02 606 1.859 10916405-32 2-5 2.313 1.599505-02 307 2-095 9o765835'03 5.2 2.163 5.905735-03. 11-5 2.215 9.518505-03 7-1 20236 10616935'02 5.7 20255 20789302902 707 20266. 300657OE'02 “07 94 TABLE 2“. 1L’I\1(p,p')wN* (2.31 MeV) plotted against momentum transfer for ED = 36.6 MeV. , 52* v DI:9:ngTIa- QiLATI/E '? 13=_{ 7?:.s 3;:TIJN 939 Czar ::/:) (vs/0Q) ERRvs ”39 1-119 ;:-3 2.7 .471 50/8b733'3: Eva 9593 503762g5'3; 1'8 -*19 3o~123.:-32 “-6 .419 1.«a25;;-33 2.1 10396 8-.313.:-33 2-9 10133 7o_€83J;-3R 80? 1.?31 9-.121g:-33 “-1 1.?3: 1-283 dz- 2 3'7 1-425 1.7asagi-aa “-3 3.a17 1.479533-32 5'5 ~-k:5 2-.729s:-32 2.5 :.s59 1-a17uuz-3? 5.5 “.773 1ob924sE-OE 5.3 10*97 10353505'92 806 1.923 1.;70235-32 6-3 1.?s8 7-aasava-33 7-8 2-113 5-;758g:-03 5.3 2.222 5-455722-33 3-5 2.35? 4.333735-3s .3 2.353 3.291932-35 16-5 95 TABLE 25. 1I"N(p,p')1uN*(2.31 MeV) plotted against momentum transfer for Ep = 40.0 MeV. veVEavxv DI:7£?;\TIA- RELATIVE T4A‘ngQ CQBSS S§ZTIBV PER CENT (t/t) (Ya/o?) ERRBQ oa~9 1-197s;:-31 2'7 .919 1o;~13;:-31 306 .611 7-6333;:-3? 2.4 .243 3.55V3;z-3» 2.5 o '39 105Q12;:'3’3 8'9 1.271 8-3347;:-33 3'7 1.1,: 7-5537;:-33 3-1 1-?35 1.114945-92 3-5 1.252 1.57.52Z-32 Boa 1.90% 8-1633-E-38 3-3 1.«%u 2.5951LE-3? 303 1.7a. 2.221343-33 3'8 ~.949 1.753322-32 3-2 1.022 10485433-32 2-3 P-dca 1.317103-32 306 P0776 7-u30935-33 3-9 2.235 40664333'33 4-1 2.319 4.33n7;_-33 «.9 h. OPTICAL MODEL ANALYSIS “-1 22:225.: An Optical model analysis was made of the differ- ential cross sections for elastically scattered protons by 1l‘LN at incident beam energies of 24.8 (Cr 70a), 29.8, 36.6 and 40.0 MeV. One purpose was to obtain optical model parameters for DWBA analysis of the measured proton inelastic scattering data. For light nuclei this is not as straight forward an Operation as it is for heavy nuclei. While it was possible to fit any one of the elastic scattering angular distributions. unrestrained mosel parameters would fluctuate widely from case to case. This sort of behavior is not unexpected since two assumptions of the optical model may not be valid for light nuclei. First the density of compound- nucleus levels is low and so nuclear structure effects not described by the model may not average out. More important for the incident proton energies involved here. is that it may not be appropriate to replace the nucleus with a potential having a simple radial form. 1LPN inelastic scattering 1h DWBA calculations of proton- require optical model parameters that describe proton- N elastic scattering for exit particles which have different energies than those for which angular 96 EE‘.WKAII‘-‘."IW 1‘ " 1 _. 9? distributions were measured. These parameters must be ob- tained by interpolating between the incident energies where data is available. If the variation with energy of the optical model parameters obtained is not smooth, the inter- mediate parameters are uncertain. To avoid singular sets of F7} parameters, an average set of geometrical parameters, radii and diffuseness parameters was sought that would fit all the data equally well. The potential strengths were varied to fit the data at each energy with the hope that well strength parameters would vary smoothly from energy to energy. h.2 Elastic Scattering Data The 1[N (p,p) data for incident proton energies of 29.8, 36.6 and 40.0 MeV were presented earlier (see Tables 3, 16, 19, and Figures 1h, 27, 30). Data at 2h.9 MeV taken by Crawley'gtlgl, is found in Table(22L The errors include uncertainty in overall normalization. The overall normaliza- tion was not varied as a part of the fitting procedure, although it was varied after the fitting schedule. There was negligible improvement in ngN for i 1% changes in absolute normalization. Since the optical model was not expected to fit the angular distributions well. past the second minima in the ratio to Rutherford cross sections, the errors on the points beyond that angle were about doubled during the searches. 98 The actual errors used in the searches are found in Tables (26 and (27) with the data. Thus these points were weighted relatively less in the search procedure. The 1x?/N values presented are for the actual experimental errors. _._.J 4.3 Optical Model Searches The main part of the Optical model analysis was done with the optical model search code GIBELUMP+ running in the M.S.U. Cyclotron 21-7 computer. The interaction of the two nuclei involved was represented by scattering from the one-body complex potential below: I d Vopt (r) = VC(r) - VRf(xR) - i (W5 - 4WD EEEEJ. 2 - .- .f(xI) +VSO m2 %£‘Ff(x50) (1.0) where: :2 I 2 2 vcm = 22: .rzRCx= W22 e (3 - {32). “Re RC = rCA1/3 f(x) 8 (1 + ex )'1 x r-rRAl/3 R 8 a 'R I - a: 1/3 _ r -z- A xSO" SO aso +An optical model search code written by F. G. Perey and modified by R. M. Haybron at Oak Ridge National Laboratory. TABLE 26. 1I+N(1:>.p )th elastic scattering for E 99 P = 24.8 and 29.8 MeV with the errors used during Optical model searches. C.M. ANGLE (DEG.) 10.66 16.01 21.35 26.69 32.01 37.32 42.61 h7.88 53.13 58.36 63.56 68.70 73.89 79.01 8h.09 89.15 94.17 99.17 109.12 109.05 113.95 118.81 123.60 128.45 133.22 137.98 1h2.70 197.41 152.09 156.79 161.h2 2h.8 MeV (MB/SR) 1.608E+03 9.607E+02 6.950E+02 n.70#E+02 2.778E+02 1.470E+02 7.268E+01 3.600E+01 2.350E+01 2.271E+01 2.522E+01 2.697E+o1 2.510E+01 2.089E+01 1.7n6E+01 1.287E+01 8.7803+00 5.3503+oo 3.395E+Oo 2.2 9B+00 1.5 5E+oo 1.47OE+00 1.785E+00 2.083E+OO 2.h55E+Oo 3.035E+00 3.288E+00 3.130E+00 2.999E+00 2.590E+00 2.322E+00 DIFFERENTIAL ERROR CROSS SECTION (%) O\O\O\O\O\O\O\O\O\\J\ANpNUNNNUUWNUNNNNNNNU coco...oooooooooooooooooooooooo COM. ANGLE (DEG.) 10.73 16.0 21.“ 26.78 32.11 37.h2 02.71 “7.98 53.23 58.45 63.65 68.82 73.96 79.07 84.15 89.19 9h.21 99.19 109.14 109.06 113-95 118.81 123.6“ 128.hh 133.22 1 7.97 1 2.70 197.91 152.10 156.79 1610““ 166.09' 29.8 MeV DIFFERENTIAL CROSS SECTION (MB/SR) 1.502E+03 1.0h5E+03 7.h73E+02 n.795E+02 2.765E+02 1.388E+02 5.9HBE+01 2.866E+01 2.09uE+o1 2.108E+01 2.2083+01 2.136E+01 1.780E+01 1.377E+o1 9.501E+00 6. 1 8234-00 3. 9 3E+00 2.59zE+Oo 1.870E+oo 1.u58E+oo 1.16IE+00 1.055E+oo 1.058E+oo 1.17BE+00 1.381E+oo 1.679E+oo 1.837E+oo 1.995E+oo 2.012E+OO 1.921E+00 1.71hE+oo 1.h28E+oo ERROR (%) OOOOOOOOOOOOOWU‘UU‘NUNUNNNNNHHHHHH HHHHHHHHHHHHH mummmmmmmmmmmkttkrtktkktkcttkttk 100 >10 TABLE 27. 1hN(p.p N elastic scattering for Ep = 36.6 and 00.0 MeV with the errors used during Optical model searches. 36.6 MeV 00.0 MeV C.M. DIFFERENTIAL ERROR C.M. DIFFERENTIAL ERROR ANGLE CROSS SECTION (%) ANGLE CROSS SECTION (9) (DEC.) (MB/SR) (DEG.) (ME/SR) 16.10 9.758E+02 5.0 16.10 9.082E+02 3.0 18.78 8.380E+02 3.0 18.78 8.077E+02 3.0 21.05 6.809E+02 2.9 21.06 ‘6.“23E+02 3.0 26.79 0.050E+02 3.0 26.80 3.516E+02 2.2 32.12 2.051E+02 3.0 32.13 1.817E+02 2.8 37.03 9.556E+01 1.8 7.00 7.580E+o1 1.7 02.73 3.8802+01 2.0 0.09 0.762E+01 1.7 08.00 2.110E+01 5.0 02.70 3.230E+01 1.5 53.25 1.721E+01 1.8 05.37 2.1 5E+01 2.0 58.07 1.717E+01 1.1 08.01 1.8 0E+01 1.7 63.67 1.593E+01 1.0 53.26 1.6 8E+01 2.7 68.80 1.299E+01 1.0 58.08 1.5 38+01 2.0 73.98 9.2552+00 1.5 63.68 1.320E+o1 2.6 79.09 6.159E+00 1.9 68.85 1.010E+o1 1.8 80.17 3.787E+00 1.0 70.00 6.939E+00 1.0 89.22 2.375E+00 1.2 79.11 0.360E+oo 2.0 90.20 1.627E+00 1. 80.19 2.567E+00 2.1 99.22 1.270E+oo 3.0 89.23 1.725E+oo 1.8 100.17 1.065E+00 0.0 90.25 1.301E+oo 2.1 109.09 8.833E-01 5.0 99.23 1.098E+00 5.0 118.83 6.106E-01 5.0 113.99 6.006E-01 5.0 128.46 heZOBE'Ol 500 137.99 0.850E-01 5.0 101 V0 static static field of a uniformly charge sphere of radius is the potential felt by a point charge Ze in the electro- (RC) and charge (Z'e). f(r, rb Ob) is the usual Woods- Saxon form factor with radius parameter r and diffuseness 00' The potentials and geometrical parameters were varied _g singly or in combinations and the code sought to minimize FEE the quantity xz/N = 1/N €— [ (6% (i) - GEXP(1))/AO’EXP(1)]2 where N is the number of experimental data points, cyTh(i) and (IEXP(i) are the theoretical and experimental cross sections at angle 61 in the center-Of-mass frame and A O’EXPu) is the experimental error in UEXP(i)°- The searches began with six different sets of Optical model parameters for the A = 10 mass region taken. from the literature (Ca 69, Sa 70, We 69, Fe 63, Ki 60, Sn 69). The object was to reach different relative minima in 'xg/N space and then to choose trial average geometries from the results. . For the 20.9 and 29.8 MeV data, the spin-orbit radii tended to unrealistically large values and the diffuse- nesses to smaller than expected values. The effect of this was to improve the fits somewhat at angles beyond the second minima. Because the optical model does not generally fit backward angle scattering data well in the mass region of 1[‘N and because polarization data are needed to convincingly 102 determine the spin-orbit well, the spin-orbit geometrical parameters were set equal to those of the real potential in the geometry finally choosen. The searches were generally two parameter searches. The pairs of parameters were usually VR VI, OR 0.1, rR WS, {71 VR V50, or rI rR' . Often the search schedule ended with a .v?"—S'.." .‘ ' '-o search on all the variable parameters just to see how good the model could possibly fit the data. Through trial and U fix, -:_'I . . 'v error an average set of geometrical parameters was obtained and the well strengths were then varied to best fit the data. The final set of parameters are found in Table (28), and the fits to the elastic scattering data, in Figures (30) and (35). To get an idea of how sensitive the fits were to changes in the final parameters, optical model calculations for the four sets of data were made with each parameter varied + and - 5%. The resultant percent change in Xz/N is also in Table (28. The results indicate that the fits are most sensitive to the real potential depth and geometry. 0.0 Spin-Orbit Form Factor It is not completely clear just what form the radial part of the spin-orbit potential should have. The argument for a form factor that peaks at the nuclear surface is made on two counts. The potential is strongest for incident nuclei with large 1 values and these spend most of TABLE 28 . Ep LAB (MeV) vR (MeV) rR (F) aR (F) (MeV) (MeV ) rI (F)' a1 (F) VSOI (MeV) rSO (F) aSO,(F) rc (F). lg/N {- 5; change in 78/11 for a 5% parameter 20.8 51.36 1.133 0.651 1.56 4.75 1.305 O. 509 1.25 31.0 ** To the nearest %. (155 * (386) < 20) ( O)** ( 18) ( 72) ( 18) 103 2908 19.09 (116) 1.133 (277) 36.6 05.67 ( 700) 1.133 (1720) 0.651 ( 18) 0.651 ( 96) 2.93 ( 2) 5.76 ( 02) 3.52 ( 9) 1.63 ( 12) 1.305 ( 70) 1.305 ( 632) 0:509 ( 11) 0.509 ( 28) 5.31 ( 0) 5.60 ( 5) rR ( 0) rR ( 8) 1.25 1.25 05.0 6.9 change. N optical model parameters found in this work 00.0 03.79 ( 702) 1.133 (1689) 0.651 ( 75) 5.75 ( 61) 1.93 ( 22) 1.305 ( 886) 0.509 ( 50) 8.61 ( 31) ( 09) ( 06) rR aR 1.25 3.9 I‘ v 100 I. 1° 1‘*N(P.P)1"N : OPTICHL flODEL FITS E 2 ‘ Q 103 E 20.8 ”EU x 9 1 I 3 5 3 ' {1' 102 8 a) S .2 “a; 3 8 2 o 10 fl _, 29.8 new a: s 5 3 E 2 E u 1 ML '3 S 3 2 10’1_ 1 .1 l 1 1, l l 1 I 114. l I. 1 I l l I 0 so so 90 120 150 180 c-r1 RNGLE — (DEGREES) FIGURE 30. Optical model fits to the 20.8 MeV and 29.8 MeV 10. . . . . N elastic scattering for the Optical model potential determined by this work with r80= rR and aso= aR. 105 I. 1" 1‘*N(P.P)1‘*N : OPTICFIL HODEL FITS 36.8 ”EU X ‘1 F /____ E 60 1 E I Z 0 £1103 8 a) 5 g 3 do: 8 U 10 2’ r: 3 5 2 * E u. 1 L‘; a 5 3 ‘I’ 2 10’! 1 1 l 1 1 l I 1 l I 1 n 1 .l l IIJ I '0 so so 90 120 150 180 c-n RNGLE — (DEGREES) FIGURE 35. Optical model fits to the 36.6 and 40.0 MeV 1”N elastic scattering for the Optical model of this work with rSO = rR and aSO = aR. 106 their time in the vacinity of the nucleus at its surface. It is also argued that only at the surface does the nuclear matter density have a non zero gradient and only there can the incident nuclei retain some sense of its direction. The Thomas form for the potential which is used in GIBELUMP was originally added to the optical potential for heavy nuclei. For these nuclei, the radius parameter is large enough and consequently the derivative of the Woods-Saxon form is small enough near (but notat) the origin to dominate the l/r term for all practical purposes. This is not true when the Thomas form is used for light nuclei. Here the l/r term dominates and the potential becomes very large well out from the origin. See Figure(36L Watson, Singh and Segel, in their optical model analysis of nucleon elastic scattering from lp-shell nuclei, used the modified spineorbit potential below: 2 l VSO (r)é~' 3.2 Vso .9 2 W50“- >395 rso(r) where f (r) is the usual Woods-Saxon shape. This modified form for the geometrical parameters also is shown in Figure (36. Bob Doering at the M.S.U. Cyclotron Lab made available a version of GIBELUMP with this modified spin-orbit potential, GIBPRIME. _ Using GIBPRIME 11: was possible to £11: the four 1"N proton elastic scattering angular distributions with the Optical model potential and parameters suggested by Watson 107 FIR] ’ [HRSITRHRY UNITS) ' SPIN-ORBIT Fonn FRCTOR 51-10 )— rna F‘ .1)- 1 I 1 l 1 - 0.0 2.0 9.0 6.0 8.0 BHDIUS - [F] FIGURE 36. Radial dependence of the Thomas form of the spin-orbit potential and of the Thomas form as modified by Watson et a1. (Wa 69) for A = 1“- 10.0 108 ‘gt‘gl. in their optical model analysis of nucleon scattering from.a number of lp-shell nuclei. The parameters found by Watson.gt'g;. are listed below. vR - (MeV) 60.0 - 0.30 ECM . 0.02/AV3 + 27 (N-Z)/A WD - (MeV) O, for ECM1<32.7 MeV; (ECM - 32.7) x 1.15. for 32.7 MeV S. ECM 39.3 MeV; and 7.5, for ECM > 39.3 MeV WS - (MeV) 0.60 ECM for‘ECM 4< 1398 Nev; 9.6 - 0.06 ECM for ECM .>. 13.8 MeV vSO - (MB) 5.5 2H = aSO = 0.57 (F) ; aI = 0.50 F rR ’3 r1 3 1'30 3 1.15 " 0.001 E F CM . The parameters are found in Table(29)and the calculated angular distributions in Figures(37)and(380 ‘While not as good as the fits presented earlier, they do reproduce the main features of the angular distributions. The minima seem to be deeper with the Watson parameters than they are in either the data or in the fits with the parameters presented in this work. When the 20.9 and 29.8 Nev angular distributions were fit with the average geometry parameters but free spin- orbit potential geometry parameters, the fits improved at backward angles but the well radii went to large values and the diffuseneSses became small. The resultant parameters are found in Table (30) and the fits in Figure (39). Since the spin-orbit force is a short range force, radii larger than 109 TABLE 29. 1“N optical model parameters from Watson gt 2;. (Wa 69) Ep LAB (MeV) 24.8 29.8 36.6 00.0 vR (MeV) 54.17 52.8 51.0 50.0 rR (F) 1.127 1.122 1.116 1.113 aR (F) 0.57 0.57 0.57 0.57 wS (MeV) 0.0 0.0 1.6 5.28 WD (MBV) 802 709 706 7.“ r1 (F) 1.127 1.122 1.116 1.113 aI (F) 0.50 0.50 0.50 0.50 * «Ii vSO (nev) 1000.0 1000.0 1000.0 1000.0 r30 (F) 1.127 1.122 1.116 1.113 ago (F) 0.57 0.57 ' 0.57 0.57 'XglN 24 25 35 43 * Modified Thomas spin-orbit potential. ** Strength for proton mass in force coefficient. 110 11 1° l"1~1(P.Pl"*1~1 5 3 OPTICHL 110051. FITS E 2 m 3 § 10 I: : U x H ' 3 g 2 F3 102 8 m 5 a) 3 i3 2 o 10 ' g 5 29.8 1150/ '3 3 5 2 5 LL 1 Us 3 5 3 8 10'1 1 1 l 1 1 1,11 1, 1‘4. 1 1 11,4, 1 1 1 l 0 30 so 90 120 150 180 c-n HNGLE - (DEGREES) FIGURE 37. Optical model fits to the 2h.8 and 29.8 MeV luN elastic scattering for the geometry and parameters from the work of Watson et a1. (Wa 69). 111 I. 1° 1"I~I(P.I=)1"N : . OPTICFIL 110021. FITS E? 2 U’ a 3 1o ,, 5 5 38.6 neu x 9 ' 3 g 2 £3 103 8 a) 5 a) 3 g 2 o 10 a:’ r: 3 E 2 35 u_ 1 fi 0 5 3 '0 2 10'1_ 1 2L1] 1 1 I 1 1 l 1 1 _l 1 1 l 124 I 0 30 60 90 120 150 180 C-H RNGLE "' (DEGREES) FIGURE 38. Optical model fits to the 36.6 and #0.0 MeV 1hN elastic scattering for the geometry and parameters from the work of Watson et a1. (Wa 69). 112 TABLE 30. 1“N optical model results for free spin-orbit geometry parameters. GIBELUMP* GIBPRIME** Ep LAB (MeV) 24.8 29.8 24.9 29.8 VR (MeV) 52.19 49.09 52.40 49.34 rR (F) 1.133 1.133 1.133 1.133 2R (F) 0.651 0.651 0.651 0.651 W3 (MeV) 1.56 2.93 1.53 2.93 wD (MeV) 4.75 3.52 4.69 3.63 rI (F) 1.345 1.345 1.345 1.345 21 (F) 0.509 0.509 0.509 0.509 V80 (MeV) 4.20 5.29 3.91 5.08 r30 (F) 1.42 1.35 1.50 1.33 aSO (F) 0.449 0.450 0.394 0.350 rc (F) 1.25 1.25 1.25 1.25 7g/N 6.7 20.0 6.4 14.0 * Thomas spin-orbit form. ** Modified Thomas spin-orbit form. 113 ’"NtP.P)“'N OPTICHL "ODEL FITS 84.8 ”EU X 9 DIFFERENTIFIL cnoss SECTION - Ins/SR) f0 10’1V14l11l11l11l11111j 0 30 60 90120150180 c-n RNGLE - (DEGREES) FIGURE 39. Optical model fits to the 24.8 and 29.8 MeV 1“N elastic scattering. The spin-orbit potential has the Thomas form with parameters varied to best fit the data. 114 that of the real well seem unrealistic. It seemed possible that the large radii and small diffusenesses were choosen by the search procedure because they would minimize the singu- larity at the origin and more nearly reproduce the form for the spin-orbit potential that results for large A nuclei. The 24.9 and 29.8 MeV data were also fit with free spin-orbit geometry parameters and the code GIBPRIME. As the results in Table(30)indicate the spin-orbit radii that best fit the data were again much larger than the real well radius although not as large as with the unmodified Thomas form for the spin-orbit well. The fits obtained with GIBPRIME were only moderately better. 4.5 Variation of Well Strengths with Energy In Figure(40)the potential strengths are plotted as a function of incident proton energy in the laboratory. The real well depth decrease with bombarding energy and the slope of a least squares fit to a straight line is -0.50. The depth of the surface imaginary well decreases with in- creased bombarding energy and that of the volume imaginary well increases. This is as expected from other optical model analyses. The real well geometry found in this work is similar to that used by Snelgrove and Kashy (Sn 69) to fit proton elastic scattering from 15N at 39.84 MeV. The slope of the 115 52- 6F W0 - - ‘ r1 = L345F 01 = 0.509F ,- 48 " a; 4 '- 2 .VR 2 . ‘ " rR = LI33F K O >44-OR=0.65lF 3 2.- “ l l I 4 l l I I 4C;20 30 40 C20 30 4O ELAB (MeV) ELAB (MeV) 6- 9- W, . . Vso . I. r1 3 L345 "' r90 3 (R = 0.509 a = a 1. 4 _ 01 A 7_ so R > 6 § 2 v I- . F' . O 8 . 3 2- > 5.. h- . - . O I I I I 3 l I I 4 20 30 40 20 30 40 EU“ (MeV) ELAB (MeV) FIGURE 40. Variation of the strengths of the optical model potential found in this work as a function of energy. 116 real well depth vs. proton incident energy plot for this analysis is closer to that found by Perey (Fe 63) in an optical model analysis of proton elastic scattering on Atarget nuclei between 27A1 and 197Au (~0.55) than it is to that found by van Cars and Cameron (0e 69) in an analysis of 23-50 MeV protons on 160 (-0.29) or that found by Watson §t_a;. (Wa 70) in an analysis of 20-50 MeV protons on a number of lp-shell nuclei {-0.30 for incident proton energy measured in the c. m. frame). 5. MICROSCOPIC MODEL CALCULATIONS 5. 1 DWBA IZOA The microscopic model DWBA calculations made for this work were done with the code DWBA 70A (Sc 70). The nuclear force can include tensor and spin-orbit terms and the exchange amplitude can be included exactly. The required spectrocopic amplitudes, equivalent to those described by Nadsen (Ma 66) were calculated with the code MULTISCAT, part of the Oak Ridge-Rochester (Fr 69) shell model code modified by Duane C. Larson. DWBA 70 used the neutron-proton formalism for the interaction. For a proton incident on a proton the force is: vpp = le + V2p Y(r,,u1)+ V3p Y(r, #2) (31. 3'2) +Vh Y(I‘, #3)-I:.‘SV+ and for a proton incident on a neutron: 2 3 vpn .-.- vn Y(r, Al) + v n Y(r, 1’42) (0'1.Q'2)+Vn y(r,,143)L'S+ 5 2 V n r Y ("9. ”4) S12 le is the coulomb potential. and 812 is the usual tensor operator. The 1{(r, /41)'s are Yukawa's e'rlfi‘i “‘3 *1) 751" 117 118 5.2 Wave Functions There is evidence that the tensor force plays an important role in the A-l4 system. The th beta decay is allowed by selection rules, but is suppressed because of the particular nature of the wave functions involved. Visscher 14C and Ferrell (Vi 57) have shown that suppression of the beta decay can be obtained with 1p shell wave functions only if they are generated with a residual interaction that includes a tensor term. Also Rose 33 a}, (R0 68) have shown that ex— panding the model space into the Zs-ld shell will not elimin- ate the need for including the tensor force. Available 14N shell model wave functions fall into two classes depending on the model space used. There are the wave functions of Visscher and Ferrell (V1 57) and those of Cohen and Kurath (Co 65) that assume a closed hHe core and 8 .particles in the ip shell, and there are the wave functions of True (Tr 63) and those of Reehal, Wildenthal, and McGrory 12C closed core and two particles dis- (Re 72) that assume a tributed among the 1p% orbital and orbitals of the 23,1d shell. A better space for IAN would be a combination of the two, that is the latter space with two or four holes in 1p3/2 orbital. Such a space would be very large but there is some hope of doing such calculations at least for the 0+ states. 119 5.2.1 1 P Shell Wave Functions The 1p shell space used by Visscher and Ferrell (V-F) and by Cohen and Kurath (C-K) contains the dominant configurations of the ground state and the excited states at 2.31, 3.95, and 7.03 MbV (Ma 68) (see Table 31). In the V-F calculation, the tensor force and the LAS force are explicitly included in the residual interaction while uncer- tainties in the central potential are removed by fitting the energy levels of the first three states in 14N and the th beta decay rate. In the C-K calculation the 15 two body matrix elements and the two single particle energies needed were obtained by fitting energy levels and binding energies of the ground states with respect to the (1s)4 core.) One set of parameters was obtained using energy levels in nuclei between A-6 and A-16 and another set using energy levels in nuclei between A-8 and A216. Because the results for A=6 and 7 were not as good as those for the other nuclei fit, the latter set of parameters was judged best for IAN. The wave functions generated with this set of parameters gave a 140 Gamow-Teller beta decay of 5.42 compared to log ft for the experimental value of 9.02 (Ba 66). Although there are 4 orders of magnitude difference between the two numbers both values represent a decay rate that is strongly suppressed. Only wave functions that reproduce the suppression of this beta decay rate are of any value in the study of the 120 dHH.O IQV NMH.OI HH0.0 HOH.O NAMQV AmQ .MQV Ana .Hmv 666.6- NmN.O 6.1.: 666.6- 666.6- 6A666 666.6 666.6 6-xs6v H .m H-“ 6 66 mMH.o smm.o 61 66 H .m 4-1 6 6V bHH.o Ann .Hmv JmH.o Ann .H Hmm.o www.01 mmH.Ol NNH.OI Nxsmv 666.6 666.6 6-xs6v bHH.OI 666.6 Nxamv Nmm.o MHm.o Adm 6H my ooo.H mmm.o my ooo.H mam.o_ Amfl .Hmv OOO.H OOO.H AHm .Hmv mqo.o emm.o 6.2 6v 666.6 0mm.01 H N A 66 OmN.O 6mm.o 6.2 66 5mm.o 500.0 H 6 A 66 mHH.o bmm.o 6-x 6c #H.m Hm.m mb.N dm.N Ao¢.Nv bq.N 0.0 0.0 0.0 0.0 % >02 v humoum .mCowvocnm o>m3 z A JV Siberia Amy MDmB Athl> AHvMIU popmHSOHmo mononomom 3H 2-2-x mama Ao .-Hv 66.6 5:3-6 mama Ao .-NV HH.6 5-3-x mama Ao .-ov Hm.6 .m a > m u 6 A6 .+HV am.m EIBIZ meme 6 u > m u 6 AH ..ov Hm.m Ao ..HV 6.0 >m>62v Lona .am mqm mm 00 OOO.H mm NE OOO.H dH.m filalm mmm.0I ©N.b QDmB AHm .Hmv JmH.O mm.h MDEB Ana .Hmv OOO.H no.5 H I U 4-xs6 .662 qu.o mm.m EIBIm 500.0! H©.b mDmB AmQ 6Hmv mM0.0 Nm.¢ ZIBIm OMH.O am.m mDmB 6x666 OOO.H m©.m 2131m OOO.H O©.m W.mH x66 . 6V A.P.coov Hm Mdmda Am 3 3. 3 AH A0 AH A0 A0 A0 A0 A0 QIJV me.m Q'Hv mo.m O'NV hm.b .+Nv no.h Q+Mv 00.0 6+Hv om.m .IMV nw.m 122 IAN (P,P') 1“N” (Ex = 2.31) reaction. 5.2.2 120 Core Plus 36 Shell Wave Functions The model space used in the shell model calculation 12 for 14N published by True consists of a C core and two nucleons free to move in the lp1/2 2 s1/2, l d5/2, or 1 d3/2 orbitals. The single particle energies are taken from the energies of levels in 13C and 13N and the residual interac- tion between the valance neutron and proton is taken as a central force made up of singlet-even and triplet-even com- ponents. The radial dependence of the force is Gaussian With strength and range chosen so that the singlet-even force is the same as that used successfully by True and Ford in 208P'b. Two parameters, the ratio of the triplet-even force to the singlet-even force and the harmonic oscillator parameter of the single particle wave functions were chosen to obtain the best fit to the levels in 14N. The model space contained the dominant configurations of all the states in 1(“N below 8.49 MeV in excitation except for the 3.95, 7.03 and 8.49 MeV states. In the shell model calculation by Reehal, Wildenthal and McGrory (Re 72) 12C is taken as a closed core and the valence nucleons are free to populate the 1191/2, 251/2, and l d5/2 orbitals. The single particle energies and the two body matrix elements were obtained by fitting energy levels 123 of states in nuclei between A-13 and A-22 that should be reproduced within the model space. These calculations 1[‘C beta decay and so would not be expected to reproduce the their wave functions for the 2.31 MeV state would not be expected to reproduce inelastic scattering. 5.3 Coupled Channels Calculations The DWBA approach to inelastic scattering is essentially a peturbation approach that assumes that elastic scattering is the dominant process and that it is sufficient to treat inelastic scattering as a first order peturbation. If there are other channels that can compete strongly with the elastic scattering, DWBA is not valid. DWBA will also fail to describe interactions for which higher than first order processes are important. An alternative for such cases is the coupled—channels approach (Ta 65) in which the total wave function is expanded in terms of wave functions for all the important channels. In the coupled channels approach the interaction is not treated to first order only but to infinite order within the space defined by the channels included (Ta 65). It was not practical to do a coupled channels calculation here, but there is evidence that such a calcula- tion would not be a great improvement over DWBA for the 1[‘N (p,pl) 14N*‘(2.3l MeV) reaction for the incident proton 124 energies involved here. F. A. Schmittroth (Sc 68) did a coupled channels calculation for the A-l4 system and com- pared the results to DWBA for the reaction 140 (p,n) 14N for 14.1 MeV incident proton energy. This reaction is the parallel to the 14N (pipi) 14N (2.31 MeV) reaction. The channels coupled were 14C + p, 1“N + n, 14N* (2.31) + n, and 14N* (3.95) + n. For the 14N (p.P}) 14N (2.31 MeV) 1[‘0 + n, reaction the appropriate channels to couple would be 14N + p, 14N* (2.31) + p, and 14N* (3.95) + p. To within the 20% accuracy of the DWBA calculation there was no effect on the 14C (p,n) 1[‘N transition due to coupling. Since the effects of coupling should decrease with increasing proton bombarding energy (Ma 71), coupling should not be important for the 14N (p,p’) 14N (2.31 MeV) reaction at the energies of this work. 5.4 Two-Step Processes For a relatively weak interaction like the 1"N (10.0") 1“N" (2.31 MeV) reaction [its strength is 1/10 that of 14N (p,p‘) 14N* (3.95 MeV)] the contribution of the two-step processes such as 14N (pad) 13‘N (dfp) 14N* (2.31 mov) should be considered. Calculation of such processes are very difficult. No proven computer code was available for such a calculation at M.S.U. and so we did not have the opportunity to look into such processes. 125 5.4 Nuclear Forces A number of different combinations of central, tensor, and spin-orbit forces were tried in DWBA calculations for the 2.31 mev state inelastic scattering. Since the shape of the calculated cross section is controlled by the interb play of the central and tensor force, central and tensor forces that had some connection to realistic forces were favored. Thus most of the.calculations were in some sense apriori. 5.4.1 Fitting Central Interactions to the Yukawa Radial Form Where necessary the strength and range of the Yukawa potential corresponding to a given central potential was found by matching the volume integral and r2 integral of that given force to those of the corresponding Yukawa. The ranges for different terms of a given potential and for the corresponding Yukawa's terms were often different (see Table 32). It was generally possible to choose some average range for the Yukawa potentials and calculate the strength from the volume integrals. This cut down calculation time. Check calculations were made to insure that the cross sections predicted by the average range potentials did not differ greatly from those predicted by the original potentials. 126 5.5.2 Serber Central Potential (5) A Serber central interaction(S) (V00: V01: V10: V11 - -3:1:l:l) with a V11 strength of 3.47 MbV was taken from the work of Love 35 3;. (Lo 70a). The range, [A , had been taken to be the pion.wavelength (1.415 F) and the strength chosen to best describe the small momentum components of the truncated Ramada-Johnston potential. Contributions to V00 central forces arising from second order tensor force terms were included. 5.5.3 Even State Ramada-Johnston Central Potential .011). A central force with a non-Serber mixture was obtained from the even parts of the Ramada-Johnston (H2 62) potential (HJ). The volume and r2 integrals were done following the Moszkowski-Scott separation procedure with a cut off distance of 1.05 F. The results are found in Tab1e(3ZL 5.5.4 Even State Hamada-Johnston Potential Plus 11? State Gaussian Potential (HJ-G) The Moszkowski-Scott separation procedure applies only to the even parts of the Hamada-Johnston potential. Owen and Satchler (Ow 70) replaced the 1P state Hamada- Johnston potential by a repulsive Gaussian [1! . 120 exp mmHm.o HO.HH 6mH6.6 o 127 mmmo mdm.o H.m mam.o Od.os 666.6 "666-656 6-66 O.H o.HH O.H O.HH O.H o.HH o.H O.mN1 Nm.o N.me1 >NM.0 N.®MH1 mwm.o N.®MH+ a 6 66.H 6.6 6.6 6a.H 6.6 6.6 66.6 6.6H 6.66 66.H 6.66- 6.66- 6.H «an. 66 66 .moouom noncov 6:6 Hmuvcoo uohmcmnp mammomH at pommcmap :HQmomH s mH¢.H h¢.m mH¢.H h¢.n mH¢.H b¢.n mH¢.H H¢.0H1 m A>ozv .¢a> .313 E a... 965 1...; E 2:. A>ozv HH> 3641 A>ozv 66> E 81 A>osv H6> Amy 00; A>ozv 66> Hmwvcopom .66 666 but for the hard core Hamada-Johnston tensor potential the integrals went in to r . 0.49 F. This was as close to the hard core radius (0.485 F) as it was possible to conveniently integrate. The tensor force is nearly independent of this choice and is similar to OPEP, in that VTT(the strength for a AT=1 reaction) is much greater than VT (the strength for a AT=O reaction). (See Table 32.) 5.5.8 Spin-Orbit Potential A spin-orbit potential was derived from the Hamada- Johnston spinporbit potential by matching the J“ and J6 integrals of the two terms of this potential to the same integrals of two Yukawas. Perhaps the best estimate of the strength was obtained for a cut of distance of 0.49 F. In 131 Table(33)are listed the J4 integrals for a number of spine orbit potentials taken from the literature (Au 72). The strength of the Ramada-Johnston spinporbit force with a 0.49 F cut off radius is in good agreement with the forces used by Love and that used by Austin. While the J4 integral for the spin-orbit potential implied by the empirical optical model is larger, it is difficult to estimate the effect of exchange for this potential. II 9'“!7.1’ " a" .. . ‘Iv 7a.! 5.5.9 "Complete" Ramada-Johnston J.-L. Escudie, F. G. Resmini, and Y. Terrien (Es 72) have made an attempt to fit the Fourier transform of the long range part of the complete Ramada-Johnston potential except for the quadratic spin-orbit term to Yukawa's and r2 - Yukawa's using three separate ranges for the Yukawas. The central potential is for a separation distance of 1.05 F and corrections for 2nd order tensor terms are included. The cutoff for determining the tensor force was 0.5 F and for the LS force 0.7 F. Thus one expects that their Les force is perhaps too weak. The method of conversion.was by fitting Fourier Transforms in a manner similar to that de- scribed earlier. 132 TABLE 33, Values of the spin-orbit force? Determination J4 (T s 0) (Nev - F5) Optical Model - 8) V30 - 607 MeV -80 Love 9OZr (p,p') b) -37.6 160(p.p') 160 (8.87, 2', 0) C) ’50'8 HJ d) rC = 1.0 F - 7.3 rC = 0.6 F -27.7 rc = 0.49 -34.9 (MeV - F5) -1502 -3202 - 6e5 ‘1307 ’16e2 a) Ref Gr 68 b) Ref Lo 71 0) Ref Au 72 d) Sc 71 LS form: VLS - [vLS (T = 0) + vLS (T = 1) 5(1. . 5(2) ,1. ‘E 133 5.5.10 Central Potential for Inelastic Scattering to States other than the 2.3;MeV State For calculations for inelastic scattering to states other than the 2.31 mev state a Serber central force with v11 of the wave functions and reaction theory. = 3.47 MeV and range 1.415 was used. Here the test was I) 6. RESULTS 6.1 Results for Calculations of Inelastic Scattering_to :- the 2.31 MeV State 1k The results of DWBA 70 calculations for the central plus tensor forces described earlier are found in Figures (43 to 47). Certain characteristics are general to all these results. It is clear that central forces alone cannot reproduce the shape of the 2.31 MeV angular distribution. In Figure 47 we have the results for the Serber central force, S, direct and with exchange. These results are typical. The calculated shape is too bread with too gentle a slope at forward angles. The tensor force alone also cannot reproduce the shape of the data. The angular distri- butions calculated for OPEP alone are found in Figurel4ll At 24.9 and 29.8 MeV these calculations overstate the shape of the experimental cross sections. At 36.6 and 40.0 MeV the situation is complicated. While OPEP alone does not fit the data, it seems to do slightly better at forward angles than central plus OPEP calculations. See Figure(4ZL The results for OPEP are very similar to those for the tensor force derived from the Hamada-Johnston tensor force (HJ-T). See Figure (42). 134 135 103 7 2&8 HEU 89.8 “EU DIFFERENTIHL moss SECTION - (pa/SR) DIFFERENTIHL cnoss SECTION - (es/3n) 0 30 80 N 120 150 180 0 30 80 N 120 150 180 C-H HGLE - (EMS) C-fl m - [MEI-TEES) " 36.8 1120 40.0 1120 DIFFERENTIRL CROSS SECTION - OLD/SR) DIFFERENTIFIL CROSS SECTION - [Fa/SR) O 30 60 90 120 150 180 C-fl ME - (DEGREES) FIGURE 41. 1L"F:(p,I.~-)1L‘1~T* (2.31 MeV) calculations with OPEP alone. 136 While the final calculations were made with the Cohen-Kurath wave functions and optical model parameters obtained as part of this work, Visscher-Ferrell wave func- tions and other reasonable sets of optical model parameters yield essentially the same results. Calculations for Visscher- Ferrell wave functions are compared to those for the Cohen- Kurath.wave functions at 29.8 and 40.0 MeV and calculations for the optical model used by Crawley 23,31, (Ca 70) are compared to those for the optical model parameters of the present work at the above energies in Figure(42) The shape of the resultant calculations and the degree to which they agree with the data is mainly a function of the interplay of the central and tensor forces and the strength or range of the central force. At 24.8 and 29.8 mev the central plus tensor direct calculations overstated the shapes of the experimental angular distributions. The rise at forward angles and the height of the second.maxima in the calculated angular distributions were too great. In calcula- tions with exchange at 24.8 and 29.8 MeV the shape is either reproduced well or washed out depending on the strength or range of the central interaction. For central plus tensor calculations at 36.6 and 40.0 MeV the direct results come closest to reproducing the tensor only shape and thus the data. With exchange included the shape of the results deteriorate in general except when the central interactions are weak. The inclusion of the spin-orbit force does not 137 U-F [H.F.) OIFFERENTIRL CROSS SECTION - [pa/SR) DIFFERENTIHL CROSS SECTION - 018/ SR] s 1.} 3 5 2 l. 3 1 20 so so so 120 ISO 190 a so so so 120 150 180 c-n fiNGLE -[DEGREES] c-n HNGLE -(o£sness) w a 3 a 2 g 5 g 102 E 109- I s I z ‘I z 0 o a 3 a U U 2 (Cr 70) 0.11. g 3 mrrmtut U) (D 3 m g m s s 4 s on.ntaan an: J 5 g - 55, ., E 3 E 3 5 2 E 2 t t S 1 3 1 5 s l'0 so so so 120 150 180 L'o so so so 120 150 180 C-fl WE - (DEGREES) C-fl FNSLE - (DEGREES) FIGURE 42. 1L‘N(p,p')1“1~:* (2.31 MeV) calculations with. OPEP and HJ-T alone at 40.0 MeV (A); V-F and C-K wave functions with S + OPEP at 29.8 MeV (B); and optical model parameters of Cr 70 and this work with S + OPEP at 29.8 MeV (C) and 40.0 MeV (D). 138 TABLE 3#. Comparison of central forces. Central Force HJ HJ-G ' BJ SMA 8 Range (F) 1.0 1.0 1.359 1.0 1.415 “1' calculated with ; exchange (mb) 2 (Ep a 29.8 MeV) 0.483 0.217 0.492 0.536 0.214 Ordered by goodness of central + OPEP fit with exchange a) 4 3 2 5 1 a) Fits to data rated by eye (1 s best) 139 change the shape of the results greatly. See Figure(48l 0f the central forces tried those most directly related to realistic forces were those taken from the even parts of the Ramada-Johnston potential (HeJ); the central force made up of the H-J potential plus a Guassion singlet odd potential (HJ-G); and the central Blatt-Jackson potential (B-J). The results for the H-J and HJ—G plus the Hamada- Johnston tensor force (HJ-T) are found in Figures(43)and(A4L The HJ-G potential was put together to see if a force with both odd and even components would make a noticeable difference. The HJ-G central is weaker than the H-J potential in calcula- tion with exchange. The total cross section for the H-J at 29.8 MeV is 0.483 mb and that for the HJ-G is 0.217 mb. See Table(34). The HJ-G thus fits the shapes somewhat better. but the improvement is not great, and is probably due to the relative weakness of the force. The results for the B-J potential plus OPEP are found in Figure(45L The H-J and B-J potentials are about equal in strength. The range of the B-J potential however is longer, ”A . 1.359 F than the 1.0 F range H—J central. For the H-J plus HJ-T force the shape of the cross section for calculations with exchange is in poor agreement with the data at all energies, while for the B-J plus OPEP calculations the shape at 2h.8 and 29.8 mev is in good agreement with the data. The B-J central plus OPEP interaction does not do as well at 36.6 and 40.0 mev. 1&0 7 29.9 nsu DIFFERENTIRL CROSS SECTION - Uta/SR] DIFFERENTIRL CROSS SECTION - (pa/SR) 0 30 80 W 120 150 180 0 30 80 W 120 150 180 C-fl FNGLE - (MGREES) C-fl FNBLE - (DEGREES) ‘* ss.s neu . ‘* mo neu h. 10 DIFFERENTIRL CROSS SECTION - Use/SR] DIFFERENTIRL CROSS SECTION - Uta/SR] O 30 80 90 120 150 180 C-fl MGLE - [E88585] n 1 .* . FIJURE #3. “N(p,p')1h (2.31 MeV) calculations for HJ central plus HJ-T. 141 2&8 HEU 29.8 [EU DIRECT DIRECT DIFFERENTIRL CROSS SECTION - (pa/SR] DIFFERENTIRL CROSS SECTION - OLE/SR) 0 30 60 90 120 150 180 0 30 60 90 120 150 180 C-fl WLE - [DEGREES] C-fl MGLE - [MST-TEES] 38.8 ”EU I. 3 DIFFERENTIRL CROSS SECTION - 0.8/an DIFFERENTIRL CROSS SECTION - boa/SR) O 30 SO 90 180 150 180 C-H m - (CEBFEES) C-l‘1 FNSLE - [MGREESJ ' * FIGURE an. 1L’N(p.p')“‘N (2.31 MeV) calculations for HJ-G central plus HJ—T. 142 29.8 ”EU E 29.8 [EU wxuw m T I - DIFFERENTIRL CROSS SECTION - 018/ SR) DIFFERENTIRL CROSS SECTION - us/sa) 0306090120150180 0308090120150180 c-n RNGLE - (DEGREES) c-n RNGLE - (DEGREES) " “ I+0.0 mu 3 5 5 a ‘ a .3 I I 5 5 H H r- t- s s U) m U) é, g 9.3 23. P E g a U IA. IL 3 a ”0 so so so 120 150 180 0 so so no 120 150 180 c-n mete - (DEGREES) c-n RNBLE - (DEGREES) ‘I' FIGURE #5. 1hN(p,p')1hN (2.31 MeV) calculations for BJ central plus OPEP. 143 The results for the central potential taken from the survey by Sam Austin (SMA) plus OPEP are shown in Figure (46L The 1.0 F range SMA central force yields a total cross section for the 29.8 mev inelastic scattering to the 2.31 state of 0.536 mb. This is slightly stronger than the H-J central potential, and it fits the data about as well as the H-J potentials. The conclusion that these results lead to is that the best central force to use should be relatively weak in strength and long in range (see Table 34). 0f the central forces tried here, the weakest and longest range force that still was derived from a realistic force, was the Serber central force (8) with V11 strength 3.47 MeV and range 1.415 F. The results of the calculations with S + OPEP are found in Figure(41L This central force plus OPEP probably best reproduced the shape of the data at the four energies con- sidered. The S central interaction seems like the best central force to use in drawing conclusions about the strength of the tensor force. When the 0.49 cutoff radius Hamada-Johnston spin- orbit potential was added to S + OPEP, the total cross sections decreased by about 25% and changed somewhat in shape. See Figure(48i Since it was felt that this was a good estimate of the spin-orbit potential, it was decided to include this potential when extracting the strength of the tensor force. The force of J-L Escudie gt 3;. produced the results 144 29.8 I'1EU OIFFERENTIRL CROSS SECTION - 048/ SR) DIFFERENTIRL CROSS SECTION - 0.9/an 60 W 120 150 180 c-n FNGLE - [DEGREES] DIFFERENTIRL CROSS SECTION - 018/ SR] DIFFERENTIRL CROSS SECTION - (pH/SR) 80 90 120 C-I'1 RNGLE ' [DEGREES] 150 180 FIGURE 46. 1“N(p,p-)1“N* (2.31 SMA central plus OPEP. 89.8 ”EU N wxmw [11!] l I I .. o ru (LT-‘01 r I [Tlllll mw:w l ..a 60 90 120 C-fl MGLE - [DEGREES] 150 90 120 C-fl RNGLE - [DEGREES] O 30 60 150 MeV) calculations for 145 3 1° 29.9 nEu ; 20.8 RED q q ‘ I )08 )02 . i ~ I q ‘ CENTRRL ONLY be r v I. I V\/ ‘ DIFFERENTIRL CROSS SECTION ' bib/SR) -‘ a; m - I - - I OIFFERENTIRL CROSS SECTION ' Dab/SR) S DIRECT '9. q DIREcT v ' J mm my CENT Rfl. MY DIRECT 1 DIRECT lo 30 so so 120 150 180 0 so so 001-: 150 100 c-n RNGLE - (DEGREES) c-n RNGLE - (DEGREES) " ss.s nEu “ no.0 "EU S 8'; , k 1' J 3 1a .3 ' ' ' ' DENTRRL MY 5 a my 3 " Exam H - m a :3 A . Q .~ 8 ’ ~ g I .- I \ g 10 ‘—,' - I g 10 I I ~ . i S d . d 1., . I H H g Q Emu-mos ‘* DERTRRL am I; DENTRRL 0m H 1 DIREcr 0 so so so 120 150 180 *0 so so 00 120 150 180 c-n RRGLE - (DEGREES) c-n RNGLE - (DEmEES) FIGURE 47. 1“N(p,p')mN* (2.31 MeV) calculations for 5 central plus OPEP and S central alone. 146 29.9 flEU 7 29.9 r1EU a . s a q E 3 s a a . . m3 me E 5 . :1‘ c 5 S s S '* ' m L. U) 3 . f a 3 g 2 - IMI’ O 2 o I I. I 5 5 1° EXCHRNGE 2’ 2’ ' E 10 H z '5 5 E E 9 u 3 DIRECT w 3 u. u. h 3 h 2 O C) 2 O 30 80 80 120 150 180 0 30 80 90 120 150 180 C-fl RNGLE - (DEGREES) C-fl RNGLE - (DEGREES) 38.8 flEU l00.0 "EU DIFFERENTIRL CROSS SECTION - [pH/SR) DIFFERENTIRL CROSS SECTION - 049/ SR) 0 30 80 90 120 150 180 0 30 80 90 120 150 180 C-l'1 RNGLE - (DEGREES) C-fl RNGLE - (DEGREES) * FIGURE 48. 1LFN(p,p')1uN (2.31 MeV) calculations for S central plus HJ-LS and OPEP. w; in Figure(49L The shape is reasonable for lower energies but deteriorates rapidly as one goes to higher energies. There is also evidence that other than direct processes are contributing to the 24.8 mev angular distribu- tion at backward angles. Central plus tensor forces that reproduce the dip at about 140° C. M. in the 29.8 mev data also predict a dip for the 24.8 mev cross section. There is no dip in the data. See Figure(47)for example. After it was established that the best essentially apriori fit to the 2.31 MeV state data is obtained with the Serber central force plus OPEP and the Hamada-Johnston spin- orbit potential (rc = 0.49 F). calculations were made in which the strength of OPEP was varied to see what ratio of central strength to OPEP strength would best reproduce the shape of the experimental data. The results for the Serber central plus the Hamada-Johnston spin-orbit plus OPEP; OPEP with a 25% increase in strength (1.25 x OPEP); and OPEP with a 40% increase in strength (1.4 x OPEP) are found in Figures 50, 51, and 52. These calculations were scaled to best fit the data, with emphasis on the foreward angle data. The scale factors are found in Table (35). Of the three tensor forces used. the 1.25 x OPEP force best fits the data overall. At 24.8 and 29.8 MeV the calculations with 1.25 x OPEP are a definite improvement over those with OPEP. The distinction is not so clear at 36.6 and 40.0 MeV, but the calculations 148 3 ‘0 29.9 nEu o-o- DIFFERENTIRL CROSS SECTION - (pa/SR) DIFFERENTIRL CROSS SECTION - 003/ SR) 0309000120150190 0309090120150190 c-n RRGLE - (DEGREES) c-n RRGLE - (DEGREES) DIFFERENTIRL CROSS SECTION - WSR] DIFFERENTIRL CROSS SECTION - (..9/ SR) O 30 80 90 120 150 180 C-fl MGLE - (DEGREES) FIGURE “9. 14N(p.p,)14N* (2.31 MeV) calculations for the complete Hamada-Johnston potential as put into Yukawa form by Escudie fl (BS 72). 149 105, 5 o 29.9 "EU x 125 :' n 29.9 (EU x 25 ..i *' A 38.8 MB) x 5 3:, H“ v 90.0 "EU 10 s :- . I I: h C) {1' 103.. U E “J - w : U) L— 00) )- 5 102E —l I: .‘E. t: t- +- E, L- S t 10? H :: C3 - 1 i_ 1 l 1 ll 1 J 1 l,_1 L, 1 n 1 l i ll J o 30 so 90 120 150 190 C-fl RNGLE - (DEGREES) ' 4!» FIGURE 50. 1LLI‘I(p.p')mN (2.31 MeV) calculations for S central plus HJ-LS plus OPEP. Calculations are normalized to best fit the data at forward angles. 150 105: ' : o 29.9 HEU x 125 5 n 29.9 REU x 25 P A 38.8 "EU X 5 - v 90.0 ”EU 10"? C )- 103:. L’ L. 108 T rlllml 10 DIFFERENTIRL CROSS SECTION - ( 9/89) I llllilll 1 1. 1 l 1 1, l 1 1, 1 .1 J. l 11 1. l 1 1.lJ 0 30 60 90 120 150 180 C-l‘1 RNGLE - (DEGREES) * FIGURE 51. 1uN(p,p')1L‘N (2.31 MeV) calculations for S central plus HJ-LS and 1.25 x OPEP. Calculations are normalized to best fit the data at forward angles. 151 105:. E o 29.8 (“EU X 125 t: a 29.9 nEu x 25 - A 38.8 ”EU X 5 (if) i” L(0.0 ”EU 10"— 5 . t 2 L CD '11‘ 103;. C) : UJ b a) C a) p- (D P 8 o 103:. .1 5 (E h— ffi F 1— .. I: w 1— 1‘5 1.. 1°? u_ _ H 1?. C3 _ 1 1 1 .1 1 '1 l 1 1 l 1 1 l 1 .1 l 1 1 l O 30 80 90 120 150 180 C-fl RNGLE - (DEGREES) *- FIGURE 52. 1L‘N(p,p')mN (2.31 MeV) calculations for S central plus HJ-LS and 1.4 x OPEP. Calculations are normalized to best fit the data at forward angles. 152 TABLE 35. Calculation normalization factors. Interaction Proton Energy Normalization (MeV) Factor 5 + L z 8 (HJ; rC = 0.49 F) 24.8 2.5 + OPEP 29.8 2.0 36.6 1.4 40.0 1.8 s + L e 5 (HJ; rc = 0.49 F) 24.8 1.95 + 1.25 x OPEP 29.8 1.40 36.6 0.93 40.0 1.18 s + L z 3 (HJ; rC - 0.49 F) 24.8 1.50 + 1.4 x OPEP 29.8 1.12 36.6 0.88 40.0 0.95 153 With 1.25 x OPEP fit the data over a slightly larger range of forward angles than do those with OPEP. There is almost no difference between 1.25 x OPEP and 1.4 x OPEP for the 36.6 and 40.0 Kev data and at 24.8 and 29.8 Rev, 1.25 x OPEP yields slightly better fits than does 1.4 x OPEP. The 1.4 x OPEP calculations overstate the forward angle drop of the experi- mental angular distributions at 24.8 and 29.8 MeV. Comparison of the 24 Rev, 1l“1\1(p,p')1’+1\'* (2.31 Kev) asymmetry data of Escudie g1_gl. (es 70) with our calculations for 24.8 Kev incident protons indicates better agreement when the spin-orbit force is included. 0f the measured inelastic scattering angular 14N only those to the distributions to the other states in 3.94 and 7.03 Rev states are expected to be properly described by Cohen and Kurath wavefunctions and consequently only these were analyzed in any detail. For both of these cases, the calculated total cross sections for 3’: 2 dominate those for the other possible 3 transfers. It is expected that these transitions are mainly S = 0, L = 2 and so the calculated cross sections were enhanced by a factor equal to the ratio of the experimental E2 reduced transition probability to the reduced transition probability calculated with Cohen-Kurath wave functions. The experimental E2 151. 3 2 o 29.9 RED )1 9 A 103 a 29.9 REU x 9 35 A 36.8 REU x 2 E 5 v 90.0 ”EU ._. 3 1 E! ' g 102 E 3,1 5 a) 3 g 2. a, 10 E 5 5 s 0: g 2 E: 1 s :3_ 1 l 1 ill 1 J - 0.0 1.0 ' 2.0 w 9.0 HOHENTUH TRRNSFER IF") it FIGURE 53. 1L’N(p,p')1uN (2.31 MeV) calculations for S central plus HJ-LS and OPEP plotted as a function of momentum transfer. The symbols are for identification only. 155 reduced transition probability for the 3.9h to g.s. transition was taken to be 9.0 1 0.6 ezFu (01 67) and for the 7.03 to g.s. transition, 3.4 1 0.9 eZFu (Cl 67). The respective calculated reduced transition probabilities were 1.7 and 0.8 22?“. The enhancement ratios were 5.3 and b.3. The angular distributions were calculated the Serber central interaction (S). For the 3.94 MeV state, the enhanced calculated cross sections are of the correct magnitude. (See Figure 5b.) This is not the case for the 7.03 MeV state. (See Figure 55.) While the remaining inelastic scattering data is yet to be analyzed in detail, it should be pointed 14 out that the calculations with the N wave functions of 14 True (Tr 63) and those with N wave functions from the work of Reehal gj_al. (Re 72) produce the same results. DIFFERENTIHL CROSS SECTION - (MB/SR] 10a 10 10"1 *I I l IIII] I *I 1’ I II III] I ITIIIq* I*T IIIIIq I Figure 5h. 0 89.8 “EU X 85 0 A 38.8 ”EU X S v H0 HEU 1 1 l 1 .1 l 1 1 1 1 1 l 1 1 l 1 .1__J 30 80 90 120 1'50 180 c-n HNGLE - [DEGREES] *- 1L‘L.\’(p,p')1ul\l (3.94 meV) calculations for S central and C-K wave functions normalized by the experimental to calculated E2 transition ratio. DIFFERENTIHL CROSS SECTION - (MB/SR] 111 1J 150 180 111111111111 1 0 30 80 90 180 C-l‘1 HNGLE - [DEGREES] 11 . * 4N(p,p')1uN h Figure 55. (7.03 meV) calculations for a central and C-K wave functions normalized by the experimental to calculated 32 transition ratio. 7. CONCLUSIONS The interaction that best fits the shape of the inelastic scattering to the 2.31 MeV state in 1“N at 24.8, 29.8, 36.6, and 40.0 MeV was a Serber central interaction plus the Hamada-Johnston spin-orbit potential (rc = 0.99 F) and OPEP with a 25% increase in strength. The overall normalization factors for the calculated angular distributions with this force are found in Table (35). The J4 integrals of the tensor potentials implied by these results are found in Table (36) along with other estimates of the strength of the tensor force as compiled by Sam Austin (Au 72). The tensor strength obtained by this analysis of inelastic scattering 1“N (probably the most complete to to the 2.31 MeV state in date) seems to be greater than that of earlier works. One must keep in mind that the spin-orbit potential was included in this analysis, but not in the other results in Table (36). Inclusion of the Hamada-Johnston spin-orbit potential re- sulted in a 25% reduction in the calculated total cross section and a 12% increase in the required tensor strength. The results of this work also included the effects of ex- change. It is not clear how exchange effects the strength of the extracted tensor force. In calculations made for this work with OPEP alone, the direct calculated total cross sections were about 25% greater than those with exchange. 0n the 158 159 TABLE 35. Values of the tensor force. Determination 1“N (p.p‘) 1“Nb?” (2.31 MeV, 0*, 1) Ep a 24.8 29.8 36.0 40.0 14c (p. n) 1“N (g.s) (b) 12.7 13.3 1803 (15.1 nev, 1*, 1) (0) Ep 3 “505 (2.31 nev, 0+, 1) (d) Ep = 24.8 MGV 29.8 VTK (MeV) «(F-1) 6.56 5.70 4.70 5.35 5.4 5.1 5.1 3.9 2.35 3.9 14.6 1.23 1.23 1.23 1.23 0.707 0.707 .o.7o7 0.707 0.707 00707 1.23 2(F‘1) 4.0 4.0 4.0 4.0 2.0 J4 (MeV-F5) 555 470 597* 454 444 420 420 321 200 290 421* 160 TABLE 36 (con't.) lp - shell, two body (e) matrix elements . 5.1 0.707 A.O 420 OPEP 318 HJ(f) (rC a 1.0 F) ‘ 288 (rC = 0.6 F) 294 (rC = 0.99 F) 295 a) Present work; only the present work includes the spin-orbit potential. Results including exchange are marked (*). b) Reference W0 71: uses ROPEP form: VT (r) = (v... + Yuk, . a2 ) 312 me) - 97 man 9": -‘I . I .A o- + i + —27 din-.- mr) c) Reference L0 700. OPEP form. d) 24.8 MeV: Reference Cr 70, ROPEP form. 29.8 MeV: Reference F0 71, r2 - Y form. 2) "Reference Sc 68, determined by Schmittroth from Cohen—Kurath lp-shell two body matrix elements involving the 1*, T=O and 03, T=1 states only. f) Reference Sc 71. For the part of the Hamada—Johnston potential with r z, rC. I'll" lull...l I II III 11:- . 1. I I'll! 161 other hand, for central force calculations the exchange total cross sections were greater that the direct. For Serber central potential plus OPEP, the direct total cross section was larger than that with exchange. It is not clear that the results of the present analysis can be directly compared to the earlier works listed 1“C (p,n) 1“N (gs) works were at proton in Table (36). The energies for which compound nuclear effects can be important. Evidence for other than direct effects in the 20.8 MeV data has already been discussed (Section 6.1). The 14N (p,p') analysis of Reference Cr 70 at 29.8 MeV used a tensor force quite different in form from OPEP. It might be pointed out that there is something of a trend toward decreasing tensor strength with increasing proton energy in the results of this analysis. It is most clear for E = 24.8 and 29.8 MeV where the fits to the data P were more conclusive than at 36.6 and 40.0 MeV. 8. SUMMARY The work of extracting the strength of the tensor force from calculations of inelastic scattering of protons from the 2.31 MeV state of th is not complete. While this is the most complete analysis to date, the fits to the data, especially at 36.6 and h0.0 MeV are not as good as one would like. The fact that OPEP alone seems to reproduce the shapes of the angular distributions better than the complete force, indicates that perhaps the wave functions are not reproducing completely enough the cancellation of the L a 0 central amplitudes. 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If one assumes that the cross section is flat, that the back aperture is a rectangle, that the front and back slits are of equal width, that the difference betwen e, e'1 , and 8“ in Figure(3) can be neglected, and that the distance between some point along the line source and some point on the back aperture does not change with the height of that point on the back aperture, the integration is simple and results in the following formula for G. can “‘17: where C a the front and back slit widths b = the distance between the front and back slits a = the distance of the back slit from the center of the gas cell h = the height of the rear aperture d20' d8 For«%fi}1and set to zero, for slits meeting the 168 conditions above, and for 9 - 90° agreement between the program G-FACTOR and the above formula was good to 3%. Al.2 Kinematic BroadeninggEstimate The analysis that leads to the full-width at half a... maximum (f.w.h.m.) of detected peaks first due to kinematic E: broadening and the acceptance angle of the slit system is 2 most straight forward at 6 . 90°. Since kinematic broadening 1 is near its maximum at this angle, this estimate is quite useful. It is carried out here only for telescopes with front and back slits of equal width. Figure (A1) shows the geometry involved. The height ‘of the peak due to particles scattered at 6L - 90° will be proportional to the length C. Particles scattered at slightly larger or smaller angles than 90° and allowed by the slits to be detected must come from slightly shorter lengths of bombarded gas. The angles that correspond to particles from lengths of gas C/2 will correspond to the half height points of the peak. The dashed lines in Figure (A1) represent this situation and from this figure it is easy to see that the A 6 corresponding to the half heighth of the peak on one side is are ten 2%. The angle corresponding to the energy spread between the two half height points is just 2A9 or 2arc tan 2%- a- g. 169 ARC TAN A6 .- c/2b FIGURE A1. Collimation slits defining the line source at 900 in the Lab. 170 A2. TRANSFORMATIONS OF NUCLEAR FORCES FROM ODDbEVEN, SINGLET-TRIPLET FACTORIZATION TO SPIN, ISO-SPIN AND NEUTRON-PROTON FACTORIZATIONS A central nuclear interaction expanded in terms of the total spin state (singlet S or triplet T) of the two- nucleon system and its relative angular momentum [even (E) or odd (0)] can be expressed in terms of exchange and spin de- pendence by means of the transformation below; tgsao,T20)-:%(3tSE+3tTE+tSO+9tTO) txsa o, T a l)-if% (tSE - 3 tTE - tso + 3 tTO) tIss 1, T - 0)-if% (-3 tSE + tTE - tso + 3 tTO) t(s- 1, T . 1)- f%»(-tSE - tTE + tSO + tTO) DWBA 70 uses neutron-proton representation for the nuclear force. The corresponding combinations of the tST's for this representation are tpp(S . o). tnn(S = o)- too + t01 tPals ‘ 1)' tnn (S ’ 1)' tlo * t11 (S s 0). t0 - t tpn 01 tpn (s . 1)= tlo - t11 The tensor and spin-orbit potential act only in O triplet or S - 1 states. Thus there are only triplet odd 171 (V1.0) and triplet even (VTE) terms in that formalism and T - 0.(V,r) and T - 1,(V.1.1) terms in the spin iso-spin formalism. The connection between the two is as follows: 1 VT - z; (vTE + 3 v1.0) 1 VT». ' 1; (’VTE * VTO) The combinations of VT and VT?» that make up the tensor force input to DWBA 70 are below: VTpn ' VT ' T‘K The same transformations hold for the spin-orbit force. 93 IIIJIIIISHLIIIIIILIIID' 31