LA-7828-T Thesis UC-34a Issued: May 1979 Neutron-Proton Radius Differences and Isovector Deformations from n+ and ir Inelasiic Scattering from 18O Steven G. Iversen* - NOTICE- This report was prepared as an accounl of work sponsored by the United Slates Government. Neither the United Stales noi the United States Depart men t of Eivrgy. nor any of their employees, nor any of their contractors, su be oni factors, or their employees, makes any warranty, express or implied, or assumes ai:y legal liability or responsibility for the accuracy, complett-wss or usefulness of any information, apparatus, product ur process disclosed, or represents thai its use would noi *Visiting Staff Member. infringe privately owned rights. Vih CONTENTS LIST OF TABLES vi LIST OF FIGURES viii ABSTRACT xi Chap ter I. INTRODUCTION 1 II. EXPERIMENTAL SET-UP 16 A. The EPICS Facility 16 B. The 18O Targets 24 C. The Spectrometer 30 D. Particle Detection System 33 III. DATA ANALYSIS 43 A. Angular Binning 43 B. Peak Fitting 44 C. Normalized Yield 45 D. Cross Sections 45 E. Corrections 47 F. Beam Contaminants 48 G. Experimental Results 50 H. Overall Errors 58 IV. THE STRUCTURE OF 18O 78 A. Experimental Information 78 B. Theoretical Description 93 V. DISCUSSION 104 A. Elastic Scattering 108 B. Inelastic Scattering 121 C. Discussion of Inelastic Results 140 iv Appendix A. EPICS OPERATION 155 B. SOFTWARE DETAILS 161 I. The EVENT ANALYZER 161 II. The TEST FILE 165 III. The DISPLAY PACKAGE 169 IV. Run Analysis I70 V. Calculation of Missing Mass 171 C. CHAMBER CALIBRATION 173 I. Front Chamber Calibration I73 II. Drift Corrections for Rear Chambers 176 D. DETAILS OF DATA ANALYSIS 183 I. Angular Binning IS3 II. Peak Fitting I88 III. Yield Calculation 191 IV. Cross Section Calculation 194 V. Total Errors 200 E. THE OPTICAL MODEL 202 I. Multiple Scattering Theory 202 II. Optical Model Potential 205 III. Corrections to the Optical Potential 208 IV. The Program DWPI 211 F. TABLES OF DATA 217 ACKNOWLEDGEMENTS 232 REFERENCES 233 LIST OF TABLES Table 1-1. Characteristics of resonances in the pion-nudeon system. 4 1-2. Fitted values for IT p and TT p total cross sections. 6 II-l. Characteristics of the EPICS pion beam. 21 II-2. Straggling AE due to substances in the EPICS beam. 21 II-3. 180 target content and target window impurities. 26 II-4. Characteristics of detectors used in these experiments. 32 II-5. Sealer, TDC, ADC quantities. 41 III-l. Summary of integrated cross section results for states 55 in 180. III-2. Experimental energies for ail states observed in the 57 present experiment. III-3. Experimental energies for the 4j,02,22 unresolved 57 triplet of states at 3.56,3.63,3.92 MeV. IV-1. Energy levels of i80. 80 IV-2. (a) Spectroscopic factors for the single nucleon trans- 82 fer reactions 170(d,p)180 and 19F(d,3He)180. (b) Spectroscopic factors for the neutron pick-up 83 reactions 18O(p,d)170 and 18O(d,t)17O. IV-3. States in 18O from 16O(t,p)18O. 84 IV-4. Experimentally determined percentages of components of 85 wave functions for states of 180. IV-5. (a) Transition strengths for the 2* and 37 states in 90 180 by inelastic scattering. (b) Transition strengths for states in 180 by lifetime 91 measurements. (c) Measurements of the quadrupole moment of the 2\ 91 state of 1&0. IV-6. (a) Theoretical predictions for electromagnetic 94 transition rates for states of 180. (b) Theoretical presictions for the quadrupole moment 94 of the 2i state of 180. VI Table IV-7. Theoretical predictions for the wave functions of the 95 Ot and 2f states of 180. V-l. Potential amplitudes used in DWPI for our analysis. 106 V-2. Deformation lengths calculated from the 164 MeV data. 124 V-3. Deformation lengths calculated from the 230 MeV data. 125 V-4. Potential parameters bo.bi used in calculations for 147 the 230 MeV data of this experiment. V-5. Calculations of transition matrix elements M and M 153 for the 2"f state of 180 using electromagnetic tran-^ sition rates. D-l. Resolution widths observed in the present experiments. 192 D-2. Ca) ir+p data fit by Dodder. 196 (b) ir~p data fit by Dodder. 197 D-3. Predicted HCrr1,^1)!! cross sections according to 198 analysis by Dodder. D-4. Hydrogen normalization factors, N, for all cases. 199 D-5. Total percentage errors calculated for the ratios p2 201 of summed cross sections. vii LIST OF FIGURES Figure 1-1. IT p and IT p total cross sections. 5 II-l. Experimental areas at LAMPF. 17 II-2. A diagram of EPICS. 19 II-3. A diagram of the EPICS spectrometer. 22 II-4. The spectrometer coordinate system. 23 II-5. An energy loss spectrum taken from a run during this 25 experiment. II-6. Exploded diagram of the arrangement used to maintain 29 18 the frozen H2O . II-7. Schematic diagram of EPICS showing the relative posi- 31 tions of the detectors and magnetic elements. II-8. Diagram of the fast electronics used at EPICS for 39 this experiment. III-l. Composite summed spectrum for 164 MeV IT scattering 51 from 180. III-2. High excitation region in ir1 scattering from 180. 52 III-3. Angular distributions for elastic scattering of 164 MeV 60 T\- from 180, for 2° binning of the spectrometer angular acceptance. III-4. Angular distributions for excitation of the 2j state of 61 180 by 164 MeV ir1, for 2° bins. III--5. Angular distributions for excitation of the unresolved 62 triplet of states in 180 - the 4f at 3.56 MeV, o£ at 3.63 MeV and l\ at 3.92 MeV - by 164 MeV TT1, for 2° bins. III-6. Angular distributions for excitation of the 3a state of 63 180 by 164 MeV •n±, for 2° bins. III-7. Angular distributions for elastic scattering of 164 MeV 64 fr~ from 180, for 1° binning of the spectrometer angular acceptance. III-8. Angular distributions for excitation of the 2j state of 65 180 by 164 MeV IT*, for 1° bins. viii Figure III-9. Angular distributions for excitation of the 3~ state 66 of 180 by 164 MeV TT1, for 1° bins. III--10. Angular distributions for elastic scattering of 230 67 MeV TT1 from 180, for 2° bins. III-ll. Angular distributions for excitation of the 2i state 68 of 180 by 230 MeV TT1, for 2° bins. 111-12. Angular distributions for excitation of the unresolved 69 triplet of states in 180 - the 4f at 3.56 MeV, o£ at 3.63 MeV and it at 3.92 MeV - by 230 MeV TT±, for 2° bins. 111-13. Angular distributions for excitation of the 3i state of 70 180 by 230 MeV TT*, for 2° bins. 111-14. Angular distributions for elastic scattering of 230 MeV 71 TT* from 180, for 1° bins. 111-15. Angular distributions for excitation of the 2i state oi 72 180 by 230 MeV ff*, for 1° bins. 111-16. Angular distributions for excitation of the 3i state of 73 180 by 230 MeV IT*, for 1° bins. 111-17. A comparison of spectra for IT scattering on 180 from 74 SIN and EPICS. 111-18. Angular distributions taken at SIN for elastic scattering 75 of 163 MeV TT1 from 180. 111-19. Angular distributions taken at SIN for excitation of the 76 2t state of 180 by 163 MeV IT*. 111-20. Angular distributions taken at SIN for excitation of the 77 37 state of 180 by 163 MeV IT1. IV-1. Energy levels and decay branches for low-lying states 79 of 180. + V-l. Experimental points for 164 MeV TT elastic scattering 113 in the vicinity of the minima. V-2. Our 164 MeV elastic scattering data with curves calcu- 115 lated with DWPI. V-3. Our 164 Me7 elastic scattering data with curves calcu- 116 lated by Liu. IX Figure V-4. Elastic scattering minima calculated with DWPI for 118 164 MeV ir* using average bo.bi amplitudes in the Kisslinger potential. V-5. Elastic scattering minima calculated with DWPI for 119 164 MeV TT° using the proper amplitudes for i& and it" in the Kisslinger potential. V-6. Our 164 MeV elastic and inelastic data with curves 129 calculated with DWPI. V-7. Our 230 MeV elastic and inelastic dita with curves 130 calculated with DWPI. V-8. Our 164 MeV elastic and 2\ data with curves calcu- 136 lated by Arima et al. V-9. Our 230 MeV elastic and 2\ data with curves calcu- 137 lated by Arima et al. V-10. The 230 MeV elastic and 2\ data with curves caicu- 138 lated by Arima et al by varying the amplitudes bo,bj in the Kisslinger potential. V-ll. Our 164 MeV elastic and 2\ data with curves calcu- 141 lated by Lee, Lawson, and Kurath using ZBM wave functions. V-12. Our 164 MeV elastic and 2\ data with curves calculated 142 by Lee, Lawson, and Kurath using LSF wave functions. V-13. Our 164 MeV elastic and 2\ data with curves calculated 143 by Lee, Lawson, and Kurath using s-d wave functions. V-.14. Our 230 MeV elastic and 2\ data with curves calculated 149 by using Arima1s adjusted parameters in DWPI. V-15. Our 230 MeV elastic and 2\ data with curves calculated 150 with DWPI using our best fit parameters. B-l.