MSU LIBRARIES ”3—. RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES wil] be charged if book is returned after the date stamped below. PARTICLE RESPONSE FUNCTION IN SAMARIUM AND EUROPIUM ISOTOPES BY James Edward Duffy A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 1986 ABSTRACT PARTICLE RESPONSE FUNCTION IN SAMARIUM AND EUROPIUM ISOTOPES By James Edward Duffy 3He) have been performed 1AH,1H8,152,15N . Sm The reactions (a,t) and (a, with 100-MeV a-particles on targets of to investigate high lying proton strength distribution in 1A5.l”9v153'1558u and neutron strength distribution in 1u5’1u9’153’1558m, respectively. The emitted particles were identified in the 8-320 spectrograph using two AE gas countersanuian E plastic scintillator. Some differences were observed in the spectra depending on the nuclear deformation. Strong transitions to high-lying proton and neutron states up to about 15 MeV excitation energy were observed. Angular distributions were measured from 2° to 25; for both (a,t) and (a,’He) reactions. The extreme forward angle data points were necessary to determine the 2- transfers. A smooth background, calculated using the a- breakup model, was subtracted from the spectra for excitation energies above 3 MeV. The background-subtracted spectra were divided into 520-keV wide bins and the angular distribution for each bin was fitted with DWBA calculations to obtain a strength distribution for each A-value. The excitation energies, angular distributions, andstrengths of the high-lying transitions suggest that they arise from proton and neutron stripping to high-spin outer subshells, 1u5’1u9’153’155 e.g. lhg/Z and 1113/2 in . _ . Eu and 1h9/2, 1113/2 145,1“9.153.155 and in Sm. The deduced proton and 1J15/2 neutron strength distributions are compared with predictions from the quasiparticle-phonon model and the interacting boson-fermion approximation model. To my wife Andrea Rose Micallef ii ACKNOWLEDGMENTS I would like to thank my advisor Gary Crawley for his guidance and direction. His constant support and inspiration provided the insight necessary to complete this Thesis. I would also like to thank Raman Anantaraman for his charitable time and friendship. There are several people to whom I owe acknowledgement: for serving on my committee, Aaron Galonsky and Alex Brown; for their recomendations regrding to this thesis topic, Sydney Gales, Patricia Massolo, V.G. Soloviev, Olaf Scholten and George Bertsch; membems of the computer group, Barbara Pollack, Ron Fox. Skip Vandermolen, Lori Fedewa and Richard Au; for members of the mechanical design group. Mike Fowler, Al Gavalya and Craig Snow; Gary Westfall, who provided emotional support; and those individuals who participated and volunteered long hours to assist in my experiments, Hans van der Plicht. Bob Tickle, John Winfield, Joe Finck and Silvana Angius; and to the dedicated staff, students and faculty of the NSCL. . With any project one endeavors, there are those individuals whose professional affiliation evolves into a social association. Special thanks for the many times iii shared with racketball buddies Don Lawton and Jack Ottarson. Through Pacman and prelims, marrage and moving, for countless fond memories I thank Mark, Mary, Mike and Pat Curtin.t Many thanks to Virginia Crawford, Ellen Frost and Tom Warren. Lastly, much love and appreciation to my parents James and Rosemary Duffy, my wife's parents Vincent and Claudette Micallef and my loving wife Andrea Micallef. iv TABLE OF CONTENTS . Page LIST OF TABLES .........................................viii LIST OF FIGURES ...................... ..... ............. xi Chapter I INTRODUCTION.................. ....... . ............. 1 II EXPERIMENTAL PROCEDURE.. .............. . ..... ....... 16 11.1 Experimental Setup................. ........... 16 11.2 Energy Calibration.. ...... ........... ........ . 29 III DHBA CALCULATIONS......... .......... ........ ...... . 37 111.1 DWBA Formalism ........ . ..... ......... ...... .. 37 111.2 Application to (a,t) and (c.3Re) Reactions on Sm Isotopes .................................. A6 IV DATA REDUCTION AND ANALYSIS ........................ 55 IV.1 Background .................................... 57 IV.2 Slicing and Fitting ........................... 62 \1 EXPERIMENTAL RESULTS ............. . ................. 67 V.1 Criterion for Accepting I-Transfers ............ 68 v.2 Background Calculations ................. ....... 70 < .3 2°°Pb(a,t)2°’Bi and 2°°Pb(a,3He)’-°’Pb Reactions 76 v.u Spectra from Nucleon-Transfer Reactions on Samarium ................. . ....... . ............. 88 v.5 l~~,i~8’152’isnsm(a’t)ius,ins lsa’issEu ReactionSOOOOOOOOO. 00000000000 O 000000 00000000.. 91 V.5.1 Low-Lying States in llolo'iloo’lsz’15~Sm(a’t)lh5’ibs’lss’lssEu a) Low-Lying States in ‘“5Eu........... b) Low-Lying Peaks in H9Eu............ c) Low-Lying Peaks in l""Eu.‘........... d) Low-Lying Peaks in ‘5’Eu;........... V.5.2 High-Lying Proton Strength in V.6 llolo’ ins 1'09 153 155 O D 3 Eu 1108.152’lSbsm(a'Sue)lb5’lh9’153’1558m ReactionSOOOCOOOOOOO......OCOOOOOOOOOOO00...... V.6.1 Low-Lying States in 1‘5,‘“’."’,1558m...... a) Low-Lying States in ‘“5Sm........... b) Low-Lying Peaks in H9Sm.......‘..... c) Low-Lying Peaks in l"‘*’Sm.......‘..... d) Low-Lying Peaks in 155Sm............ V.6.2 High-Lying Neutron Strength in lhs.‘~9,:53’lsssmOOOOOOOOOOOO VI COMPARISON WITH NUCLEAR STRUCTURE MODELS.. ......... V1.1 The 1““Sm(a,t)‘“5Eu Reaction at 80 MeV and 100 MeVOOOOIOOIOIOOOIOOOIOOI......OOOOOOOOOIOOOCOO V1.2 Models for Position and Width of Single PartICI-e EXCitationSOOOOOOOOOOI0.0000.00.00... V1.2.1 The Quasi-Particle Phonon Model'(QPPM).... Comparison between theoretical (QPPM) and experimental proton strength distributions in ‘“5Eu:................................. Comparison between theoretical (QPPM) and experimental proton strength distributions for the high-lying region in ‘5’,‘55Eu:... Comparison between theoretical (QPPM) and e:tpeari.m£ant;al. riethrcon str~er1gt11 distributions for the high-lying region in ‘5’,“’Sm:................................ V1.2.2 The Interacting Boson-Fermion Approximation Model (IBFA)................ V1.3 Conclusions.................... ..... .......... V1.3.1 The Background.................. ..... .... V1.3.2 Low- Lying Peaks Observed in the (a, t) and ' (c.3He) Reactions. ........ ....... .... .... V1.3.3 High- Lying Strength Observed in the (a, t) and (0,3He) Reactions..................... V1.4 Future Directions............................. A~Ii>pendix 1 Tables of Angular Distributions ............. H5Eu low-lying states...................... ‘“9Eu low-lying peaks. .............. ........ 153Eu low-lying peaks... ...... ... ....... .... 15$Eu low-lying peaks....................... vi 92 96 101 102 103 10“ 118 119 123 126 128 129 130 1H1 142 mu HIS 1N6 149 152 156 157 159 160 16” 167 170 171 172 173 17“ ‘“SSm low-lying states. ‘“’Sm low-lying peaks.. ‘s’Sm low-lying peaks.. lssSm low- lying peaks.. Elastic scattering of the HI. 9 l o b. Isotopes..............00.0.0.0... -’°’Bi and 2“Pb low-lying states. Appendix 11 Program Algorithms and Examples. A. Calibration program.......... B. Slicing and Fitting programs. C. DWBA program examples........ D. Program example for SIGCALC.. E. Program example for WRITECHEX. F. Program example for the 68K... References... ..... .... vii 175 176 177 178 179 180 181 182 186 190 192 195 197 199 Table 11.1 111.1 LIST OF TABLES Page Typical S320 magnet settings for ‘“°Sm(a.t) and ‘“°Sm(a,’He) reactions at Ta- 100 MeV and elab' 60.0.00000000000000.0.0.0.........OOOOOOOOOOOOI. 22 Optical model potential parameters used for the (a,t) and (a,’He) reactions on samarium and lead targets for a 100 MeV a-particle incident energy. (In the case of proton particle states in 2”Bi a different geometry was used, with roa 1.28 fm, a - 0.76 fm, r - 1.09 fm and a - 0.60 _ 0 so . so fm0)00000......OOOOOOOOOOOO.....OOIOOOOOIOOOOOO. ”9 List of the C28 values obtained from the minimum-x: fits to the angular distributions for low-lying states in 2“Bi and 2“Pb. The two columns labeled A and B are the results of using two different sets of bound state parameters given in Table 111.1............................ 82 List of the possible CZS values, using the 1- mixtures indicated, for the low-lying states in 2”Bi. The 028 values are determined using the set B of bound state parameters (see Table V.1). 8A Results of the analysis of the summed angular distributions of the first two low-lying state in 2“'81 and 2°’Pb, when the A-values were selected by the best-fit requirement. The results are compared with those obtained when each state was individually analyzed using the known I-transfer. The x: values of the fits are shown in parenthesis. The labels A and B refer to the two sets of bound state parameters used in the DWBA calculations (see Table V.1)........ 86 List of the extracted C’s values, for the summed angular distribution of the first two low-lying viii A-1.1 states in 2”Bi, when the L-mixtures were fixed at the values indicated. The correct L-values aresand 30.000000000000000000.00.000.000000000 List of the spectroscopic strengths (C‘S) obtained from minimum-x: fits for the low-lying states of ‘“’,‘”’,‘5’,"5Eu. The x: values of the fits are given in parenthesis............... List of the possible C’s values, with the 1- mixtures indicated, for the low-lying states in l~SEUOOOOOO0.00.0000...0..........OOCOOOOOOOOOOO List of C28 and X3 values of single L-transfer fits for each peak listed in Tables v.5 and v.6. List of the possible C’S values, with the 1- mixture indicated, for the high-lying region at Ex.7018Mev1n1saEUOOOOO0.0.0.0000000000000000 List of the summed transition strengths for the high-lying regions of ‘“‘,‘“°,“’,‘55Eu from this experiment and from other work. The uncertainties in the summed strengths are given in parenthesis. They are calculated using the uncertainty in the fitted parameter and in the target thickness................................ List of the spectroscopic strengths (C28) obtained from.minimum-x: fits for the low-lying states of ‘“5,‘“’,‘53,‘5‘Sm. The x: values of the fits are given in parenthesis............... List of C25 and x: values of single L-transfer fits for each low-lying peak from the (c.3He) reactions on the samarium isotopes.............. List of the summed transition strengths for the high-lying regions of ‘“’,’“’,"’,‘558m from this experiment and from other work. The uncertainties in the summed strengths, which appear in parenthesis, are calculated using the uncertainty in the fitted parameter and in the target thickness................................ List of cross sections for the low-lying states in, 1“’sEu popiilat;ed by ‘the reaictican 1““SM(a,t)l“sEU 000000000000000 0.0..00...00.0.000 ix 87 98 99 100 106 117 12A 125 13A 171 A.1.2 List of cross sections for the low-lying peaks in ‘“ ’EL: pcaptilatLed by trie 1~eaict.1011 l~.sm(a’t)1~98u000.0.0.0....IOOOOOOOOOOOOOOOOOI. 172 A.1.3 List of cross sections for the low-lying peaks i.n ‘5 ’Et: pcaptilatsed by true r°eawati.on ‘szsm(a't)‘s’Eu00000000000.0000000.000.00.000... 173 A.1.A List of cross sections for the low-lying peaks in ‘5”Eu poy>ulaitec1 by' trie r‘ea<:ti.on ls~Sm(a’t)‘ssEuotc.OOOl000......OOOIOOOOOOOOOOO. 17“ A.1.5 List of cross sections for the low-lying states in ‘“ sSm p<3ptalatLed by trie r~ea<3ti.on lhusm(a’3He)l~ssmO0.0.0.0...OOOOOOOOOOOOOOOOO... 17S A.1.6 List of cross sections for the low-lying peaks in 1"’S'Sm p<>ptllatLed by trie r'ea<:ti.on lbssm(a,3He)lbssmOOOOOO0.0.0.000...0.00.00.00.00176 A.1.7 List of cross sections for the low-lying peaks i.n ‘5 3Sm p<3ptilat;ed by trie r~ea<3ti.on tszsm(a.3He)lsasmOOOOOO.....IOOOOOOOOOOOO ....... 177 A.1.8 List of cross sections for the low-lying peaks in ‘5 58a: p()lelat;ed by' time reaict.ic>n ls“sm(a,3He)1sssmOOO............OOOOOICOOCOOIOOO 178 A.1.9 List of the cross sections for the elastic peak in the reactions ’““,‘“°,"2,’5“Sm(a,a)......... 179 A.1.10 List of the cross sections for the low-lying peaks in 2°9Pb and 2°°Bi populated by the respective reactions 2°°Pb(a,’He)2°’Pb and 2°°Pb(a,t)’°9Bi.. ........ ..... ............ . ..... 18o 1\-11.1a Calibration program input example..... .......... 184 .A.-11.1b Calibration program output example....... ..... .. 185 ll..11.2 Slicing and fitting program example.. ........... 189 A-- 11.3 DWBA program example... ........... . ...... ....... 191 A - II.Aa SIGCALC program input example...... ....... . ..... 193 A - JEI.Ab SIGCALC program output example .................. 19A A- 11.5‘ Program example for WRITECHEX. ........... 196 A*- 111.6 Program example for the 68K......... ...... ...... 198 Figure 11.1 11.2 11.3 II.” II-7 [LI - 8 LIST OF FIGURES Fragmentation of a single-particle excitation.... View of the NSCL S320 spectrograph [Be83b]....... View of the NSCL S320 detector box.......... ..... FWPC -> Front wire proportional counter. FIC -> Front ion chamber. BIC -> Back ion chamber. BWPC -> Back wire proportional counter. SC .) Scintillator. PM a) Photo multiplier tube. A view of the monitor detector................... Typical spectra from the monitor detector. The ‘“°Sm(a.’He) monitor events with the $320 scattering angles at 7° and 12° are displayed on the left. The blank frame [empty(a,°He)] monitor events with the S320 scattering angles at 7° and 12° are displayed on the right................... A schematic view of the electronic set up for the 33200000000000.00000 0000000000000000 0 000000 0 00000 LL6a The top figures display the particle identification for the reaction ‘““Sm(a,t) at 2° and 1""Sm(on,°11e) at 3.5°. The axes are labeled TOF (time of flight) for the y- axis and ENERGY (total energy loss in both ion chambers) for the x-axis. 11.6b The bottom figures display the typical spectrum for the reaction H"Sm(m,t) at 2° and x""Sm(on,°He) at 3.5°................... Mylar(a,t) spectra are displayed from 2° to 12°.. Energy calibration for the triton spectrum from the l""Sm(o¢.t)"“Eu reaction. ‘The arrows point to known states in H5Eu, HN‘and 17F. The ‘3N and HF states were obtained by the mylar(a,t) xi Page A 19 20 25 26 28 30 32 III.1 III.2 IV.1 IV.2 IV.3 reactionIOOOOOOOOC......OIOOOOO.........OOOOOOOOO Calculated angular distributions for the case of 1-3 transition in the l""Sm(a.t)""’Eu reaction at excitation energies of 2.0 and 10.0 MeV, for a beam energy of 100 MeV. The calculations were done using the code DWUCKA [KuBA]................ Calculated angular distributions for i-transfers of 0, 1, 2, 3, A, 5, 6 and 7 in the ‘“°Sm(a,t)1ASEu reaction at an excitation energy of 8.0 MeV, for a beam energy of 100 MeV. The full single-particle strength (CZSh1) was used for each I-transfer. The calculations were done using the code DWUCKA [Ku84]..................... Energy spectra of residual nuclei ‘“3,‘“’,‘5‘Sm from the 100,1100’1528m(3He’a)1b3,lh7’1Slsm reactions at a beam energy of 70 MeV, taken from Gales et al. [Ga81]. The dashed lines that appear under the spectra are hand drawn backgrounds. Also shown are the gross structure gaussians A and B which were used to fit the Spectra.’00............IOOOIOOOOOI......OOOOOOOIO A schematic representation of two projectile breakup processes, sketch (1) being the elastic breakup and (2) the inelastic breakup............ Illustration of the slicing of spectra into bins. A bin width of 1 MeV is used for clarity. The spectrum displayed is the triton spectrum from the l"°Sm(m,t)"’°Eu reaction at 5°. The dotted curve is the total background that is obtained by the procedure described in the text.............. Triton spectrum from the ‘5“Sm(a,t)‘°5Eu reaction at 5° showing the a-breakup plus evaporation calculation (dashed curve) for the background. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in the figure. The sharp peaks near Q-values of -35 and -A8 MeV are spurious and are due to a defect in the focal plane detector................................... Triton spectra from the ‘“°Sm(a,t)‘“9Eu reaction at eight angles. The estimated total backgrounds are shown by the dashed curves. The a-breakup contributions at angles of 18° and 25° are shown by the dot-dashed curves. At more forward angles the contribution from the compound nucleus evaporation process is small relative to that from a-breakup and therefore the total background xii 33 51 52 56 59 6M 72 v.3 V.6a is essentially equivalent to the a-breakup contribution. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in each panel of the figure....................................... Same as Figure V.2, but for the H°Sm(a,.°He)”’Sm reaction. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are shown in each panel of the figure. The break near the middle of the spectra is due to a defect in the focal plane detector............... Spectra from the 2°°Pb(a,t)’°°Bi and 2°°Pb(a,°Re)2°°Pb stripping reactions at a scattering angle of 5°........................... Angular distributions from the 2°°Pb(a,t)2°°Bi and 2°°Pb(a,’He)z°°Pb reactions for low-lying proton and neutron states in the final nuclei. The L-transfer and excitation energy (in MeV) are indicated in each panel. The solid curves are the normalized DWBA predictions for these I- transfers........................................ Triton spectra at 7° for proton states excited by the lhh’lha’lsz’lsusm(a’t)ibs,lh9,153’lSSEU reactions. The horizontal scale gives the reaction Q-value (in MeV). The corresponding excitation energies in the residual nucleus (in MeV) is also shown in each panel of the figure. The a-breakup plus evaporation calculation is shown as the dashed curve........................ Spectra of 3He at 7° for neutron states excited by the in»,ina’isz,is~Sm(a’3He)i-os’i~9’isa'isssm reactions. The horizontal scale gives the reaction Q-value (in MeV). Excitation energy (in MeV) is also shown in each panel of the figure. The break near the middle of the spectra is due to a defect in the focal plane detector. The a- breakup plus evaporation calculation is shown as the dashed curve............................ ..... Triton spectra at 5° showing the low-lying proton s t ea t e :3 p o p L1.l a t e (1 b y t h e lbh,lb8.152’15Msm(a’t)lh5,1'09,l$3,ISSEU .stripping reactions.... ..... . .......... . ..... .... Angular distributions of some low-lying peaks (indicated with arrows in Figure V.7) which are excited in ‘“5,‘“°,‘53,‘55Eu. The curves are the minimum-x: fits with DWBA predictions; the xiii 7a 77 79 81 89 9O 93 v.9 'V.13 V-1u v-15 corresponding 1 values are indicated............. Angular distributions of some high-lying regions in ‘“5,‘“’,‘5’,‘55Eu after background subtraction. Each region is 520-keV wide, centered at the excitation energy Ex(in MeV) indicated. The curves are the minimum-x: fits using the DWBA angular distributions. The 2 values thus determined are indicated............. Angular distributions of the under-lying background for typical high-lying regions in the in»,lb8,152’15hsm(a’t)ibs’109’153,1558'1 reactions. The term "scale x 0.1" in some of the panels means that the indicated scale must be multiplied by 0.1 to get the actual scale........ A 3-dimensional plot ( do/da vs 00 m vs Excitation energy) of experimental angular <1 i s t r‘ i b 11 t i <3 n s f o r' t 11 e 1'0“.1&8’152’15§8m(a.t)1b5,1b9’153’1558u reactions. 00 m varies from 0° to 30° in all four panels of the figure........................ Spectroscopic strength distribution of the fragmented 2-3. 5 and 6 proton single-particle excitations in ‘“5,’“°,‘5’,‘55Eu obtained by performing minimum-x: fits to angular distributions measured in (a,t) reactions on ‘““,‘“°,‘52,‘5“Sm targets. i=3 corresponds to the 2f.“2 and 2f5/2 single-particle states, i=5 to 1h9/2 and 1:6 to 1113/2. in some of the panels means that the indicated scale must be multiplied by two to get the actual Scale000..00000.00..000000.000000000000000o000000 The term "scale x 2" As for Figure V.12, except that the strength distributions were obtained by fitting the measured angular distributions with single 2- transfers (2=3, 5 and 6). The terms "scale x 2", "scale x 3" and "scale x A" in some of the panels mean that the indicated scales must be multiplied by two, three and four, respectively, to get the actual scales.............. ...... ................ The minimum-x: distribution corresponding to the fit that produced the C28 values in Figure V.12.. The x: distribution corresponding to the single-2 xiv 9A 108 109 113 v.19 -.22 fits that produced the C28 values in Figure V.13. Spectra of ’He at 5° showing the low-lying nae ut.rc>n st.at.es p<>ptileateed by tile iuu'iba’isz.isusm(a’SHe)i~s,ius'isa’isssm stripping reactions. Besides the Q?values energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in each panel of the figure ............................. Angular distributions of some low-lying peaks (indicated with arrows in Figure v.16) which are excited in ‘“5,‘“°,’5°,‘558m. The curves are minimum-x: fits with the DWBA predictions; the corresponding 2 values are indicated............. Angular distribution for the Ex- 0.98 MeV state in H9Sm. The solid curve is the minimum-x: fit with the DWBA prediction for the 1:1 angular distributionSOOOO......OOOOOOCO......OOOCOCC.0... Angular distributions of some high-lying regions in ‘“’,‘“°,‘5°,’558m after background subtraction. The curves are the minimum-x: fits using the DWBA angular distributions. The indicated 2 values determined by this procedure are indicated 0. ..... 00...........OOIOOOIOOOOOOI. A 3-dimensional plot ( do/dn vs 00 m vs Excitation energy) of experimental angular d i s t r i b u t i o n s f o r t h e 1'05,108,152’l5~Sm(a,3He)lhs’lb9’153’1558m reactions. 00 m varies from 0° to 30° in all four panels of the figure........................ Spectroscopic strength distribution of the fragmented Ls3, A, 6 and 7 neutron single- partdxile excitations in 1°5,1“°,‘5’,‘558m obtained by performing minimum-x: fits to angular distributions measured in the (c.3He) reactions on ‘““,‘“°,‘52,15“Sm targets. 2:3 corresponds to the 2f7/2 and 2f5/2 Single-particle states, is“ to 239/2, I=6 to 1i13/2 and 2:7 to 1315/2. The term "scale x 2" in some of the panels means that the indicated scale must be multiplied by two to get the actual scale.......... ..... .............. As for Figure v.21, except that the strength distributions were obtained by fitting the XV 115 120 121 127 131 133 135 V1.1 V1.2 V1.3 VI.“ V1.5 measured angular distributions with single I- transfers (1-3, A, 6 and 7). The terms "scale x 2" and "scale x 8" in some of the panels mean that the indicated scales must be multiplied by two and eight, respectively, to get the actual scales.........OOOOCOOOCIO......OOOOOOOOOOOOOOOOO The minimum-x: distribution corresponding to the fit that produced the C28 values in Figure V.21.. The x: distribution corresponding to the single-2 fits that produced the 0’s values in Figure v.22. Comparison between theoretical and experimental- proton strength distributions for the high-lying subshells in ‘“5Eu. The theoretical distributions [St83] are the thick smooth curves and the experimental distributions are in histogram form. The term "scale x 2" in some of the panels means that the indicated scale must be multiplied by two to get the actual scale........ V1.1a. (Top figure) Experimental distributions ‘ ' obtained from the ’““Sm(a,t)‘“5Eu reaction at 80 MeV incident energy [Ga85a]. V1.1b. (Bottom figure) Experimental distributions obtained from the same reaction at 100 MeV incident energy (present work). Comparison between the experimental spectrum (solid histogram) for proton states in ‘“’,‘5°,‘55Eu and the predicted spectrum (thick dashed histogram) obtained by the conversion of theoretical strength functions at three angles. The theoretical strength functions for ‘“5Eu are those shown in Figure V1.1 [St83] and for ‘5’,‘55Eu are those shown later in Figure V1.3 [Ma86]............ ..... .......................... Comparison between theoretical [Ma86] and experimental proton strength distributions for the high-lying subshells in ‘5’,‘55Eu............ Comparison between theoretical [Ma86] and experimental neutron strength distributions for the high-lying subshells in ‘53,1558m. The term "scale x 2" in some of the panels means that the indicated scale must be multiplied by two to get the actual scale................................. Same as Figure V1.2 applied to the high-lying neutron states in 153,1558m ........ ......... ..... xvi 136 137 138 1N3 148 150 153 V1.6 Comparison of the experimental 2-5 proton strength distributions in ‘“’,‘°’,‘°’Eu (shown in histogram form on the left hand side) with the corresponding IBFA-model prediction for the 1h9/2 strength distributions (shown on the right hand Side)OOOOOOOOOOOOOOOIOIO0.0.0..........OOOOOOOOO.158 A.11.1 Calibration program algorithm.................... 183 A.11.2 Program algorithm for SMASHER.................... 188 xvii CHAPTER I INTRODUCTION The study of elementary modes of excitation, particularly in many-body systems, is of great interest in several areas of physics. 1n nuclear physics, there are numerous examples of such simple structures, including isobaric analogue states, giant resonances and single- particle and single-hole states. The concept of single- particle motion in the mean field of the nucleus is perhaps the most fundamental idea in nuclear structure physics and is the basis for the highly successful nuclear shell model. Experimentally, single-nucleon transfer reactions [Au70] have been the probes most extensively used to study the properties of single-particle and.single-hole states. These reactions are of two types: stripping and pickup. In :stripping, a nucleon is transferred from the projectile to tan unoccupied single-particle state in the target, thereby Probing the distribution of particle strength in the final nucleus. In pickup, a nucleon is transferred to the I>rojectile from an occupied state in the target, thereby 2 probing the distribution of hole strength in the final nucleus. Since the early 1960's, many single-nucleon transfer reaction studies have been performed on nuclei throughout the periodic table, with low energy light-ion projectiles (p, d, t, ’He, “He), to examine low excitation energies (less than 5 MeV) of the nucleus. Only recently, with the help of higher energy beams, have such studies been extended to explore single-particle and single-hole strength at higher excitation energies. This Thesis describes the investigation of single-particle states at high excitation energies (up to 15 MeV) in a set of samarium isotopes whose shapes range from spherical to deformed, using the (a,t) and (c.3He) reactions. The a-particle beam was chosen because it provides the lightest projectile with which both proton and neutron stripping can be studied using the methods of charged-particle spectroscopy. In this Chapter, the techniques that have been developed over the years to investigate particle and hole states by means of single-nucleon transfer reactions will first be presented. Next, brief reviews of the results of pickup and stripping reactions on medium-heavy targets will be given, including the use of nuclear structure models to understand the results. Finally, the goals of this Thesis - - the investigation of particle states in the samarium isotopes -- will be discussed. 3 In reality, nuclear states are seldom true single- particle states. Most commonly, as sketched in Figure 1.1, a given single-particle (or single-hole) excitation spreads over many states of the fanal nucleus. Transfer reactions then study the distribution of the single-particle strength over a finite energy interval. Such mixing of simple states with more complicated underlying states is a problem even at low excitation energies, and it becomes worse with increasing excitation. In a single-nucleon transfer reaction, each state in the final nucleus is populated with a strength proportional to the square of the amplitude of'the single-particle component of that state. This strength is usually expressed in terms of the spectroscopic factor S for that state. The precise mathematical definition of S will be given in Chapter III, in equation (111.13). Qualitatively, the spectroscopic factor Snij for a state IJB,MB> in the residual nucleus B, of angular momentum JB' is the B,MB> "looks like" the target ground A’MA> plus a particle p (or hole) in the single particle state |nlj>. Here B=A+p. The angular momenta probability that |J state |J -> -> satisfy the relation JB = JA + j. The technique used to extract the spectroscopic factor is of a state is the following. From spectra taken at Various angles, the experimental angular distribution for Figure 1.1 Fragmentation of a single-particle excitation. an; scam: g EHBéUxW _ _ _ _ WIS EDIIHVd-S'ms ‘- . U A\U .5 I1)! 0.. .\5 5 the state is obtained. It is characteristic of the orbital angular momentum (1) of the transferred particle; the j must be inferred from other considerations, such as the use of polarized beams. This angular distribution is compared with a theoretical one calculated in the Distorted Wave Born Approximation (DWBA) in which it is assumed that the entire spectroscopic strength is concentrated in that of a given single-particle (or single-hole) excitation inlj), gives the energy of that excitation. The width of the distribution is a measure cm‘ ‘the spreading of the single-particle (or single-hole) excitation. The sum of the spectroscopic factors of all frhagments of a given single-particle (or single-hole) AA ' h 6 excitation measures the extent to which that excitation is empty (or occupied) in the target ground state. The total width of a nuclear state is the sum of two parts: the; decay width and the spreading width. The decay width or escape width of a state is a measure of the probability that the state decays to a lower energy state either in the same nucleus (by Y emission) or in another nucleus (by particle emission). The spreading width is the probability that the state decays through the development of more complex excitations such as vibrational states, compound nuclear states, etc. In this mixing, the angular momentum of the initial single-particle is preserved: a state of angular momentum j mixes only with background states having the same total angular momentum. When the lifetime of a state is known, its decay width can be easily calculated using the uncertainty principle. This is given by the following. £3 = 197 (MeV fm) (1.1) ct 3x1077(fm/sec)xt(sec) fl 1: «Is: :1 Here t is the mean lifetime in seconds, which is related to the half life by the expression t=1.AAt1/2. In this Thesis, we shall concentrate on the spreading width of the single-particle excitation, which is measured by the width of the distribution of all the complex states (:shown in Figure 1.1) into which the excitation fragments. 7 Each of these complex states has.a width which arises from its decay to lower-lying states (the decay width). When the state is bound with respect to particle emission so that it decays only by Y-ray emission, it has a negligible decay width. For example, the first excited state of (“58m has a half life of 36x10.12 seconds [Tu80] and decays by Y-ray emission to the ground state with an energy of 0.883 MeV. Its decay width, calculated using equation (1.1), is 1.3 x 10.8 keV. When the state is unbound with respect to particle emission, the decay width is much larger. It depends on the energy available for the decay, on the angular momentum in.the decay channel, and FIC => BIC => BWPC => SC => PM => 20 Figure 11.2 the NSCL S320 detector box. Front wire proportional counter. Front ion chamber. Back ion chamber. Back wire proportional counter. Scintillator. Photo multiplier tube. N.HH onmmdm Eo scan ‘1 .523. Eu 2...». v. n 1 J 11 1v. u .30 . filV. . _ E . .AIV. . 52...“ “n usual. .3 so .. .. _ 30 .8 “.....E u“ n .F «2.3. “muons " n n n can“... .. . __ .< ... ......u 259. 5......“ Hh n: \ 29:8 6 a . .. 25... a... 0... 111mm,. son—3m & we” . 0&5“. , . >11 Ago-Q 08560. >11 05¢...» n—OF 6.5...— 593.3»: 21 Typical settings of the spectrograph magnets used for 3 the (a.t) and (a, He) reactions of interest are given in Table 11.1,, in terms of both potentiometer and digital voltmeter (DVM) readings. These settings were used to focus the highest energy tritons or 3He onto the focal plane of the $320, which is at the position of the front position sensitive wire chamber. The highest energy particles emitted were focused near one end of the focal plane because this enabled the examination of the excitation energy range from 0 to 15 MeV. The settings were obtained from a program called S320 [Va85a]. A more detailed description of the S320 spectrograph is given in another NSCL Thesis [Sh85]. Two collimators of different sizes, one narrow and one wide, were used during the experiment. The narrow one was used to decrease the count rate at the forward angle of 2° and the wide one was used for the other angles. The narrow collimator was made of copper, with a thickness of 0.125 3He) and an aperture of 1.0 by inches (enough to stop 90 MeV 2.0 inches. The wide collimator, which was the most frequently used one, was made of brass with a thickness of 0.25 inches (enough to stop 90 MeV tritons) and had an opening of 1.6 by 1.6 inches. Both were located 78.5 inches from the target ladder. A number of different Faraday cups were used in the (experiment. In the first two runs, two Faraday cups were ‘u—— _——“4——— __———_-““__— __— ‘—-— Typical S320 magnet settings for ("8Sm(a,t) and Sm(a, 22 Table 11.1 1A8 reactions at Ta= 100 MeV and O = 6°. lab 3 $320 Reaction Magnet ‘“°Sm(a,t) ‘“°Sm(a,’Re) Pot DVM Pot DVM 0,, (Y) 12.A8 1.221 v 5.72 0.559 v Q21 (X) 3.001 -27.835 V 1.375 -12.752 V Dipole 7.3“ 13.UO7 kG 3.25 6.1U2 kG Octupl. 297. 12.638 V 136. 5.790 V Sext. 390. 15.508 V 179. 7.105 V He) 23 used for different angles of the spectrograph. One cup was located in the target chamber and was designed to measure charge for scattering angles of 12° and larger. This Faraday cup did not have an electron suppressor, thus posing a problem with normalization. The other cup was located in the wedge and had an electron suppressor. This cup was used to measure the charge for scattering angles from 2° to 9°. In the third run, we used a single Faraday cup with an electron suppressor. This was located in the target chamber and was designed to measure the charge for scattering angles of A° and larger. It was called the zero degree Faraday cup. It did not fulfill all of our needs, due to its inability to allow the particles of interest to travel freely to the focal plane of the spectrograph for angles of 2° and 3°. 'ha obtain spectra at 2° and 3°, we removed the zero degree Faraday cup and normalized using the wedge Faraday cup. All of the measurements carried out for this Thesis were normalized using the zero degree Faraday cup. Short runs of spectra at the larger angles (2 12N’) for the (a,t) 3He) reactions were reactions and at all angles for the (a, taken using this Faraday cup, and these were used to normalize the spectra taken before the third run. Errors in this relative normalization are included in all the cross sections quoted in this Thesis. 2A Because of the problem in measuring the charge during the first run, a monitor detector was used to check the normalization in the second run. The monitor detector was used before the zero degree Faraday cup was installed and so was the only means available at the time to check the normalization. It was a simple device, consisting of a single piece of plastic scintillator, as displayed in Figure 11.3. It had dimensions of 0.25 by 0.25 inches by 0.75 inches thick and was made of NE102. The light pulses from the NE102 were transferred through a fiber optic cable to a photomultiplier tube. The monitor was positioned at 18° in the plane of the beam and subtended a solid angle of about 0." msr. We chose the angle of 18° because the angular distribution of o /o for the elastic cross section on el Ruth the Sm isotopes is predicted to be flat at 18°. Typical spectra from the monitor are displayed in Figure 11.“. Note the difference between the monitor spectra when the S320 spectrograph was at 7° and at 12°. When the S320 angle was 12° or larger, the monitor spectra showed some background. At the time, as mentioned before, there were two different Faraday cups to read the charge: a wedge Faraday cup and a target chamber Faraday cup. At an angle of 12°, the latter was only about an inch away from the monitor. The background in the monitor spectrum was presumed to be due to Y-rays and neutrons emitted from the 25 Figure 11.3 A view of the monitor detector. mamm1mummwm mgnoo ciao Loo: .... meoiba x. ‘Uiiwg 11111" oao+ n3+mofi. \\ 1 a ‘11 ! 1 (\i ,1“ 11 mo_mz 1 wonoc.mm. 26 Figure II.A 3 Typical spectra from the monitor detector. The ‘“°Sm(a, He) monitor events with the S320 scattering angles at 7° and 12° are displayed on the left. The blank frame [empty(a,3 He)] monitor events with the S320 scattering angles at 7° and 12° are displayed on the right. 2300 1300 Counts 2000 100 21—25 350 Channel Number Figure 11.4 27 Faraday cup. This was confirmed by putting a blank frame in place of the target and measuring the monitor spectra when the S320 spectrograph was at 7° and 12°; see the right half of Figure 11.“. In view of this, we concluded that the added background was due to the Faraday cup in the target chamber. , A schematic view of the electronic setup for the S320 focal plane detector system is given in Figure 11.5. The signals from the electronic modules were digitized with an ORTEC A0811 12bit analog to digital converter (ADC) and were (read by a program called ROUTER [Sh85] in the LSI—11 microcomputer as part of the data acquisition system. Two different data acquisition systems were used, the first being the CAMAC system [Sh85] and the second being the 68K data acquisition system [Va85b]. The latter was used for the third run, with a series of reads and clears for each of the ADC and QDC modules used. An example of the setup program for the 68K is given in Appendix II. The example is appropriate for the measurements described in this Thesis. Both data acquisition systems needed an LSI-11 microcomputer to communicate with, and transmit data to, the vax 11/750. Then the computer program Router [Sh85] sent the data to the tape drive unsampled and to an on-line (and off-line) data analysis program called SARA [Sh85]. Among the signals recorded for each detected particle, one was its time of flight (TOF) through the system, which 28 Figure 11.5 A schematic view of the electronic set up for the S320. mamm-mmma«u 03010 01.0.0311. .. Li.n. N u ta .QEOO ...Eom L0 0 mugoomlll. m A rJ .. I «a _ 000:0 :3. z33 . >33 «mu, ..A ..A 3 £38 .285.— . . ta k (va In. m..a._00m....lllH a o mvv. 3 you 23.9.5 mh2. 8. n 5.. 31 same as for a Sm target. The second way was by moving an elastic peak through the counter by changing the dipole field B. The first method was the one used most often. Identification of peaks in the spectra was carried out using the kinematic shift in the centroids of different peaks as the scattering angle was changed. Examples of this shift are evident in the 13N and 17F ground state peaks shown in Figure 11.7. A peak corresponding to a heavier-mass target will move a smaller distance across the focal plane as the scattering angle changes. Once we were confident about the identification of peaks in the mylar and samarium spectra with particular levels in carbon, oxygen and samarium, we then determined a best-fit calibration curve. The calibration curve is an equation expressing the kinetic energy T of the outgoing particle in terms of channel number, the relation used being a quadratic one: T = a + b x channel number + c x(channel number)2 (11.1) The parameters a, b and 0 were calculated by a program called SPECCAL. A typical fit is shown in Figure 11.8. To complete the calibration, the excitation energies in the different residual nuclei were expressed in terms of channel numbers, using the following expression. 32 Figure 11.7 Mylar(o,t) spectra are displayed from 2° to 12°. Mylar(a,t) Ta: 100 MeV 400 W. 1 0: 12° "N 1 . » (3.55) 200} “N "F 175m: : (5.52) r .. o- c. .s. 1 a I g.s. g ’ L. , - 1 '9: 7° 17F ”N ‘ (3.55) 1 1000 7 .. 1 . gs. 1 500 : 13N 17F ‘1 U) g 3" (5.82): H ’ ' ' 1U LA :1 ’ 1 . ‘ :1 {0: 3.5? 1°N 3 O L 4 L) ; (3.55) 1 1000 f- 1 n .71, ~ E a”. .. F (5.52)} f gsu gs. .. j 2000 r 1 17 ‘ 3" F (5.52). 1000; 1+ '- 1 gs. U gs“ *1 0 , 20 400 600 Channel Number Figure 11:1 33 Figure II.8 Energy calibration for the triton spectrum from the 1H“ 5 1M Sm(a,t) Eu reaction. The arrows point to known states 13 17 1&5 13 17 N and F states were obtained in Eu, N and F. The by the mylar(a,t) reaction. 90‘“Sm(a.t)“°Efi T¢= 100 MeV ::“Eu 8: 20 : b 60 AA.I....I....I. 200 400 600 Channel Number Figure II.8 34 Ex = u + v x channel number + w x (channel number)2 (II.2) The terms u, v and w were also calculated by the program SPECCAL using the relation (11.1) and are related to a, b and c by a straight-forward kinematic relationship. Finally the spectrum, which to begin with was expressed in terms of counts versus channel number, was converted to a spectrum of counts versus excitation energy by the program WRITECHEX. The calibration process discussed above may be summarized in the following three steps. 1) We identified peaks of carbon and oxygen in the mylar spectra. We also identified known peaks in the samarium isotopes whenever possible. 2) The program, SPECCAL. was used to obtain the equation for excitation energy versus channel number. 3) The equation of excitation energy versus channel number was used in the program, WRITECHEX, to convert a spectrum of counts versus channel number to a spectrum of counts versus excitation energy. A description of the SPECCAL program is given in Appendix I and a sample input file for this program is given in Appendix II. The second method of calibrating the spectra involved moving the elastic peak across the focal plane of the S320 sgzectrograph as a function of the dipole field B at a fixed 35 angle. We plotted B versus the channel number for the elastic peak. The equation, P‘DQB ‘ (11.3) .relates the momentum p (MeV) of the emitted particle to the radius of curvature p (meters), the magnetic field B (kc). and the charge q (MeV/(mokG)) of the emitted particle (units are in 0:1). The equation, p = po + KX (II.N) expresses the radius of curvature. p (meters), in terms of a constant po and the channel number x (K is in meters/channel number). The equation 2 (N T + 2 mnV (11.5) P relates the kinetic energy T with the momentum p, m being the mass of the emitted particle (all units are in MeV since c=1). From equations (11.3), (II.H) and (II.5), we deduced a relation between the kinetic energy T and the channel number x. We then proceeded, as we did in the mylar case, to acquire a spectrum of counts versus excitation energy. The two methods gave excitation energies which agreed vuith each other to within 50-100 keV, depending upon the 36 position in the detector. The closest agreement (50 keV) was at the center of the detector. 3 Triton and He spectra from the (a,t) and (c.3He) reactions on the Sm isotopes are shown in Chapter V. CHAPTER III DWBA CALCULATIONS In this section, we will discuss the Distorted Wave Born Approximation (DWBA) calculations used to analyze the stripping reactions (c,t) and (c,’He) employed in this work. In both reactions, a nucleon is removed from the projectile: a proton in the (a,t) case and a neutron in the (a,’He) case. We therefore discuss first the DWBA formalism of single-nucleon transfer reactions, including a definition of the spectroscopic factor already introduced in Chapter I. Then we discuss the application of this formalism, using the DWBA program DWUCKH [Ku69], to the specific cases of interest to us. Reasons for our particular choice of optical parameters will be given, followed by details of the calculation of the DWBA angular distributions for different excitation energies and different i-transfers. III.1 DWBA FORMALISM Let us consider the reaction A(c.B)B, where A is the target nucleus, 0 the projectile, B the emitted particle and B the residual nucleus. If particle a consists of B+x then 37 38 the reaction (a,B) is a stripping reaction which strips the particle x. For our cases, x is a proton (p) when 8 is a triton (t) and x is a neutron (n) when 8 is a ’He particle. If 8 consists of c*x, then the reaction (c,8) is a pickup reaction in which the projectile picks up a particle x from the target. We will concentrate on stripping reactions here. This direct reaction process allows one to investigate the excitation energy levels of the residual nucleus B and determine the extent to which they are single- particle states built on the ground state of the target A. The DWBA involves three basic physical assumptions listed below [Ma69]: 1) Nucleon transfer occurs directly between two active channels (A,a) and (8,8), 2) Optical-model wave functions for A+a and B+B are correct in all relevant regions of the configuration space, 3) The transfer process is weak enough to permit a first-order treatment. To find an expression for the angular distributions of such direct reactions one must first consider the transition amplitude, which may be expressed as + + + + a 3 3 + T J Id rBB (d rmA ¢BB(kBB,rBB)¢aA(kaA,raA) (III.1) 39 Here J signifies the Jacobian that transforms the center of momentum system to the lab system. is the matrix element for the transition from the state |aA> to the state |BB> through the potential W. ++' ¢i(k,r) are the (incoming ) distorted waves (plane wave outgoing plus spherical scattered wave) describing the motion of a in the entrance channel and of B in the exit channel. The o are assumed to depend only on the separation of the centers of mass of the colliding pairs and to be independent of the spins. In DWBA, they are taken to be the distorted waves which describe the observed elastic scattering. They are solutions to - :33 WM) ¢(k,r) =0 (111.2) hZ (V2 + k2 where V(r) is the optical potential. Let La and L denote the orbital angular momenta in the B incoming and outgoing channels of the reaction A(c,B)B and let 1 denote the transferred angular momentum. These angular momenta must satisfy the conservation laws for angular momentum and parity + L + 1 = L . (III.3a) L (-1) °‘ = (-1) B (III.3b) NO The elastic scattering in the channels (A,a). (8.8) is dominated by a few partial waves a a (III.M) close to those whose classical impact parameters correspond to a grazing collision with the surface of the nucleus. Higher partial waves give no contribution to the cross section because the centrifugal barrier excludes them from the region of the interaction, while lower partial waves are completely absorbed and do not reappear in the elastic channel. If conditions in case of the transfer reaction are such that the conservation laws (III.3) are satisfied for angular nmmenta close to those favored in elastic scattering, that is, if kaR - kBR | = 1 (111.5) then the transfer cross sections are integrated over the internal co-ordinates of the core nucleus A and of the lighter projectile B. If the effective transition operator W is taken to be the interaction VBx between projectile B and the transferred nucleon, the effective matrix element separates into a product of two disjoint form factors A = A8, (111.9) with the nuclear form factor A independent of VBx' The projectile form factor B is evaluated tusing suitable internal wavefunctions for a and B and with suitable assumptions about the range of V8x|a> as a function + -> of rx- r8. We shall use the zero-range approximation = 111.10 f(r8x) 6(r8x) ( ) for time projectile form factor, since past work by Gales et al [Ga85a] has shown that the DWBA angular distributions cualculated within the zero-range approximation and the ffiinite-range approximation have the same shape. We have now isolated the single-nucleon form factor ”3 o A(x) = A = (111.11) It is an overlap integral (integrated only over the internal coordinates of the core nucleus A) or, equivalently, a 9 matrix element of the operator aT(x) that creates a nucleon .9 with co-ordinates x. Its angular momentum decomposition is + lj Ij A(x)= ) FB A(x) 1m (x) (111.12) where Y is a spin- angle function and Clebsh-Gordon coefficient. The radial form factors F are unnormalized; the normalization constants necessary to introduce normalized form factors f 23 _ lj 1/2 13 FBA(x) - (SBA) fBA(x) (111.13) are the spectroscopic amplitudes (S§%)1/2. SE1 is the spectroscopic factor. The differential cross section for the reaction A(a,B)B may be expressed in terms of the transition amplitude T as (111.1u) an where isj 2J + 1 isj do 3 2 92 a (2JA+1)(2j+1) N'C Slj d9DWBA (111.15) dolsj HEDWBA is the reduced differential cross section which the program DWUCKH [KuBH] calculates using (111.1) through (111.9). (3 is a Clebsh-Gordon coefficient which describes the isospin coupling between the target, transferred nucleon and residual nucleus: 0 ll <1 1 t t |T Tz > The literature is marred by a good deal of confusion between the use of S and C28. In the case of neutron stripping reactions C2 has the value of unity, but not in general for proton stripping reactions. As equation (111.15) shows, C28 is the quantity directly entering in the cross section. In this Thesis, we shall present results for Gas, which we call the spectroscopic strength. Since the Sm targets used in this study are all even-even nuclei, they have J =0; so j A must equal J and the spin statistical weight factor B (2JB+1)/(2JA+1)(2j+1) in equation (111.15) is unity. Thus knowledge of the j value is not needed for obtaining C28. N is a normalization factor which incorporates the effect of the zero-range approximation for the light-ion NS vertex. Its value depends on the specific light ions, a and 8, involved in the reaction, but is independent of the target A. A value of N836 had been calculated previously [FP77,G&858] for the (a't) and (0.3 He) reactions, with an error of 151 due mainly to the uncertainty in the optical model potentials [Fr77]. This value oflivndl be used to determine C28 values for low-lying states populated by'tflue 208Pb; we shall compare them (c,t) and (c.3He) reactions on with C28 values from previous work. The same value of N will be used for both the (a,t) and (c.3He) reactions. This is because the bonding potentials for the two reactions are very similar: the mass difference for (c,t) is ma-(mt+ mp) = 3He) is ma-(m3He+ m ) = -20.58 -19.81 MeV and that for (c, p MeV. Equation (111.15) provides us with the means to extract from experiment the spectroscopic strengths Czsgj, by olsj dolsj comparing the experimental cross section -- with —- DWBA, d9 an whicni is the calculated DWBA cross sections for a state lsj which has the full single-particle strength. In Chapter IV we shall describe in moreedetail this method of extracting the experimental spectroscopic strengths. The sum of the spectroscopic strengths of all fragments in the residual nucleus for a given single-particle (or single-hole) excitation nlj measures the extent to which orbit nij is empty (or occupied) in the target ground state |A>. In the case of neutron (proton) stripping reactions, the sum of F—r—r—v— A‘A“; H6 spectroscopic strengths for a particular orbit (nlj) over the entire excitation energy region is equal to unity or less depending upon whether the ground state of the target nucleus is empty or partially occupied with neutrons (protons) in that orbit. This is clear from (111.13) and it is expressed by the inequality 2 c=s£.(e) s 1 (111.16) 8 J ' ‘ The limited range of excitation energies which can be studied experimentally may also contribute to this inequality. Chapter VI will be devoted to the predictions of the spectroscopic strength using two models and their comparison with the experimental spectroscopic strengths extracted from this experiment. 3 III.2 APPLICATION TO (a,t) AND (a, He) REACTIONS ON SM ISOTOPES The program DWUCKN requires an input of optical model parameters to calculate the angular distributions. Parameters obtained from elastic scattering experiments as described in the literature were used. The entrance channel (u+A) and the exit channel (8+8) each has its own optical model set. The former was obtained from the elastic scattering of 81.u MeV a-particles on Pb [Pe81,Ga85a]. The "7 exit channel parameters were those determined from the elastic scattering of 3He beams of 130 MeV on Pb [Dj77,Pe81]. There are no data for elastic scattering of triton beams at high energies and so the triton exit channel 3 parameters were chosen to be the same as the He parameters. The justification for this is that both t and 3He are mass-3 particles and also there is very little difference between the energies for stripping a proton or a neutron from an a- particle (see above). The difference in the Coulomb potentials for the two particles was of course taken into account. There are three parts to the optical potential, as given in equation (111.8). The Coulomb part is expressed as Z Z 2 2 - 2 / R2 , V (1~)={ ( p T e )/( RC) ( 3 r c ) c C ZF’ ZT 82 / r , C (111.17a) 1/3 with RC= r A The central nuclear potential is C expressed as a Woods-Saxon shape with a volume absorption part: VN(r)= (111.17b) 1 + exp( £-:-B ) 1 + exp( £-:—Ei) rrr—rr A8 The spin-orbit part of the potential is expressed as V2.8(r)= Vso £L§ d_ 1 (111.170) r dr r R 1 + exp( —~§——so ) so where R. = r: A”3 and R = r A1/3. 1 so so Different sets of optical model parameters were tested by comparing the corresponding DWBA angular distributions with experimental angular distributions for low-lying states (with known l-transfers) from the 11MSm(o1,t) reaction measured in our experiment. The set given in Table 111.1 [Ga85a] is the one that best reproduces the measured angular distributions. Figures showing the quality of the fits of the DWBA calculations to the experimental angular distributions are given in Chapter V. Bound-state wave functions are also needed in the DWBA calculation, to describe the binding of the transferred nucleon x to the core nucleus A. They were calculated in a bound-state potential for which a Woods-Saxon shape was used. The radius and diffuseness parameters of this potential are given in Table 111.1 and the depth was adjusted to fit the empirical binding energy of the transferred nucleon [Pe81]. Using these optical-model and bound-state parameters, DWBA angular distributions were calculated for various 149 Table III. 1 Optical model potential paraneters med for the (a,t) and (61,3 He) reactions on sanariun and lead ta'gets fcr a 100 MeV a-particle incident energy. V r a W ' ' a r ° ° ° r a Vso 1”so so c Channel (MeV) (fm) (fm) (MeV) (fm) (fm) (MeV) (fm) (fm) (fm) a 158.u 1.32 0.62 30.02 1.35 0.85 - - - 1.u t 125.u 1.18 0.86 17.20 1.55 0.77 - - - 1.u, ’He 125.1 1.18 0.86 17.20 1.55 0.77 - - — 1.u Bound state paraneters p Vh 1.25 0.65 1-25 1.25 0.65 In the case of proton particle states in 20981 a different geometry was used, with ro- 1.28 fm, ao- 0.76 fm, rso' 1.09 fm and a - 0.60 fm. so IA. :- .5- \\v ma V 1 A“A_‘_‘_ 50 excitation energies from 0 to 20 MeV. For a given 2- transfer, they change in shape and magnitude as a function of excitation energy. This is evident from Figure 111.1, in which the 2=3 angulardistributions at excitation energies of 2.0 MeV and 10.0 MeV for the case of ‘”‘Sm(a,t) are compared. The angular distributions changed in magnitude by about 4% when the excitation energy changed from 2 MeV to 3 MeV. In order to keep the the error in the DWBA calculations less than u%, an interpolation scheme was set up as follows. The DWBA angular distributions were calculated in one MeV steps from 0 MeV to 20 MeV and the angular distribution at any intermediate excitation energy was obtained by linearly interpolating between adjacent integer excitation energies. Additionally, the DWBA calculations showed that, for a fixed spectroscopic strength, there were large variations in the cross sections for different I-transfers at the same excitation energy. This can be seen in Figure 111.2. Generally we observed that with increasing 2, the cross section also increased. This favoring of high-i transfer is a result of the fact that the angular momentum matching condition (111.5) picks out high R values for single-nucleon transfer reactions induced by 100-MeV a particles. For the same C23, the 2 = 6 or 7 cross sections are two orders of magnitude larger than the £=O or 1 cross sections. This has the consequence that the reactions studied are not sensitive 51 Figure 111.1 Calculated angular distributions for the case of i=3 . 1AA 1M5 . . transition in the , Sm(a,t) Eu reaction at excitation energies of 2.0 and 10.0 MeV, for a beam energy of 100 MeV. The calculations were done using the code DWUCKN [Ku8u]. 144Sm(0(, 01451311 T = 100 MeV‘ 10° —-E = 2.00 -; A ---E: = 1000 s... . 1 (I) "x \ \ 4310"1 - \ E C: “U \10'2 ' b x i "U \ : 10-3'-LL.1...11..-. O 10 20 30 80m. (degrees) Figure 111.1 52 Figure 111.2 Calculated angular distributions for l-transfers of O, 1, 2, 11“4Sm(01.t)1u5E:u reaction at an 3. A, 5, 6 and 7 in the excitation energy of 8.0 MeV, for a beam energy of 100 MeV. The full single-particle strength (028:1) was used for each A-transfer. The calculations were done using tflua code DWUCKN [KUBN]. do/dQ (mb/sr) 144Sm(cx,t) 1451311 Ta: 100 MeV H O (D ...-L O .L H O A 10"3 \—\ ,_ [11): ' 13;;— ’820' 1 \ ". \‘-Z=1 \' d \./‘\ LLgL\ 80m. (degrees) Figure 111.2 53 to low A in the presence of high 2, even though the two may be present with comparable spectroscopic strengths. It must also be noted that the shapes of the angular distributions are distinctive for low l-values (i=0, 1 and 2) but become rather similar for £23. Thus identification of 2 values (for £23) on the basis of angular distribution shapes alone was very difficult. The DWBA code was used to calculate angular distributions for both bound and unbound states. An unbound state is one whose excitation energy is greater than the separation energy of the transferred nucleon. The separation energy is the amount of energy necessary to separate a particle from a nucleus. For instance, the 1N5 separation energy for a proton in the Eu nucleus is 3.25 MeV. So states in lusEu at excitation energies greater than , 1AA 1&5 3.25 MeV populated in the Sm(a,t). Eu reaction are unbound to proton emission. To calculate angular distributions for unbound states, the DWBA program used the Vincent-Fortune method [V170]. The form factor distribution was used to monitor the convergence of the calculated solution for all the I- transfers considered and for all excitation energies above the separation energy. If the form factor does not converge at some excitation energy, then the angular distribution cannot be calculated by DWUCKA for the given l-transfer. All excitation energies above this one will also not be 5H calculable for the given nlj (one must increase the number of nodes n to regain the convergence, like (n+1)2j). The lack of convergence is associated with the onset of the inability of the centrifugal-plus-Coulomb barrier to hold the nucleon inside the nucleus. Since the barrier increases with increasing 1 and is higher for protons than for neutrons, the cutoff excitation energy is higher for high 2's than for low 2's and, for a given I, is higher for protons than for neutrons. Thus, for instance, for the case of proton states in Eu, the l-transfer of 3 (2f ) cannot 7/2 be calculated by DWUCKH above an excitation energy of 12 MeV; the corresponding form factor distribution does not converge and has a large magnitude for oscillations at distances of 15 to 25 fm from the nucleus. But higher 2- transfers can be calculated. Similarly, for neutron states in the samarium isotopes, l-transfers of 3 (2f7/2) and u ) cannot be calculated above the excitation energy of (239/2 7 MeV, whereas the cutoff for an Z-transfer of 6 (1i13/2) is 12 MeV. Chapter IV DATA REDUCTION AND ANALYSIS In many previous studies of single-nucleon transfer reactions, the extraction of informathm1f¥pm experimental spectra seemed to be somewhat arbitrary and subjective. For example, one would hand draw a background and use gaussians to fit gross structures. Angular distributions obtained from the gaussian fits depended on the background drawn. The widths of the gaussians used to fit the gross structures were rather arbitrary. One rather extreme example of these procedures is illustrated in Figure IV.1 [Ga81]. 1n the present work, in an attempt to be more systematic in the analysis than was generally the case in the past, the background was estimated by a calculation instead of by hand drawing it. Also, a slicing technique was used instead of gaussians to calculate angular distributions. Both these techniques have been used in recent work on particle states [Ga82b,Ga83,Ga85a,b]. The goal of our analysis was to determine the single- ;Darticle strength as a fUnction of excitation energy using the angular distributions obtained from the systematic 55 56 Figure IV.1 Energy spectra of residual nuclei 1u3'1u7’1518m from the 1““:1u8’152 3 1N3’1u7’1518m reactions at a beam energy Sm( He,a) of 70 MeV, taken from Gales et al. [Ga81]. The dashed lines that appear under the spectra are hand drawn backgrounds. Also shown are the gross structure gaussians A and B which were used to fit the spectra. 2133‘ 109‘ “N‘ NW4 (”KNOW 3133-1 1' 1525,“ o 9=8° 2.9 _ an A ' 'c l . i To C 1:: A ’ 3O 3113.1313‘3 C 3 L L L L L L acumen mv in “'9- ' V3 . Hesm e=e° 2‘ 21 1. 15 I! 3 r. a 3200‘ . 3l33'1 1N7 L margin-1111011111 1111’s)» ‘ '7: L 1 C C o :5 j 1' “”5!“ .fl e=6° "‘ ’ v t v ‘ S ' O O t ,A ‘ . --.. . .-...r--- 21 12 I? 12 9 C 3 L l J; L L ucxnuon spam :1. “‘snmm Figure IV.1 57 procedure mentioned above. IV.1 BACKGROUND Cross sections obtained from a measured spectrum clearly depend on the background which is subtracted from the spectrum. In order to try to be less arbitrary than in earlier analyses, an attempt was made to treat the background systematically and calculate it with few arbitrary assumptions. The model used for the calculation was the plane wave breakup model (PWBM) applied to the case of u-particle breakup [Wu79]. Work carried out by Wu et al. [Wu 79] has shown that, when fast 0 particles (80 and 160 MeV) are scattered from medium-heavy nuclei, the breakup process yields a significant contribution to the reaction cross section. The a-breakup model is analogous to the deuteron [Seu7] and 3He [Me85] breakup models. In the deuteron breakup model, the proton and neutron are scattered and in the 3He breakup model, the deuteron and proton are scattered. 1n the c-breakup model, the projectile (an a particle) peripherally collides with the target nucleus and then divides into two constituents. The constituents are a triton and a proton or a 3He and a neutron.. The (c,tp) or (a,’He n) reaction can leave the target nucleus either in its ground state or in an excited state. These two processes are called elastic and inelastic breakup, respectively. 58 Schematic illustrations of these processes are given in Figure IV.2 [Me85]. The S320 spectrograph was set up to detect either the tritons or ’He's in the singles mode. A coincidence experiment to study the breakup processes, although interesting, would have been very difficult and time consuming, in view of the small solid angle of the $320 spectrograph (S 0.6 msr). Recent 3He breakup work has been carried out by Aarts et al. and Meijer et al. [Aa82,Aa8u,Me85], using a 52-MeV beam of 3He bombarding 2881. Coincidence experiments were 2881(‘He,dp) used to study the breakup of 3He by the reaction and various models were developed to explain the data. These experiments show that the elastic breakup process is more dominant than the inelastic process [Me85]. a breakup coincidence experiments cH>1uot exist at the present time. Our procedure then was to use the 3He breakup model as a guide to develop a parallel a-break up model. In view of the 3He results, we considered only the elastic breakup in our model. The elastic breakup cross section is given by the expression [Wu79,Me85J 820/8938 = c 0(xA) <0(q)>2 p (IV.1) Here, 0 is a constant. 0(xA) is the total reaction cross 59 Figure IV.2 A schematic representation of two projectile breakup processes, sketch (1) being the elastic breakup and (2) the inelastic breakup. Torgef (.4 i I) 1“ elosflc ale 2) M inelosflc Figure 11!. 2 E 60 section for the interaction of the transferred nucleon x with the target A. A sharp cut-off geometrical model [8153] was used for 0(xA). 0(q) is the wave function of the constituents of theprojectile, q being the internal momentum in the projectile. We used a wave function of the Eckart fxnun [Wu79] for ¢(q). p is the phase space factor, for which an analytic expression [0165] was used. The constant c was determined by normalizing the elastic a- breakup calculation to the measured spectrum from the 1u8Sm(a,t) reaction at a small scattering angle (5°) and a high excitation energy (28 MeV). The high excitation energy parts of our spectra do not display any significant structure or peaks. This featureless character was confirmed up to especially high excitation energies (2 35 MeV) in the case of the 1u8’15u8m(a,t) reactions by measuring spectra with two (sometimes three) dipole field settings and then joining them together. The elastic breakup calculation gave an acceptable fit to the shape and magnitude over the entire high-excitation (Ex> 28 MeV) region of these spectra. In fact, it fitted the high-excitation regions of all the forward-angle spectra from the (a,t) reactions on all the Sm targets. (The (a,3He) reactions were not measured for excitation energies above ~15 MeV.) It was found that the elastic a breakup calculation was not sufficient to account for the observed cross section at large angles (0= 18°-25°). So we also considered compound 61 nucleus evaporation, which was found to be an important 3He-induced reactions process at backward angles for [Aa8u,Me85]. Such an evaporation process would give rise to an isotropic angular distribution in the center of momentum system, as was shown to be the case for 3He [Aa84]. A Fermi-gas model was used by Aarts et al. [Aa8u] to predict 3 the compound nucleus evaporation in ( He,dp) reactions. It was further shown through kinematics that the phase space 3He for the evaporation process is the same as for the breakup. However, when the Fermi-gas model was used to calculate our stripping reaction background with a Fermi energy parameter of 42 MeV [M071] and a temperature of 8 MeV, it did not predict the shape or the magnitude of the cross section in the high-lying region of the spectrum. So for the evaporation contribution to the background we arbitrarily used the magnitude of the background observed at 25° (corrected for the small c-breakup contribution at this angle). At high excitation energy, all of the cross section at 25° was assumed to be due to the evaporation and a-breakup processes. The evaporation cross section thus determined was taken to have the same magnitude and shape at all angles. At forward angles it was small compared with the elastic a-breakup yield. A comparison of the full background calculation with spectra from the 1u8Sm(c,t) reaction at various scattering angles is shown in Chapter V (Figure v.2). It is demonstrated there that the background calculation, which 62 includes the large angle evaporation contribution, predicts the spectral shape as well as the magnitude of the cross section at high excitation energy reasonably well at all angles studied. IV.2 SLICING AND FITTING In extracting cross sections we again used a more systematic approach than had been the case in earlier work. In most previous analyses, it was assumed that the spectra consisted of a few broad structures which were then fitted by gaussian shaped peaks, generally of different widths [Ga81,Ga83]. An example of this approach is displayed in Figure IV.1. The peaks labeled A and B are gaussian peaks chosen by the authors to fit the gross structure at 7””‘1u8'7523m(3 excitation energies above 3 MeV in the He,a) [Ga81] reactions. This same fitting procedure was carried out at various scattering angles. The gaussian fits yielded cross sections. For the regions where the gaussians were fitted, angular distributions were produced by plotting the cross sections as a function of scattering angle. The spectra from the present experiment may be divided into two regions, one where discrete distinguishable peaks were present and another where no distinguishable peaks could be observed. On the average, the discrete distinguishable peaks were in the excitation energy range of 0 to 2 MeV. By fitting them with gaussians, their angular 63 distributions were obtained. The rest of the spectra, from about 2 to 15 MeV excitation energy, was analyzed using a "slicing" method to deduce cross sections. The slicing was in bins of 520 keV excitation energy, corresponding to twice the width of the experimental resolution. (Figure 1V.3 displays bins of 1 MeV width for the sake of clarity.) Cross sections were obtained for each bin and the angular distributions were plotted. Other choices for the bin width were investigated and the results were checked with one another. Results of this comparison are given in Chapter V. As discussed in Chapter III, the number by which one must multiply the DWBA calculation to fit a particular experimental angular distribution is called the spectroscopic strength 0‘s; see equation (111.15). The goal is to obtain strength distributions (C’s as a function of excitation energy) over a large excitation energy range (from ~2 to 15 MeV) for different i-transfers. This was achieved by fitting the experimental angular distributions with the contributions from various i-transfers calculated using DWBA. Because of the overlapping nature of the single-particle resonances, in general more than one 2- transfer contributed in each energy slice. The fitting procedure was carried out by minimizing the following quantity [8e69,Ge70]: 2 - . IV.2 (( y(xj) yJ)/AyJ) ( ) (b N 11 Q IIMZ 6“ Figure IV.3 Illustration of the slicing of spectra into bins. A bin width of 1 MeV is used for clarity. The spectrum displayed 1118S 1N9 m(a,t) Eu reaction at is the triton spectrum from the 5°. The dotted curve is the total background that is obtained by the procedure described in the text. 1', = 100 Mev 14BSm(a.t) IBOOIII1IIIITITIFIIII -o- ' a = 5° X ' - 1 an A 5 *1 I geno— o 0 ll 0 L l 1 l --1 Excitation Energy (MeV) Figure IV.3 65 Here, AyJis the error in the data point yJ; N is the number of data points, and y(xj) is defined such that 2 y(xj) Zmax a(1,.£x) r(1,.xj.sx) (IV.3) i,=0 f(2,,xJ,Ex) are the DWBA cross sections (calculated with the DWUCKA [Ku8u] code) at position x.j (where xj may be either scattering angle or, equivalently, momentum transfer) mm" angular momentum transfer 11 and excitation energy Ex' The quantities a(£,,Ex) are free fitting parameters which contain the spectroscopic strength information. They are determined by minimizing (IV.2). The minimization procedure is carried out by finding the extremum of (IV.2) which is, an/aal = a 2( y(xj) - yj)/Ay3{f(l,x.,8x)} = 0 (1v.u) J 11 M2 j 1 To be sure that 32 is a minimum, one must show that Baez/aakaaj > 0 at the point where (IV.M) is true. Note that N 2 2 = 2 a e /3alx8a12 a 121 21(i,,xi,Ex)r(12,xi,EX)/Ayi > 0 (1v.5) since f(l,x ,Bx) > 0. This means that the extremum at (1V.N) i is a minimum. So the solution of (IV.M) is 66 N 1 2 {max a(l,,Ex)f(l,,xi,Ex)f(lz,xi,Ex)/Ayi 1-1 1,-0 N . 121 y1f(lz,xi,Ex) (1v.6) (1v.6) is a matrix equation in which the known quantities are the data points yi and the DWBA cross sections f(11,x ’Ex) at angles x for various l-transfers and J J excitation energies. One can determine the parameters a(£,,8x) by this means. The above procedure of minimizing (IV.2) is known as the least squares X2 method of fitting [8e69,Ge70]. The quantity a in (IV.2) is 1/0 where v is the number of degrees of freedom in the fit (i.e., v a N [data points] - number of fitting parameters). The quantity 22 obtained by minimizing (IV.2) is commonly called the "reduced X2" or the "X2 per degree of freedom" and denoted by the symbol x:. The X2 value is related to x: by the equation; x2 = v x ,2 (1v.7) A program called SMASHER was written to calculate the background, "slice" the spectra and fit them with the DWBA angular distributions. A program example to use SMASHER is given in Appendix 11. CHAPTER V EXPERIMENTAL RESULTS The experimental results from the stripping reactions 3 1NA,1H8,152,1SASm and 208P (c,t) and (c, He) on targets of b are presented in this Chapter, which is separated into six sections. In the first section, the criterion used to accept a particular set of i-transfers for a given angular distribution is discussed. Background subtraction is discussed in the second section. In particular, the a- breakup calculation described in Chapter IV, the method of normalization and the uncertainty in the background calculation are presented. In the third section, our data for the well resolved low-lying states excited in the 208 93 208pp 3 209Pb reactions are Pb(01,t)20 1 and (01, He) discussed. These data are used to test the DWBA calculations performed with the code DWUCKH [Ku8u], both as regards angular distribution shapes and as regards predicted magnitudes (by comparing spectroscopic strengths obtained from the present measurement with those from previous work). In the fourth section, the overall spectral shapes and their variations from isotope to isotope are discussed for the 144,1”8,152,1Su 3 stripping reactions Sm[(c,t) and (a, He)]. 67 68 3 The results from the (c,t) and (a, He) reactions on 1uu,1u8,152:15“3m are presented in the fifth and sixth sections, respectively. The spectroscopic strengths for the low-lying states of 1”Eu, 1u98u and 1u5Sm obtained from the ‘ 11111 1115 present measurement, through the use of the . Sm(a,t), Eu, °u88m(a,t)1u98u and 1uuSm(a,3He)]uSSm reactions, respectively, are compared with those from previous measurements. The well resolved low-lying states of °u58u u and 1 5Sm are used to provide a check on how well the predicted DWBA angular distributions agree with the measured angular distributions. Spectroscopic strengths for the low- 153Eu ISSEU 1‘19Sm 153 155 lying states of , , , Sm and . Sm are reported for the first time. The spectroscopic strength distributions at high excitation energies for the proton and neutron states built on the samarium target ground states are also presented. The summed transition strengths (2 C28) 145 for Eu obtained from this study are compared with those from previous work. V.1 CRITERION FOR ACCEPTING R-TRANSFERS As described in the previous Chapter, the high-lying regions of the spectra generally involved a mixture of £- transfers which were sought to be identified by fitting the measured angular distributions with a set of DWBA calculations for different l-transfers. The strength parameters a which are related to the spectroscopic 2' 9 69 strengths, were determined by requiring that Eakggz (with DWBA 2 d9 the set of allowed 1's chosen on the basis of shell model considerations) provided the best fit to the shape and magnitude of the experimental angular distributions. The most common criterion used for this was the minimization of the quantity x: ("reduced x2") defined by equations (IV.2 and 1V.7). Each of the al values corresponding to the minimum x: has an associated error or width [Be69]. The error (da ) in the parameter a was approximated by the A 1 standard deviation of the fit, which is determined by the inverse matrix elements of the fit; it was not weighted by xv. This error is included, along with other experimental errors, in the results which are tabulated and plotted in the following sections of this Chapter. Since the calculated angular distributions for the different i- transfers were rather similar, it was difficult to be sure that the correct set of i-transfers was selected by following the best-fit criterion. Acceptance of slightly worse fits (slightly larger X3) would have led to a different set of l-transfers. In order to assess the difficulty of this procedure, the experimental angular distributions were also fitted with single l-transfers. The al's and the x: from these fits were obtained as a function of excitation energy. For each combination of i-transfers, the program calculates various local minima. The minimum x: is the 70 lowest of these local minima. This minimum x; will be listed in all the tables in this Chapter except for Tables v.1, v.9 and V.12, while the X3 values corresponding to the other local minima will be listed in a few selected cases (Tables V.2, V.N, V.6 and v.8). v.2 BACKGROUND CALCULATIONS As mentioned in Chapter IV, the backgrounds used in previous experiments were often arbitrarily drawn by hand. In an attempt to be more systematic in handling the background, we peformed an a-breakup calculation, as described in Chapter IV, and the results are presented hi this section. We discuss first the results for the (c,t) reactions. With a single normalization constant for each reaction, the c-breakup calculation predicted the shape and magnitude of the high excitation energy region of the spectra reasonably well for forward angles out to 12°. The calculation predicted only about 50% of the observed cross section at 18° and about 10% at 25°. This suggested that while the breakup calculation may explain the background at forward angles, some other contribution was present at larger angles. As mentioned in Chapter IV, the unexplained part of the background at 18° and 25° was thought to be due to a compound nucleus evaporation process. However, a simple Fermi-gas calculation of this process did not explain the 71 shape of the spectra in the high-lying region [Aa8U,Me85]. Therefore the empirical shape and magnitude of the spectrum at large angles and high excitation energies was used for the contribution of this process, and the contribution was taken to be constant at all angles. The net background was taken to be the sum of the a- breakup part and the angle-independent part. In Figure V.1, this net background is compared with the spectrum shape over a particularly large range of excitation energies measured in the 1511S 155 m(c,t) Eu reaction at 5°. We note that the background calculation follows the shape of the spectrum from about 28 MeV to about “3 MeV in excitation energy. Thus the excitation energy at which the background calculation is normalized to the spectrum is not important, as long as:H;is high enough. In fact, the normalization was done at an excitation energy of 30 MeV in jssEu, corresponding to a Q-value of —U3.2 MeV. For the (a,t) reactions on the other three samarium isotopes, normalizations were carried out at the same Q-value of -43.2 MeV. We believe that this procedure led to greater consistency in the analysis, since the phase space of the a- breakup begins at the same Q-value for all of the europium isotopes. In order to keep the number of free parameters in the background calculation to a minimum, for each reaction we used a single normalization which was the average of the values obtained at different angles. (1n the case of the 1lmSm(01,t)1u5EIu reaction, the high-lying position of the 72 Figure V.1 15“ 5 Triton spectrum from the Sm(c,t)15 Eu reaction at 5° showing the a-breakup plus evaporation calculation (dashed curve) for the background. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in the figure. The sharp peaks near Q-values of -35 and -N8 MeV are spurious and are due to a defect in the focal plane detector. 9 154Sm(rx.t)°°°1~3u Ta: 100 MeV 1D 15 1 351359?!{JJQ'JLJE' ' 2 . 10 20 3O ' L‘ . U) . 9: o . \\\ _ q .0 10. 8 El - ,- 1 q "d 5 . [I C: ’ / 4 "d , 1 \ 1 053 “J+~:-1~---l---.1.- - “o ‘10 ~35 -60 Q-Value Energy (MeV) Figure VLl 73 spectrum was measured only at 7° and so no averaging was possible.) The normalizations used for the a-breakup contributions 1AA,1A8,152,154$m(a’t)1"5,149,153,155 in the Eu reactions were 7.1, 8.7, 6.8 and 8.3. respectively. Note that they u are slightly lower for the reactions on ] IJ’ISZSm than for 1u8’15u8m. The uncertainties in the the reactions on absolute cross sections for the reactions may contribute to these differences. We recall from Chapter 11 that for reactions on 152Sm there is a 20% uncertainty in the absolute cross section values. The results of the background calculation are compared with the measured spectra from the 11°88m(01,t)1_u913u reaction at various angles in Figure v.2. The a-breakup contribution dominates at forward angles but falls at larger angles, as shown by the dot-dashed curves at 18° and 25°. The compound nuclear evaporation process, on the other hand, contributes very little to the background at forward angles (3 12°) but dominates at 25°. Together, these two processes predict the spectrum shape as well as the magnitude of the cross section at high excitation reasonably well at all the angles studied. Because the background calculation did not give a perfect fit to the high-lying part of the spectra at all angles and energies, an uncertainly is introduced into the cross section determination. Of course, the high-lying part of the spectra might not result solely from elastic a 7“ Figure v.2 u Triton spectra from the 1u88m(a,t)1 98u reaction at eight angles. 'Nmeestimated total backgrounds are shown by the dashed curves. The c-breakup contributions at angles of 18° and 25° are shown by the dot-dashed curves. At more forward angles the contribution from the compound nucleus evaporation process is small relative to that from a-breakup and therefore the total background is essentially equivalent to the a-breakup contribution. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in each panel of the figure. 0 .... V n... m 1 m . a. T m 1. \u’ b." 0 a 3 m . I. J 11.1111-1111-1111 1111.1111-1111.1111-1111.1111 1111-1111-1111.111.111.1111 11 1.111-.--11-11 1.1111 0 1 nu .0 .0 _ .u a. 10 9.... RES mace}... Energy (MeV) Q-Value v12 P8 -Figu 75 breakup and compound nuclear evaporation. There may be some single particle states or other background process which contribute to the spectrum in this region. However, until more definitive coincidence measurements are made, we assume that our normalization of the background calculation is reasonably correct. The uncertainty in the background normalization contributes some uncertainty to the relative cross sections. We chose to take half of the percentage difference between the spectra and the predicted background at the position of normalization as the relative error. An interpolation of the error was carried out for all angles for which the measured spectra did not extend to an excitation energy high enough to reach the normalization point. Figure V.2 indicates that for °u98u, the cross sections at 2° and 9° would have the largest error bars, 13% and 12% respectively, since they are the angles for which the calculated backgrounds are furthest from the spectra at the normalization point (Q-value of -A3.2 MeV, Ex: 27.7 MeV). We now turn to the estimate of the backgrounds for the 3 (a, He) reactions. The procedure used to calculate the a- breakup contribution was similar to that for the (a,t) reactions, except that the normalization was obtained in a different way. This was because no high-lying spectra (Ex) 3He) case, partly due to the 15 MeV) were measured in the (a, lack of time and partly due to experimental problems. The normalization for each target was obtained by assuming that 76 the ratio of total yield to background in the (0,3He) reaction was the same as that in the (c,t) reaction at a selected angle (7°) and excitation energy (~1H MeV). The normalizations used for the (c.3He) reactions on 1uu']u8’]52°°5u3m were 5.5, 6.3, “.9 and 3.6, respectively. The evaporation part of the background was adjusted such that the ratio of total yield to background at 25° in the (a,3He) reaction was the same as in the (c,t) reaction. As an example of the results obtained, the estimated u backgrounds are compared with spectra from the 1 8Sm(a,3 He)]ugEu reaction at various angles in Figure v.3. The backgrounds estimated for the (c.3He) reactions on the other Sm targets showed the same behavior. The uncertainties of 3He) reactions were the background subtraction for the (0, obtained in the same way as for the (c,t) reactions. After the calculated backgrounds were subtracted from 3 the measured spectra for both (c,t) and (a, He) reactions, the remaining parts of the spectra were assumed to consist only of particle states populated by a direct nucleon transfer mechanism. V.3 208PB(01,t)20981 AND 208Pb(c,3He)209Pb REACTIONS . . . . . 208 . Many Single particle stripping reactions on Pb which populate the low-lying states of 20981 and 209Pb have been reported [Ma77]. [Pe81,Ga85a]. 131the present experiment, 3 these states were measured by the (c,t) and (c, He) 77 Figure v.3 u Same as Figure v.2. but for the 1u88m(a,3He)1 9Sm reaction. Besides the Q-value energy scale along the horizontal axis, excitation energy scales (in MeV) are shown in each panel of the figure. The break near the middle of the spectra is due to a defect in the focal plane detector. mSrn(01.°I-Ie)“°Srn T,= 100 MeV 11?.)111-1111 11>1b1pb>bbhub->>1>-prppn>h>1 11-1111b1111-1111 5 5 $62 .aEEV Sagan“. x~ .0 .fl .0 -30 -20 Q-Value Energy (MeV) -20 -10 F1 ure v.3 78 reactions on 208Pb for three reasons. First, they are well separated even with the modest resolution available in the present experiment. Therefore they provide a check of how accurately the angular distributions predicted by the code DWUCKA match the experimental angular distributions for states whose J" values are well known. Second, the spectroscopic strengths (C23) measured for these states in this investigation can be compared with other work. Such a comparison provides a check on the overall normalization of the DWBA calculations, in particular the value of N (occurring in (III.15)) which in previous work [Ga85a] was determined to be 36. Third, the slicing method used for the higher excitation energy regions of the Sm and Eu isotopes (sections V.5.2 and V.6.2) can be tested by summing the angular distributions of two low-lying states to find whether the x: fitting program can select the correct 2- transfers for this summed distribution. Three distinct low-lying states are populated in both 20981 and 209P1) , as shown in Figure V.U. We note that the resolution for the (c.3He) reaction is somewhat better than that for the (a,t) reaction. This may be explained in the following way. The spectrograph was focused using the elastic peak. The spectrograph settings were then sealed according to the ratio of the rigidity of the particle of interest to that of the elastically scattered ”He. The 3 rigidity of He is closer than that of the triton to the u rigidity of He. Thus the extrapolation is greater for 79 Figure v.u 208 Spectra from the Pb(a,t)2098 208 209 i BDG Pb(a.3He) Pb stripping reactions at a scattering angle of 5°. Ta=100MeV 000 W1 Elk-1.61 «L 400 r . Q: 50 . 200 ’ 1---- Counts 400 ; 206Pb(01,:°He)2°9Pb 200 o 1' 1 - 1 20 350 500 Channel Number Figure v.u 80 tritons, and this is the probable cause of the worse resolution. The experimental angular distributions obtained for the low—lying states of 20931 and 209Pb are shown in Figure v.5. 208P 209 DWBA calculations were made for both the b(d,t) Bi and 208Pb( 3 209 a, He) Pb reactions using the optical model parameters listed in Chapter III (Table III.1). A different 20981 (see set of bound state parameters was used for footnote to Table III.1) [Ga85a]. Use of the first set of bound state parameters gave a low DWBA cross section so that the 0‘s value obtained for the ground state of 20981 was significantly higher than unity (see column A in Table V.1). Recall that unity is the theoretical maximum, as shown by equation (III.16). Results of the "minimum XS" fits for the low-lying states of 20981 and 209Pb are shown in Figure v.5. The fits have rather large x: values ranging from about 2.3 to 8.5. The 023 values obtained from these fits (using N=36) are 20981, two sets of bound-state listed in Table v.1. For parameters, labeled A and B, were used. They are the first and the second set given in Table 111.1. C28 values from other recent measurements and from the Nuclear Data Sheets [Ma77] are also tabulated in Table v.1. We note that the C25 values from the present experiment (with bound-state 20981 and A for 209Pb) parameter set B for are slightly lower than the values from other recent work and that they are at the lower end of the range quoted by the Nuclear Data 81 Figure v.5 Angular.distributions from the 208Pb(a.t)20981 and 208 O Pb(a,3He)2 9Pb reactions for low-lying proton and neutron states in the final nuclei. The l-transfer and excitation energy (in MeV) are indicated in each panel. The solid curves are the normalized DWBA predictions for these 1- transfers. do/dfl (rnb/sr) 10. 1.0 2°°Pb(a,t)z°°Bi 2°°Pb(a .3He)z°°Pb v v ' "v v v v vvvvv' - p 1! l D p D ht.‘ A A A A A AA ' - ' VVV'V' V V v 3,: 0.0 rfrfir A1 A | A A A A A A A A. i A A A -li-- 10 20 10 69¢... (degrees) Figure v.5 20 30 82 :35 C. J76: Hung—«Logo u58gm A. ”apex“ Ac H5£HA9 me m8 Am mm..-mm.o mm.o~\m.q_ m=.o 5 ~:.. =o.o-~m.o m~.o =~.om\m.a_ mm.o no.0 o ._o._ ~m..-m~.o ca.o~\m_a. oc.o o m~.o m_._-ms.o m~.o o~.o N\~a~ mm.o m~.o m om.o \ ma..-mm.o mm.c Nxmmm mc.o z oo.o 5...-zm.o mm.o oo.o N as, ow.o a:.. m co.o x x m3 090 1.: .90 a :2: m .93 om.u «$0 2: .mb .m.u a :3: m 302...... < 302m m < sumo x8: £85..on 2:... some x83 985.898 3:... .3033: .850 .5332 .650 . o .5 .5 £8~A =m vamom d£83 Vemow ...H: v.33. 5 53m 983.5ng woman 058 .3 moon 85.8.23 oz» 939 .«o 338.. on» 0.3 m was < «53an 2:530 oz... on... .nmmom new Baom .3 883m 92:-on no» 8033238 .5155 2» 3 BC Q2555... 9: .8: 8538 832 mac 9: .0 $3 —.> $.32. 83 Sheets. However, our C’S values are consistent with the others within the range of uncertainty (151) in the value of N at our energy. We conclude that although the absolute cross sections predicted by the DWBA calculations are slightly high, they are resonable. Our C23 values could have been made higher by decreasing the value of N, but we decided it would be better to use the standard value than to increase the number of variable parameters in the analysis. These data served to test, for cases where the correct answers were known, the reliability of l-transfer values obtained by fitting measured angular distributions. Table v.2 lists the complete range of x: values for different 20 mixtures of l-transfers for the three low-lying states in 981. We note that in all three cases, the correct (single) l-transfer gives the minimum x: and that the next nearest x: corresponds to a mixture of Q-values that includes the correct l-value. Also, the added mixture of other £- transfers reduces the 0’s value for the l-transfer selected by the minimum-x: fit. The need to test the slicing method used in sections V.5.2 and V.6.2 provided a further reason for studying the lead target. The angular distributions for two known low- lying states in 20981 and in 209Pb were summed and the fitting program was used to analyze them. This procedure of decomposing the summed angular distribution of low-lying states reproduced, to some extent, the situation wherein 8“ Table v.2 1.1.: o! the possible c's vsi’ues. using the 111an indicted. ta- the low-lying states in 20931. The c‘s values ere determined using the set 3 of bomd stete pr-etrs (see Table 11.1) . 1 Hi" 3 3 "iv B B 1' 1r . "‘-’ 3" 0.00 1 C S xv 1 0'8 x: 2‘ 0.90 1 0'3 x:' l C'S {:7 5 0.60 3.87 6 0.25 3.5 3 0.53 2.3 7 0.23 3.7 3 0.1“ 5 0.05 3 0.39 6 0.12 H.“ 7 0.12 16. u 0.06 2.“ H 0.23 16. 5 0.30 “ 0.15 3 0.00 M 0.03 6 0 09 ‘4 11 6 0 311 26. 6 0 02 3.0 5 0.511 82. 5 0 1M 3 0 50 6 0.11 7 0.18 5 0.05 31 6 0 28 172 5 0.39 5.0 3 0. 31 3 0.139 3 0.02 7 0.03 5.7 u 0.23 50. 7 0.01 3.2 7 0.27 308. 5 0.5“ 3 0.51 6 0.20 S 8 7 0 3“ 13“ u 0.09 7 0.0“ 6 l1 3 0.117 135 5 0.U9 11 0.01 HOV B B B B . I T x I z z .. ‘F Ex 1.61 l C S xv l C S xv 1 C S xv 2 0‘3 xv 6 0.53 3.7 7 0.27 3.5 5 0.9“ 67. u 0.39 192. 5 0.fl8 7 0.02 3.8 7 0.35 113. 7 0.52 67. 3 0.88 359. 6 0.51 H 0.15 7 0.0“ “.9 T 0.39 20. 6 0.“8 3 0.26 n 0.01 85 angular distributions of high-lying regions with unknown 2- transfers were fitted in order to determine the i-transfers and their individual contributions to the cross section. It gave an indication of the accuracy of the fitting procedure in selecting an i-transfer or a mixture of i-transfers. Results obtained by using the minimum-x: method are shown in Table v.3. It is observed that the i-transfers obtained by fitting the summed angular distribution are off by one unit from the correct i values. This suggests that the selection of an i-transfer made by the fitting procedure is probably only accurate to within :1, consistent with Huafact that the angular distribution shapes for neighboring i-transfers are similar (see Figure III.2). Also, the fit to the summed angular distribution with the incorrect 2's has a x: value that is HHHHT smaller than the x: values for the individual angular distributions with the correct 2's. More importantly, the inaccuracy of selecting an i-transfer implies that the C35 values determined will not be valid, since they may be associated with the wrong i-transfers. Table V.“ lists the range of x: values for the summed angular distribution in the case of 20981 for all combinations of i-values from the set i=3,fl,5,6,7 which gave positive values for C28. Hence, the reader can evaluate the reliability of the l-transfer values obtained by the fitting procedure. Thus we see that CZS values are hard to deduce in regions where different i-transfers overlap (Tables v.3 and 86 .—.> 03m... 6.; Lo>o 32:8 mead? man I. .853» 93:..on oz» gas: on» min—83m + 3.385 s 2.5 3.285 m as 35 a. $5 .. 3.39.5 m and 5.3280 9.0 6.386 a 8.0 8.286 m 86 < goixm < $5M. m 93.3.. m 923M 238va a 233.0 a 23863 a 236.0 a Emowxmzm BEEN 8253 3968 . :5 03m... 003 93.5338 423 on» 5 009 983.5ng 33m 258 ha neon 0:» on» 0.... Logo; m 05 < nHBmH 9:. 63935ng ca :39; mum 3: 9.3 yo mead: ”x on... 3.0.35.3; 2306. on» 939 ufiaficm 3:83:93 mm: mega some can: 02.3.50 anon... 5 a: 89.328 one 333.2 mg... 6:83:39. 3.7... men on» 3 uoaomaon one: 333?... 2: con: .nmaom one «maom 5 sum: mcgauaa or» can: 05 go 9833238 6.39.5 3335 on» go «Suzanna 23 no 3 33: m .> $33. 87 Table v.u List of the extracted c's values, for the canned angular dietrlhutlcn of the first two law-lying states in 20931, when the lemixttra wa'e fixed at the values indicated. The correct l-values are 5 and 3. eff-0.115 MeV 9. c‘s x: 9. c's XT 501 0.10 0.91 F 0.39 3 0. 33 0. 96 0.33 5U! wU'I .... 0.1“ 0097 0.30 0.15 Wmfl O 8 J: .0 g ax 0.07 0.99 0.13 0.36 2.0 zmm DUI-'0‘ 0.10 1.00 0.15 0.26 0.16 00sz ms: 0 0 Cd \0 4-.- m 0.02 1.0 5 1.2 8.5 0.25 0.35 cmq 0.311 1.1 3 1.0 18. 0.31 0.03 0.03 1.2 6 0.63 311. 0.28 . 0.30 0.07 0.061.2 7 0.61 86.’ 0.112 :4 01.1sz but-‘U'I 0.15 1.11 WWO‘ O u» U.) 88 V.“) but that the correct l-transfer and C23 value are obtained by the fitting procedure in regions where only a single i-transfer is present (Table v.2). Keeping these conclusions in mind, we shall now proceed in attempts to obtain the spectroscopic strength for single-particle states built on the ground states of the samarium targets. V.“ SPECTRA FROM NUCLEON-TRANSFER REACTIONS ON SAMARIUM 3 Spectra at 7° from (a,t) and (a, He) reactions on qu,lu8,152,15“Sm targets are displayed in Figures V.6a and V.6b, respectively. The (a,t) reaction populates proton 3 states in europium and the (a, He) reaction populates neutron states in samarium. We observe differences among the proton and neutron single particle states as a function of deformation (which increases with mass for the nuclei considered here). Figure V.6a shows the presence of a gross structure (labeled A) just to the right of a pronounced minimum in all four Eu nuclei. This structure occurs at around a Q-value u of -23 MeV for 1 5Eu, corresponding to Ex= 6.” MeV. As the (“SEu to 155E deformation increases from u, the gross structure "A" moves closer to the corresponding ground state. Accordingly, it resides in the unbound region of the 1M5,1M9 spectrum for Eu and in the bound region of the 153,155 spectrum for Eu. 89 Figure V.6a Triton spectra at 7° for proton states excited by the 1uu’1u8’152’15u8m(c,t)1“5’1u9’153’155Eu reactions. The horizontal scale gives the reaction Q-value (in MeV). The corresponding excitation energies in the residual nucleus (in MeV) is also shown in each panel of the figure. The a- breakup plus evaporation calculation is shown as the dashed curve. dzo/deE (mb/sr MeV) ASm(ont)‘MEu T¢= 10 5 .. 10 20 - 0: 7°- 5 - A B _ /” 7 \‘ - // / 1 E! __ 10 20 _ 10 - (9: 7°- ._ A .. 5 _ B _ 10 - 5 .- 0 -1o -30 -50 100 MeV 155Eu 153 Eu 149Eu 145 Eu Q— —Va1ue Enesrgy (MeV) Figure V. ...-“E: 90 Figure V.6b Spectra of 3He at 7° for neutron states excited by the 1uu,1u8,152,15u8m(a,3fle)1u5,1u9,153,155 Sm reactions. The horizontal scale gives the reaction Q-value (in MeV). Excitation energy (in MeV) is also shown in each panel of the figure. The break near the middle of the spectra is due to a defect in the focal plane detector. The o-breakup plus evaporation calculation is shown as the dashed curve. ‘Sm(a,3He)‘“Sm Ta = 100 MeV 10 A .'> 0) :3 5 L. (I) \\\ “E v 1:”: ‘ . 5 10 * . «149 [.51 ’_ e: 7. i Sm C'. ' 1 13 5 _ J \\\ A‘ ‘ b r m .. ,4 13 y ,’ « T ’l i :“:;~:1‘:‘*‘ ‘ 5r iors' I ; i 145 r 9: 7. - Sm 5 L U i ,’ 0b .l....L/.. .1..-.‘ ’10 -20 -30 —V (Q edgiginghgfzgguy (AAEflV) 91 There is also a second gross structure "bump", LLabeled "B" in Figure V.6a, that is centered at a Q-value of about - 32 MeV in (“SEu (Ex- 15 MeV). It resides in the unbound region of excitation energy in all four Eu isotopes. This bump also moves closer to the ground state as the deformation increases. We also observe a gross structure, labeled "A'" in Figure V.6b, around the -25 MeV Q-value region (Ex- 11 MeV) u in the 1 5Sm spectrum. This gross structure also moves closer to the ground state as the deformation increases in the odd-mass Sm nuclei. It resides in the unbound region of the spectrum for 1u5’1u98m and in the bound region of the 153.1558m. spectrum for The i-transfers in each region of the spectra will be determined by the fitting procedure (to within an uncertainty of :1, as discussed before) in the third section for the (a,t) reactions and in the fourth section for the 3 (a, He) reactions. Thus the i-transfer(s) associated with each of the gross structure "bumps" will be identified. 1HH,1U8,152,15M 145.189.153.155 v.5 Sm(o,t) Eu REACTIONS This discussion of the results from the (a,t) reactions on the samarium isotopes is divided into two parts: 1) The results for the low-lying states, including the extraction of angular distributions, assignment of l- transfers and determination of C28 values.' 92 2) The results for the high-lying portion of the spectra, including the extraction of angular distributions using the "slicing" method described in Chapter IV and the determination of the C28 distribution as a function of excitation energy for different i-transfers. V.5.1 Low-Lying States in 1HM,1H8,152,15H 145.149.153.155 Sm(a.t) Eu The low-lying portions of the energy spectra from the 1UN,1N8,152,15H (a,t) reactions on Sm are displayed in Figure v.7. It is clear from this figure and an examination of other work [Tu80], that in the case of (usEu the states are well separated up to an excitation energy of 1.2 MeV, whereas the states in the other three nuclei are not well resolved. With increasing mass, and thus increasing deformation of the isotope, the density of low-lying levels also increases. So the levels are not well resolved within our limited experimental resolution. The angular distributions obtained by fitting gaussians to the (mostly) unresolved collection of low-lying states are shown in Figure v.8. In principle, the fitting program should pick out the correct mixture of l-transfers for states within a peak. If the decomposition works well for the low-lying states we may be more confident about applying this method to higher lying regions. 93 Figure v.7 Triton spectra at 5° showing the low-lying proton states populated by the 1“1"1u8’152’151‘Sm(a,t)1“5’1“9’153’155E3u stripping reactions. .v': dza/dfldE (mb/sr MeV) W 0 l 2 3 3‘ 20 _ i t 1 6: 5° 10 - 15‘Sm(a,t)155Eu Q‘_..'=- 13.2 ‘ Qu.=-13.9 148Sm(o:,1’.)1"'9}':‘.u ‘ Que-15.4 144'Sm(on,t)1'"5Eu Que—16.6 '75 - ®= 5° 1 50 L 25 t o l I —13 -15 -17 Q—Value Energy (MeV) Figurg_v.7 9N Figure v.8 Angular distributions of some low-lying peaks (indicated with arrows 1J1 Figure V.7) which are excited in 1“5’1“9'153’155Eu. The curves are the minimum-x: fits with DWBA predictions; the corresponding 2 values are indicated. da/dfl (mb/sr) '“5m(a.t)j“zu “‘mgahmzu ‘°'3m(a.t)‘”au ‘“sm(a.c)‘“eu - 0.05‘ l;- 0-1111' ' l :- 0331 4.3.3.0 f i t' .. - 1.. . " - ' 5.- “31.35 --~\ "'"" .m "-‘-. ---!.-e. ’I 1 r ..l.’ I;- 1.411 -- l-O 8,,JIIL (degrees) El§2:s_!;§ 95 The Z value (proton number) of europium is 63. In the simple shell model theory, the 1g9/2 orbit is filled at Z-SO. The next subshell (between Z-50 and Z=82) contains the single-particle orbits 1g7/2, 2d5/2, 1h11/2, 2d3/2 and 331/2 [8075a]. It is in these orbits that the 13 valence protons of Eu (outside the Z=50 shell closure) are distributed to form, by coupling with the valence neutrons outside the N=82 shell closure, the low-lying levels of the Eu isotopes. That is the picture according to the spherical shell model which, however, is not valid for the heavier Eu isotopes because of the effects of deformation. The Nilsson model, which incorporates these effects, shows that the single-particle orbits shift in energy depending upon the deformation. The energies of the lower orbits in the next higher subshell (above 2282), 2 and 1 f7/2’ ”19/2 113/2' decrease as the deformation increases, so these orbits can occur at the same energy as the subshell that contains the and 3s orbits. Therefore the 137/2’ 2d5/2' 1h11/2' 2013/2 1/2 i-transfers expected in proton transfer to the low-lying u 1 states in the lighter europium isotopes 1 5’1 9Eu are 2, u and 5 (2 1h11/2 proton excitations) d5/2' 2d3/2’ 1g7/2’ 153.155 whereas those expected in Eu are 2, 3, M, 5 and 6 2f 1h ( and 11 2 proton 2d5/2' 2d3/2’ 7/2’ ‘87/2' 11/2’ 1h9/2 13/ excitations) [Bo75a]. The i=0 transfer corresponding to the 331/2 proton excitation is weak at our high bombarding energy (see Figure III.2), so this i-transfer was not included in the analysis. 96 We now present the results.for the four Eu isotopes individually. In this discussion the reader should remember that the ability to select an z-transfer (and hence to determine the C28 values) using the minimum-x: criterion, when unuting with other l-transfers is involved, is probably accurate only to within :1. Also, it should be noted that in addition to allowing the above mentioned set of 2- transfers to fit each of the low-lying peaks, each peak was also fitted separately by each of the individual l-transfers from that set. This allows the reader to better evaluate the reliability of the l-transfer values obtained from the fit and to have available the C28 values if a different 2- mixture is assumed. u a) Low-lying states in 1 5Eu Since the low-lying states of ?u5Eu were well resolved in the present experiment, the angular distributions measured for them provided a means for checking the angular distributions calculated by the code DWUCKH, just as in the case of the low-lying states of 20981 and 209Pb discussed before. In addition, the spectrOscopic strengths obtained were compared with previous measurements [Tu80,Ga85a]. The four states analyzed are indicated by arrows in Figure v.7. By an examination of the Nilsson model predictions [8075a], we see that i-transfers of 2, N and 5 ‘4 are the only p0331b111t1es for the low-lying states of 1 5Eu 97 (see discussion above). These E-transfers were used to fit the angular distributions for the low-lying states using the "minimum x3" criterion. The fits are shown in Figure v.8 and the extracted CZS values in Table V.5, where the x: values from the fits are shown in parenthesis. Table v.6 lists the range of x: values for the four low-lying states for all combinations of 1 values from the set 2=2,u,5 which gave positive values for C28. (A negative value for 028 is, of course, unphysical.) We note that, 20981, the just as was the case for the low-lying states of x: value nearest to the minimum x: corresponds to a mixture of i-values which includes the one identified as the correct l-value by the best fit (minimum x ). Also, as we would 2 v expect, the effect of the additional l-values in the mixture is to reduce the C28 value for the l-transfer which corresponds to the best fit. Table v.7 displays the czs values obtained when the angular distribution for each state was fitted with a single l-transfer chosen from the allowed set (i=2, u or 5 in the case of 1u5Eu ). At least some of these single-2 fits are clearly unphysical, since they give 028 values considerably above the theoretical maximum (unity). As shown in Table v.5, the results from the present experiment agree quite well with those from previous measurements. The states at Ex: 0.05 and 0.37 MeV have strengths quite close to the values determined in previous measurements, while the states at Ex: 0.73 and 1.04 MeV have S)8 Table V. 5 use d :1. spectroscopic strangul- (6'8) obtained from minima-x; - fits for the low-lying out. “105.109.153.155“. 1'1. x: vainl- 0r :7- fitl to given in {Ir-um“. This «peril-It 11me atm- Pk I (9940:»)' Data Shots wa-k Final 8 ' Burma) ‘v 31:01.1!) “’1 c's c's Nmicu 2 0.37 H 0.23 (1.3) 0.329 137/2 0.2! 0.17 3 0.73 5 0.70 (6.9) 0.775 ”11120-95 0.32 ”530 H 1.0” 2 0.53(‘1.0) 1.0332 2d3/2 0.73 0.98 c 1 0.11 2 0.25 (32.) 0. 265,2 0.22 n . I I 0 an o 15 737/2 0 12 2 0.51 50.172 (36.) 0.1196 tun/20.63 2 0.82 1:79 3 1.07 2 0.08 (16.) 0.811 265/2 0.03 Eu 5 0.08 0.876 " 0.051 1.221 " 0.21 1| 1.1)? 2 0.33 (22.) 1.31 2d5/2 0.01 5 0.111 1.399 291/2 0.08 1.13140 2pU2 0.07 1.503 1n'1/20.11 5 1.711 11 0.32 (27.) 1 0.33 2 offiTm.) 2 0.70 a 0.25(36.) 153:0 3 0.71 3 1.20 50.08019.) 3 0.12 1 0.185 50.15 (7.7) 3 0.07 2 0.20 2 1.07 60.05(7.6) "5520 u 0.26 2 0.23 3 1.111 50.11 (9.1) 3 0.21 a) [03531; b) [111807; c) {SW9}; 7 Using the minimum 1;. 99 m=.o m s.m o_.o : 2.6 N 26 m ..m o..o m a... 86 m ..S. o.m m;. 85 m .... 3.0 ._ o.= 86 m ...m ad ad 2.6 m > 9 who a in; mac n 8...». ”x «.00 ...x mwo a 2.5 km 35 w 55 m we. 8.0 m Z. 85 a 85 .. 35 m .3 36 m ~.m 85 m .3. 86 a... 85 m m.m mod m. a; $5 a ..3 8.0 m... .3. m 11 ”x 90 a ”x 9.0 a and .xm ”x «.0 ”x at. a 8.0 .xm >0: >0: .smma— cu magnum 9.2.3-33 0.: 8c 63885 8.53.35 05 5:. o.> mHQMH .mm:~m> mno manummoa onu mo and; 100 Tmzv mmd A.=ov o~.o A._mv aa.o A._mv sm.o A.~mV mo._ .=.. :mmm. “.mmv =..o A.-v m..o A.=~V ao.o A.omv =~.o A._wv -.o eo.. A._mv o~.o A..mv m~.o A.=~V =a.o A.mmv mm.o “.mmv .m.o mz.o A.m__v ...o A.aov m_.o A.mov oo.o A.mcv m~.o “.mev ac.o =~.F smmm. A.m._v o_.o A.ao. =_.o A.mmv mm.o A.mzv om.o “.mzv mm.o oa.o A.mm_v m_.o A.m._v m..o A.oo_v oo.o A.mo_v =N.o A..o.v o~.o mm.o A.-V o_.o A.-v ~=.o “.smv em.o :~.. A._mv m..o A.~mv a~.o A.msv 5°.. ~:.. sums. A.omv o_.o A.=~V mm.o A._o_v m:.o 20.. A.m=v mm.o “.mzv =m.~ A._o_v .m.~ _m.o A.¢mv ...o A.m=V m=.o A.mmp mm.o ._.o A._mv o_.o A.o=V o=.o Ao.=v no.0 so., 2mm..— 8.3 2.6 7:3 310. Two: 65 $6 Am.mv oo.o Am._v =~.o A.mov a~.o em.o A.¢mv mo.o A.==v m~.o A~.=p .m.o mo.o 9282 ”x was ”x ....0 Q at “x ....o ”x ....o £053 suede m m a m m .u b.> oanmh .c.> new m.> moanmk cu noun: xmma some so.“ no?" 3.35.5-.. mam—Zn no nmzam> 2“; new mac ..o on: 101 strengths only slightly lower than those previously measured. The fact that the 0.73-MeV state has i=5 and a C23 value not far from unity means that it exhausts most of the 111‘1/2 strength. (It appears as the largest peak in the spectrum (Figure V.7). 0n the whole, the present work gives C‘s values somewhat lower than previously reported. We have already seen this feature in connection with the low-lying 209 209Bi states in Pb and , where possible reasons for the tendency were given. 0 b) Low-lying peaks in 1 9Eu u . Five peaks in the 1 9£u spectrum at the positions indicated by the arrows in Figure v.7 were analyzed. These peaks correspond to unresolved clusters of low-lying states. Their angular distributions were fitted by a mixture of i=2, 4 and 5 DWBA angular distributions since, as we have seen, these are the only l-transfers likely to occur for the low- lying states of 1N9Eu. Angular distributions for four of the peaks are shown in Figure v.8. The C28 values obtained using the "minimum X3" criterion are given in Table v.5. Table v.7 lists the 0‘s values obtained when the angular distributions were fitted with single l-transfers from the allowed set. We note from Table v.5 that the best-fit x: values are large compared to unity; they range from about 16 to 36. The probable reason for this is that the peaks are very 102 poorly resolved, making it difficult to extract accurate cross sections. Probably because of this, the Z-M 028 value for the ground state is considerably larger than that found ) contribution 11/2 to the peak at Ex- 0.51 MeV, which is the largest peak in in other work. There is a large 2-5 (1h the spectrum. The table shows that the 1-5 (1h11/2) proton excitation in 1H9Eu is fragmented, its strength being spread over at least three of the low-lying peaks. Once again we note that the present strength values are generally lower than those previously reported. As another test of our procedure for determining 2 values, the allowed set of l-transfers (i=2, 11, S) was enlarged to include i=3 and 6 as well, and the angular distribution for the state at Ex= 1.7“ MeV was fitted using i-transfers from the larger set. The minimum-x: procedure then selected i-transfers of 3 and 6 instead of 2 and 5. This test reinforces the conclusion already arrived at in 20981, that the our analysis of the low-lying states of fitting procedure is reliable in selecting i values only to within :1. c) Low-lying peaks in 153Eu Three peaks were analyzed, as indicated by the arrows in Figure v.7. No strength values are available from 153Eu. previous studies for any state in As we have seen, the Nilsson model prediction is that only 2-transfers of 2, 103 3, A, 5 and 6 are allowed for the low-lying states of 153Eu. This set of i-transfers was used to fit the angular distributions for the three peaks. The fits using the "minimum X3" criterion are displayed in Figure v.8. The corresponding C‘S values, reported here for the first time, are listed in Table v.5. Table v.7 lists the 0’s values obtained when single E-transfer fits were made. Note that the x: values are very large for the best fits (Table v.5). The peak at Ex: 0.33 is not fitted well by any mixture of i-values. As seen in Figure v.8, the angular distribution in the neighborhood of 9° is especially poorly fitted for this peak and, in fact, it is the deviation between experimental calculation and the theoretical calculation at 9° which makes the most significant contribution to the overall x:. The other two peaks are better fitted with a mixture of i values. They show some i=3 strength, which supports the Nilsson model prediction that neighboring subshells of the spherical shell model mix at low excitation energy as the deformation increases. The Nilsson model predicts the i=6 orbit to be lower in energy than the i=3 orbit, but we find no i=6 strength. d) Low-lying peaks in 155Eu Three peaks were analyzed and the regions are pointed out in Figure v.7. No strength values have been previously 104 reported for any of the states in 155Eu. The Nilsson model shows that i-transfers of 2, 3, A, 5 and 6 are possible in the region of the low-lying states of 1SSEu. This set of £- transfers was used to fit the low-lying peaks, using the "minimum X3" criterion. The resulting fits to the angular distributions are shown in Figure v.8. The corresponding CZS values, reported here for the first time, are listed in Table v.5. Table v.7 displays C’s values obtained by single i-transfer fits. Note that the x: values are large. Note also that a mixture of three l-transfers was selected for the peaks at Ex: 0.45 and 1.07 MeV. Examination of Table v.7 shows that no single-i fit to any of the low-lying peaks is very good. However, mixtures of 2 values give much better fits (Table v.5 and Figure v.8). As in the case of 153Eu, we find i=3 strength (in agreement with the Nilsson model prediction) but no i=6 strength (in disagreement with the Nilsson model prediction that the (i=6) orbit is lower in energy 113/2 than the 2f7/2 (i=3) orbit). 1M5,1H9,153,155 V.5.2 High-Lying Proton Strength in Eu High-lying spectra from the (a,t) reactions are displayed in Figure V.6a. Angular distributions, obtained by "slicing" the spectra from about 2 MeV to about 15 MeV excitation energy in 520-keV wide bins, were fitted by mixtures of DWBA angular distributions corresponding to 105 different i-transfers. An examination of the expected single particle levels in the Nilsson model [8075a] shows the allowed set of i-transfers to be 3, 5 and 6 for 185.1“9 1S3’155Eu. (In our analysis Eu and 2, 3, 5 and 6 for we extracted no i=2 strength, probably because cross sections an‘ i=2 are much smaller than for the other 2 values, as shown by Figure III.2.) A number of different bin widths for the "slices" were tested to see whether the resulting strength distribution depended on the bin width. Bin widths of 280 keV, 520 keV, 1 MeV and 2 MeV were used. The general characteristics of the resulting strength distributions were similar. The decision to select the 520 keV bin width was arbitrary. A. width of 280 keV would have been roughly equal to the experimental resolution and thus seemed too small, whereas a 'width of 2 MeV might haverresulted in averaging of states. A width of 520 keV thus appeared to be a good compromise. Table v.8 lists the complete range of x: values for the high-lying region at Ex: 7.18 MeV in 153Eu. Some of the fits give x: values which differ only slightly from the minimum x: value. Therefore, combinations of i-values other tfluum the particular mixture selected by the minimum-x: fit are quite possible in this region. The minimum-x: requirement may not be the best criterion to use for deducing C28 values in high-lying regions. However, since no other criterion was used hitfius Thesis, the minimum-x: 106 Table V.8 List of the possible c's values, with the l-mixture indicated, for the high-lying region at Ex- 7.18 MeV in 153 Eu. 1 I I T I 7 l C S xv 1 C S xv l C S xv 6 0.03 3.? 5 0.25 5.5 3 0.25' 7“".2 3 0.16 2 0.10 2 0.18 5 0.16 u.0 6 0.002 5.7 6 0.05 8.5 3 0.011 5 0.26 2 0.31 6 0.02 u.0 6 0.001 6.1 6 0.07 8.7 5 0.011 5 0.25 3 0.111 2 0.10 5 0.27 5.2 3 0.29 6.9 2 1.19 15. 107 results will be displayed for the sake of completeness, along with the fits obtained using single t-transfers. Examples of calculations using the "minimum x3" criterion in different regions of the background-subtracted spectra are shown in Figure v.9. The excitation energies labeled are those at the center of the energy bin "slice", e.g., the energy bin for the 7.30 MeV region in TNSEu is the interval from 7.0" MeV to 7.56 MeV. Note that in some cases the program picked out only one i-transfer. In the case of 153Eu, the angular distributions for the high-lying regions in the neighborhood of 9° are poorly fitted, just as for the low-lying peaks. Therefore the maximum contribution to x: comes from the 9° point. Figure V.1O displays the angular distribution of the under-lying background for typical high-lying regions in the spectra of the four Eu isotopes. Generally, 1rrth a few exceptions, the angular distributions for the background have similar shapes. At the larger angles we observe the effect of including the angle-independent evaporation 153'15530, the 105,1M9Eu process. We note that, at Ex= 7.18 MeV in shape of the background is different from that in at nearly the same Ex' This shape difference is primarily 011e to tt1e love g170L1nd-staate Q-v jiue in trie 152’15u8m 153.155 (a,t) Eu reactions (08 = -13.9 and -13.2 .S. 14U,1U8Sm(a’t)145,1u93u MeV, respectively) compared to the reactions (Q8 3 = -16.6 and -15.N MeV, respectively) where 108 Figure v.9 Angular distributions of some high-lying regions in 1u5'1u9'153’155Eu after background subtraction. Each region is 520-keV wide, centered at the excitation energy Ex(in MeV) indicated. The curves are the minimum-x: fits using the DWBA angular distributions. The 2 values thus determined are indicated. wam1mtausm Ameoumovv .....0 on e. 8 ‘1‘1 5.2:. 3.5.... 52. . ism... 5.3:. 35m... awn: 3. 359:6 (IS/am) 09/09 109 Figure v.10 Angular distributions of the under-lying background for t;y'p i c a l 111 g h-1.y i n g r'e g i<>ris i n t h e 144.1UB.152.15uSm(a’t)1“5,149,153,155 Eu reactions. The term "scale x 0.1" in some of the panels means that the indicated scale must be multiplied by 0.1 to get the actual scale. on ON :— 0— .> 0.5070 $02003 .800 cu ON 6— ON A: 1111.11.11.1“9 1111.1090‘1l‘1 1111.1111‘1111 1111.0411‘1111 A v . v v . . v v I l" I- .l I. v . C v v v v v 2 . .v v v v ' I. L- l .35.. an... . .0 u e ' 00mg 11m 00mg .110 0.00."- . . . 11n>11Php>pp ppbnprpbpbihbp 1-»)151 . A v .v . v v v v v v A ' 1' I- I l A v 2 . f . . v v . C . v v r A A II ll- 1 l . I . . I aballm v0-allw.m 000110 3 >1 uppppbbfbp . nub->phb .71-.»1>-->11> 11 111 1111 111 1111 1111 1111 .1 n . q 1 q .11 i .v u L... .1 ..m v e v L AV 7 v I... ll 1 V A O acne-eo- V .330 .330 . can: u : w h. a V e v e a 0d um .0vhlm .cnhnm v 5E0— ha. 5vemv0u ”H00— Aa. Xvvia-mm0u Hum—avg Aa. EVA-Hume: sumo: 3.35m... 72 O C en. (.Is/qtn) up7op O G 0-1 7 C 0-1 O C 1-1 .2 110 the background is low and the angle-independent process does not have an effect. Not all the fits for every region and for every target. are displayed, since each reaction has about 25 "sliced" angular distributions. Instead, a 3-dimensional plot of the "sliced" experimental data of d0/dn versus ec.m. versus excitation energy in MeV is shown in Figure v.11. 00/09 is plotted along the z-axis, 00 m. along the y-axis and the excitation energy along the x-axis. The scales for all three axes are linear. The conventional experimental angular distribution at any excitation energy is the projection onto the y-z plane. The range of excitation energies is plotted on the x-axis and listed in Table v.8. High-lying proton strength distributions in the europium isotopes are displayed as a function of excitation energy in Figures v.12 and v.13. In Figure v.12, the 023 values are those obtained by performing minimum-x: fits to the experimental angular distributions with a mixture of allowed i-transfers (i=3, 5 and 6); Figure v.11 displays the corresponding x: as a function of excitation energy. In Figure v.13, the 028 values are those obtained by fitting the experimental angular distributions with a single 1- transfer from the allowed set; Figure v.15 displays the corresponding x: as a function of excitation energy. Note in Figure v.15 that the x: distributions for the i=5 and i=6 transfers appear very similar. This meant that it was difficult to distinguish between the adjacent 1 values of 5 Figure v.11 A 3-dimensional plot ( do/dfl vs 0C m vs Excitation energy) of‘ eicper'imeantaal aangLilar' diflstr'ibliticans for‘ true 1uu,118.152,1sus 1‘45-1“9"53-‘555u reactions. ac m m(o.t) varies from 0° to 30° in all four panels of the figure. LIQELLLu Figure v.12 Spectroscopic strength distribution of the fragmented i=3, 5 anci 6 pr<3tc>n sirig].e-;>ar*ti<:le ex1zitLat:ioris in 1u5'1u9’153’155Eu obtained by performing minimum-x: fits to angular distributions measured in (a,t) reactions on 1UU,148,152,154 - Sm targets. i=3 corresponds to the 21"7/2 and 2f5/2 Single-particle states, i=5 to 1h9/2 and i=6 to 1i13/2. The term "scale x 2" in some of the panels means that the indicated scale must be multiplied by two to get the actual scale. 3r: am..." _ a... 52. cu m..>IM2:msu 302V mwuocm um IIII'I'TN - .ou. .. . ca 1. _ . NNo—dca meio- - -L . . - _ .141. ._ Ci? 1 Nuondoa we?! ... -- .--; -.-. - . - .1..- . ..:.:1 .. . . .. .1 ~88. .. 1 p . ..- p - . >1»-- . . . . .m 1.. - q . u' .. — m V. . - t a “Ho NAy VAV NAV VAV NAV v.0 NAV ¢Av GAV (,_A9N) szo 113 Figure v.13 As for Figure v.12, except that the strength distributions were obtained by fitting the measured angular distributions with single l-transfers (i=3, 5 and 6). The terms "scale x 2", "scale x 3" and "scale x A" in some of the panels mean that the indicated scales must be multiplied by two, three and four, respectively, to get the actual scales. ON cu A: as... am... was. sane m—.> otsmdm 302V 233:0 a m 2...; .7. 59.3.38? I | I I | v v v I | u v . . . v ’ ’ b b ' 0 ‘ ‘ ‘ - ‘ ‘ ‘ - u | ' - . l v v . ' . v . . w b ' ’ P ’ . b ‘ ‘ ‘ ‘ . 0 . . v I v . v ' . v v I - v v w l I . v I v v . . . b ’ ‘ b D 0 I u 1 1‘ . 0 9 . v I - . v v w I ' - . | ' | .. N I O—doa u 010. v ' ’ ’ ’ ’ * ' ’ p r ’ ' - $ ’ b ’ b. as so so (,_Aew) szo Figure v.14 The minimum-x: distribution corresponding to the fit that produced the C25 values in Figure v.12. ‘20 Ex Energy (MeV) Figure v.13 Figure v.15 The x: distribution corresponding to the single-i fits that produced the C28 values in Figure v.13. m_.> 053 933 >395 am cm 3 S 3 _. - . . 1.11-2. ---..-111. ....- 1. O.“ 3r: 2 \<,\\\<< .3 ...-.-. 1.1-1:“.-.- . o.“ 1D 1D 1 1 1 1 1» 1 1 1 - L...- 1....-- ‘ O O 1-1 d— 2 ma: SENS-{1-- . 116 and 6. We also notice that it was not very difficult to distinguish between 2-3 and 5 or between i=3 and 6 using the x: distribution. Note also that the i=3 transfer does not have any Gas or x: values above Ex- 12 MeV. As mentioned in Chapter III, DWBA angular distributions for 2-3 could not be calculated above 12 MeV excitation energy and thus a C28 value for 1-3 could not be determined in that region. Comparison of the plots of 028 with plots of the respective spectra shows the regions of the spectrum in which the various l-transfers dominate. The sum rule limit of the spectroscopic strength for a given j-transfer in stripping reactions is unity, as expressed by equation (111.16). The predicted DWBA angular distributions shapes depend only on the 2 transfer, not on the j-transfer. In particular, the predicted angular distribution shapes for the 2f.”2 and 2f5/2 transitions look very similar. (They are not identical because the bound state part of the potential contains an Ros term (see Table III.1 and equation III.17c) which has different values for the two transitions.) A given i-value would correspond to either j=2+1/2 or to j=i-1/2. We must remember this ambiguity when summing the transition strengths. A summing of the strength was carried out for each of the four Eu nuclei and is tabulated in Table v.9. Results from previous studies for TuSEu [St83,Ga85a] are also given. The theoretical sum rule limit is 2 for i=3, since for this l-transfer there are two possible associated j-transfers, Table v.9 List of the sunmed transition strengths for the hi gh-lying regions of other wa‘k. 1315,1119.153.155 Eu fran this experiment and tron The mcertainties in the smmed strengths are given in parenthesis. uncertainty in the fitted parameter and in the target They are calculated using the tmcmas. This experiment Other work Ex(MeV) 203$ 00's 0013 Final interval 1. nil-j Nuclem 1 5 - 1n 5 ° ° . . 3 1.8811.uu) 2:7/2 0.13 0.86 . 1. - 11.5 5 o.53(0.15) 109/2 0.75 0.51 ‘“°£u 1. ‘1“.5 6 1.03(0.01) 1113/2005“ 0.88 - 15 3 3.5(0.811) - 15 5 1.1u(0.10) '“930 2 - 15 6 0.70(0.01) 1.5 15 2 0.0 1.5 15 3 3. 2(0.80) 1.5 - 15 5 2.ue(0.55) ‘5350 1.5 - 15 6 0.05(0.01) 1.5 - 15 2 0.0 1.5 - 15 3 1.27(0.uu) 1.5 15 5 1.33(0.37) 15550 1.5 15 6 1.53(0.17) a) IGaEa] b) [3083] 118 2f.”2 and 2f5/2 [8075a]; for i=2, 5 and 6, the limits are 1. In our analysis, these limits are exceeded to some extent for l-transfers of 3, 5 and 6 in most cases, whereas for i=2 no strength is found. )These results show the limitations of the analysis. Some of the possible reasons for the discrepancy are: (i) not enough background may have been subtracted; (ii) the i=5 and i=6 strengths may need a slight redistribution; (iii) we may need to introduce another 2- transfer from another subshell; (iv) the reactions are not sensitive to i=2 strength, since i=2 cross sections are much weaker than those for higher i's (about a factor of four weaker than i=3 cross sections, see Figure III.2); (v) in view of the uncertainty of $1 in i determination, the i=2 153’15uEu in the excitation energy strength expected for region considered (4 to 15 MeV) may have been misidentified as i=3 by the "minimum X3" procedure. This last possibility would account both for the lack of observed i=2 strength for 153,155 . . . . Eu and, Since the m151dentification would effectively raise the i=3 sum rule limit to about 2‘/~ (The ’/“ is used because the i=2 cross sections is about a factor four less than the i=3 cross sections), for the observed i=3 strength in the two nuclei. 1UM,lN8,152,15N (a,3He)145,lN9,153,15 v.6 Sm 5Sm REACTIONS We shall discuss the results from the study of the (c.3He) reactions on the samarium isotopes in two parts: 119 1) The results for the low-lying states, including the extraction of angular distributions, assignments of 2- transfer and determination of C28 values. 2) The results for the high-lying part of the spectra, including angular distributions extracted using the "slicing" method described before and 0’s distributions obtained as a function of excitation energy. V.6.1 Low-Lying States in 1u5’1u9’153’1558m The low-lying parts of the energy spectra from the u (c.3He) reaction on 1 “’1u8’152'15u8m are displayed in Figure v.16. Note that the states in THSSm are well resolved up to an excitation energy of about 2.5 MeV. As the mass, and thus the deformation, of the isotope increases, the density of the low-lying levels also increases and so the levels are not well separated due to limitations of our experimental resolution. The angular distributions obtained for these unresolved states are shown in Figure v.17. The DWBA program should pick out the correct mixture of i-transfers for the states within a peak. If the decomposition works well for the low-lying states, we can be more confident about applying the method to the higher lying regions of the spectra. The N (neutron number) values of the samarium isotopes 1N5,1N9,153,155 Sm are 83, 87,91 and 93, respectively. In simple shell model theory the level is filled at 1h11/2 120 Figure v.16 Spectra of 3He at 5° showing the low-lying neutron states Inu'1“8’152’15“Sm(a.3He)1”5'1u9'153’1558m populated by the stripping reactions. Besides the Q-values energy scale along the horizontal axis, excitation energy scales (in MeV) are also shown in each panel of the figure. 40 dZU/deE (mb/sr MeV) 25 0 - - . -13 -15 -17 ..l---- --. v I v v v v 14-L-lmmxxll--- 15“Sm( o1, 3He) 155Sm 3 Q‘,,,=-14.8 Q-Value Energy (MeV) Figure [ng 121 Figure v.17 Angular distributions of some low-lying peaks (indicated with arrows in Figure v.16) which are excited in 1lfih1u9’153'1558m. The curves are minimum-x: fits with the DWBA predictions; the corresponding 2 values are indicated. da/dfl (mb/sr) “‘Sm(a.’He)ern ‘“Sm(a.’l-ie)m8m mSrn(¢x.’fle)'“$m mSm(a.’l'ie)'“8m io 20 i0 20 so Gen. (degrees) Figure v.11 122 N=82, and the valence neutrons in the Sm nuclei (ranging in number from 1 to 11) are distributed in the next subshell (between N=82 and N=126). This subshell contains the orbits 2f7/2, 1h9/2, 1113/2, 3p3/2, 21“5/2 and 3p”2 [Bo75aJ. As was the case for the proton orbits, the Nilsson model shows that the neutron orbits also shift in energy depending upon the deformation. As the deformation increases, the 2g9/2 and orbits from the next higher subshell (above 1J15/2 N=126) occur in the same energy region as the orbits listed above. Therefore, the i-transfers expected for the low- 1N5,1N9Sm lying states of are 1. 3. 5 and 6, while for 153’ISSSm, the expected i-transfers are 1, 3, A, 5, 6 and 7. Results for the low-lying states will be presented individually for the four Sm isotopes. As mentioned earlier, the ability to select an i-transfer (and thus to determine the C28 value) by the "minimum X3" criterion, when other l-transfers are also involved, is probably reliable to within :1. In addition to allowing the set of i-transfers mentioned above to fit each of the low-lying peaks, each peak was also fitted separately by each of the single 1- transfers from that set. This allows the reader to better evaluate the reliability of the i-transfer values obtained from the fit and to have available the C28 values if a different i-mixture is assumed. 123 a) Low-lying states in THSSm Since the low-lying states of 1u58m were well resolved in the present experiment, the angular distributions measured for them provided a means for checking the angular distributions predicted by the code DWUCKH for different i- transfers. In addition, the spectroscopic strengths obtained were compared with previous measurements [8075b]. The five states that were analyzed are indicated by arrows in Figure v.15. The allowed set of R-transfers (i=1, 3, 5 and 6) was used to fit the angular distributions for the low-lying states. The fits are shown hingure VJ7B The CZS values extracted using the minimum x: method are shown in Table v.10. Table v.11 lists the C28 values 2 obtained when single l-transfer fits were made. The xv value for each fit is shown in parenthesis. As shown in Table v.10, the i-value for the ground state is correctly identified but the strength is less than half the value determined in earlier work. The peak at 0.98 MeV is identified as having i=5; it probably corresponds to the known state at 1.099 MeV, which has i=6. (Recall the :1 uncertainty in l determination.) The 0.98-MeV peak is the largest one in the 1u58m spectrum, consistent with the fact 3He) reaction at 100 MeV favors high-2 tJiat ‘the (a, transfers; this is due to the angular momentum matching condition (111.5). It is for the same reason that the known 3133/2 level at 0.89 MeV does not appear to be excited in the 1211 W List of the spectroscopic strengths (C‘S) obtained from fits for the low-lying states of minimum-y; 1.5-”9-‘53-‘55sg. m x; values of the fits re given in prenthesis. This experimmt Nuoler Other Pk i C'S(exp) Data Sheets wa'k Final 8 t ExmeV) 11.W 3,01") “’13 c's Nuclei: 1 0.00 3 0.38 (5.9) 0.0 2:7,2 0.853 2 0.98 5 0.88 (12.) 0.899 303,2 0.53 1.099 11‘3/2 0.96 3 1.20 5 0.53 (9.3) 1.93 1119,2 0.69 ‘”53m 9 1.67 5 0.26 (9.5) 1.620 301,2 0.63 0.23 1.676 2:5/2 0.21 2.350 (as/2.7a) 0.09.0.03 2.999 cars/2.7,2) 0.07.0.05 5 2.58 5 0.55 (2.9) 2.679 (311,,2 3,2) 0.11.0.05 1113/2 0.25 1 0.00 3 0.25 (2.0) 2 0.29 5 0.38 (5.8) 3 0.91 6 0.13 (11.) 5 0.96 9 1.91 5 0.38 (6.5) ‘ugsm 1 0.76 5 1.89 6 0.11 (13.) 3 0.29 1 0.03 50.9T(9.S) 2 0.95 5 0.17 (9.1) 3 0.95 5 0.25 (6.0) 1533111 9 1.79 5 0.98 (6.6) 1 0.36** 6 0.13 (1.1) 2 0.95 7 0.02 (3.2) 1553111 9 0.02 3 1.71 60.1o(2.8) 1 0.61 a) WT 125 TNfleV.” values (I single i-trmsfc- fits for esch low-lying peak from the 8 V ((1.31%) resctiom on the SII'ILI isotopes. List d C‘S lid x Final to 11ml eta 0'5 8 XV 8x04“) C'S 175$fl ))))) I 0319 52... 2e|u62 ((((( 3 7s 2%?35 0.00.00. W9- \.I\.I\-I\.I\l .8 .6 O 8 e2 e3 “5.182 (((I\I\ 38 el 13%9fi C I O O C 00000 ..... Lo C'S I XV Ex(HeV) C 1S 0.118 (9.5) 0.17 (9.1) 0 25 (6 0) 0.148 (6.6) 155Sm 0.10 (12.) 0.03 (11.8) 0 08(81) 0 (5.3) 1 (3 2) 0.13 (1.1) u 0 e e 00 ))) ee .20 6.111 039 e e e 000 ))\II .0. 003 222 ((( 585 202 0.0.0. ))) 3 M 798 ((( 55 30 Q01 eee 001 126 0.98-MeV peak. Indeed, when we tried to fit the angular distribution for this peak with a pure i=1 transfer, the attempt failed: the shape was wrong (Figure v.18) and the extracted C’S value (1N.7, as shown in Table v.11) was unphysically high. The peak at Ex- 1.28 MeV, if identified with the known level at 1.43 MeV, agrees best with 1h9/2 previous measurements. Note from Table V.10 that the sum of the C28 values for i=5 determined in this work exceeds the sum rule limit of unity. This implies that some of the strength identified as i=5 is probably 2:6 (for which the minimum-x: fits did not find any strength). b) Low-lying states in 1”93111 Five low-lying peaks in the 1“98m spectrum were analyzed as indicated by arrows in Figure v.16. They were taken to correspond to unresolved groups of individual states and their angular distributions were fitted by mixtures of i-transfers from the allowed set (i=1, 3, 5 and 6). The fits using the minimum-x: criterion are also shown for four of these peaks in Figure v.16. The C28 values obtained are shown in Table v.10. Table v.11 gives the C28 values from single i-transfer fits. Note from Table v.10 that for the first two peaks single l-transfers are selected by the minimum-x: procedure (with very low xi), implying that the peaks corresponding to individual states. The other three peaks appear to 127 Figure v.18 u Angular distribution for the Ex: 0.98 MeV state in 1 58m. The solid curve is the minimum-x: fit with the DWBA prediction for the i=1 angular distributions. p_s O da/dQ (mb/sr) 0““10“"20“”3o 96m. (degreeS) Figure V.18 128 correspond to groups of states. We have the most confidence in the C28 values and i-transfers determined for the first two states, since fits with other possible i-transfers are much worse (see Table v.11). The state at 0.29 MeV appears to have 2-5. For the peak at Ex- 0.91 MeV, which has the largest cross section in the spectrum, the minimization procedure selected a mixture of 2-5 and 6. fun; it is very possible that the peak is a single level having either i=5 or i=6, since the x: values with these single-2 fits are only marginally worse than the best fit value. c) Low-lying states in 153Sm Four peaks were analyzed as indicated by arrows Figure v.16. No previous strength measurements are available for 153Sm. The set of 2 values suggested by the any state in Nilsson model (i=1, 3, A, S, 6 and 7) was used to fit the low-lying peaks. The fits to the angular distributions are shown in Figure v.17. The corresponding C’S values, reported here for the first time, are listed in Table v.10. Table v.11 gives the C28 values obtained from single 2- transfer fits. The minimum-x: procedure selected the i-transfer of 5 for all the peaks, with no admixture of any other i-transfer (Table v.10). But the sum of the 028 values exceeds the sum rule limit for i=5. From Table v.11, we see that the x: value for the i=6 fit to the Ex= 1.79 MeV peak comes closer 129 to the minimum-x: value than in all the other cases. If, on this basis, we assign 2-6 to the peak at Ex- 1.79 MeV, then the sum of the C28 values for the other three peaks does not exceed the sum rule limit for i=5. d) Low-lying states in (SSSm Three peaks were analyzed, as indicated by arrows in Figure v.16. No previous strength measurements are available for any state in TSSSm. The set of possible 2- transfers (i=1, 3, A, 5, 6 and 7) was used to fit the low- lying peaks. Fits to the angular distributions are displayed in Figure v.17 and the corresponding C‘s values, reported here for the first time, are listed in Table v.10. Table v.11 lists the C23 values for single l-transfer fits with the x: value from each of the fits given in parenthesis. The x: values listed in Table V.10 range from 1.1 to 13, indicating the quality of the fits varies from good to not so good. No i=5 (1h9/2) strength is found. We notice that as the deformation increases with the mass of the &n isotope, the i-transfers for the analyzed peaks are generally of higher value. The i-transfers of M and 7. which correspond to orbits in the next higher subshell above N=126, seeuitxa be present for the Ex= 0.95 MeV peak in 1555m. However, because the peaks are poorly resolved and 130 because of the uncertainties of the procedure used, it is not possible to make definite i-assignments. 1HS,1H9.153.15SSm V.6.2 High-lying Neutron Strength in 3He) The high-lying portion of the spectra from the (a, reactions are displayed in Figure V.6a. Angular distributions were obtained by "slicing" the spectra from about 2 to 19 MeV excitation energy in 520-keV wide bins. DWBA fits were made to the angular distribution of each slice. As we have seen in Table v.10, the C28 values for i=5 (7“9/2 195,199,153Sm ) exceeds the sum rule limit in the low-lying peaks of Therefore, the £85 possibility was excluded from the set of possible i-transfers when fitting the high- 195,199.1535m. Through examination of the lying regions of expected single particle levels [8075a], i-transfers of 1, 3, A, 6 and 7 were used to fit the high-lying regions in these three nuclei. For 1558m, i=5 was also included. Typical fits using the minimum-x: criterion for different regions of the spectra are shown in Figure v.19. The excitation energies indicated are those at the centers of the energy bin "slices", e.g., the energy bin for the 6.99 MeV reghniis the interval from 6.68 MeV to 7.20 MeV. As was the case for the (a,t) reactions, in some cases the program did not pick out more than one i-transfer. 131 Figure v.19 Angular distributions of some high-lying regions in 14 N . 5’1 9’153’1558m after background subtraction. The curves are the minimum-x: fits using the DWBA angular distributions. The indicated 1 values determined by this procedure are indicated. Amway—~03 ...-8Q ‘ o—.> on: a Fldl..l ..dl... on...) 9:11 w . I. I _. 8.” U.” .. 8.0 U.“ 89>“ b p .1111 1)) p111). 111)»)111- r assesses... 52.3.5.5... In" v' med SwaonZnévEm-z Smacks—fiver. (Js/qm) UP/DP 132 Not all of the fits for every region for every isotope are displayed, since each reaction has about 25 "sliced" angular distributions. Instead, a 3-dimensional plot of the "sliced" experimental data of d0/dn versus ec.m. versus excitation energy in MeV is shown in Figure v.20. 00/09 is plotted along the z-axis, ec.m. along the y-axis and excitation energy along the x-axis. The scales for all three axes are linear. The conventional experimental angular distribution at any excitation energy is the projection onto the y-z plane. The range of excitation energies is plotted on the x-axis and listed in Table v.12. High-lying neutron strength distributions in the samarium isotopes are displayed as a function of excitation energy in Figure v.21 and v.22. In Figure v.21, the C28 values are those obtained by performing minimum-x: fits to the experimental angular distributions with a mixture of allowed i-transfers; Figure v.23 displays the corresponding x: as a function of excitation energy. In Figure v.22, the C28 values are those obtained by fitting the experimental angular distributions with a single l-transfer from the allowed set; Figure v.29 displays the corresponding x: as a function of excitation energy. Note in Figure v.29 that the x: distribution for i=6 and i=7 appear very similar up to a certain excitation energy. This is due to the difficulty in distinguishing between the adjacent i-transfers of 6 and 7 in that excitation energy region. We also notice that, except for i=6 and 7, it is not very difficult to 133 Figure v.20 A 3-dimensional plot ( do/dQ vs 00 m vs Excitation energy) of ex;>erinner1ta]. arigu iar diustr'ibtiti<>ns for' tlie 199,198,152.15“Sm(a’3fle)1”5'1u9'153'TSSSm reactions. 0 0.111. varies from 0° to 30° in all four panels of the figure. ___..F 1 8“" E-!:.3.°. 1314 Table V. 12 List of the sunmed transition strmgths for the him-lying regions of fran this experimmt and true other wcrk. The uncertainties in the sunmed strengths, which appear in parenthesis, are calculated using the uncertainty in the fitted paraneta' aid in the ta'get thickness . Thi s exper i ment 1u5.1‘19.153.1553m Ex(MeV) 2013 Final interval 9. Nuclem 2.7 - 19 3 0.0 (0.0) 2.7 - 19 9 1.61 (0.29) 2.7 — 19 6 1.39 (0.10) 1“53111 2.7 - 19 7 0.26 (0.02) 2 - 19 3 0.58 (0.31) 2 - 19 6 0.88 (0.08) ‘”93m 2 - 19 3 0.0 (0.0) 2 - 19 9 0.0 (0.0) 2 - 19 6 1.06 (0.22) 1538m 2 - 19 7 0.39 (0.07) 2 - 19 3 0.32 (0.30) 2 - 19 9 0.31 (0.20) 2 - 19 5 0.10 (0.09) ‘553m 2 19 6 0.26 (0.11) 2 19 7 0.83 (0.10) 135 Figure v.21 Spectroscopic strength distribution of the fragmented i=3. 9, 6 and 7 neutron single-particle excitations in 1u5’1u9'153’1558m obtained by performing minimum-x: fits to 3 angular distributions measured in the (a, He) reactions (”1 199.198.152.1548m targetso i=3 corresponds to the 2f7/2 and single-particle states, i=9 to 2g9/2, i=6 to 2r5/2 1113/2 and i=7 to The term "scale x 2" in some of the 1315/2' panels means that the indicated scale must be multiplied by two to get the actual scale. cm a: Ems: Ema: Ems. am... —N .> 0.28am $33 hmmonm am as as cu ‘ ‘ q .- ‘ ‘ J 9 4 J .1 ‘ < 6 9 ‘ 9 1 (q 9 1 ‘ ‘ ‘ ‘ ‘ 9 ‘ ‘ - FL .. I 0 I ' I | I 1 N u eases N w 010- .. 0 ’ ’ D I. 1’ 1 ’ D D ’ b 0 b i ‘ ‘ 1‘ 9 ‘ 1 ‘ q l ' - I - ' | ' ' - N M £3. . - _ I i ' I ' ' . ' ' ' L ’ D b F ‘ 1 ‘ .11 . .0 i | ' - ' ' ' ' - ' - N." .eua -eua 89:33.38? 136 Figure v.22 As for Figure v.21, except that the strength distributions were obtained by fitting the measured angular distributions with single L-transfers (i=3, 9, 6 and 7). The terms "scale x 2" and "scale x 8" in some of the panels mean that the indicated scales must be multiplied by two and eight, respectively, to get the actual scales. NN .> 0.28:. C35 >3on um ON ca 2 H 8mg: 9 9 9 9 . 9 9 9 N 9 9 9 9 q 19 9 9 w 9 9 9 5- 9 9 9 9“ 9 19 1 ' 1 s ' ' ' | 1 N u 010- a w 070. 1 ’ P ’ ’ - I1 P ’ b ’ F ’ k - ’ b r ’ - i. . 1 u n .. n 1 ' 1 N w 010- c w 810- 1 D ’ ’ F - 0 D ’ D '19 9 9 9 .- 9 9 ' I ' ' . | ' I O 1 N u 0.00- o w 010- 1 i b P 0 .- b D b b ’ 0 D - i [P ’ P u 9 9 919 ‘ 9 9 9 9 9 9 ‘ 1 9 ' r- - I ' I - | W N w eases . o w 070- 1 ¥ ’ ’ r)? p ’ (I le)b(p D - ’ L * ’ ’l) - D ’ 1? r h D ’ - b P ’ and «flu Em_+3on um ON A: cu cu o” H v 4 1 q 1 1 1 11 1414 .1 4 .1 .- 11 1 r m w w. . Sue—eon .\\._ v p > p p 1 p b b b 1 1 1 1 1 )1 1 1 1 d 0 1 (P d 1 1 11“ ._ L Sue—sou \._ p p > P p 1 b p n p 9 P p b . 1 1 11 1 1 1 1 q 1 4 1-1 11 . m 3 union \h 1 p p 1 pl! 9 p 1 P 1 b p p p p p Pb bu 1 1. 1 q 1 1 1 1 11 1 1 . . 1) 11m Mane—so- \h .1 . . 1 11. 1 1 1 .1 1 1 1 1 . .1 1 F1 end end awrxomnésm. 139 distinguish between any two l-transfers. Recall, from Chapter III, that above 12 MeV excitation energy, DWBA calculations were feasible only for £87 and thus C‘S values could be determined only for is? above that excitation energy. Comparison of the plots of C28 with plots of the respective spectra shows the regions of the spectrum in which the various i-transfers dominate. A summing of the strength was carried out for each of the four odd-mass samarium nuclei and is tabulated in Table v.12. There is very little i=5 strength observed in TSSSm. In the three lighter Sm nuclei, as mentioned earlier, most of the i=5 strength is observed in the low-lying region of 1555m the spectra. The lack of i=5 neutron strength in suggests that the orbit becomes occupied as the Th9/2 neutron number increases. The summed i=3 strength has large 1558 uncertainties; in m, the uncertainty has about the same magnitude as the strength. The sum rule limit is exceeded for l-transfers of H and 6 in juSSm. This may be explained in two ways. First, perhaps not enough background is subtracted in the excitation energy region (2 to In MeV) under consideration, or second, the i=3 and u strengths may need to be slightly redistributed. Very recently, theoretical predictions [Ma86] were made for the strength distributions of neutron single-particle excitations in deformed samarium (153’1555m) and proton single-particle excitations in deformed europium (T53’155Eu) isotopes. The C28 values presented in this Chapter will be 1H0 compared with these and other nuclear structure calculations in the next Chapter. CHAPTER VI COMPARISON WITH NUCLEAR STRUCTURE MODELS This work, which represents the first attempt to find high-lying particle state strength in deformed nuclei, is also unique in that it presents a systematic study of both proton and neutron particle states using the same set of isotopes (samarium) as targets. In this Chapter, the strength distributions already obtained in Chapter V are compared with two nuclear structure model calculations. This discussion contains four sections. In the first section, a comparison of the results obtained from the 1M‘Sm(m,t)1.u5E2u reaction at 80 MeV [Ga85a] and our work at 100 MeV (discussed in Chapter V) is presented. The second section gives a brief summary of two theoretical models that predict strength distributions for particle states in the samarium isotopes. These are the quasi-particle phonon model (QPPM) and the Interacting Boson-Fermion Approximation model (IBFA). Comparison of the theoretical (QPPM) and experimental strength distributions for protons in 1H5,153,155 153,155 Eu and neutrons in Sm are presented. Also, the IBFA model predictions are compared with the 1N1 1H2 proton strength distributions in Uflh153,155 Eu. The third section presents the conclusions. Finally, in the fourth section, suggestions are made for improvement in the analysis of single-nucleon transfer data to extract spectroscopic information at high excitation energies. mu V1.1 THE Sm(a,t)1us Eu REACTION AT 80 MEV AND 100 MEV In this section, we compare the results of the 1H“ 5 Sm(a,t)1u Eu reaction at 80 MeV and 100 MeV. The histograms in Figure V1.1 display the C23 values determined at the two energies as a function of excitation enerSY; the top part of the figure gives the results obtained at 80 MeV [Ga85anuuithe bottom part the results obtained from the present experiment at 100 MeV. For the C28 values from the present work, error bars are shown which reflect uncertainties due to both the fitting procedure and the absolute normalizations. For the i=3 and 5 transfers, there are differences between the 80 and 100 MeV data sets. Compared with the 80 MeV data, there appears to be more i=3 strength and less i=5 strength above Ex8 6 MeV in the 100 MeV data. The distribution of i=6 strength in the two data sets is somewhat similar, except that the data taken at 100 MeV show more strength above 11 MeV of excitation energy. Besides the difference in the bombarding energy, the analyses of the two data sets were also somewhat different. For example, the background 143 Figure VI.1 Comparison between theoretical and experimental proton strength distributions for the high-lying subshells in 1MSEZu. The theoretical distributions [St83] are the thick smooth curves and the experimental distributions are in histogram form. The term "scale x 2" in some of the panels means that the indicated scale must be multiplied by two to get the actual scale. FWgure\M.1a.(Top figure) Experimental distributions obtained from the juu8m(a,t)1u53u reaction at 80 MeV incident energy [Ga85a]. Figure V1.1b. (Bottom figure) Experimental distributions obtained from the same reaction at 100 MeV incident energy (present work). ”1.3.31.3 936 mmuocm um >3. 2: u.... . >3. 8 .... H 1AA subtractions were carried out differently. As mentioned before, the results at 80 MeV were obtained using an empirical background subtraction. Another difference is the uncertainty in the A-values obtained from the 100 MeV data. This uncertainty is 11 and it critically affects our entire determination of C28 values. V1.2 MODELS FOR POSITION AND WIDTH OF SINGLE-PARTICLE EXCITATIONS The two models discussed here are the quasi-particle phonon model (QPPM) [Ma76,SoBO] and the Interacting Boson- Fermion Approximation model (IBFA) [Sc82]. Both models are derived from a particle-core coupling scheme and predict single-particle strength functions. The spectroscopic strength (defined in Chapter III) as a function of excitation energy is called the strength function. In the models the strength function takes on the Breit-Wigner form [8069] F2(w) 02(w) (V1.1) [e - w]2 + F2(w)2 Here we shall only discuss the assumptions and the input each model uses to calculate the strength distribution. The derivations of the two models are discussed in the references given above. 1N5 VI.2.1 The Quasi-Particle Phonon Model (QPPM) The quasi-particle phonon model describes the fragmentation of the quasi-particle strength due to the interaction of the quasi-particle with the phonon excitation modes of the core. ‘The term "phonon" used here describes excitations of the core. Among the phonons included in the model are the low-lying quadrupole (J-Z) and octupole (J-3) phonons, multipole phonons with J > 3, and spin-multipole phonons. Both isoscalar and isovector modes are considered for the phonons. The effect of the odd quasi-particle on the phonon structure is discounted, since the effect is minimal. The Pauli principle is only taken into account to a limited extent. These features of the model influence the results in the low (~1 - 2 MeV) excitation energy region. The interaction of the quasi-particle with the phonon does not use any free parameters. The model predicts the position w, width r,(m) and magnitude Cz(w) of the strength function. The relation between these quantities is given in equation (V1.1). The comparison of the QPPM predictions with the experimental proton and neutron strength distributions for 1N5.153,155 153.155 the high-lying excitations in Eu and Sm is presented in three parts. Parts one and two discuss the u results for the proton strength distributions in 1 5Eu and 153’155Eu, respectively. The third part discusses the 153.155Sm. in results for the neutron strength distributions'in 1H6 £222a:$222-9.922222_2£22222i23l_i93Efl1-222-25222122229.}. proton strength distributions in 145Eu: In Figure V1.1, the predictions of the quasi-particle phonon model for the 2f (2-3), 1 (1-5) and (i=6) 7/2 h9/2 7113/2 proton strength distributions in jusEu are shown by the solid curves. They are superimposed on the data plotted as histograms. The experimental i=3 CZS distribution extracted at 100 MeV agrees, within the uncertainties of the measurement, with the prediction. For 2-5, there seems to be a large strength missing in the experimental distribution at 100 MeV in the excitation energy region from 6 to 10 MeV. This may be due to the uncertainty in determining 1- transfers to within :1 in regions where different 2- transfers overlap, which would affect the magnitude of the C28 values extracted. For i=6, the experimental distribution from the present work agrees with the prediction up to about Exa 11 MeV but is larger than the prediction at higher excitation energies. This may be because the estimated background was not high enough at the larger excitation energies.or because the determination of C23 values is difficult in excitation energy regions where: different l-transfers overlap. Thus the comparison between the strength distributions for individual i-values predicted by the QPPM and those determined experimentally at 100 MeV in the present work is not satisfactory. As we have pointed out, the experimental 147 distributions are suspect because of the uncertainty in identifying 121-transfers. But it is possible that the QPPM predictions are also not very reliable. In order to assess this, the model was tested in a manner that bypassed the difficulty with the experimental distributions for the individual i-transfers. It was concluded that the model predictions for 145Eu are quite satisfactory. The test also shed greater light on the limitations of our technique for determining i-values and C28 strengths. The test was performed in the following way. A theoretical spectrum was obtained by starting with the and predicted 2f strength distributions, 7/2’ 1h9/2 1113/2 which overlap in excitation energy, and converting them using the DWBA calculations (with N-36) into a double differential cross-section (mb/sr MeV). This was done for angles of 2°, 7° and 12°; the excitation energy range covered was from 0 to 13 MeV. The comparison between the background-subtracted experimental spectrum and the theoretical spectrum at 2°, 7° and 12° for jusEu is shown in the left panels of Figure V1.2. (The excitation energy range from O to 1.5 MeV is not plotted, as it is dominated by orbitals not included in the theoretical spectrum.) There is good agreement at all three angles. This demonstrates the validity of the QPPM model and confirms the strong and 11 proton strength 7/2' ”19/2 13/2 functions in the energy range from 3 MeV to about 11 MeV. overlap between the 2f The width of the overall distribution is about the same in 1N8 Figure V1.2 Comparison between the experimental spectrum (solid 145,153,155 histogram) for proton states in Eu and the predicted spectrum (thick dashed histogram) obtained by the conversion of theoretical strength functhnmsat three angles. The theoretical strength functions for jusEu are those shown in Figure V1.1 [St83] and for 153’155E2u are those shown later in Figure V1.3 [Ma86]. “Sm(mt) ‘uEu T.= 100 MeV. 1“3111011) “‘zu _ O .... 7 ... -. ._ w .9 PI. .uu. .. ....IIIIIH... In. +bDb-’D 1111 1 mSm(a.t) “’Eu e'= 7° 3.12 .385 wagons 151'x Energy (MeV) Fi ure VI.2 1N9 the theoretical and experimental spectra, though slightly smaller in the latter. This may indicate that the damping of the high-lying orbitals considered is slightly smaller experimentally than is predicted theoretically. The excess experimental cross section seen at all three angles for Ex) 10 MeV may be due to some orbital(s) not included in the theoretical spectrum. 99.9225:122ansiasss_£s22£2£issl_i9.££21122235223222.22I proton strength distributions for the high- lying region in 153.155Eu: Figure V1.3 displays both the predicted (QPPM) [Ma86] and experimental strength distributions for the high-lying 153.155Eu proton orbits in . The predictions are for the (i=3) and 1h (i=5) orbits. As before, the 2f7/2 _ 11/2 experimental C28 values are greater than the predicted values. At least part of the disagreement in the case of i=3 is due to the fact that the experimental strength distribution has contributions from both 2f,”2 and 2f5/2, whereas the theoretical distribution hascnfly'the former. Similarly, in the case of 2=5, some of the strength in 153Eu below 10 MeV of excitation energy may be due to the 153.155 7h9/2 orbital while the strength in Eu above 10 MeV of excitation energy may actually be due to the 1113/2 orbital (in view of the uncertainty in the determination of 2- transfer values). The Nilsson model shows that the 1h9/2 150 Figure VI.3 Comparison between theoretical [Ma86] and experimental proton strength distributions for the high-lying subshells 153.155Eu om Damn“ Hammond VV'VVVVIVVVV'V'VVIVVVVI waH> Menusm Cross zmsocm um A: OH 9.0 Nd v.0 Nd v.0 (,_Aew) szo 5:13.31... m6 151 and excitations are possible in the high-lying 153.155 1i13/2 excitation energy region of Eu. But the theoretical strength distributions for the and orbitals ”19/2 1113/2 were not calculated in [Ma86] and so are not shown in Figure VI.3. It is interesting to note that the theoretical proton 153Eu a 155 strength distributions are similar in nd Eu for both the 2f,”2 and 1h11/2 orbitals, whereas the experimental strength distributions are different. The similarity seen in the theoretical calculations is probably a consequence of the fact that the deformation parameters for the two nuclei are very similar, while the difference in the experimental strengths may be due to the uncertainty of :1 in determining i-transfers. 1A As in the case of 5Eu, a comparison was made (Figure V1.2) between the experimental spectra (background- 153.155 subtracted) taken at 2°, 7° and 12° for Eu and the corresponding theoretical spectra obtained by adding up the contributions of the predicted 331/2, 2d5/2, 2d3/2, 2f7/2, and 1 strength distributions [Ma86]. The low 2- 187/2 h11/2 transfers (i=0 and i=2) contributed only about 10% to the total cross section of the theoretical spectrum. Unlike the 1N5 153.155 Eu case, the plots for Eu in Figure V1.2 extend u down to Ex: 0 MeV. As in the 1 5Eu case, the theoretical cross sections have generally the same magnitude as the experimental cross sections at all angles for low excitation energies, but there is a marked (and systematic) 152 disagreement for excitation energies above 3 MeV. This is at least partly due to tnua neglect (because of nonavailablity) of the and 1 strength 1h9/2 i13/2 distributions in the theoretical spectra; both of them would have made substantial contributions to the spectra. gegtgog_§332hgth distributions for the high-lying region in 153’1558m: Figure V1.11325 um— 15“ strength. The Nilsson model shows that the 1J15/2 excitation should be present in the high-lying region of 153’1558m. However, the strength distribution for this excitation was not calculated in the recent work by Malov et al. [Ma86]. As was the case for the theoretical proton strength distributions, theoretical neutron strength distributions 153Sm 155Sm are similar in and . For example, the 2f and 7/2 . 153 155 2f5/2 strengths in Sm and . Sm have the respective centroids separated by the same amount, about 3 MeV. These similarities in the neutron strength distributions suggest that there is little difference in the structurecfl?these two deformed nuclei (1538m and 155Sm). As before, theoretical spectra were obtained at angles of 3°, 7° and 12° by adding up the contributions of the and strength 3p1/2' 3p3/2' 2f5/2' 2f7/2’ 239/2’ 1h9/2 1113/2 distributions.. The i=1 cross section from the 3p”2 and 3p3/2 strengths is only about 2% of the total theoretical cross section. In Figure VI.5, the theoretical spectra at the three angles are compared with the corresponding background-subtracted experimental spectra. The theoretical spectra have somewhat higher cross sections than the experimental spectra at very low excitation energies (Ex< 1 MeV), about the same cross sections for Ex: 2-5 MeV and considerably less cross sections for Ex> 5 MeV. As in the 1 1 53’ 55Eu cases, there is not much difference between the 153.155S theoretical spectra of m; the experimental spectra 155 Figure VI.5 Same as Figure V1.2 applied to the high-lying neutron states 153.1558m. dza/dOdE (Inb/sr MeV) I 10~ 1 .I' 1 1',= 100 MeV °°°Sm(a,°lie) 16°Sm “53,91“: 3’1“.) 1563’“ 'fr- A I .- - a; 35 -I- A- v'vvvv l--- -.--v A A vv'vvv E, Energy (MeV) Figure VI.5 156 are also rather similar to each other but not, as Just mentioned, to the theoretical spectra. The excess experimental cross section occurring for Ex) 3 MeV may represent the contribution of the 1315/2 neutron excitation. Until the 1j15/2 strength calculation is made, it would be premature to draw a conclusion about the spreading widths of individual single-particle excitations. The IBFA model is a particle-core coupling scheme. Its predictive power depends upon parameters in the Hamiltonian some of which are constants while others are allowed to vary slowly with the mass number of the nucleus [8082]. The Hamiltonian contains a boson core, a single-particle fermion component and a component describing the coupling of the fermions with the bosons. The monopole-monopole interaction term in the fermion-boson coupling component is weak enough to be ignored. The Pauli principle is automatically incorporated in the coupling component. The model predicts the excitation energy m and Strength C2(w) of various single-particle excitations but does not treat their widths properly. To begin with, the entire predicted strength is concentrated at certain discrete energies m. For comparison with experimental data, each of these "spikes" is then spread out over a range of excitation energies using the 157 Breit-Wigner form (V1.1) with an arbitrary, energy independent spreading width T2(m). This model was used to predict the 119.153.155 1h9/2 proton strength distribution in Eu [Sc85]. (Because of certain computational difficulties, the model was not applied to the nearly spherical jusEu nucleus or to neutron strength distributions in the odd-mass Sm nuclei of interest to us.) The predicted 2 proton strengths were spread 1h9/ out using a width T2(m)= 0.5 MeV. The results are shown in the right half of Figure V1.6. They are to be compared with the experimental i=5 strength distributions we have obtained 1149’153'155Eu, which are shown in the left half of the for figure. These data were already presented in Figure v.12. Even though a few centroid positions seem to match well, the overall comparison between the experimental strength distributions and the IBFA predictions is poor. We have not pursued this matter further. VI.3 CONCLUSIONS As mentioned in the Introduction, our goal was to obtain systematic information on high-lying proton and neutron particle states over a range of spherical to deformed nuclei. Single-nucleon stripping reactions provide the only convenient and generally applicable means presently available for this purpose. The reactions we chose were 3 14“.148.152.15H (d,t) and (a, He) on targets of Sm at a 158 Figure V1.6 Comparison of the experimental i=5 proton strength 1A9.153.155 distributions in Eu (shown in histogram form on the left hand side) with the corresponding IBFA-model prediction for the 1h9/2 strength distributions (shown on the right hand side). mammnmLsusm 9.25 Ammsocm Am cm 1 1o“ 1. .. cs 1 159 constant bombarding energy (100 MeV). We also wanted to reduce the ambiguities of previous analyses. This was accomplished in two ways. First, an attempt was made to calculate the background using the a breakup model instead of by drawing a background by hand, and second, a slicing method was used to obtain the strength distribution without making any assumptions about specific peak shapes. This concluding discussion is separated into three parts. The first part describes the calculation of the background. The second part discusses the strength found 3 for low-lying peaks using the (a.t) and (a. He) reactions on nu 1 ’1u8’152’15u8m. The third part presents the results for the systematics of the strength distributions of high-lying single-particle excitations obtained using these reactions. VI.3.1 The Background The background calculation was developed to explain the shape and magnitude of the measured spectra at high excitation energies. The calculation included contributions from an elastic d-breakup process and an angle-independent evaporation process. The evaporation process is not totally understood, at least in terms of the Fermi-gas model. The background fitted the shape of the spectra at high excitation energies well (see Figure V.1). With a single normalization for each reaction, the background also reproduced the variations in the magnitude of the high-lying 160 spectra from angle to angle fairly well (within 201, see Figure v.2). The normalizations used for the background varied ffiwnn target to target by less than about 20% in the (a,t) reactions and by less than a factor of 2 in the 3 (a, He) reactions. Reactions The (a,t) and (c.3He) reactions were performed on 1uu,1u8,152,1548m 208Pb targets of nd . The reactions on 208Pb populated the well-known single—PartiCJ-e levels or 20981 and 209Pb. Among the Sm targets, the only complete study so far has been for the °uuSm(a,t)1usEu reaction; data for the low-lying levels of jugEu and TMSSm have also been obtained previously. For all the other cases, strengths are reported here for the first time. The results obtained with the 208Pb target were used for checking the predictive power of the distorted-wave code DWUCKH as regards angular distribution shapes and cross section magnitudes. Additionally, since previous work had determined the angular momenta and single-particle strengths (C28) for the low-lying levels of 1u5Eu and since those levels were well resolved in our experiment, our data for these levels were also used for checking the DWUCKA predictions. In all these cases, which involved individual levels and therefore single i-transfers, the best fit to the 161 angular distribution shape (as determined by the minimum-x; procedure) was provided by the correct (single) l-transfer even when the possibility of a mixture of l-values was allowed; see Tables V.1 and v.5. The C’S values corresponding to the best fits, though somewhat on the low side, agreed with previous determinations within the range of uncertainty of our measured and calculated cross sections. Generally, however, the reactions on the Sm targets populated (mostly) unresolved collections of low-lying states; this was also invariably the case for the high-lying (Ex> 2 MeV) regions. In principle, the fitting program should pick out the correct mixtures of l-transfers for states within a peak. This was tested in two ways. The first way was to carry out a complete search of x: 20981 and M5Eu values for each of the low-lying states in using a variety of 1 mixtures. The purpose was to investigate whether other combinations of l-transfers gave acceptable x: values relative to the best-fit value. The results, listed in Tables v.2 and v.6, showed that the x: value nearest to the minimum x: corresponded to a mixture of l-values which included the one identified as the correct A- value by the best fit. The second way was to sum the measured angular distributions for two states in 20981 and in 209Pb and then to decompose them using the fitting program. The results (Table v.3) suggested that the selection of an l-transfer 162 made by the fitting procedure was probably only accurate to within :1. This fact severely limited our ability to determine i-values and, consequently, strength distributions, in regions where different i-transfers overlapped, i.e. over most of the excitation energy range studied. The basic reason for the limitation lay in the similarity of the angular distribution shapes for neighboring i-transfers for 123; see Figure III.2. The shapes for 2(3 were distinctive but, as also shown in Figure III.2, the single-nucleon transfer reactions induced by 100- ihfv a particles are not sensitive to low 2 in the presence of high A. In other words, the kinematic conditions of the experiment1rwestricted us in effect to a study of high-spin single~particle states. The Nilsson model was used as a guide to select the range of allowed i-transfers for both the low-lying and high-lying states. Due attention was paid to the effect of deformation in bringing down single-particle orbits from the next higher subshell above the proton shell closure at Z=82 and the neutron shell closure at N=126 into the low-lying regions of the heavier Eu and Sm isotopes, respectively. In order that the reader can better evaluate the reliability of the i-transfer values obtained by the fitting procedure, the results of single-i transfer fits -- C28 and x: values --1were tabulated for all the low-lying peaks in the Eu and Sm isotopes (Tables v.7 and v.11). These tables are of some LHHB, in that large values of x: (say 3 20) 163 associated with a particular A rules out that A-value. But the use is limited, since (as mentioned before) most of the low-lying peaks consist of migtgggg of l-values. There are dramatic differences in the width and position of the low-lying particle states in 1A5,1N9.153.155 1N5.1N9.153'°553m as a function of Eu and nuclear deformation; see Figures v.7 and v.16. It is known from earlier investigations that similar effects are seen for hole states. Mixtures of i-transfers were selected for most of the °u9’153’1558u. Notice in Table v.7 that low-lying peaks in single-2 fits to the data with the adjacent i-transfers i=u and i=5 resulted in similar x: values. This shows that it was difficult to distinguish between these two A-transfers. 1u9’1538u are The x: values listed in Tables v.5 and v.7 for all very high (16 to 183), which indicates that l-value selection was difficult for the low-lying peaks in these two nuclei. 11e tur"n nc>w to trie love-l.yixig p13a101 .12070 0.724303E»01 .15202 0.549019E>01 17724 0.526401€.01 .22752 0.4411555.o1 .30230 0.1440026101 .37041 0.1004896101 .91300 0.7248096400 .44942 0 5006015400 .52110 0 207761E.00' .61462 0.9007505-01 - 0.70 Mev .05007 0.7141995101 .07529 0.602093E»01 .50090 0.702009E401 .12704 0.537606E401 .15230 0.3903076401 .17704 0.2902608101 .22002 0 2079048-01 .30305 0.1215575-01 .37725 0.7392496~oo .91397 0.5690485-00 .4504! 0.503077E.00 .52234 0.1779076-00 .61590 c 8495535-01 0000000000000 0000000000000 un0011|1n1y .0704533100 .3330795400 .2978345000 .Z‘BI‘OEOOO .2080565100 2286705000 10792‘5-00 .5207305-01 .2724295-01 .2308115-01 .2323805-01 .613277E.02 .3273045-02 3761065100 2930005100 250772E000 .1635205100 .'500055100 .l305425000 .5373‘95-0' .4392095-01 .2053035°01 .1886‘25-0’ 72335086-01 .5307575-02 2900005-02 1552 1 Sm(o,t) 538n. E. - 1.24 HOV an 0:111. en‘”"" 2.05103 0.0503578401 3.07053 0.5450000401 3.50927 0.0544040401 5.12745 0.5723332.01 6.15205 0.451412Ev0! 7.17021 0.3005720401 9 22575 0.3230945401 12.30403 0.1155503401 15.37540 0.5414075.oo 15.91531 o.oaozeze~oo 10.45100 0.4ssasoe.oo 21.52402 0.1070055400 25.01790 0.9741145-01 ISBEU uncer1sin1y 0000000000000 .302710E400 .2780i4E400 .2411ose.oo .17374ze.oo .1725505.oo .1essass~oo .aossosE-01 .4255552-01 .23124ze .2052575-01 .2120915~01 .5533295 .3290646-02 ~01 ~02 List of the cross sections for the low-lying peaks in Eu. 1 70 Table A.I.u populated by the reaction I. . 0.45 MeV do .an. d0 “mu” 2.04991 0.0700516-01 3.07405 0.002911Eo01 3.50731 0.042555E-01 5.12405 0.730040E~01 0.14950 0.6045015>01 7.17430 0.4600325-01 9.22373 0.3470695-01 12.29735 0.1041278-01 15.37016 0.1250396-01 10.90019 0.0003076-00 10.44195 0.5002665-00 21.51252 0.3691216-00 25.00440 0.1703406-00 E' - 1.07 Mev 2.05010 0.721061E~01 3.07513 0.640937Ev01 3 50763 0.6623215-01 5.12511 0.5015716-01 6.15004 0.415079E~01 7.17494 0.3120116~01 9.22455 0 233077E~01 12.29044 0.137109Ev01 15.37151 0.9394445-00 16 90760 0.6007975-00 10.44357 0 5262318-00 21.51440 0.3262535-00 25.60662 0.1507SZE-00 0000000000000 0000000000000 un001101n1y .9501108000 .322027E400 .2604516-00 .18'3855~00 .1595955-00 1047065-00 7560135-01 $87‘SSE-O' .3171325-01 249'3'5-01 .1579085-01 9436115-02 .7501795-02 .3707355000 .2432255400 .2115470400 .1255500.00 .1163025400 .710726E-01 .5243916-01 .3720130-01 .2404700-01 .1949935-01 .1443325.o1 .040949E-02 5451775-02 15” Sm(o.t) '2. 16. '8. 21 25. 155 6.1“. .05020 .07520 .50701 .12537 .15035 .17530 .22502 29900 .37220 90052 44440 51540 60707 OVCUUUN 1.01 0000000000000 NOV 2: (m0!!!) do .‘OOC'OEOOZ .92‘3995101 .9032072403 .0774975901 .0987903401 .53!3|¢E>01 .3425525401 .2130735101 .1250605101 .003'655~00 .037850E100 3475248400 .1793002400 155Eu uncer1sin1y 0000000000000 .5233120400 .3437070.00 .300560£>00 .217177e.oo .1010466.oo .11017oe.oo .7475625-01 .5500006 .3t70206-01 .2040408-01 .1714795 .0959046 .7620716 01 .01 -02 ~02 List of the cross sections for the low-lying states Table A.I.5 175 populated by the reaction 0‘00“” 12. 15. ”0‘00“” 15. 10. ”0‘00“” 15. 10. ~10.00 Iov do 00.111. 00 (”I") .05344 0.9394005401 .59340 0.719503£~01 .13345 0.512093E.01 .10000 0.2370205401 .23953 0.1919150-01 31035 0.1305105-01 39029 0.0024778400 .47315 0.57723IEo00 - 0.09 MeV .05372 0.10943GE.02 .59397 0.1707606-02 .13410 0.1002050-02 .10700 0.1090320~02 .24000 0.034121E.01 .32004 0.4100450401 39040 0.2109028401 47507 0.1215225101 - 1.00 MQV .05370 0.1301720402 .59404 0.114301E.02 .13425 0.9024046401 .10772 0.6107025401 .24090 0.4200095401 .32025 0.2031905~01 39007 0.143926Eo01 47590 0.0991758400 00000000 00000000 00000000 0000110101y .7519038400 .5555543400 .2954GBEtOO .0306005-01 .1207005v00 .800737E—01 .5406045-01 .3245015-01 .1297726101 .9092076400 .620007E.00 .207133E~00 .3105360400 .197002£.00 .9000046-01 .5114325-01 .1007325901 ,7091§OE.OO .0005235900 .120091Eo00 .1997085000 .1105178000 .7316235-01 .423024E-01 “Sm(c. 3 He) OMNOVDNN 0 ”0‘00“” 105 Sn. . 1.11 MeV 0 2: (Mb! 1) c.m._ 001 . .05379 0.1072070402 .59409 0.0975200401 .13433 0.0553040~01 .10704 0.4149402401 .24111 0.321470£.01 .32045 0.1923000401 .39091 0.1050090401 .47027 0.0305700400 - 1.42 Mev .05309 0.1219190102 .59427 0.110002E-02 .13459 0.963437E~01 .10019 0.0021050401 .24157 0.4206950.01 .32100 0.2335020401 39907 0.144441e.o1 47710 0.0101025400 1115sm uncertaunty 00000000 00000000 .0290435400 .0309006400 .3430908400 .9479933-01 .1701406-00 .1122756-00 .0004725-01 .343030E-01 rr .914235E-00 .733500E-00 .4406785-00 .1360488-00 .199904E-00 .1204265-00 .7331295-01 .3991598-0' Table 0.1.6 List of the cross sections for the low-lying peaks in ”880(0.3He) populated by the reaction . 0.00 00V ac .c.m. 001(Mb”') .0703? 0.3049378401 .10445 0.2954030401 .13051 0.205349£~01 .15052 0.100240E.01 .10249 0.122099E~01 .23425 0.9023516400 .31133 0.7309376400 .30755 0.4505206400 .40271 0 2005505400 .53060 0.1724060~00 .63200 0.9945595-01 . 0.29 MeV .07051 0.7715355.01 10404 0 6092040-01 .13074 0.5021158-01 .15000 0.5270210-01 .10201 0.4615005-01 .23400 0.275270E~01 .31107 0.1470070401 .30023 0.9337536-00 .40353 0.6114606.00 .53755 0.3253505.00 .03391 0.1302276-00 - 0 91 MeV .07000 0.157504E402 .10502 0 1590616-02 .13122 0.1320435-02 .15737 0 1205356-02 .10340 0.1110600-02 23552 0.7350018-01 39302 0 4097900-01 38960 0 2102296-01 .40523 0.13943SE~01 53953 0 0091205-00 .03624 0 3453375-00 00000000000 00000000000 00000000000 uncer1ain1y .1390315000 .1042055100 .5075995-01 401571E-01 .2513325-01 .2509255-01 2235275-01 .190197E-01 .9212256-02 6853655-02 ,6143175-02 .3436665400 2204925~00 ,143194E.OO 110099E.00 7719416-01 .5933495-01 .3808475-01 .3551675-01 .1597195-01 .1052305-01 .7976515-02 .6962165100 4908525400 .3208615100 .2722125100 1756695.00 .145737Eo00 .9600215-01 .7579455-01 .3150606-01 .2120275-01 .1754605-01 176 OVOM‘U 12. 15. 10. 21. 25. 10 980. ac 00.111. 00 (1110191) .07904 -0.0735375401 .10534 0.0500910101 .13102 0.5409455101 .15700 0.5044995401 .10404 0.4355915101 .23024 0.3030095401 31390 0.1440500401 39000 0.1002515101 40000 0.0000790100 54110 0.4327496400 63020 0.1764358400 . 1.09 Mev 07920 0 0305290401 .10505 0.00009ZE.01 .13200 0 6403905401 .15031 0 0113530101 10450 0.527001E>01 .23693 0.3550040401 .31409 0.245001E~01 .39190 0.1002202401 .40001 0.9200720400 .54274 0 4934006100 .64004 0.31027OE~00 1119sm 00001101nly 00000000000 00000000000 .3000005400 .2115925c00 .1390745400 .1114505o00 .7324925-01 .0457505-01 .3022925-01 .3709025-01 .1749535-01 .1295905-01 .9750045-02 .3729555-00 2777895100 .1623055o00 .133476E~00 .072711E-o1 .7447046-01 .0031905-01 .4004406-01 .2234105-01 .1431105-01 .1593560-01 List of the cross sections for the low-lying peaks in He) populated by the 0 2! m0! 0.5. on ( ") 2.05090 0.1024102402 3.07033 0.9001225401 4.10173 0.037099Eo01 5.12711 0.7169508s01 0.15244 0.020020£~01 7.17773 0.500200E101 9.22014 0.340907Eo01 11.27027 0.200079E401 12.30321 0.102154E.O1 15.37745 0.1100910401 10.45005 0 01900GE»00 21.52202 0.301175E>00 25.61031 0.10170SE~00 EI - 0.45 Mev 2.05102 0.4113005-01 3.07052 0.379997Eo01 4.10199 0.2060398-01 5.12743 0.2471136401 0.15203 0.2119156o01 7.17010 0.1024005o01 9.22072 0.11009BE.01 11.27097 0.0436065400 12.30390 0.5720506400 15.37040 0.4170125.00 10.45179 0 2697270-00 21.52394 0.1221510-00 25.61706 0.5092005-01 1'77 Table A.1.7 reaction 0000000000000 0000000000000 unCOIIIInly .BOJZTBEoOO .3531005o00 .2601315900 .171091E400 .1630705400 .9211825-01 .1054115100 .1077035>00 .6682415-01 .2523455-01 2467416-01 .1440305°01 6627715-02 2466825-00 .1510015400 .9437795-01 .6176075-01 .6090655-01 3205110-01 3004000-01 .4560‘85-01 2260345-01 .1116545-01 1133025-01 .5289475-02 .2771605o02 1528m(a, 3 11. 12. 15. 10. 21. 25. OVQMOUN OVOMOUN 1553 Sm. 0000000000000 .5240170.o1 .4023405001 .3940025e01 .3527095401 .3004405501 .2770175r01 .100290Ev01 .1109095'01 .9400055r00 .5923705o00 .3109100~00 .1838025100 .0155615-01 ' 1.74 MeV 05142 .07712 .10279 .12643 .15402 .17950 .23051 .20116 12. 15. 10. 21. 25. 30030 30137 45533 52004 62271 0000000000000 9355255-01 757184E401 .7‘5‘585901 .5302105001 .5286175401 .5259255101 .2957005401 .213590E>01 71710285101 -1°6771E*O1 .6586915400 .3939805t00 1661685.00 153Sm 0000110101y 0000000000000 0000000000000 .3120000.oo .1757400.00 .1200730.00 0037540-01 .0404508-01 .4997646-01 .536560E~01 .509410E-01 .3593226-01 .140037E.o1 .1313266-01 .7476400-02 .3620906-02 .5516975400 2961945100 .2327385-00 .150917Eo00 .1407‘05'00 .8000975-01 .9050055-01 .110‘855>00 .6289075-01 .2055615-01 2653095-01 .1685645-01 .0790075-02 List or the cross sections for the low-lying peaks in 178 Table 0.1.8 populated by the reaction - 0.30 MeV ac .c.m. 00(m’") .07551 0.7711345401 .10004 0.0070500401 .12574 0.0490440401 .15001 0.5035225401 .17503 0.5107400401 .22570 0.3054908401 .29990 0.201050E.01 .37341 0.1209220401 .44503 0.0791506-00 .51702 0.3719535400 .00971 0.1927105400 - 0.95 MeV .07570 0.23107BE~01 10100 0 1930765-01 .12019 0.200459E.01 .15134 0.1010035101 .17045 0.145301E>01 .22050 0.110500Eo01 .30103 0.0070976400 .37473 0.3727220400 .44741 0.2905770.00 .51000 0.161370E~00 .61107 0.7014030-01 00000000000 00000000000 un001101011 .3470015400 .1771305400 .2149905400 .1300005-00 .0450055-01 .9720525-01 .0262095-01 .4211315-01 .32493‘5oo1 .2690705-01 .1000905-01 .1003490400 .555597E~01 .7460505-01 .5410493-01 .3414525-01 .3745340-01 .273141E-01 .1990395-01 .2010020-01 1338205-01 .0705045-02 15H 1 Sm(o.3He) 5580. a. . 1.71 MeV 9 2! ma! 1) c.m. 00 ( 3 3.07012 0.5042405401 4.10140 0.5154090401 5.12077 0.4029195401 0.15204 0.4049105401 7.17720 0.4130115401 9.22754 0.2000935401 12.30241 0.1590095101 15.37045 0.9000205100 10.44940 0.022419EoOO 21.52124 0.3309045100 25.01400 0.1750945100 155sm uncer1a1n1y 00000000000 .2044000400 .130091E.00 .1550500400 .107445£.oo .7102025-01 .720351E—01 .503097E.01 .35102IE~01 .294727E-01 .244012E'01 .1257308-01 '7 179 cc.wmuvou..o v92wna.ome.c sc.mso—Os~.o >.c.u..ooc: Qo4maovnv—.o mo4wovosw..o oo4movnoa..c >.c.e..ooc= 005mmnonwn s04wmnnww. uo4wh.vmo~ ..0295..mw bu ...”.Emcm. @o4wwmvmom ~04m~movo~ calmcmmncw. ..m‘oevamw co .e.a.sm~m_ .o .o .O .o .O O .oom..u mama..v onnmo.~ .5.u Q co..oao¢ .m.w..m mOQO-.v movmo.w .5.0 G co..omom .Ae.avam v°.wmo.mm~.o vc.w~@oo_v.o mo2wco.mm~.c >.:.a..ooc: volwcm~o_m.o molmvanso~.o holwn.mao..c >.c.a..ouc: =m_.~m_.mz_.==_ cc.w-..nv. sc.wvccmn.. cc.w.vnm.n. ..m‘oE.fiww cu .n.a.Emov. mo.uom4.-. ~o.wo~okn.. oclwoohusa. :39... MN on .a.u.Emvv. 000 000 maow..w ome...v «mmmc.m .E. u 0 co..uaom macs—.0 ccv.—.v sasmo.N .E. U Q co..oaom acouuommp on» :H xmoa ofiuanm on» 000 ncoduoom nmogo on» no and; m.H.< mamas 180 Table 0.1.10 09 List of the cross sections for the low-lying states in Pb 209 . 208 3 209 and Bi populated by the Pb(o, He) Pb and 208 209 Pb(o.t) Bi reactions, respectively. 000011011 : 20.11010,” 1000011011 : 20.1%”.31-1.) el - 0.00 HOV { EI - 0.00 Mbv e 91 1 c . e 95 1 ' c.1n. 00 (m0 51') 00 011011119 0.111. 00 (Mb 01) 00001101n1y 2.03747 0.9005076101 0.1015190100 2.03701 0.4373905401 0.2572935-00 3.56555 0.0740006401 0.209509E»00 3 05040 0.4092020101 0.192071E.00 5.09350 0.765519E401 0.15606OE~00 3.50579 0.3914400101 0.1347335.oo 7 13000 0.600024EoOI 0.1554416-00 5.09392 0.3020426401 0.9090025-01 9.16797 0.409030E101 0.005019E~01 7.13133 0.2294595401 0.2792535-01 12.22324 0.2140105401 .0.7415150-01 9.10050 0.1792425401 0.2909146-01 15.27791 0 1370325401 0.414727E-01 12.22404 0.104479E>01 0.27433OE-OI 10.33101 0.06311ZE~00 0.206057E.01 15.27090 0.1106025401 0.2441936-01 20.30724 0.5271205400 0.4700935-01 10.33299 0.9311000100 0.2510946-01 E . 0 90 MeV E. - 0.70 MeV 1 2.03700 0.122403E>02 0 210416Ev00 2.03779 0.0010240-01 0 300904E400 3 56591 0.110324E~02 0.241570E400 3 05067 0.9037240-01 0.2060645~00 5.09409 0.0420OSE.01 0 1600905400 3 50010 0.0500225u01 0.1992596-00 7.13157 0.521543E.01 0.1400905.oo 5 09437 0.6959038401 0.150000£~00 9.16009 0.3020075401 0.7492935-01 7.13195 0.5732505401 0.4413715-01 12.22440 0.210000Eo01 0.7500190-01 9.10930 0.3994400401 0.4342426-01 15.27941 0.100035E~01 0.3020275-01 12.22511 0.2573120401 0.3430035-01 10.33301 0.0194IOE~00 0.2701010-01 15.20023 0.1792056401 0.300150E-01 20.35923 0.49106OE.00 0.4692795-01 10.33450 0.1117145401 0.275020E-01 E. - 1.61 MeV E: . 1 42 MeV 2.03704 0.134244E-02 0.224974E~00 2 03794 0.130137E>02 0.4572295-00 3.56619 0.1425525-02 0.270951£~00 3 05609 0 1519015402 0 3716105-00 5 09450 0.1325005-02 0.2000245-00 3 56635 0.1477655-02 0 2617305-03 7.13214 0 1171a4e.oz 0 2044105-00 5 09474 0.1290535-02 0 2043715-00 9.10952 0 0432995401 0.1200026-00 7 13247 0 1175565-02 0 6322536-3' 12.22543 0 4472495401 0.100073Ev00 9 17005 0.9090018~01 0 6550458-31 15.20063 0.203663E~01 0.5015776-01 12 22600 0 5757025~01 0 5131336-01 10.33506 0 171047E~01 0.3790966~01 15.20134 0.3795705o01 0.430767E-01 20.37004 0.103754E.01 0.0000650-01 10 33590 0.220203E401 0.3930436-01 ”PBIDIX II PROGRAM ALGORITHMS and PROGRAM INPUT EXAMPLES. The codes developed in this thesis were carried out for use on the VAX 11/750 and VAX 11/780 computers at the NSCL. All input data for programs and output data from programs were written to the disk of the VAX computer in the file format. This appendix is separated into six sections. I’h the first section the program, SPECCAL is outlined in an algorithm format and a program input and output is also presented. The second section outlines in an algorithm format the program SMASHER and a program input and output is presented here. The third section gives and example of the data files needed to run the DWBA program DWUCKH [KuBH]. The fourth section gives an example input and output cfi’ the data files needed to run the cross section code SIGCALC [St82]. Imitlw fifth.section. an example input and output is displayed to use the program WRITECHEX, which converts a spectrum which is expressed in terms of counts versus channel number to a spectrum expresse0.in terms of counts versus excitation energy. In the last section, an example input that was used to setup the 68K data aquisition program, used to collect data in the third experimental run. 181 182 A. CALIBRATION PROGRAM. The calibration procedure is outlined in Chapter II. The program developed to calculate a set of calibrations for each reaction is called SPECCAL. As mentioned in Chapter II, the program fits a quadratic curve through a set of energy calibration points given by the mylar target iflld low lying states in the reaction of interest, if any exist. The algorithm of the program SPECCAL is given in Figure A.II.1. The input data file required to run the program SPECCAL is presented here as a case of 96.9 MeV 0 particles 100 bombarding mylar and Sm. In this case, the input and 1a output files obtain a calibration equation for the 5Eu spectra at a laboratory angle of 2° and target angle of 2° for all spectra angles will be given. There are eight calibrated peaks positions corresponding to those in Figure II.8. The input andioutput sample files for this case is given in Tables A.II.1a and A.II.1b respectively. 183 Figure A.11.1 Calibration program algorithm Program SPECCAL REACTION READ: Experimenfol poromerfers I [ Redd: no. of looIIbro'rlon p?s.] LReodz coubroflon p10] Colculofe beam energy loss In forge? CALL Colculo‘re Ktnemoflcs coefficients To Te vs cnonnel no. 40"”pr O'D'CH CALL .LKInemoflcs Cotculo‘re coefficients 1° {oufpuf u.v.w}-—D Ex v0 channel no. Nexf onque. Figure A. 11.1 180 Table A.II.1a Calibration program input example. 7 0110110500? gaunt. 40 v v v 1440M(4H0.T1 1.05 . 101901 1nickness in mglcmz 90.9 -’beem energy in MeV 1 Y 200..900. ’ 2 - order 01 100 polynomial 111. 0 - number 01 00110101100 poin1s. 1 252.009. 201.153. 271.443. 200.475. 329.010. 300.510. -O60.O..1448M - 04110101100 in1orme1ion: ensue.» 01c. .040.0.3295.144SM .040.0.710.144su .040.1.0419.144SM ' .00.0..12¢ .00.0..10O 449.293. .00.3 547.12C 503.173. . .00.5 017,100 2..2. - L40 9. target 0 252.009 201.153 271.443 200.475 329.010 300.510 449.293 503.173 040.000 722.009 735.530 00000000 0 0. V NNNNNNNN NNNNNNNN 77..59. moer 185 Table A.II.1b Calibration program output example. '10010. ‘9“. '11" '0 V. Ch.nn.| . 1440u(4H0.T) '0- 0.:51711925-00 l" 2 e 0.100500025000 0" 1 e 0.71500053I003 T.- 0.10022000£-00 l" 2 e 0.00510277£°01 0" 1 O 0.090202005402 xe"°°.‘3°3.91.£¢01 ‘b’ .7700'0.‘173725'E.0' “.1 ."°"°‘54“3095-03 EI- °.113’2‘785°°‘ I" 2 o 0.007502315-01 8" 1 4 -.90.017755401 L00 C.M. T0 Ova! 5: To 079 Ch 0 R00011on angle angIe [MeVI [MeV] [MeVI [MeV] [MOVI 2.000 2.054 00.1710 -10.559 0.000 90.0507 0.0250 252.01 1448M14HE.T1 rho 0.1x . 1.040 mglcm'°2 2.000 2.055 79.0404 -10.559 0.330 90.0507 0.0250 201.15 144SM(4HE.f1 rho 041x 4 1.040 mglcm"2 2.000 2.055 79.4517 -16 559 0.710 90.0507 0.0250 271.44 144SM14HE.T1 rho OQIX - 1.040 mglcm"2 2.000 2.055 79.1230 -10.559 1.042 90.0507 0.0250 200.40 144SM14uE.11 rho 001x - 1 040 mgrcm"2 2.000 2.654 77.4336 -17 071 0.000 90.0403 0.0354 329.01 12C14HE.T1 rho 001x . 0.000 mg :m"2 2.000 2.497 70.3901 -19.214 0.000 90 0497 0.0340 300.51 10014HE.Y1 rho oelx . 0.000 m97cm'°2 2 000 2.070 73.0100 -17.071 3.547 90.0403 0 0354 449.29 12C14HE.V1 '00 GOIX . 0.000 mglcm"2 2.000 2 523 70.2173 -19.214 5.017 90.0497 0 0340 503.17 100(4HE.T1 rho 0.1x - 0.000 mglcm"2 rho 001x - 1.040 mglcm°'2 2 000 0.000 00.1004 ~15.559 0.003 90.0507 0250 252.01 144$M(‘HE.T1 2.000 0 000 79 7007 ~16.559 0.383 90.8507 0250 201.15 144SM(4HE Y. 2 000 O 000 79.4230 ~16.559 O 740 90 0507 .0250 271.44 144$M1‘HE.71 2.000 0.000 79.1110 ~16.559 1 051 90.8507 0250 200.40 144SM14HE 71 2.000 0 000 77.4370 ~10 559 2.719 90.0507 3250 329.01 '44SM14HE 7- 2.000 0.000 70 4232 ~10.559 3.720 90.8507 0250 360 51 144SM14~§ ' 2.000 O 000 73 0039 -15 559 5 525 90.0507 0250 449 29 1445M14~E '~ 2 000 0 000 73 2374 -15.559 9.052 30 050’ 3250 553 17 144SM14~E ’» 2.000 0 000 00.1013 ~10.559 11.902 90 0507 3250 530 as 144$M14HE '1 2 000 0 000 60.0107 ~10.559 14.004 96 0507 0250 722.01 144$M(4HE ' 2 000 0 0:0 65 5759 -10.559 14.399 96.0507 0250 735.54 1445M14HE ‘. 2.000 O 000 01.9533 -10.559 -1.000 90.0507 0250 200.00 144SM14HE 71 2.000 0 OOO 61.9231 -10.559 17 900 90.0507 0 0250 900 00 144SM14HE '3 000000000000 186 B. FITTING and SLICING PROGRAMS. Chapter IV made reference to a slicing and fitting of I)WBA l-transfers using the x; method. The program that performs these operations is called SHASHER. The algorithm of SMASHER is given in Figure A.11.2. The program SMASHER was designed to calculate the spectroscopic factors (C’S) by means of fitting a set of 2- transfer angular distributions calculated by DWUCKH with the experimentally deduced angular distributions. The experimental angular distributions were calculated by either a slicing method or by gaussians. The input example that its given here will use the u typical case of slicing the 1 58m spectra using the 1uuSm(a,3 He) reaction. The slicing of 520 keV bin widths begins at 1.7 MeV and is concluded at about 10 MeV. The IDWBA i-transfers that were selected to fit this excitation energy region are the 2-3, u, S, 6 and 7 values. The input data file for this case is given in Table A.11.2 and is called ASMAHBF.DAT. To run the SMASPHHR program interactively one would type in: ANALYS:: @SMASHER1 The program then asks (with your response underlined): 187 ‘ihat is the name of the *.DAT file to be run by SHASHER? ASMAHBF Theoutput of the program write a set of output files of the calculation which contain the information from all of the fits and of the background calculation. 188 Figure A.11.2 Program algorithm for SMASHER. Program SMASHER Fitting criterion code READ: Experimental parameters Background calculation READ: Slicing size " subtract background 'siice spectra“ and calculate experimental angular distributions DWBA htransfers READ' selected to fit angular distributions Fit experimental angular distributions with DWBA OUTPUT a, . do, Figure A. II.2 18!? Table A.11.2 Slicing and fitting program example IIIV‘50‘ goerv.eirw4wc.04t41 g. 1.0 95.9410.19.77 3.5.2. 1.0 . 144.0717.0.74 5..2. 1.0 201.2140.5.35 7..2. 1.0 354.1145.5.00 9..2. 1.0 417.3974.50.95 12..2. 1.0 344.9075.13.40 15..2. 1.0 477.0900.24.00 10..2. 1.0 571.2793.40.94 1445M14H0.3H0) 90.9 1.05 .9047 (’VOHOUON' I 11 1 11 1 1010 on 23 111110.. RUGIOI 01 00.100 0.0011. 1110 OUR. 00‘. 140 0. 1erge10 charge (06). rele1ive 01101 (BC) DOOM 00.197 1010 On I-D'Ollufl 1U!" 00 - .VIDO'I11OH ma1CB CdlCull1100 01 54429 MeV 51011 5110109 41 1 7 MeV number 01 DWBA 1-1ranslers 103 1e‘ 1-5 1-0 107 Fl 4' . 190 C. DWBA PROGRAMS. DHBA programs are made easy to run on the Vax 11/750 and 11/780 computers. [The DWBA calculations needed for this thesis involve many cases of t-transfers (1. - O + 7) and a long range of excitation energies (Ex' 0 + 15 MeV) for one reaction (see Chapter III). Setting up the data file for the DWUCKH [KuBIi] program involving many cases for one reaction and is very time consuming if this work was to be carried out by hand. This gave rise to the development of a program, called DWKREACT, that would make the setting up of the input data file for the DHUCKli program very easy for the many cases involved. Hence. the DWBA inelastic calculations where performed using two different programs. The first program, called DWKREACT. would set up the input data file for the second program called DWUCKll. No algorithm of the DWKREACT is necessary because all it does is write to disk, in the format form, an input file for the DWUCK‘i program. The typical case of an input file for DWKREACT is given in TABLE A.II.3. This is a typical case to calculate the 1h9/2, 1111/2 and 1315/2 at the excitation energies of 0.0 and 5.0 MeV using the Optical parameters given in Table III.1. 191 Table A.II.3 DHBA program example 144$m(4He.3He)1455m “boas-Saxon 42 100. , deepneu1225.00000.0000 0. 30. 0. 25 1. .1, C 1 2 3 4 5 0 .1. o. -L 0. -L 0. 1.4 1 4 0.0 .150 4 1.32 0.02 o -3c.02 1.35 0.05 .25 4 1.10 0.00 o .17.: 1. s 0.77 .. 1 25 0.05 23 o o. c. 192 D. PROGRAM EXAMPLE FOR SIGCALC. The program SIGCALC has been used throughout the NSCL to calculate cross sections using the experimental parameters and extracted peaks. The typical example that will be given here, is, the examination of three low lying peaks in 1“5811: obtained by the inelastic reaction of 11mSm(o:,3He) with an a beam energy of 96.8 MeV. In particular, the three low lying peaks energies are; 0.0 MeV, 0.88 MeV and 1.17 MeV and cross sections are computed for eight angles that range from 2° to 18°. The name 0: the input file is Aéfllfléiflflfl and is tabulated in Table A.II.11a. SIGCALC is an interactive program in which one must input data file and type in what form the output must be in. Table A.II.hb tabulate the procedure to obtain labcmoss sections by running the program on the VAX computer. SIGCALC program input example. “05m 4115. 3110) 1 g 0.000 3 0.002 3 1.107 - . 100.000 1.000 1'le .9047 3 2.000 2 5 3.500 2 g 5.000 2 g 7.000 2 10 9.000 2 13 12.000 2 18 15.000 2 19 10.000 2 END 195.80 1992- 220.92 13190. 229.09 4959. .1.0 0. 200.52 3541 224.38 13794 232.12 9977. .1.0 0. 200.39 2803. 224.18 12965. 231.70 19175. .1.0 0. 200.51 2745. 224.53 15823. 231.83 22258. .1.0 0. 200.69 2732. 225.08 13280. 232.13 18468. .1.0 0. 200.79 1433. 233.31 8023 226.04 5818. -1.0 0. 202.38 1281 227 74 6033. 235.58 3882. -1 0 0. 203.39 1056. 228.97 3204. 238.53 4606. [EOBI 1 93 13019 A. II. 11a .000 .000 .000 .000 .000 .000 .000 52 30 .72 .15 50 19 64 50 10 a1 85 21 53 01 73 .03 49 .00 35 21 33 89 01 0. 410 233. 200. 247. 330. 420. 590. 007. 1023 7312 7100 0750 2042 0000 0020 0090 .1002 S1. 199. 249. 60. 260. 482. 197. 352. 59. 204. 371 50. 197. 340. 42. 320. 175. 36. 120. 205. 38. 141. 239. ‘-“““ .00000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 “““‘- .20000 .00000 .00000 .00000 .00000 .00000 .00000 .00000 mmmommcoouuuouuu OOIOOOVNVOUIUIMOUUUONNN O‘DWUU‘UIMONNN 190 Table A.II.HD SIGCALC program output example. To ,un 100 910.10. 000 lyeee (the undetlinod 1.15.); vs; 2 c (Cb :::t 15 1010 10001 1110 nen0 7 W<¢b MENU 51011 0010111011011 L191 10 111. L151 10 screen P101 30110 10 Rutherlord snow commiete 0010 501 ' 5 L151 10 OMUCK4 111. . 9 (CR) #3 “001 15 1h. n0me 101 the DMUCK4 111. 001901 7 A§MAHI3AC.OUT MENU OQD‘PIO S1UW cumulanon L151 10111. L151 10 screen P101 30110 to Rutheriora Show comoIete 0010 501 L151 10 0WCK41110 OWDVF'IIO g (CR) snoCALC 15 11015000. The 1050115 01 rue calcula11on are stored 1n the 1110 called ASMAHBJAC.OUT 195 -. '3. PROGRAM EXAMPLE FOR waxrscnsx. The program HRITECHBX was designed to convert a - spectrum which was expressed in terms of counts versus channel number into a spectrum expressed in terms of counts versus excitation energy. This was carried out for all or the spectra that where sliced and used the calibration output of SPECCAL. Table A.II.S list the command file that was used on a VAX 11/750 or 11/780 computer for the typical case of converting spectra of the three angles of 2°. 9° and 18° 7 obtained from the reaction 1l‘uSm(01.t) using the 96.9 MeV beam. The name of this file is called CHEXASMT.COM. This command file requires file names of spectra to exist in the computer. These names are ASMATBOZ.SPC,ASMATBO9.SPC and ASMATB18.SPC in the subdirectory called [DUFFY.ALPHAT.DATA]. To run this program on the VAX computer one types in (5119 underlined part): ANA LYS : : @CHEXASMT The output from this program will write the corrected spectra to disk in the subdirectory called [DUFFY.ALPATC. DATA]. 196 Table A.II.5 Program example for HRITECHEX ' 5 307 DEFAULT SYS5ANALY818:[DUFFY.ALPHATC.DATA| 3 sun [ouFFY.PLOTSIWR1TECHEx '0‘ ‘ '50 Site in 00V 3.000. 11.040. 2 : g:”:;.f;"?:f:;i 1'1311:1°,M."' 00.11052470240-04 7 ‘"°“"" 4 20¢ order 00110. ,m. .1 é1.000.17.040.5 0.11321744095100 0.4000301202Eo01 . 0.94522140195101 4.400.15.200.10 -0.01549510795.05 0.37222009542-01 -0.11015397205102 ASMATB (DUFFY.ALPHAT.DATA| [DUFFY.ALPHATC.DATA| (600] 197 -_ F. PROGRAM EXAMPLE FOR THE 68K. Table A.II.6 outlines the steps that are taken to program the 68K data aquisition program for the stripping reaction run. 198 Table A.II.6 Program example for the 68K 73. 10110010. 15 00 0000010 101 501110. 00 the 00K 0010 0001511100 eyetem. we 1111110012 400(00011‘51 10 51010 4 000 5 000 2 men 12240111'5) 10 5101 41 0 .110 1 10 100 500 01010. 711.1110! 11110.10 00 10 10 1393101111111 0090111110111 0660. 010050 1y90 100 Iollowtnq. And 005w01 100 qugg1iong .3004. saflMOJflHWIHT o 610010 0 001111 0011011000 1110?(YIN) .......... Y ( 11 N - type [050011m001 0|.00K ) . 610010 1011101 FNA’e 7 (YIN) ............ Y 1 . F:20 . £00010 LAM (500 m00001 101 00811'51 N:4 a Slot 0 on 0101.. ‘ 0:12 a 0001055 NAM£: .......................... .. .. SAVE’: tyne ...Y ..... 01 the 000 11 «111 050 CONTINUE7: tyne ...Y 900001 101 011 FNA's. 010001 01 the com001100. 1500 001001 2 - F:11 - C1001 011 109151015 (500 M00001 101 A0011'51 N:4 A212 3 ~ F:20 N:5 ~-----: 00 the same 101 the 1051 01 the ADC‘5 : Az12 . 4 - Ft11 I 5 - F-25 ~ 500 M00001 101 2249W'5 N25 - ----- N‘0 A: 12 A.0 . 01 the comolet100 01 thus 0055. type N 01101 CONTINUEY' Tn. 011 0011. “n 010 05109 only 2 0115. 000 15 101 the 5320 events and the other one 1:1 --9 mo01101 (AE.E1. 000 AS 0505 0 2249w and the other E 0505 the other 2249a On. “06 "‘0'. 1110111101310! 0113171.” 061031 1'30 309(09'1010 001011101015 4 TyDO 1015 0011 811 11 311 2 1 311 3 O Table A.II.6 continued 31.1.1" .111 (11000 01 LAW” 00 1011. 51015101 011 2 00 119111. 4 Type 1010 0011 4 Type 1015 0011. 1 1 0 5101 1 0 :::1 2 0 0101 2 0 5101 3 0 5101 3 0 3101 4 1 3101 4 0 5101 5 1 5101 5 0 5101 5 0 5101 0 1 5101 -7 0 0101 7 1 5101 8 0 5101 0 0 5101 9 0 5101 9 0 5101 10 0 5101 10 0 5101 11 0 $101 11 0 5'0! '2 0 $101 12 0 $101 13 0 Slot 13 0 5101 14 0 $101 14 0 Slot 15 0 $101 15 0 $101 10 0 5101 10 0 11101111110 00111 5100 15 10 1000 0010010005 01811 L 10 m 01001 900001 the 50m0 010000010 05 above 101 010010M1ng 1n. sun-,, 1 - F:0 u 0000 command 101 40811’5 (500 m000011 N35 00510: D 4 - F 0 7 - ‘10 A;o N24 SAVE?:Y N:4 SAVE’:Y NAME: 0‘5 A22 NAME; NAME: 2 - F10 5 - 0‘0 0 . 5:0 0:4 SAVE?:Y ~:4 SAVE?.Y N14 SAVE?:Y A27 A:4 A:1 NAMEz NAME: NAMEz 3 F;0 6 - F10 9 - Fro N:4 SAVE?:Y N;4 SAVE?:Y N:4 SAVE"Y A:6 A:3 A.O NAME: NAME: NAME1 Don't 101951 to 50v Ntno1 01101 the CONT1~UE7 51010m0n1' In 1000130 01001 load 311 g. 1 . F o N.6 SAVE’ v A I NAME. A:0 NAMEL -, Table A.II.6 continued 011'(ev0011 0501057 ................................ v ., .... .109 15 10 01001 FNA’e 101010011y 101 0000 00.01 0,010,, . 0:11 0 01001 commend (500 00011 m000011 N:4 - 5101 0 A:12 5AMl: - 0:11 . N:0 0AV07zY A112 NAHE: 0 5010 1001 you type in N(001 101 the CONTINUE 51010m001. o INA'5 010 000000 to 01001 5101 0 5 00100 5. 1°, tn. 22‘,“r. (0°C..). '70. 1001 15 0000 051010011y. . Do you 0001 FNA-s 101 the 000 01 0.1.3 ey010g 0fl1y, '_. N 1 5010 900? (1.0. 1015 005571 .. ....................... v [Aa82] [Aa8fl] [A070] [Be69] [Be79] [Be83a] [8983b] [Be86] [8153] [8069] [8075a] [Bo7SD] [C069] REFERENCES E.H.L. Aarts. R. Malfliet, S.Y. van der Werf and R.J. de Meijer, Nucl. Phys. A380. 465 (1982). E.H.L. Aarts, R.A.R.L. Malfliet, R.J. de Meijer and S.Y. van der Nerf, Nucl. Phys. A025, 23 (198“). N. Austern, "Direct Nuclear Reaction Theories" (John Wiley and Sons, 1970). P.R. Bevington, "Data Reduction and Error Analysis for the Physical Sciences", (McGraw Hill, 1969) p. 89 ' .F. Bertsch, P.F. Bortignon, R.A. Broglia and .H. Dasso, Phy. Lett. 808, 161 (1979). .F. Bertsch, P.F. Bortignon, R.A. Broglia and H Dasso, Rev. Mod. Phys. 22, 287 (1983). G.F. Bertsch, private communication, 1986. J.M. Blatt and V.F. Weisskopf, "Theoretical Nuclear Physics" (John Wiley and Sons, 1953) p. 32M. ‘ A. Bohr and B.R. Mottelson, "Nuclear Structure", Vol 1 (Benjamin,1969) p. “32. A. Bohr and B.R. Mottelson, "Nuclear Structure". Vol 2 (Benjamin,1975) p. #22. w. Booth and S. Wilson, Nucl. Phys. A2”?, 126 M. ConJeand, S. Harar and E.Thuriere, Nucl. Phys. A129, 10 (1969). 199 [Cr80] [D377] [Fr77] [01-1] [G1-2] [Ga81] [Ga82a] [Ga82b] [Ga83] [Ga8u] [GaBSa] [Ga85b] [Ge70] [0e80] [0072] [He7u] 200 G.M. Crawley, in Proc. Int. Conf. on Structure of Medium-Heavy Nuclei, Osaka, Japan (1980) p. 590. A. Djaloeis, J.P. Didelez, A. Galonsky and W. Oelert, Annual Report of Kernforschungsanlage Julich, 1977. p. 2. E. Friedman, A. Moalem, D. Suraqui and S. Mordechai, Phys. Rev. C15, 160“ (1977). ' Ref. [C069,He7N,Se77,We77,Cr80,Ge80,Sa81,Ga81, Ga83] ' Ref. [Ga826,Ga8u,Ga85a,Ga85b] \ S. Gales, Nucl. Phys. A35“, 1930 (1981). \ S. Gales, G.M. Crawley, D. Weber and B. Zwieglinski, Nucl. Phys. A351, 173 (1982). \ S. Gales, (J.P. Massolo, S. Fortier, E. Gerlic, J. Guillot, E. Hourani, J.M. Maison, J.P. Schapira and B. Zwieglinski, Phys. Rev. Lett. "8, 1593 (1982). ' ' ‘ \ S. Gales, G.M. Crawley, D. Weber and B. Zwieglinski, Nucl. Phys. A398, 19 (1983). \ S. Gales, Journal de Physique, cu, March 198R. \ S. Gales, C.P. Massolo, S. Fortier and J.P. Schapira, Phys. Rev. C31, 94 (1985). S. Gales, in Int. School of Nuclear Structure, Alushta, USSR Oct 1985, IPN Report IPNO-DRE/85-31. C.P. Gerald, "Applied Numerical Analysis", (Addison-Wesley, 1970) p. 28“. E. Gerlic, G. Berrier-Ronsin, G. Duhamel, S. Gales, E. Hourani, H. Langevin-Joliot, M. Vergnes and J. Van de Wiele, Rhys. Rev C21, 12A (1980). U. Gotz, H.C. Pauli, K. Alder and K. Junker, Nucl. Phys. A192. 1 (1972). W.H.A. Hessenlinck, B.R. Kooistra, L.W. Put, R.H. Siemssen and S.Y. van der Werf, Nucl. Phys. A226, 229 (197“). [K074] [K085] [Ku69] [Ku84] [La82] [Ma69] [Ma76] [Ma77] [Ma86] [Me85] [M071] [0165] [Pe81] [Sa81] [Sa85] 201 D.G. Kovar, N. Stein and 0.x. Bockelman, Nucl. Phys. A231, 266 (1974). N. Koori, T. Ohsawa, S. Seki, H. Yokota, T. Yanabu, Y. Deschamps, E. Hourani, H. Langevin- O Joliot, F. Reide and M. Roy-Stephan, Phys. Rev. CB1, 246 (1985). P.D. Kunz, University of Colorado, program DWUCK4 (1969) unpublished. P.D. Kunz, private communication, 1984. H. Langevin-Joliot, E. Gerlic, J. Guillot, M. Sakai, J. van de Wiele, A. Devaux, P. Force and G. Landaud, Phys. Lett. 1148, 103 (1982). M.H. Macfarlane, in Proceedings of the International Conference on Properties of Nuclear States, Montreal, 1969, p. 385. L.A. Malov and V.G. Soloviev, Nucl. Phys. A270, 87 (1976). M.J. Martin, Nucl. Data Sheets 22, 545 (1977). L.A. Malov, N.D. Vinh and V.G. Soloviev, preprint (1986). R.J. de Meijer, Rev. Mod. Phys. 51, 147 (1985). E.J. Moniz, I. Sick, R.R. Whitney, J.R. Ficenec, R.D. Kephart and W.P. Trower, Phys. Rev. Lett. 26, 445 (1971). ' G.G. Ohlsen, Nucl. Inst. and Meth. 37, 240 (1965). R. Perry, A. Nadasen, D.L. Hendrie, P.G. R003 and N.S. Chant, Phys. Rev. 024, 1471 (1981). H. Sakai, R.K. Bhowmik, K. van Dijk, A.G. Drentje, M.N. Harakeh, Y. Iwasaki, R.R. Siemssen, 3.x. van der Werf and A. van der Woude, Phys. Lett. 1038, 309 (1981). ' Ii. Sakai, R.K. Bhowmik, S. Brandenburg, J.R. van Dijk, A.G. Drentje, M.N. Harakeh, Y. Iwasaki, R.R. Siemssen, 8.1} van der Werf and A. van der Woude, Research Center for Nuclear Physics, Osaka University, RCNP85-1. [8080] [$082] [8085] [8e77] [Se47] [Se85] [sn85] [8080] [St79] [St83] [Tu80] [Va85a] [Va850] [V170] [Wa77] [We77] [W072] [Wu79] 202 0. Scholten, M.N. Harakeh, J. van der Phicht, L.W. Put, R.R. Siemssen and S.Y. van der Werf, Nucl. Phys. A348, 301 (1980). 0. Scholten and N. Blasi, Nucl. Phys. A380, 509 (1982). O. Scholten, private communication, 1985. M. Sekiguchi, Y. Shida, F. Soga, Y. Hirao and M. Sakai, Nucl. Phys. A278, 231 (1977). R. Serber, Phys. Rev. 72, 1008(1947). B. Seligmann, J. Ernst, J. Kleinfeller, K. Keller, L. Lassen, W. Lucking, R. Schreck and H. Gemmeke, Phys. Lett. 157B. 345 (1985). B.M. Sherrill, Ph.D. Thesis (Michigan State University, Department of Physics, 1985). unpublished. ' V.G. Soloviev, Ch. Stoyanov, and A. I. Vdovin, Nucl. Phys. A342, 261 (1980). 0. Straum, G. Lovhoiden, D.G. Burke, B.R. Flynn and J.W. Sunier, Z. Phys. A293. 75 (1979). Ch. Stoyanov and A.I. Vdovin, Phys. Lett. 1308, 134 (1983). J.K. Tuli, Nucl. Data Sheets 829. 533 (1980), A=145, and references therin. H. van der Plicht, private communication, 1985. A. Vander Molen, R. Au, R. Fox and T. Glynn, Nucl. Inst. and Meth. £236, 359 (1985). C.M. Vincent and H.T. Fortune, Phys. Rev. CZ, 782 (1970). A.H. Wapstra and K. 803, At. Data Nucl. Data Tables 19, 215 (1977). S.Y. van der Werf, M.N. Harakeh, L.W. Put, 0. Scholten and R.R. Siemssen, Nucl. Phys. A289, 141 (1977). P.B. Woollam, R.J. Griffiths, F.G. Kingston, C.B. Fulmer, J.C. Hafele and A. Scott, Nucl. Phys. A179. 657 (1972). J.R. Wu, C.C. Chang, R.D. Holmgren and R.W. Koontz, Phys. Rev. C20, 1284 (1979)