"HFSYS ‘. .11.“. ‘ _ .._ -........... .. "y P} LIBRARY ”3 ; Michigan State " ‘Vl flfflb V—p—v-‘———~' This is to certify that the thesis entitled 232 234,236,238U Multipole Moments of Th, Using Proton Inelastic Scattering presented by Robert Clare Melin has been accepted towards fulfillment of the requirements for Ph. D. degree in Physics W % Qééficfi / V C 6/ Major professor 0-7639 w: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records .1/ fl\\ ‘A({ u\{\\‘ A .. “T‘ul"ll 232 MULTIPOLE MOMENTS OF Th, 23u’236’238U USING PROTON INELASTIC SCATTERING By Robert Clare Melin A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1981 ,. .1/ (‘1' \__A (37 // ABSTRACT 232 23u,236,238U MULTIPOLE MOMENTS OF Th: USING PROTON INELASTIC SCATTERING By Robert Clare Melin The multipole moments of 232Th, 23u,236,238 U have been determined using proton scattering at 35.3 MeV. The angular distributions of scattered protons for the elastic (J1T = 0+) and ground state rotational band states (JTr = 2+, H+, 6+, 8+) were extracted for laboratory angles from 20 to 144.5 degrees. The targets were UP” and ThFu 2314’236U. The scattered and isotopically separated for protons were detected using a position sensitive detector in the focal plane of an Enge split-pole spectrograph. The typical energy resolution of 15 keV is made possible by using dispersion matching for the entire range Of scatter- ing angles. The data were analyzed using coupled channels calcula- tions for scattering from a rigid rotor via a deformed optical model potential. Automatic searches were made on Robert Clare Melin a number of model parameters, including the deformation parameters 82, Bu, 86 for both spherical and deformed Spin— orbit potentials. The quadrupole hexadecapole and hexa- kontattetarapole moments were calculated from the parameter values and compared with the results Of Coulomb excitation, electron scattering, inelastic alpha scattering and with predictions of microscopic calculations. Improved fits to the data were obtained by including the higher order deformations. Comparisons were made for a full deformed spin-orbit potential and a spherical spin-orbit potential, with the deformed Spin-orbit yielding improved fits. The resultant quadrupole moments increase in magnitude with increasing nuclear mass in agreement with Coulomb excitation results but systematically 3% to 5% lower. The present results are 3% to 6% higher than those predicted by micro- scopic calculations. The hexadecapole moment from this study 2h; largest for A = 23A in agreement with the trend predicted by the microscopic calculations and from the Coulomb excitation results, although the magnitudes of the latter exceed the present results by as much as 25%. In general, the quadrupole and hexadecapole moments deduced in this work disagree in trend and magnitude with the inelastic alpha scattering results. The hexakontat- tetarapole moments of these nuclei are extracted for the first time and reach a maximum for A 236 and approach zero for A = 238, a trend which can be explained by a Robert Clare Melin Simple model which also predicts the quadrupole and hexadecapole behavior. ACKNOWLEDGMENTS During my years at Michigan State University I re- ceived assistance from many friends and colleagues. My thanks go out to all of them with special acknowledgments to the following. To Dr. J. A. Nolen, Jr. who advised me and assisted in choosing and completing this project. By working with Jerry, I gained an immeasurable wealth of knowledge about experimental methods, techniques and equipment. To Drs. R. G. Markham and R. G. H. Robertson with whom I worked throughout my graduate career. Roger taught me much of what I know about particle detectors as we designed and developed new detectors. The experiments I worked on with Hamish provided exciting challenges and an excellent Opportunity to broaden my education. Without the timely guidance of Dr. R. M. Ronningen this project would have been difficult. Reg was extremely help- ful in understanding and completing the calculations leading to the experimental results. For his assistance in writing this thesis, for his constructive comments on presentations of this work, and for his friendship, I am forever indebted. To the National Science Foundation which supplied operating funds to the Cyclotron Laboratory and to Dr. H. Blosser, the staff and faculty of the Cyclotron Laboratory, ii for making it an excellent facility in which to work and learn. A special thanks to Peter Miller, Jones Chein, Harold Hilbert, Dan Magistro, Bill Harder and their helpers who maintained and kept the cyclotron and experimental equipment running and to Dick Au and Tim Glynn who worked diligently to keep the computer running. To Mr. Norval Mercer and his machine Shop crew who fabricated much of the experimental equipment I used. Besides teaching me the art of working in the machine shop and giving guidance on my mechanical projects, Merce is a good friend with whom I shared countless stories and dis— cussed innumerable football and basketball contests. For my undergraduate education which carried me so far, I thank the members of the Physics Department at the Uni- versity of Wisconsin-River Fa/ls. Special thanks go to Dr. Neal Prochnow who helped open a number of doors which led to my graduate education. To my parents, Clare and Dorothy Melin a Special ap- preciation for allowing me to choose my own paths and for instilling in me the value of hard work, knowledge and experience. To Jan and ZOphia Porzuczek for their con- tinued encouragement. To Paul, Jim, Joe, Steve, Wayne and all my friends and members of the Nuclear Beer Group whose companionship will always be remembered. So much of an education comes outside the classroom and laboratories and it is with these people that I have enjoyed this facet of my education. iii To my wife, Teresa Porzuczek, for her constant support and help, I dedicate this thesis, for it is She who sacri- ficed the most and worked the hardest in order that I could complete this work. She kept me going when the work was the hardest and supplied the motivation to continue. iv TABLE OF CONTENTS Chapter Page LIST OF TABLES. . . . . . . . . . . . . . . . . . Vii LIST OF FIGURES . . . . . . . . . . . . . . . . . iX CHAPTER I INTRODUCTION. . . . . . . . . . . . . . . . . l MOTIVATION. . . . . . . . . . . . . . . . . . 6 ORGANIZATION. . . . . . . . . . . . . . . . . 1“ CHAPTER II. . . . . . . . . . . . . . . . . . . . 15 THEORETICAL METHODS . . . . . . . . . . . . . 15 Optical Model Potential . . . . . . . . . l5 Deformed Optical Model Potential (DOMP) . l9 Multipole Moments . . . . . . . . . . . . 23 COUPLED CHANNELS CALCULATION. . . . . . . . . 27 CHAPTER III . . . . . . . . . . . . . . . . . . . “1 EXPERIMENTAL METHOD . . . . . . . . . . . . . Al Introduction. . . . . . . . . . . . . . . Al Dispersion Matching . . . . . . . . . . . A2 Particle Detection. . . . . . . . . . . . 51 Target Thickness Monitor. . . . . . . . . 62 Beam Current. . . . . . . . . . . . . . . 65 Targets . . . . . . . . . . . . . . . . . 65 Chapter CHAPTER IV. DATA REDUCTION. Optical Model Search. 238U Analysis 232Th Data Reduction. 23A CHAPTER V . RESULTS AND DISCUSSION. APPENDICES APPENDIX A. INTRODUCTION. CONSTRUCTION AND PERFORMANCE. ELECTRONICS RESULTS APPENDIX B. POSITION READOUT. DESIGN. . . . . . TIMING CALCULATIONS ELECTRIC FIELD DISTRIBUTIONS. ELECTRONICS CONSTRUCTION. RESULTS AND DISCUSSION. APPENDIX C. REFERENCES vi U and 236U Data Reduction. Page 71 71 78 78 9A 10A 115 115 125 125 128 136 1AA 1A6 1A8 15A 155 157 169 182 189 200 218 Table IV—1 IV-2 IV-3 IV-A LIST OF TABLES Results Of fitting scaled 'data' with DSO calculation and actual 'data' with 880 calculation. The 'data' are calculated values for 238 deformed spin—orbit in a calculation using the parameters of King, et a1. [K179]- Best fit parameters resulting from fits to 238U data with deformed spin orbit (D80) and Spherical spin orbit U using O-2—A—6-8 couplings with (880) calculations. . . Values of optical model parameters, deformation parameters, chi square values and moments corresponding to the extreme values of 82. Best fits spin spin fit parameters resulting from to 232Th data with deformed orbit (D80) and spherical orbit (SSO) calculations vii Page 8A 87 91 105 Table IV-5 IV—6 Best fit parameters resulting from 236U data with deformed fits to spin orbit (D80) and spherical spin orbit (SSO) calculations Best fit parameters resulting from fits to 23“U data with deformed spin orbit (D80) and spherical spin orbit (SSO) calculations Estimation of contributions to line width for thin proportional counters. All contributions in Um are added in quadrature. Time and spatial resolution for leading edge and constant frac- tion timing . . . . . . . . Calculated active wire Operating voltages, gain ratios, and trans- parancies for various active and guard wire diameters. viii Page 113 11“ 127 160 181 Figure I-3 LIST OF FIGURES Angular distribution for ground 238U for state rotational band of proton scattering at 35 MeV a) Quadrupole moments of rare earth nuclei. From Reference [R077]. b) Hexadecapole moments of rare earth nuclei. From Reference [R077]. 0) Prediction of trends in quadrupole and hexadecapole moments using formulation of Bertsch a) Quadrupole moments of actinide nuclei. b) Hexadecapole moments of actinide nuclei. See text for references. a) Prediction of the trends of the quadrupole, hexadecapole, and hexa- kontattetarapole moments using formula- tion of Bertsch. b) The predicted 86 values [Ni69] for the rare earth nuclei. 0 O O O O O O C O O 0 O O O O . ix Page 88 13 Figure Page II-l Calculation of Woods-Saxon term and its derivative for a number of dif- fuseness values. The radius used is R0 = 1.17 A1/3, where A = 238 . . . . . . . 18 II-2 Comparison of lowest 0+, 2+, and A+ angular distributions for 238U and 208Pb. The lead data is from reference [Wa731. . . . . . . . . ... . . . . . . . . 22 II—3 Calculated surface shapes illustrating the contributions of the 82, BA, and 86 deformation parameters. The sym- metry axis is the horizontal axis . . . . . 25 II-A Schematic illustrating various coupling routes included in the coupled channels method. The energy level spacing cor- responds to that of a deformed rotor. . . . 36 III—l Schematic illustration of Enge split— pole spectrograph and scattering chamber. . AA III-2 Experimental layout showing the beam transport system used with the Spectro- graph . . . . . . . . . . . . . . . . . . . A7 III—3 Illustration of the two modes used for dispersion matching. For forward angles (6 < 90°), the transmission geometry a) is used. For back angles Figure III-A III-5 III-6 III-7 (e > 90°), the reflection geometry b) is used. . . . . . . . . . . . . . Spectra resulting from 35 MeV protons 176Yb target for the scattered from a two modes of dispersion matching; a) transmission, b) reflection, and c) target rotated for reflection mode with the beam transport system set up for transmission mode. Figure III-Ac represents the worst possible case where the beam energy Spread is enhanced rather than cancelled Schematic cross section of the inclined cathode delay—line counter. Labeled parts are: a) window frames, b) anode support, c) separator foil, d) anode wires - five active and A guards, e) anode wire for,AE counter, f) pickup stripe board, g) frame for delay line and board, and h) delay line. From Reference [Mk75]. Schematic (plan view) of counter. From Reference [Mk75] Schematic of electronics used to acquire the proton scattering data. xi Page 50 53 57 58 61 Figure III-8 III-9 IV-1 IV-2 IV-3 IV-A Page Comparison of wing and data (good) energy loss bands . . . . . . . . . . . . 6A Spectra for 35 MeV protons scattered from a 23“U target for a number of lab angles showing kinematic Shift of target contaminant peaks. . . . . . . . . 68 + Spectra and fit line to the O , 2+, and A+ states Of 238U(p,p') at 57.5°. . . 73 Calculated cross sections Showing the best fits to the data with and without the B6 parameter. The best fit for 86 = 0.0 is calculated using the parameters of King et a1. [Ki79]. . . 77 Illustration Of the result of adding additional excited states to the coupled channels calculation. . . . . . . . . . . 81 Illustration of the ratios of a O-2—A-6 calculation to a O-2—A-6-8 calculation for each state in 238U. The ratios were used to scale the experimental data to compensate for the omission of the 8+ state in further calcula- tions . . . . . . . . . . . . . . . . . . 83 xii Figure IV-5 IV—6 IV-7 IV-8 IV—9 238U Comparison of the best fits to using the deformed Spin orbit (D80) and spherical spin orbit (SSO) cal- culations . . . . . . . The X2 values for the 0+, 2+, and A+ angular distribution data for two ranges of 82 with corresponding optical model parameters. Illustration of the fit to the data resulting from the use of the B2 parameter which yields a minimum X2 value for the 2+ data in Figure IV-6. . . . . . . . . . . . . Illustration of the ratio of a 0-2- A—6 calculation to a O-2-A-6-8 cal- culation for each state in 232Th. The ratios were used to scale the experimental data to compensate for the omission of the 8+ state in further calculations. The X2 values for a 0+, 2+, and A+ angular distribution data for two ranges of 62 with corresponding optical model parameters. xiii Page 89 93 96 99 101 Figure Page IV-lO Illustration of the fit to the data resulting from the use of the B2 parameter which yields a minimum X2 value for the 2+ data in Figure IV—9. . . . . . . . . . . . . . . . . . . 103 IV-ll Best fits to the 232Th data for the deformed spin orbit (D80) and spheri— cal spin orbit (SSO) calculations . . . . 107 IV-l2 Best fits to the 236v data for the D80 and SSO calculations. . . . . . . . . 110 IV-13 Best fits to the 2324U data for the D80 and SSO calculations. . . . . . . . . 112 V-l Calculated moments for this work using the parameters which give a best fit to the data for D80 and SSO calculations. . . . . . . . . . . . . 116 V—2 Comparison of the moments resulting from this work with previous experi- mental results and microscopic cal— culations. See text for references . . . 119 V—3 Comparison of the moments obtained using a-particle scattering at 50 MeV . . . . . . . . . . . . . . . . . . . 121 A-l Exploded view of 1 mm thick resistive division counter. . . . . . . . . . . . . 129 xiv Figure Page A-2 Position Spectrum for 35 MeV elastically scattered protons . . . . . . 132 A—3 Photographs of 2 mm thick resistive division counter. Lower (close-up) photograph is about twice the actual size. . . . . . . . . . . . . . . . . . . 133 A-A Photographs of 2 mm thick delay line counter. Lower (close—up) photograph is about twice the actual size. . . . . . 135 A-5 Position spectra using 2 mm thick resistive division counter. . . . . . . . 138 A—6 Position spectra using 2 mm thick delay line counter. . . . . . . . . . . . 1A0 A-7 Schematic of electronics used with a) resistive division and b) delay line position encoding. . . . . . . . . . 1A3 B—l Schematic view of wire plane for MWPC. . . . . . . . . . . . . . . . . . . 1A7 B—2 Schematic of active and guard wire connections. . . . . . . . . . . . . 1A7 B-3 Illustration Of the times measured to derive position. . . . . . . . . . . . 152 B-A Geometry of the counter Showing dimensions important to the electrical characteristics of the counter. . . . . . 152 XV Figure B-7 B-8 8-9 B—10 B-11 B-12 Illustration of the calculated field lines for the counter wire plane. Fraction of the particle track length arriving within a time segment. Results of the pulse modeling calcula- tion illustrating the effect of the integration and differentiation time constants on the resolution and pulse height. Potentials resulting from the preliminary relaxation calcula- tion. Potentials resulting from the relaxation calculation with the addition of field shaping planes. Parallel plate capacitor, a) without and b) with the dielectric material inserted. The electric field in the air-gap increases with the dielec- tric slab . . . . . Schematic of preamplifier used in the MWPC. . . Photograph of a) bobbin and b) pot- core used to make an isolation pulse transformer xvi Page 15A 15A 159 16A 166 168 168 172 Figure B—13 B-lA B-15 B—16 B-17 B-18 B-19 Page Frequency and phase response for pot-core transformer. . . . . . . . . . . 173 Photograph Of toroidal pulse trans- former used in high voltage isola— tion. . . . . . . . . . . . . . . . . . . 173 Frequency response curve for a toroidal pulse transformer for various trans- former turn ratios. . . . . . . . . . . . 17A Frequency and phase response curve showing the effect of additional cable . . . . . . . . . . . . . . . . . . 17A Schematic of high voltage supply network . . . . . . . . . . . . . . . . . 178 Schematic cross section of MWPC. Labeled parts are: A) gas windows, B) ground foil, C) wire plane, D) wire support insulation, E) covers, F) active wire matrix circuit board, C) energy loss counter, H) separator foil, 1) delay line circuit board, and J) field shaping planes . . . . . . . 183 Photograph showing a portion of the wire plane and the electronics housed in the vacuum box . . . . . . . . . . . . 185 xvii Figure B-20 B-21 B—22 B—23 B-2A Schematic of electronics used with MWPC. The time digitizer and ADC'S are part of a CAMAC system connected to a PDP 11/A5 computer Comparison spectra for MWPC and delay line counter. Spectrum is of protons scattered from a UFA target Thick gas cell and spectrograph showing relationship between locus of the scattering and the angle of incidence on the detector Spectra whose abscissa is angle of incidence on the detector Position spectra contrasting the result of gating with angle of inci— dence on the detector xviii Page 188 191 19A 196 199 CHAPTER I INTRODUCTION The shape of the nucleus is one of its most fundamen- tal properties, although precise determination of Shape properties remains an outstanding problem. In this thesis, the nuclear shape will mean the radial and angular distribu— tion of nucleons, the nuclear matter distribution. The distribution of protons makes up the charge distribution. These distributions are parameterized; nuclear shape de- termination means the measurement of parameter values within the framework of the model, some given parameterization. One of the basic influences the nuclear Shape can have is on the stability of nuclei. The stability is related to the balance between the Coulomb repulsion and the sur- face binding energy. Theoretical calculations have been made for the charge and matter distributions for heavy nuclei, and these calculations have been used to predict the masses and possible stability of superheavy nuclei. The reliability Of these predictions is very dependent on the accuracy with which the calculations agree with known nuclei. Hence, it is of considerable interest to systemati- cally measure the shapes of nuclei, especially massive nuclei, in as much detail as possible in order to test and refine these theories and thereby improve the accuracy and reliability of their predictions. Nuclei with proton and neutron numbers near closed shells tend to be spherical in Shape, while those far away from closed shells tend to have permanent deformations and energy level structures which display rotational bands. The energy level spacings of these bands, electromagnetic transition rates between states in the bands, and the angular distributions of particles inelastically scattered from states in the bands all provide various details of the in- trinsic nuclear deformations. In classical physics it is well known that the results of scattering experiments con- tain shape information. For example, light diffracted by an Object carries information about the size and shape of that Object. Consider the elastic and inelastic proton scattering angular distributions in Figure I-l, which dis- play a diffraction-like variation of cross section with angle. This distribution of particles scattered from a nucleus can be used to describe the nuclear surface or details of the deformation if the interaction is adequately modeled. The scattering angle is related to the interaction distance between the projectile and the target in such a way that the scattering data, covering a range Of angles, map the surface of the nucleus in the form of the scattering cross sections. The measurement of the shape of the Figure I-l. Angular distribution for ground state rota- 238 tional band Of U for proton scattering at 35 MeV. do/dQ [mb/sr‘] 10“ I I I I I I: -I 238Lllp p] 1 103 '5 "g _ 100 o 'E ' ..=. ' Z 0*. _ 1o 0 —= o 5 o .0. Z O 5 .- . _ 10 O f. . E E .. O. .”.. E 5 "'%5 o 7 I- . .- O 1? ’1 W W ... 0+ : V v .. ' I ' I" 9-. ’ .. v. v , + .— 'wfi' ... 2 0.1:— ¢~ 'WW' ..45 k8 _ : v 1 : o 5”,. 'v"v., 4+ : g It! ‘1 .4“. I48 kevI 10'2 P z ' '00" 6” 1 I33517! 307 kevg 5l8 iev T11”. fin, - 10-3 1 l F4 I so 100 150 9c.m.[degrees] Figure I—l. nucleus is an indirect measurement because the projectile interacts with the field or potential resulting from the distribution of nucleons. The observed data may be des- cribed by modelling the interaction, which is a function of parameters related to the shape of the Object causing the scattering. A deformed optical model potential (DOMP), is used to describe the particle scattering data in the present work. Similar to light scattering, the model con— tains terms to describe the scattering and absorption of the projectile nuclei by the target nuclei. As the name implies, the surfaces in this model can be deformed with the deformations expressed as a deviation from spherical shape. The surface can be expressed as an expansion in terms of spherical harmonics. The coefficients in this expansion are the deformation parameters. The shape can also be expressed in terms of the multipole moments, which are related to the deformation parameters. For example, to first order, the quadrupole moment is proportional to the quadrupole deformation parameter 82. Using this model, information about the shape Of a nucleus can be determined much like the reconstruction of the details of an object from tHe observation of the light that it reflects or scatters. To summarize, the measurement of the deformation of a nucleus is carried out by describing the elastic and in- elastic scattering cross sections with a model which has parameters explicitly related to its shape. MOTIVATION Both the rare earth and actinide regions lie between closed shells and are known to contain permanently deformed nuclei. Systematic studies of these nuclei have shown trends of large quadrupole deformations between closed Shells and a Sign change of the hexadecapole deformation in the same region. Bertsch [Be68] has explained this systematic behavior using an observation of the effect on the nucleus by adding nucleons into the unfilled shells. In filling the Shell, the nucleons are added nearest the symmetry axis, which increases the quadrupole moment. The addition of more nucleons fills the orbits near the equatorial region result— ing in a tendency toward a more spherical shape. Figure I-2 shows the measured quadrupole and-hexadecapole moments for the rare earth nuclei and Bertsch's predictions of these systematics. Moments for the actinide nuclei have been measured by a variety of experimental techniques. Methods used include proton scattering at 23 MeV [M071] and at 35 MeV [Ki79], a—particle scattering at 50 MeV [He73,Da76], Coulomb excita- tion [Be73], and electron scattering [C076]. The values of the moments from these measurements are plotted in Figure I-3 in addition to predictions based on microscopic calculations [Ne7A,Ne76]. The microscopic calculations (a) Quadrupole moments of rare earth nuclei. From Reference [R077]. (b) Hexadecapole mom- ents of rare earth nuclei. From Reference [R077]. (0) Prediction of trends in quadrupole and hexadecapole moments using formulation of Bertsch. Figure I-2. omsmfim IH .m E V I Coul ex 9 ( a.a') . (p.p') . (e.e') (b) Q4 1.0- L; \ (ebzl ’ 0r 0.0 (ha) . ’1°° : : : t : t : (a) (12 ‘l.O~ _ . I I I/_ (eb) ' or 3.0- ’ /‘—LO/‘/— 0)) . 2.0t W'Zfib ‘WITSU A (a) Quadrupole moments of actinide nuclei. (b) Hexadecapole moments of actinide nuclei. See text for references. Figure 1-3. 10 involve minimizing the nuclear potential energy as a function of the deformations and evaluating the moments. Although there is qualitative agreement between the measured and predicted values, the results of the measurements show some disagreement in both trends and magnitudes. The Coulomb excitation measurements follow the trends of the theoretical predictions but differ in magnitude. The a— particle scattering [Da76] results Show disagreement with the previous d-particle scattering [He73] results and with the Coulomb excitation measurement in both trend and magni- tude. Since the experimental methods are different, with each method having a different sensitivity to the proton and neutron distribution, the difference in the results may be attributed to a difference in the shape being measured or to a possible breakdown of the model used in the analysis. The proton is used in this work because it is a simple hadronic probe which may lead to a fairly unambiguous model independent analysis. At a beam energy sufficiently above the Coulomb barrier the proton is more sensitive to the neutron matter distribution of the nucleus than it is to the proton or charge distribution [Ma77,Ma78]. Coulomb excitation and electron scattering (e,e') reactions are only sensitive to the charge distribution, whereas a- particle scattering at an energy of 50 MeV is about 50% Coulomb excitation. Proton scattering at an energy Of 35 MeV is sufficiently above the Coulomb barrier so as to be 11 dominated by the nuclear potentials. Most measurements to date in both the rare earth and actinide regions have been concerned with the quadrupole (Q2) and hexadecapole (QA) moments, whereas very few have had any sensitivity to the hexakontattetarapole (q6) 238 moment. Previous work on U (p,p') indicated the pos- sible need for a 86 deformation [M071], while a subsequent 238U indi— survey of (a,d') reactions on rare earths and cate a general improvement in fits to the data by including a 86 term [He73]. The proton scattering by King et a1. [Ki79] at 35 MeV shows considerable structure in the higher excited state angular distributions which is necessary to have sensitivity to the higher order deformations in addition to the quadrupole and hexadecapole deformations. By extending Bertsch's idea to the B6 deformations and values of the Q6 moment, Figure I—A, the 86 value can be expected to change Sign twice in a region where the hexa- decapole deformation changes Sign once. In addition the first Sign change can be expected in the portion of the region near uranium. Figure I-A also contains microscopic calculations [N169] for the B6 parameter for the rare earth nuclei showing a trend similar to that predicted by the Bertsch formalism. The purpose of the present work was to extend the survey of King, et al. to demonstrate the sensi- tivity of using proton scattering in the study of Shape properties of the actinide nuclei and to do a systematic 12 Figure I-A. (a) Prediction of the trends of the quadrupole, hexadecapole, and hexakontattetarapole moments using formulation of Bertsch. (b) The pre- dicted 86 values [N169] for the rare earth nuclei. 13 0.020- I 86 \\ / 0.000 \ / \ / / -0.020- \/ moi ‘ If 0‘ ‘ ‘1W 0 A A _ (a) L /Qz Q Ox \6 r \Q4 A Figure I-A 1A study of the moments to test various experimental results and theoretical predictions. ORGANIZATION The following chapter discusses the theoretical model, its derivation and use, and techniques used to describe the data. In this work, the deformed optical model is used with a coupled channels formulation to describe the scatter— ing cross sections for protons from the actinide nuclei. Chapter III describes the experimental setup and procedures used to gather the experimental data. The technique of dispersion matching, particle detection, and the targets used are described. In Chapter IV the data reduction and analysis are described. Chapter V contains the results of the analysis and a discussion of the significance of the results. In addition to the scattering experiment des— cribed in this thesis, Appendices A and B contain descrip- tions of the work associated with the development of position sensitive proportional counters. The first appendix deals with short high position resolution proportional detectors, while the second reports on the design, development, and testing of a multiwire proportional counter. CHAPTER II THEORETICAL METHODS Optical Model Potential The optical model potential for proton scattering from nuclei is analogous to light scattering from a cloudy crystal ball. The potential has a real part which accounts for scattering and an imaginary part which accounts for absorption of nucleons incident on the target nucleus. A summary of the optical model formalism is based on dis- cussions by Hodgson [H063] and a number of textbooks [Pr62,MS70]. The general expression for the potential of the target nucleus is vo(¥) = v - vr<¥> - 1(wg(¥)+ngI(?))—(vso+iwso)h(?) (II-1) C The terms in this equation will be defined in the following text. The Coulomb interaction potential VC is ' 1 i 3 I v = zIzTe2 fo Rc(0,¢) where Rc is the Coulomb radius. The angular dependence of the radii will be defined below. By using the expansion u m R 1- P‘ * < > < > < u) l = N Z Z Y 6' ' Y 6 II- ‘Trf:—— 2:0 m=_£ 22+1 r 2+1 2m ’¢ 2m ’¢ where r< (r>) is the smaller (larger) of IT] and IT'I. The Coulomb potential becomes 3 2 fl 2 122 .. __ I v I Vc ' II'IFZIZ'I'e 2§,/;z+1 “111 ”(r ’6 ’¢ ) X m 1‘) v v v _ Y£m(6 ,¢ )Y£m(6,¢)dr d0 (II 5) The real well has a depth V and a radial form which may be defined using a Woods—Saxon form f(r) = {1 + exp[(r-I=I)/a]}"1 (II-6) where R is the radius and a is the diffuseness. An l7 illustration of this function appears in Figure II-la. The imaginary portion of the potential has two terms, a volume term with well depth W and a surface term with well depth ND. The surface term is used to include the effect of strong absorption at the nuclear surface. The form for the shape of the volume term is identical to the form for the real volume term although the radius and dif- fuseness may be different. The surface imaginary term requires a radial form which is surface peaked. A possible expression is the derivative of the volume term r.—R r.-R l ){l+exp( ai 8.1 -2 g'(r) = -Aai 5%g(r) = exp( )} (II-7) The normalization factor Aai causes the maximum value to be unity. Although there is no theoretical basis for this definition, the parameterization has the advantage of in— troducing no new variables and maintaining consistency in the model. Figure II-lb illustrates various calculations of the derivative of the volume term for a number of dif— fuseness values. Another possible form for g'(r) is a Gaussian term but this appears to have no added advantages. The spin-orbit portion with well depths VSO and wSO are used to explicitly include the interaction between the spin of the projectile and its orbital angular momentum relative to the target nucleus. This portion of the l8 l I I I I I I I: ‘III - fiflé‘k ‘ d'flr‘! I," g: ‘I‘\\\ d" I]; 55 I\\ _ 0.50l- I ' g : | \ III E E \\\ I” 'l ,E E \\\\ _ I” ’l I: :3 ‘s‘ \ d / / I, 5 'l \\ \ o oo 5’ 5 ,1 .-" [I ‘Plx J I . [II—4‘ I F 'L T —_-+_— l I 1.00 ...-am; ------- ‘ .. \§\\ 0.. 0 \§\ ': ---------- 0.10 - \\‘ ': """ 0.60 - m] ‘1‘: — — —o.7s {I —-—- 0.90 0.50I— \\ _, §\ : \ I- E \&\ ‘l I. \\ '. ‘.\ 0.001 I I .‘~. ‘\~ \ _. l . o 5 10 15 RADIUS [fm] Figure II-l. Calculation of the Woods-Saxon term and its derivative for a number of difiggfeness values. The radius used is R = 1.17 A , where A = 238. 19 potential is also surface peaked. An expression for the shape term h(r) is the Thomas form, - 2 1 _d_ h(r) - - (‘h/mflC) I. dr f(r) (II-8) where mTr is the pion mass. The radius and diffuseness may be different from those of the real and imaginary portions. The spin-orbit radius is typically 20-30% smaller than either the real or imaginary radii. The imaginary spin-orbit term will be neglected since it is not required unless pol- arization data is being fitted. Deformed Optical Model Potential (DOMP) For deformed nuclei, the surface of the nucleus is defined by the expression of R. For spherical nuclei, R would be independent of angle and only depend on the nuclear 1/3 where r is a mass for constant densities, R0 = rOA o constant and A is the nuclear mass. The existence of rota- tional energy levels in some nuclei indicates that the ground states of these nuclei can be treated as permanently deformed rotors. The deformation of the potential surface may be introduced by expressing the radius as a function of angle (assuming axial symmetry), R = rOAl/3 (1 + EBAYAO(§)) (II-9) 20 where BA are the deformation parameters, and 9 is the angular component of P. To maintain consistency this form will be used to express the angular dependence of the radii in Equation II-l. This expression is simplified by includ- ing only the even 1 terms. The A = 0 term is excluded since this term would only serve as a normalization term. The A = 1 term corresponds to the motion of the center of mass of the nucleus which can be eliminated. The A = 3 term corresponds to an octupole deformation of the nucleus. Since there has been no observation of an octupole moment in the ground state of nuclei this term is also neglected. The odd terms would result in a form which would violate parity. In general, the odd terms are neglected to maintain a symmetry for rotation by N. For rotational nuclei, the excited States of the rota- tions of the ground state have the same intrinsic structure, with the excitation energy appearing as rotational energy of the nucleus. The elastic scattering is defined by the diagonal elements of the effective interaction in the in- trinsic ground state. The angular distribution for each state contains information such as the phase, amplitude, and frequency of the oscillations, and the slope and magni- tude of the cross sections. Consider Figure II—2 which +, and A+ shows angular distributions for the lowest 0+, 2 states in 238U and 208Pb [Wa73]. The difference in the structure of the angular distributions of all states is 21 +, and A+ angular 208pb Figure II-2. Comparison of lowest 0+, 2 238 distributions for U and The 208Pb data are from Reference [Wa73]. 22 (39/qu esp/op [.Is/quu] tsp/op Figure II—2 ‘TTTT'F'l—‘l'l'ITIIII l IIIIIIII I [nun I I IIIIIII I I pnnrr IV‘WHIYTT WWII I I [I > > o 0 + 2 12 I- N + n In 6’ d’ + Q N 0 l0 - r—~ O o oq: o q. -° 0. . o o 3 .9. Q 0 a z . °. 5—! O. . . " .O o o o ‘ 0- .. O. .. (I) o o C) o o o O '- o . o. 0. i "'O N . O C _. m 0 O O . O O. O I o. o ' ‘ O O 0.4 O 0.4 O IIII I I llllllll l hm“. I hm“ I I Inn“ '4‘ [“1111 1 1 1111111 1 1 1111111 1 1 * "a, ° 2 a c —: I.“ 2 o-o O O 2 I [I1 V—I'I'I'ITT'II l I'lll'lll I "I W! I IIIIIIII I WWII} I llllllII T will ' ' l"" > : z E + '332* +‘Em o a) “I °*- 5 . ° :" :3: 3 ..." O. O O O H o o . o H O O D I D: 4 o o ,b C {' r—\ 0.. ‘8 C): . . .‘ i ..E f F‘ 0. O 5 fs 5 °’ ~ - a) .o ' s " 9 g m ‘ '. .3 or ”-0 N o { .D ‘8 Oc.m.[degr‘ees] ecmjdegr‘ees] 23 due to the difference in the Shape of the two nuclei, the lead nucleus being spherical and the uranium nucleus being permanently deformed. From the analysis of the angular distributions, information about the shapes of these nuclei can be obtained. Multipole Moments The contributions of the various BA terms to the Shape of a surface, Figure II-3, can be related to the multipole moments of the nucleus. For example, the 82 term reflects an elongation of the nucleus giving rise to a quadrupole moment (q2), and the BA term gives rise to a hexadecapole moment (qu). The moment is defined by the relation in Equation II—lO. The integral of the potential over the nuclear volume is used to evaluate the moment _ A A _ 3_ qA - r YXOtr)o(r)d r (II-10) For a Sharp edged distribution with deformation parameter 82 the corresponding quadrupole moment is given by 2 2 R0 (82 + 0.360u 82 + ...) (1 + 0.2387 82 + 0.01u3 822) 3 (312 = fl? (II-11) The 86 term leads to the hexakontattetara moment (06). 2A Figure II-3. Calculated surface shapes illustrating the contributions of the 82, BA’ and 86 deformation parameters. The symmetry axis is the horizontal axis. 25 B, = 0.226 2380 B4 = 0.054 as =-0.0II R : Rd ' +BZY20+E4Y4O+BGY60+'”) Figure II—3 26 The values of deformation parameters extracted from scat— tering experiments are model dependent on the distribution used, as well as the model of the interaction. The ambiguity of the model dependent parameters is illustrated by the coupling of the deformations and the nuclear radius. The cross sections depend on B but through the term R8, where R is the radius. A defined quantity, the deformation length, 6A = RBA is a less ambiguous param— eter and can be used to compare results of various experi- ments. The deformation length may be compared to the dis- placement of the surface, OR = RBAY:O(r), which may be a physically significant term. This factor may still contain ambiguities as the value of R81 may also depend on the other optical model parameters. Mackintosh [Ma76] has used a theorem due to Satchler [Sa72] to state that a folding model with a density in- dependent interaction leads to folded potentials with the same multipole mements as those of the nuclear density. The assumption that the DOMP is derivable from a folding model leads to quantities which are more significant than the potential deformation parameters and should be related simply to the underlying nuclear moments. Mackintosh [Ma76] has found reasonable agreement for the folded quadrupole moment and the underlying nuclear moment for light nuclei. For heavy nuclei, alternative arguments point to either a breakdown of the application of Satchler's theorem or that 27 the nuclear deformation of the proton component is greater than the neutron component for the hexadecapole degree of freedom. For the actinide nuclei the q2O moment for the neutron distribution was about 10% higher than that of the proton distribution [Ma76]. The qAO moment for the proton distribution was found to be about 20% larger than the neutron distribution. An additional finding is that for a-particles the theorem application breaks down for heavy nuclei. COUPLED CHANNELS CALCULATION For proton scattering from a nucleus, the interaction strongly depends on the energy of the incident projectile. For energies below the Coulomb barrier the proton inter— acts only with the Coulomb field of the nucleus. At higher energies it interacts with the nuclear field where it can be either scattered or absorbed. The nucleus may be left in an excited state if the proton deposits energy in the nucleus. At sufficiently high incident energies, the number of excitation channels becomes infinite as the nucleus may be excited to any of its discrete or continuum states. Excitations may be direct or involve a cascade through two or more states (multistep excitations). When a cascade is involved, the interaction is a result of the coupling of the involved channels. The coupling is a complicated 28 mechanism and requires a special formulation. The method of coupled channels consists of explicitly considering transitions between a number of strongly coupled states during the scattering process. In practice, the coupled channels space is severely truncated by the consideration of a limited number of channels. An important effect which is omitted is the excitations which involve the neglected channels as intermediate states and reactions such as (p,d), (p,t), etc. The truncation will lead to in- accuracies due to limitations placed on the vector space. To improve the accuracy an effective interaction which com— pensates for the neglected channels is desired. This inter- action would be a complex non-local potential. It has been shown that an equivalent complex local potential can be used to replace the non-local potential. The DOMP contains a complex local potential which makes up its absorptive portion. The optical model is a phenomenological potential, not currently totally derivable from first principles. The parameterization is obtained through the fitting of the ex— perimental data. Consequently, the fitting of the data will produce the effective interaction to compensate for the truncated space considered with the coupled channels calculation. The coupled channels calculation entails a quantum mechanical solution of the Schrodinger wave equation (SNE). The eigenfunctions for the nucleus are defined by 29 HA¢GJ(A) = EQJOGJ(A) (II-l2) where HA is the Hamiltonian for a nucleus with mass A, EaJ are the energy levels of the nucleus, and A are the internal coordinates of the nucleus. The quantum number J denotes angular momentum of the nucleus with a containing all other quantum numbers required to describe the nucleus. To consider the interaction of the nucleus with the projectile, in this case a proton, the total Hamiltonian becomes H = HA + T + V(P,A) (II-13) where T is the kinetic energy of the proton and V(P,A) is the interaction of the projectile with the nucleus. The solution to the scattering problem is defined by (H—E)w(?,A) = O (II—1A) with the appropriate boundary conditions. The quantum numbers aJ describe the nuclear state and the incident proton can be described using three additional quantum numbers jls. For simplicity in notation let 0 = quls denote the nucleus and projectile in their initial state and 0' denote any other possible state for the target and projectile. 30 The nuclear wave functions ¢QJ(A) form a complete orthonormal set so that w(;,A) may be expanded in terms of the wave functions for the nucleus and for the incident proton. It is advantageous to express the solution in terms of the total angular momentum I and parity N . n = (-1)2 (II—15) HI H uI + 9+ Thus we have m + + ‘_ 2 ¢ + + 6 chN(P’A) - c' ¢0J CIfl(r’O)’ (II-1 ) where the term ¢cIW describes the relative motion between the nucleus and projectile. The term 6 has been included to explicitly include the spin of the projectile. The wave function describing the relative motion may be expanded to separate out the spin and angular dependent terms . .. Uc ¢CIH(P’O) = —_;_— ¢CIU(9’3) (II-17) where T (9,6) = CYQm-EC.>UC.(r> = - z v§.C.Uc. (II-19> C"#C' where 2 2 EC = -EaJ + E _ A 2 TC, =‘gfi(g§_ + —i—%ll), (II-20) I” I” k2 = 2WE 0/62 where E is the bombarding energy and m is the reduced mass. The matrix element chcn is I A" ++ A") v0.0" = <¢C,In(r,A)IV(r,A)I¢CnI"(r,A)> (II-21) The integration implied is only over the polar coordinates of P and over all the internal coordinates A. The resultant matrix element is a function of r = |;I. Since V(P,A) is a scalar potential, V is diagonal in I and N and C'C" independent of m. 32 Two effects have been neglected in the above derivation. Since the proton is treated as a free particle, reactions such as pickup are excluded. Proton exchange with one in the target is also excluded by not allowing the overlap of the two wave functions. The number of channels in equation II—19 is equal to the number of possible couplings between the excited states which includes both the discrete and the continuum states yielding an infinite number of possible channels. To reduce the magnitude of the problem, the number of inelastic channels is limited to those with large cross sections and to other states of interest. In the present work, only the states of the ground state rotational band are included. The wave function is expanded in terms of the wave functions of the elastic scattering channel and one or more of the inelastic scattering channels. This leads to a finite problem which can be solved numerically using a computer. When considering a certain number of states, the number of channels far exceeds the number of states. Recall that c = aJljs labels a particular state and angular momentum of the scattered particle. For the total angular momentum I and parity n and for each state aJ there are a number of scattered particles jls which satisfy the quantum number relationships in Equation II-15. For a spin 1/2 particle there are 2J+l couplings allowed. For each I,N value there are 33 N = Z (2J+1) (II-22) states coupled channels, where the sum is over the states of the nucleus. A calculation involving the 0+, 2+, A+, and 6+ states contains 28 coupled channels. Adding the 8+ state increases that number by 17. The number of differential equations also depends on the angular momentum of the inci- dent particle. The angular momentum of the incident partial waves ranges from O to 2ma where lma = 2kR, where R is X X the radius at which the interactions are effectively zero. For each A there are 2j states giving a total number of dif— ferential equations of AkRN2. In solving the equations there is a coupled differen- tial equation for each channel involved. Each equation has two boundary conditions, the first at the origin where the wave function must vanish. The second boundary condition exists at the exterior of the nucleus where the nuclear force vanishes. The wave functions become decoupled and the solutions are the Coulomb functions when the projectile is a proton. For a more detailed discussion of the boundary conditions and methods of solution, see Glendenning [G167], or Hodgson [H071]. An additional simplification leads to a well known method used to solve certain types of scattering problems. The Distorted Wave Born approximation (DWBA) is the result of considering only the transition which go directly from 3A the ground state such as transitions 1, 2, and 3 in Figure II-A. This reduces the differential equation for the tar- get channel to an uncoupled differential equation and also the excited states channels are coupled only to the ground state channel. The coupled differential equations become (TVIE)UO()-O 2 c7 00- c c r - target channel (II- 3) (T -VI -E )U0 (r) = -V U0 excited state channel 0' c'c' c' c' c'c c (II-2A) where 0 denotes the ground state and c' is an excited state. This method is suitable if excited states are not strongly coupled so that higher order transitions as A, 5, 6 and 7 in Figure II-A may be neglected. Qualitatively, collective transitions in vibrational nuclei are not too strong, allowing the use of the Dis— torted Wave Born Approximation (DWBA). The transitions in deformed nuclei are quite strong. For 238U the strength of the first excited state (2+) always exceeds that of the ground state for scattering angles beyond 90 degrees. At more forward angles, the cross sections of the ground state and 2+ are also comparable, as in the region of 70 degrees. Higher order transitions which involve the 2+ level as an intermediate state cannot be neglected. Thus additional channels must be considered for deformed nuclei than are 35 Figure II-A. Schematic illustrating various coupling routes included in the coupled channels method. The energy level spacing corresponds to that of a deformed rotor. 36 eIHH oesmfia +mw To 37 considered using the DWBA. For example, transitions which populate the 2+ state includeld 2+A, 3+6, 1+7, . . . in Figure II-A. The inclusion of the additional channels com- plicates the solution of Equation II—l9 as the equations are numerous and coupled. The solution for the wave function should be a plane wave plus an outgoing wave given by .+ to = eXp(ik-?+in£n(kr-E°F))lo> GU.(6>exp(ikr-intn(kr))lo'> (II-25) + 2 l F O r where o is the component of the spin at infinity, k is the momentum, and n = ZtZieZ/h2k the Coulomb parameter. The angular-momentum expansion of the solution becomes To = %%Xi£exp(16£)U£J(r)<£su'o'I£m> A A ' - x Y£u(k)Y2u,(r)lo > (II 26) where 02 is the Coulomb phase shift. The asymptotic expres- sion for the radial wave function can be expressed in terms of the regular and irregular Coulomb functions Uj,(r) = F,(n,kr) + Ci x Y£u(k)Y£u,(r)Io'> (II-28) where Fc(e) is the Coulomb amplitude -n 2ksin 2 1 Fc(e) = exp(-in(sin g8)+2ioo) (II-29) 2 1 50 For a spin 1/2 particle, the spin can couple in two ways with the angular momentum i to give a total angular momentum j = 2+l/2 and the eigenvalues of which correspond to these two spin orientations are 2 and —(2+l). Two scattering amplitudes result Q 1 1 1 . + 2 ’— A(6) = Fl 1 = FC(0) + R i exp(21o£){(9,+l)Cz +SLC£ } 2 2 (II-3o) 1 “+2 £‘2 8(a) = Fl 1 = E z exp(2102{C£ -c2 }chos(0) (II-31) —— 1 2 2 The cross section is given by 2 2 0 = |A(e)| + |B(e)| (II—32) The boundary conditions require that the solution for the initial channel is of the form of Equation II-27 and 39 all other channels be outgoing waves _ i . yi — F11 + Ci(Gti + ing), (II-33) _ i . From these, the amplitudes can be found, (6) “"I (11 < > = 1 exp 10 +io “FGFuiOi E1 11 gr -gF) * O O A <21811101'J1m1><3111miuiIJM>Ytiui(k1) * ' A (QFSUFCFlJFmF> (11‘35) where O and u are the projections of the spins of the projectile and target and i and F refer to the initial and final states. The cross section becomes 9982-” l 1 szIF (e)!2 d '§§:T EIIIT RI UFOFU1°1 The code ECIS [Ra7A] uses a different method to achieve a solution. The ECIS method involves an iterative pro- cedure to obtain a Solution to the coupled differential equa— tions as opposed to integration of the solutions. The usual method of solving coupled equations results in as many solutions as there are equations, although only one is needed. The ECIS method involves a search for this A0 solution by iteration. This method results in a reduction of computational time but has the disadvantage of larger storage requirements than the standard coupled channels methods. The ECIS method gives better results than DWBA codes after the first iteration, while the second itera— tion gives the same result as the standard coupled channels method. A complete description of the ECIS method is contained in reference [Ra72]. CHAPTER III EXPERIMENTAL METHOD Introduction The measurement of elastic and inelastic proton scatter- ing from the actinide nuclei presents various experimental problems. The major one is the spacing of the states in the ground state rotational band. The excitation energy of the first excited state (2+) is roughly A5 keV for uran- ium and thorium. An energy resolution of about 15 keV is adequate to resolve the first excited state from the ground state, which permits accurate determination of the peak areas. Since the Coulomb barrier for protons on uranium is about 13 MeV, particle energies sufficiently above this are required for strong nuclear as well as electric inter- action. The 35 MeV proton beam from the MSU cyclotron is well suited to these studies as its energy is well above the Coulomb barrier and sufficient energy resolution is achievable. In fact, an energy resolution of 1.5 keV [N07A] for 35 MeV protons has been obtained in test situa— tions using the MSU cyclotron and the Enge Split-pole A1 A2 spectrograph [Sp67] by utilizing the technique of dispersion matching [B171]. The energy resolution in the focal plane depends on both the beam resolution and the position resolu- tion of the particle detector. The beam resolution is enhanced with the dispersion matching so that the detector resolution becomes a significant problem. Detectors routinely used in the spectrograph focal plane have an optimum position resolution of about .25 mm which results in an energy resolution of less than 10 keV for 35 MeV protons. The target thickness can degrade the resolution further by a maximum of 5 keV for almg/cm2 target. How— ever, the expected data rates are high enough that thinner targets may be used. Dispersion Matching Dispersion matching [C0591 involves spatially dispers- ing the beam at the target so that the image contains in- formation about the energy of the beam. The dispersion of the spectrograph is used to cancel the coherent energy spread of the beam. Effects which make the beam incoherent such as multiple scattering in the target cannot be can- celled, however. Consider (Figure III-l) a point image at the focal plane with an energy spread equivalent to that of the beam. The high and low energy particles at this image A3 Figure III-1. Schematic illustration of Enge split-pole Spectrograph and scattering chamber. AA 23.550 05.238 .om.o .8 5 £80 85> £20m 3.8280 ozoEosx 5. 8:22 so: ./. .\x \\ . n 83 sod zfi - . c983: \. a I -\I\\\ ’ \ V :00 «93> EEom .. .\ Figure III-l “5 must originate from different positions on the target. If the beam from the cyclotron is dispersed to match this dis- persion by the Spectrograph, the high and low energy par- ticles in the beam at the target will arrive at the same position at the focal plane. The standard procedure is to adjust the focussing elements of the beam transport system, depicted in Figure III-2, to obtain an accurate image of BOX 5 at the target location. The production of an image at the target may be observed by the insertion of an object at the BOX 5 location and observing the resultant image on a scintillator at the target position. The beam at BOX 5 is dispersed by the analyzing magnets M3 and MA so that the horizontal position at BOX 5 is dependent on the energy. It is possible to vary the energy spread of the beam at the target by adjusting the width of slits at BOX 5. A small energy spread may be obtained only with a substantial loss of beam current. Additional fine tuning of the beam trans- port system is done to obtain a narrow image of an elastic scattering line or the beam at the focal plane of the spectograph. When the dispersion matching parameters are optimized it is possible to use the full beam intensity extracted from the cyclotron without any deterioration in energy resolution observed in the inelastic scattering spectrum in the Spectrograph focal plane. Detectors used in part of this tuning procedure are discussed in Appen- dix A. A6 Figure III-2. Experimental layout showing the beam trans- port system used with the spectrograph. A7 «an \ a\\\\\\\\ \ \ \ s a $523 \ W \\\L \ \\\\\.\\\ o . s ., / o2 ' s» O 0 X0 I ”(‘31 fl’ ddddddddd \\ \ \ W. M A8 Different angular ranges of the data dictate different modes of dispersion matching. The standard procedure is to rotate the target such that the target angle relative to the normal to the beam is one half the scattering angle. Keeping the target angle at one half the scatter— ing angle maintains constant effective dispersion over a range of scattering angles. Consider Figure III-3a for scattering at 90 degrees. The geometry used for forward angle scattering is the transmission mode where the scattered particles pass through the target. This mode has an advantage that the effects of the target thickness are minimized as the maximum total thickness seen by the incident and the scattered particle is equal to the target thickness. When the scattering angle is greater than 90 degrees, causing the target angle to exceed A5 degrees, the width of the beam Spot may exceed the horizontal extent of the target material. When the target is not rotated, scattering to angles near 90 degrees cannot be done since the scattered particles are blocked by the target ladder assembly. An alternative is to use a reflection mode as in Figure III-3b. In the reflection mode the particles entering the Spectrograph come from the same side of the target as the beam is incident. This has two major difficulties, the first being that the maximum thickness seen by the incident and scattered particle is twice the thickness of the Figure III-3. A9 Illustration of the two modes used for dis- persion matching. For forward angles (0 < 90°), the transmission geometry (a) is used. For back angles (6 > 90°), the re- flection geometry (b) is used. ENGE SPLIT-POLE SPECTROGRAPH GROUND \ATE / 8) " t /?/°QFI\’ E-AE EtAE REFL E CTI ON 5+ BEAM ,‘ g_ TARGET GROUND b) \ATE / , / I, / ’/ $VF“€ .06” E-AE E+AE TRANSMISSION E- ______—A BEAM ’g’ TARGET + Figure III—3 51 target material. This is relatively minor when compared with the effects caused by the dispersion matching being wrong. The beam is dispersed such that the beam energy spread is now enhanced rather than cancelled. The spectro- graph views the opposite Side of the target where the energy spread is effectively reversed. To correct this, it is necessary to reverse the sign of the horizontal magnifica- tion of the beam between BOX 5 and the target. Beam optics calculations were done using TRANSPORT [Br7A] to determine the correct beam-line settings. Two additional quadrupoles Q7' and Q8' placed near M5, as seen in Figure III-2, are required to produce a horizontal crossover prior to two of the existing quadrupoles, Q9 and 010. The beam trans- port system prior to BOX 5 remains unchanged. The reflec— tion mode produces a comparable image to the image pro— duced by the no-crossover mode, with no loss of energy resolution. Figure III-A shows spectra for protons scattered 176Yb target [Me79] for the reflection and transmis- from a sion mode and also for the target in reflection mode with the beam transport system setup for transmission mode. Particle Detection To take full advantage of the high quality beam, dis- persion matching requires measuring the position of par- ticles at the focal plane with a high degree of accuracy. Figure III-A. 52 Spectra resultigg from 35 MeV protons scat- tered from a 17 Yb target for the two modes of dispersion matching; (a) transmission, (b) reflection, and (0) target rotated for reflection mode with the beam transport system set up for transmission mode. Fig— ure III-Ac represents the worst possible case where the beam energy spread is en- hanced rather than cancelled. COUNTS/CHANNEL 53 '75Yb (0,0') 0: 90° Ep= 35.3 MeV 103 0+ 2+ NOT DISPERSION MATCHED a) 100 '-++ 6+ 10 l .' I 3 I . I AW, ‘5 l.) ; H I I] . , INA: III II b) 2+ H‘REFLECTION GEOMETRY + 100 8+ 10 I l l i ll ‘ I I I C) 0+ TRANSMISSION GEOMETRY 100 10 H+ 8+ I, .I I I I J ' III II" . ALI I II 1‘ l 0.00 0.50 1.00 EXCITATION ENERGY [MeV] Figure III-A 5U Photographic emulsions in the focal plane have extremely good position resolution and linearity. However, in this experiment their usefulness is limited. The position of each track is measured directly. The tracks appear in an emulsion deposited on a glass plate and the position is found using a microscope and mechanical readout. The emul- sion can become saturated with tracks from the particles, limiting the number of distinguishable events per unit area. High resolution enhances this effect as a particle line such as the elastic scattering line may have a total width of 100 um. Track saturation prevents the acquisition of both strong and weak states on the same plate. To recover the data requires the scanning of the plates, which is time consuming and may be impossible for strong lines. Also, the use of plates prevents continuous monitoring of the experiment and the resolution cannot be checked or tuned without an additional detector. The disadvantages of plates make a position sensitive detector with direct position readout useful. To observe both elastic and inelastic scattering where the excited states may have cross sections four orders of magnitude smaller than the cross section for elastic scattering, re- quires a position sensitive detector which has a much better dynamic range. The detector used was the inclined cathode delay-line counter [Mk75]. This device utilizes a more sophisticated 55 readout scheme than the standard charge division propor- tional counter and is illustrated in Figures III-5 and III-6. A particle passing through the detector leaves a track of dissociated electrons. The electrons are col- lected and multiplied on the active wires. The guard wires are for field shaping only, having no appreciable gain. The avalanche at the active wires induces a signal on the cathode. The cathode is made position-sensitive by dividing it into sections and connecting the sections to- gether using a tapped delay line. The cathode consists of stripes parallel to the particle trajectory (“5 degrees from normal to the detector) to minimize the projection of the particle track onto the position readout. By measuring the relative time delay between the par- ticle passing through the detector and the signal emerging from the end of the delay line, the position is obtained. A method used to derive the position is to use the signal from one end to start a time to amplitude converter (TAC) and the signal from the other end, delayed in time by the total delay of the delay line, to stop the TAC. The Optimal resolution obtained is less than the tap spacing because of an interpolation property of the delay line readout. Although an event is localized on the anode wires, the charge induced on the cathode is over a region roughly equal to the cathode—anode spacing. The centroid of the induced charge carries accurate position information Figure III-5. 56 Schematic cross section of the inclined cathode delay—line counter. Labeled parts are: (A) window frames, (B) anode support, (C) separator foil, (D) anode wires-five active and U guards, (E) anode wire for AE counter, (F) pickup stripe board, (G) frame for delay line and board, and (H) delay line. From Reference [Mk75]. ////////z¢/ w§\ 58 .wmhxzw mocmummwu Scum .Hmpcnoo mo A3wfl> :mHmv owumfimnom .oIHHH musmflm mthDOU ....O A30.) 5:: 0....4—2wIUm I z 3353 8%. 89.6 I 8:83:32 / 1.9.on / / ‘5 J ”0.3; ocm>h=ae< III: Nb Mr SSSS *Illlllllllll P % 59.953 w Boo... I N //55 z 3...; 20:0 \ ~ \. z . ¢ . £05qu $2959.... /30... 2.3 3.00 o... 3852, 3283:. 22:8 59 and through suitable electronic shaping this information can be preserved. In addition to the position from the delay line counter, a second proportional counter gives particle energy loss (AB) information. The counter is also backed with a plastic scintilator which yields timing information and particle energy. From the timing information, the time of flight of the particle through the spectrograph rela- tive to the cyclotron RF is determined. This is possible because the beam from the cyclotron comes in bursts with the frequency of the cyclotron RF. A schematic of the electronic setup used is shown in Figure III-7. In order for an event to be valid it must satisfy E, AE and time- of-flight requirements. The requirements placed on each event are useful in rejecting unwanted particles and gamma- ray background events. The counter electronics were modified from the orig- inal description. Signals were obtained from the active wires, and the delay line was terminated using pulse trans- formers [Bk76] and Radeka [Rd7h] 'electronically cooled' preamplifiers, which eliminated the resistive delay-line termination and gave an increased signal to noise ratio. The signal from the active wires was used to determine the energy loss in the delay line portion of the counter. It has been found that the high and low energy tails on the peaks correspond to events with higher energy loss 60 Figure III—7. Schematic of electronics used to acquire the proton scattering data. 61 .1: 00.2.0 out: also ‘5 >193. N 00‘ . 00‘ no _ ~ 30:39. la . _ u:- oxuu .8838 - w 3...: :3: <0: ] moo-... ua» _ 39:8.”— . . , 35 }\ l j hahn 04» umSI— u:- puo: 3 0250 .0» cow to» ~11 .285 >159 oo. _ _ .3203 _ FL .8. E, E , 53 ac —‘ J. ... I -IL .86 02... :38... H >1 8.5:: tat-.8 tag 448 Ono 5.40.3122: can. ...: I... a: . :5: oil: ZOGFOJU>U .2...» mac «.2 .34 4...» uni Eu: 4...» a .13.! I!!! cordgg 5: . 13¢. can! .3! RV cuhzaou wd » «. >2 Figure III—7 62 in the counter. Two position spectra were recorded, one corresponding to the high energy loss in the front counter and the second containing all other valid events. The high AE band, called the wing band, was set to contain about 5 percent of the total events. Figure III—8 il- lustrates the results of the high energy loss selection. The gating has the effect of reducing the extent of the high and low energy tails, which simplifies the fitting of the data. The fitted peak areas were corrected by scaling the areas by a factor generated by determining the frac- tion of events in the wing band for each spectrum. Target Thickness Monitor A NaI(T£) detector was installed in the scattering chamber at a scattering angle of 90 degrees to monitor the target thickness. Particles scattered from the nuclei in the target have different energies from those scattered from the nuclei of the backing material or contaminants, which are measured using the NaI(T£) detector. The area of the peak corresponding to scattering from the target material is extracted and the effective target thickness calculated. The scattering data measured in the spectro- graph are scaled relative to the effective thickness determined by the monitor detector. 63 Figure III-8. Comparison of wing and data (good) energy loss bands. 6A I IIHITT T r [mu I I mmmznz IEZZ2 mm u w .08 ... m 2.33% n 'IBNNVHD/SINFIOCJ Figure III—8 65 Beam Current The beam current was monitored using a water—cooled Faraday cup to stop the beam. A current integrator de- termined the charge collected at each scattering angle. The beam current was adjusted to maintain a maximum of three percent dead time for the position TAC or the com- puter ADC. The scattering data were deadtime—corrected by scaling the data by a factor equal to the current integrator output scaled in a scalar inhibited by the ADC busy signal divided by the output scaled in a free scaler. Typical beam currents ranged from 50 nA to 3 uA. The lower currents were used at forward angles where high particle count rates would contribute to large dead times. Targets The target material is radioactive and in the case of 23uU and 236U, quite difficult to obtain. The pro- duction and handling of radioactive targets must be done with care to prevent contamination of the target-making equipment or the experimental apparatus. The angular range of the data to be covered, where the elastic scatter- ing cross section covers at least five orders of magnitude, requires that the target be sufficiently thick to keep the time required for acquiring the angular distribution 66 within reasonable limits. The need for relatively precise inelastic scattering data, where the strength of the 8+ may be as much as four orders of magnitude less than the elastic sets a lower limit on the thickness of the target material. It has been shown [Wa73] that targets with thicknesses less than “00 ug/cm2 have little effect on the energy resolution for 35 MeV protons. Targets with a thick- ness in this range are also well suited to these experi- ments in allowing efficient use of the available beam current. The effects of contaminants in the target are not as important for the actinide nuclei as for lighter nuclei due to the kinematic recoils of the nuclei in the target. The competing elastically scattered particles from con- taminants have lower energies than the particles scattered from the target material being studied with the energy difference increasing with angle. Figure III-9 shows 23uU target at a spectra of particles scattered from the number of angles illustrating the kinematic shift of the contaminant peaks. A relatively straight forward way of Sidentifying the contaminants is to display the raw data in this form and identify peaks which shift relative to the elastic as a function of scattering angle. It is apparent that contaminants with small mass present less of a problem making it beneficial to use target backings and target making procedures which do 67 Figure III—9. Spectra for 35 MeV protons scattered from a U 23 U target for a number of lab angles show- ing kinematic shift of target contaminant peaks. COUN TS/CHANNEL 68 “:MUIF-JI'} 0‘ 2‘ Sue : 120. 11‘ I v 6. a' ‘ I U ' I II I III I » I ' I 23“UIp.p'I 0’ 2* one = 110‘ E " C 5‘ I I °' 1 T '| I III' I - IIIII'I II II ‘ I , 23“ulp.p'I 0* 2° 0 = 100' E .. LAB 35c 2.5: 22~° . 6° ' I I ' ' a‘ I . , * | . H." I: -II III HI ‘tllll I II ' I 23". ' O 9 = O ’ Ulpvp) o 2 OLAB 90 285. E ‘0 I ZZNo E , .. I * [I I H. I- III IIIIII '-| I‘IIII II . 23"UINJ’I 9m, = 80' E 35(:I as. 22940 I I I E 1 r ' l L l I I . I I I I l III III I I‘ III‘ II II III : ZBNUWIP.) OLAB = 70. '60 Isc E I "N I . M I A I I I I ' I I I ., I“ i I I ‘Ihl I II 'lIlIIIIH‘I IIIIIII I ZJHUIP-P.) GLAB = 80. .60 l3c 2c 3 I4" ii In I ‘ I ‘ 'I H II II Mull , 33”UIp.p'l one - 50' no 'Zc g I E I i I ‘I III I “MIMI I I IIIIII F 23~U[pop.) OLAB = ”0. ‘0 cc 1 1 .I III. .II "II win. .I III... IMI Imus-I IIIIII I I 5...... "WW-IT"! - 23”UIp.p'l l‘ m‘Ju‘ H‘ A . ~ ‘ .' -- ... c~s+ .'\t .C‘AL (.‘\\ 31“.? . ‘. ." Figure III-9 69 not introduce heavy contaminants. Uranium and thorium metal are difficult to prepare into relatively thin (<500 ug/cm2) self-supporting foils. An 800 ug/cm2 rolled thorium foil was used although it degraded resolution and contained a number of contaminants introduced by the rolling procedure. Since suitable self—supporting foils are not available car- bon foils were chosen as the backing material to support the target material. A sputtering device [N078] was used to deposit uranium metal on carbon backings but yielded thin targets (lOO ug/cm2). The pure metal targets on carbon backings broke due to strains induced by the oxida— tion of the metal. The high melting temperatures of the pure metals make vacuum deposition of the pure metal dif- ficult and may introduce undesired contaminants from the tungsten or tantalum boats required in the evaporation. The metals are also quite reactive, which quickly strains and breaks the backing foils. Natural uranium and thorium tetrafluorides are suitable target materials with rela- tively low melting points for clean vacuum deposition. The fluorine contamination is observed at only forward scattering angles. The targets produced were 250 ug/cm2 in thickness on 20 pg/cm2 carbon backings making them well suited to this experiment. Contaminants in the target include fluorine, carbon and oxygen. 23“ The U and 236U targets were made [Be73] by deposit— ing the material onto HO ug/cm2 carbon backings using an 7O electromagnetic isotope separator. These targets are relatively free of contaminants, except those introduced by the backing foil and vacuum system. The observed con— taminants include sodium, chlorine, and silicon, in addi- tion to carbon and oxygen. However the thickness of the target material was only 30 ug/cm2 which severely limited the statistics. The targets were originally made for (a,a') Coulomb excitation studies where the 30 ug/cm2 iS about the thickest that might be used. The thicker back- ings on these two targets were used to add strength to the target to avoid possible breakage and loss of the target material. The amount of target material on the backing was small so that extreme care was taken to prevent dis- crepancies in the measured scattering cross sections, in- troduced by the motion of the beam spot relative to the target material. The monitor spectra were fitted and the resultant effective target thicknesses used to correct the data except at forward angles (a < U5 degrees). At forward angles, cutting back the beam current produces a smaller beam spot,:mflchu;the cross section less sensitive to_beam spot motion. CHAPTER IV DATA REDUCTION The position spectra were fit using an interactive peak fitting code SCOPEFIT [Dv78]. The code is used to fit the background, fit the peaks with an empirical peak shape, and sum the peak area in the background-subtracted data. The first order reference peak for fitting is generated by using the elastic scattering peak. The reference peak shape was then adjusted to obtain a best fit to the elastic peak and the inelastic states with which the elastic peak overlapped. A typical fit is shown in the Figure IV-l. The cross sections are calculated from the areas by using the standard relation N 2. 67 A coscb .9 ._. T Q IV-l Q dQDQ GET Q where N is the peak area, A is the target atomic mass, ¢T is the target angle, Q is the charge in uCoulombs, p is the target thickness in mg/cm2, and QDT is the charge scaled with a scalar inhibited by the ADC-busy signal. 71 72 Figure IV-l. Spectra and fit line to the 0*, 2+, and u+ states of 238U(p,p') at 57.5°. 73 mwd “>23 Omd HI>H waswfim >omwzw 20:45:83 mmd 0.0 O. 00. COO. 0000 '13NNVHO 83d SanOD 7A The solid angle dQ is defined by the spectrograph accept- ance aperture. A majority of the data was taken using a 0.69 msr (1° x 2°) aperture. Data for 125° < 6 < 1AA.5 23“U was taken using a 1.2 msr (2° x 2°) aper- degrees for ture to speed data acquisition. The data are scaled by a factor to correct for the number of counts in the "wing" band described above and for target thickness variations as determined by the monitor spectra. Typical corrections are 0—3% for the dead time, and 2—5% for the wing band. An uncertainty of 3 percent was folded quadratically with the statistical or fitting error to account for possible systematic errors in the normalization. Several targets of 232Th and 238U were used. The data were normalized by comparing common angular points. The overall absolute normalization was obtained by comparing the data to coupled channels cal— culations using Becchetti—Greenlees optical model param— eters [Be69]. The normalization was reevaluated following preliminary searches on the optical model and deformation parameters. The forward angles (6 < 50°) only are used as these points are least sensitive to the model param- eters. The scattering angles are checked from the spectra 'by taking advantage of the large kinematic shifts of the lighter mass impurity peaks for forward angles. This is ianortant because the elastic cross section is a very strong "ffiinction of the scattering angle at forward angles. The 75 initial deformation parameters were obtained from the Coulomb deformation parameters of Bemis [Be73] using 'BR scaling'. This scaling was accomplished by keeping RCBC = R8 where RC and R are the Coulomb and volume term radii, respectively, and BC and B are the Coulomb and volume term deformation parameters. The deformation parameters for the volume, imaginary, surface-imaginary, and spin- orbit are set equal. The volume, imaginary, and spin—orbit radii were fixed at the Becchetti-Greenlees optical model parameter values. The Coulomb radius and deformations (82, BA) used were those of Bemis [Be73]. Because of the ambiguity involving the imaginary well depth and the dif- fuseness, the volume imaginary well depth was fixed at the Becchetti-Greenlees value of 5.0 MeV for a majority of the searches. The cross sectional data appears in tabular form in Appendix C. In order to extract the deformation parameters for the nuclei being studied, the optical model parameters must be optimized by obtaining a best fit for the ground state data. The excited state cross sections are more sensitive to the deformation parameters, which are optimized for best fits to the inelastic scattering data. In addition to the (quadrupole (82) and hexadecapole (BA) deformation parameters, the hexakontattetarapole (B6) deformation parameter were in— cluded. Figure IV-2 illustrates the sensitivity of the 238U ciata.to the inclusion of a non—zero 86 deformation param- eter in the calculation. 76 Figure IV-2. Calculated cross sections showing the best fits to the data with and without the B6 parameter. The best fit for 86 = 0,0 is calculated using the parameters of King et a1. [Ki79]. 77 mI>H mgswflm Hmmmcmmnficao¢ .mwocmouacaoo on" 93 on o9 oc— fll. _’ u _ J .l . cu q a q IOum d >2. em ...- a n do n v we. I a ”>9. 2.... P m .. fl W . >9. 9. 3 m 2 . .N 8°. "mm H w: Ia. "a I q mmm. "Nu m / ..o 3 95.--: 2: II a S 1 N. me. "an 1 $6. "a .. wmm. "Na ”2 m EI v o— . 1 3.388 .2 n u n. u _ . _ t C . a: 78 Optical Model Search The angular distributions were fit using the Deformed Optical Model Potential (DOMP) in the coupled channels code ECIS [Ra7A]. The parameters were adjusted using the auto- matic search option of the computer code. First parameters were searched on by preferentially weighting the state which is most sensitive to the parameters being searched on. For example, the elastic scattering cross section data were fitted by varying the optical model parameters V, WD’ VSO’ a and a1. The 82 search was conducted with the 2+ angular distribution weighted. For the optical model parameter and 82 searches the calculation included couplings between the 0+, 2+ and A+ states. The 6+ state was included in the calculation when fitting the A+ angular distribution by varying BA° 238U Analysis The full calculation required to search on the B6 parameter exceeded the available size of the data processor. Alternatives include scaling the experimental data or omitting portions of the potential such as the deformation of the spin—orbit potential. Scaling the experimental data can be done to account for the omitted 8+ state. It was found that the inclusion of an additional state tended to 79 reduce the cross section in states with lower excitation energies in the rotational band. Figure IV—3 illustrates the effects of adding additional excited states in the coupled channels calculation. The data was scaled using a O-2-A—6-8 calculation and a O—2-A-6 calculation for 238 U with all potentials deformed (these calculations were test calculations carried out on a larger computer at Daresbury) [R079]. The parameters used in the calculations are the best fit values for 238U re- ported by King [Ki79] with 86 = 0.00. The scaling factor consists of the ratio of the two calculations for the par— ticular state and angle involved. Figure IV-A shows the cor- rection factors for the O+ through 6+ states for the full range of angles. The scaling is largest for the A+ at back angles and the 6+ state. The 0+ and 2+ states are changed by less than 1 percent throughout the angular range. To test the scaling method, the cross sections from a O—2-A-6-8 calculation with 86 set to -0.02 were scaled using the above described technique. The resultant calculated 'data' was fit using O-2-A and O-2-A-6 calculations with the values for 82, BA’ and 86 listed in Table IV-l. The same angular range as the actual data was used and the optical model parameters and deformation parameters not involved in the search were the same as used to generate the 'data'. .The results show agreement with the starting deformation parameters. Thus by using the scaling 80 Figure IV-3. Illustration of the result of adding additional excited states to the coupled channels calcula- tion. 81 mI>H oLzmfim . . .86 308338ko HmmwcmoE ¢ on; 2: on . o9 2: on III. — _ _ q _ . A Du - _ q — . _ u >mx 90m m- . I +0 Hmmmflfim 1 n u do m “~wa “ . >m u I W. x BOOM-O H INIou H +® O 0 j H I W - w. H I>ox m! I 0. I H +v. m M”, H w 1.3 m n 2 ”>8. 9. H w: m ..m m fl 2: w In" 9 m... H HHDolnwm mo“ m the. urn w mwm. "Na 2 ...: n ad 0 u H. _ _ HM :Immmm_ .m . L p _ p _ . m2 [JS/QUJ] (Sp/DP Figure IV—A. 82 Illustration of the ratios of a O-2-A-6 cal- culation to a O-2-A-6-8 calculation for each 238U. state in The ratios were used to scale the experimental data to compensate for the omission of the 8+ state in further calcula- tions. SCALE FACTOR 83 238U I I 1 r l r r I _ 8+ _ 1.10 .— 1.00 -- .. I I I 4r a I I I 1.05 - L} + - 1.00 _/_VW_\/\/\< 0'95 — i I l I 1 I 1 l .- l I I f F l I I 1.05 - 2 + .. 1.00 A M 0'95 - 1 l 4 I l l 1 I - I [ l [ r r I I 1.005 v w 0'95 '— 1 4 1 l 1 L l I d 0 ‘IO 80 120 160 9 (degrees) cm. Figure IV-A 8U Table IV-l. Results of fitting scaled 'data' with DSO calculation and actual 'data' with SSO calcula— tion. The ‘data' are calculated values for 2380 using 0—2-U—6-8 couplings with deformed spin-orbit in a calculation using the param— eters of King, et al. [Ki79]. RESULTS OF FIT DSO sso (scaled 'data') (actual 'data') 82 (expected) 0.2320 0.2320 82 min x2(0+) 0.2320 0.2270 32 min x2(2+) 0.2320 0.2310* 82 min x2(u+) <0.2000 0.2219 Bu (expected) 0.0U20 0.0U20 Bu min x2(0+) 0.0u20 0.0753 Bu min x2(2+) 0.0u20 0.02u5 Bu min X2(u+) 0.0U10* 0.0396* Bu min x2(6+) 0.0u00 0.0390 Bu min x2(8+) ------ 0.0381 86 (expected) -0 0200 -0.0200 86 min x2(0+) -0 0200 >0.0000 66 min x2(2+) -0.0206 >0.0000 36 min x2(u+) -0 0201 —0.02u2 86 min x2(6+) -0.0180* -0.017u* 66 min x2(8+) ------ —0.0175 *Indicates value which would be most significant. 85 approximation reliable deformation parameters may be ex- tracted even though the actual calculation required to extract the deformation parameters is impossible to carry out. The 238 U data were scaled and fitted using the deformed spin-orbit (DSO) calculations, including the 6+ state. Searches on the well depths, the diffusenesses and the deformation parameters 82 and Bu were done separately using a D80 calculation until a X2 value convergence was ob— tained using the search procedure described above. The 86 parameter was calculated by fitting the scaled 6+ an— gular distribution. The data were then fitted by varying V2 WD, V30: a, a 32 and Bu simultaneously minimizing the + 1, total X2 value for the 0+, 2 , and u+ states with the actual data. The 86 parameter was held fixed for this search pro- cedure. By including only a spherical spin orbit (SSO) inter- action in the potential rather than the deformed spin-orbit (DSO) interaction, the magnitude of the calculation is greatly reduced. This makes the 0—2-U-6-8 calculation pos- sible using the available computer, although the quality of the fit to the ground state data is reduced by using this method. To investigate the effects of the elimination of the spin orbit deformation, the calculated 'data' described above were fitted by varying the deformation parameters individually using the SSO calculation. The results are 86 listed in Table IV-l. There are deviations between the fitted deformation parameters and the initial deformation parameters but this method may still be viable for obtain- ing relatively accurate values for the deformation param- eters with a considerable savings in computational time. The SSO fits were done without readjusting the optical model parameters which may account for some of the dif- ferences. The spherical spin-orbit (SSO) calculation was used to fit the unscaled 238U data by searching on the parameters V, WD, VSO’ a, a 82, Bu, and 86 using a similar procedure i’ described for the deformed spin orbit searches. The result- ant best fit to the ground state yields X2 values which are a factor of 2-3 greater than the X2 values for the deformed spin orbit calculation. The excited state angular distributions could be fit with comparable x2 values. The best fit parameters and results from the spherical spin orbit calculations are compared to the results from the deformed spin orbit calculations in Table IV-2. Figure IV-S contrasts the best fits to the data for the D80 and SSO calculations. The search procedure used to obtain best fits to the data yielded results which require care in interpretation. Comparable fits could be obtained for continuous values of the product W and ai. This is of no great consequence, but %_has nearly the same effect on slope of the 0+ and 2+ 87 Table IV—2. Best fit parameters resulting from fits to 380 data with deformed spin orbit (080) and spherical spin orbit (SSO) calculations. RESULTS OF FIT Parameter D80 D80 V (MeV) 52.963 (190) 52.93“ (3&0) w (MeV) 5.000 5.000 WD (MeV) U.U77 (220) “.021 (U30) VSO (MeV) 6.756 (170) 6.603 (2MB) a (fm) 0.756 ( 11) 0.718 ( 26) a1 (fm) 0.807 ( 19) 0.8U2 ( 31) r (fm) 1.170 1.170 ri (fm) 1.320 1.320 rSO (fm) 1.010 1.010 82 0.226 ( 1) 0.226 ( 2) Sq 0.052 ( l) 0.0u7 ( 2) 86 -0.011 ( 1) -0.013 ( l) 88 Figure IV-5. Comparison of the best fits to 238U using the deformed spin orbit (D80) and spherical spin orbit (SSO) calculations. 89 Hmmmcmogéao mu>H ttsmwa om_ oo_ om . u a a d . d In: >9. 2mm m I u 1 s an an. , > I 'II' I, \ III-\\ I. m u .02; En “swim I“ 2 NO 1,. . m m I ldoc mu .m— n m m. .uos _ “ Ammocmogédc [II1 b °m_ co" on d d d . a . m. to m. s .mofi .992 mp no" I w. yo” mos 90 data as does the B2 deformation parameter, so that erroneous results for 82 could be obtained by allowing a to deviate continuously and compensating with 82. For the searches w was fixed at the Becchetti-Greenlees value of 5.0 MeV and 81 allowed to vary. Limiting the number of states included in the coupled channels calculations had some adverse effects on the fit- ting of the data. It was observed that improved fits to the ground state (0+)resulted in a worsened fit to the first excited state (2+) for the Optical model parameter searches. 2 for The results Of the 82 search would give a smaller x the 2+ data, while increasing the X2 for the 0+ angular distribution. The searches were repeated a number of times using the results of the previous calculation as the start- ing parameters for the search. The 82 parameter oscillated about a value which is nearly equal to the final parameter obtained. The Optical model parameters also oscillated in value to compensate for the 82 values. The value of BM was not as subject to change as the 32 parameter, showing no oscillatory tendencies. Table IV—3 lists values of the parameters and chi square values resulting from two search sequences, showing the results of the fits for two extreme values of 82. A phenomenon to note is that the higher values of 82 yield higher x2 values for the h+ angular distribution, whereas the lower values result in a de- creased X2 value for the U+ data. Figure IV—6 shows the 91 Table IV-3. Values of optical model parameters, deforma- tion parameters, chi square values and moments corresponding to the extreme values of 82. Parameter 238U 232Th V (MeV) 53.599 53.686 52.671 53.276 wD (MeV) u.036 u.050 5.193 u.753 vSO (MeV) 6.605 6.991 5.830 6.213 (fm) 0.7u9 0.75M 0.723 0.725 1 (fm) 0.811 0.795 0.797 0.791 82 0.22u 0.233 0.206 0.212 Bu 0.052 0 052 0.067 0.067 86 —0.011 -0.011 0.009 0 009 x2(0+) 72. 75. 103. 106. x2(2+) 261. 291. 2M6. 2M6. x2(u+) 380. 1862. 560. 1782. Q2 (eb) 3.215 3.3U6 2.872 2.261 qu (eb ) 0.860 0.893 0.972 0.99u q6 (eb ) 0.097 0.107 0.298 0.309 92 Figure IV-6. The x2 values for the 0+, 2+, and u+ angular distribution data for two ranges of 82 with corresponding optical model parameters. 93 wI>H mpzwwm mm mm oorwd ooNNd ooomd oorwd ooNNd oooNd 4 . a q a a q _ a do .68 I law I I 1 48.. I 18.. Nx Nx 1 .I l ITSm I 458 J I l mN.x++.4 mN.X++_< om.x+No om.x+No +9 0 8m I B 0 8m _ P) h b _ L _ » 9H +, and 8+ angular x2 values as a function of 82 for the 0+, 2 distributions for the 2 different 82 searches. Since the parameters are correlated, the results of the search pro- cedure is the production of a series of values for the optical model and deformation parameter, 82 which yield good fits to the 0+ and 2+ angular distributions. Figure IV-7 illustrates two fits to the data with 82 values which differ by about U percent. The optical model parameters for each 82 are different which indicates that the other param- eters in the optical model compensate for a change in a particular parameter. This discrepancy in the moment may be the result of the fitting procedure rather than inac- curacies in the measurement. Since there is considerable interplay between the parameters, the inclusion of the 6+ state into the calculation and the simultaneous search on a number of parameters yields an unique value for 82 with errors much smaller than u percent. 232Th Data Reduction The data were fit using a deformed spin orbit calcula- tion with both scaled and unscaled data. The unscaled data were fit with the optical model parameters V, WD, VSO’ a and a1 and the deformation parameters 82 and Bu 238 varied with the same method as was used for the U data. In order to search on the B6 parameter, and use the full 95 Figure IV-7. Illustration of the fit to the data resulting from the use of the 82 parameter which yields a minimum X2 value for the 2+ data in Figure IV—6. 96 Hmoocmogédw Ti 6.53,. AmmocmmEédo cm“ God on cm" as c—W . _ _ a _ q _ — q T >8. 9.... mes I I H I. I . I .6 an mm... - I, ,I. h w 2!.) m >3. Sm ”mg n I u v m n +m .......) H m NIOH W- +0 .5 I >8. m... .....I: I W I 0. ..I / n. +v ”3.5.4 1... . U D m ....) m ...-..I.-..,.. ... ...—T w. / m x ..I “If I IIIII ”V ' lac p W “wouluwm O .... III 433. 1 MO I Nmo. urn IIIIIIIIII r I 6 9. a. -. .. . I J I> .. a ... I ) I mmN. umn . fl +N .. 5.? w y l w H. i h I q W m it) K. M m / II . Inna”. s n .....Iuwn I a {.1 Illvl III. NWO. "rm lllll I (3.x - ..NN. ”a... I : I m :7) .....mm x: w . . .. ...é .. g H C». - 3.3.68 I a I n ....asmmm ” _ _ p L p _ 1 r _ p _ p h . H6 3 GS no. no. N9 /qu ESP /Dp 97 deformed potential, the data were scaled. The scaling is 232Th test calculations the same as done for 238U except that done at Daresbury [Ro79] were used. Figure IV-8 shows the correction factors as a function of angle for the four states included in the calculation. The fitting to the scaled data was done with the imaginary volume well depth set equal to 5.0 MeV. The value of this parameter was previously searched upon with it showing little change from the 5.0 MeV value predicted by Becchetti-Greenlees calcula- tions. This data also shows a tendency for the 82 value to oscillate. The variation was about U percent of the value Of 82. An improvement to the x2 value for the 2+ data with an increase in the x2 values for the 0+ and 9+ data is evi- dent for larger values of 82. Table IV-3 contains sets of parameters resulting from the 82 search. Figure IV-9 dis- plays the X2 values for the 0+, 2+, and 9+ states resulting from 82 searches about the extreme values in the oscillation. Figure IV—lO shows the different fits for the different deformation parameters. A calculation of the quadrupole moment shows a variation of about 5 percent. The oscilla- tion may be in part due to the effect of not including the 6+ state in the calculation when searching on the 82 param- eter. The inclusion of this state changes the fit to the 14+ angular distribution quite dramatically. The case of the + higher 82 value which yields a larger X2 value for the u angular distribution will be improved as the effect of the Figure IV-8. 98 Illustration of the ratio of a 0—2-9-6 cal- culation to a 0-2—9-6-8 calculation for each state in 232Th. The ratios were used to scale the experimental data to compensate for the omission of the 8+ state in further calcula- tions. SCALE FACTOR 232 99 1.10 1.00|- I I I I I I I I 1.051- "H’ " Loom/WA 1.05- 2+ _ local—‘2’ ‘ V o'ssl— IL I % J I I 1 I ‘- LOSE 0+ I I I I I _ Loon ——\___.—- O'SSI— 1 I l I l I 1 I d 0 “IO 80 120 180 6mm. (degrees) Figure IV—8 100 Figure IV—9. The x2 values for a 0+, 2+, and U+ angular distribution data for two ranges of 32 with corresponding optical model parameters. 101 Na oomwd 836 80—6 _ . . a a. ... loom 18: N .68 mm. x ...: 4 CW. x +N . o 0 8m comma . mm 83.9 82.9 a 4 1 40 SN 18... NX 180 mm. x +... 4 cm... x +N 0 +0 0 090 L b » IV- 9 Figure 102 Figure IV—lO. Illustration of the fit to the data resulting from the use of the B2 parameter which yields a minimum X2 value for the 2+ data in Figure IV-9. 103 Hmwohmmgédo 3.2. is... .mmmcmmgédo cm: 93 cm cm..— o“: o_m.. I _ . _ . . . I>..:. mam . _ INT... I I .m u. u. m /. I H I H .II n n. r was. mm. M. H I Io ..... IN-.. .II .o 1...... $3. um. I} m I c H 4.? but DD 0 UN H p V H ”Human... . I .. L n o (.... m>ox av) .15» .00 mflo / r I IN ... A. 6...... I 0. 8.. I... . I .. ..., .....ch I 6 no... I... .......... .8... H (I part»! H 1w} Nam. “Na 0 m ...... . 2 m fl .... "I . r... rum. 3 .8. I... I W... ...... H... um... I... IIIII I ”....I mom. "Nu a ... w ( ... .. I J . I m — m J, .. ... ._ -... . a Q ... w... H ... 3:8... I ad II. p _ _ Hn— HJHNm—N F” H p p _ p _ . ... . p w 2 0. M0 .0. 8. fl 3 III... no. .2 n2 10“ added 6+ state is to lower the u+ cross section at back angle where the disagreement is worst (Figure IV-lO). The use of a simultaneous search on a number of parameters with the full calculation eliminated this situation for 238 U and should be no different for 232Th. The scaled data were fit until a convergence was ob- tained with the Bu and 86 values not changing appreciably during the search procedure. Using these best fit param- eters from the scaled data searches, the actual data were fit by varying V, WD, V50, a, a B2, and Bu simultaneously 1) using a 0-2—9-6 deformed spin orbit calculation. The 232Th data were also fit using a SSO calculation with searches on the optical model parameters V, W VSO’ a and a., and the D’ 1 deformation parameters 82, Bu, and 86’ using 0—2—u and 0-2—u-6-8 SSO calculations respectively. The best fit parameters for the scaled data (D80) and the actual data (SSO) searches appear in Table IV—U with the best fits to the data illustrated in Figure IV-ll. 239 236 U and U Data Reduction The starting points for the searches were the Becchetti- Greenlees optical model parameters with the B2 and Bu deformations parameters a result of 'BR scaling' of the Coulomb deformation parameters of Bemis [Be73]. The data were fit similarly to the other nuclei with the optical 105 Table IV-U. Best fit parameters resulting from fits to 232Th data with deformed spin orbit (D80) and spherical spin orbit (SSO) calculations. RESULTS OF FIT Parameter DSO (error) SSO (error) v (MeV) 52.973 (780) 53.02u (300) W (MeV) 5.000 5.000 WD (MeV) H.960 (M20) “.860 (280) VSO (MeV) 6.097 (350) 6.080 (170) a (fm) 0.730 ( 17) 0.723 ( 10) ai (fm) 0.792 ( 19) 0.801 ( 10) aSO (fm) 0.750 0.750 r (fm)- 1.170 1.170 ri (fm) 1.320 1.320 rSO (fm) 1.010 1.010 82 0.202 ( 2) 0.20M ( 2) Bu 0.068 ( 1) 0.067 ( 1) 86 0.009 ( 2) 0.010 ( 2) 106 Figure IV-ll. Best fits to the 232Th data for the deformed spin orbit (D80) and spherical spin orbit (SSO) calculations. 1137 IIIITI I I IIWIT T I 1‘ I T 11 ”moocmooacsoo cod ......fimmm ..II. IIIIIII I I IIIIIII I I IIIIIII I I IIIIIII I I l aaI>H otsmaa a-.. N-.. _1o o“ IIIII Hmootmouactoo . emu oo~ ow J A d I— d J [IIIIIII I WI1T IIIIII I 11 IIIfi 3.32:me fio o-l o— cod no. ... no“ 108 model parameters V, WD, VSO’ a and a1 searched on separately with a 0—2-9 calculation for the 0+ angular distribution. The 2+ angular distribution was fitted with the same cal- culation with the deformation parameter B2 varied. The Bu search was made using a 0-2-U-6 calculation with the b+ data weighted. This sequence was repeated until the param- eters stabilized and the normalization rechecked for the forward angle elastic scattering data. A value for the B6 parameter was found using a spherical spin-orbit (SSO) in a 0-2—9—6-8 calculation and searching for a minimum X2 value for the 6+ state. The change in B6 affects the fit of the other states so that the search procedure on the other parameters needs to be repeated until the values of the search parameters including 86 stabilize and a 2 value is obtained for the 0+, 2+, 4+, minimum total X and 6+ data. The data were fit using a SSO calculation with couplings up to the 8+ included. The optical model 2 value for parameter values were found by minimizing the x the O+ angular distribution using a 0—2-U calculation. The deformation parameters were evaluated using a 0-2-U-6-8 calculation to minimize the total X2 value for the 2+, u+, and 6+ angular distributions. Figure IV-12 and Figure IV— 13 show the best fits to the data. Tables IV—5 and IV-6 list the parameters yielding the best fit to the data for both the D80 and SSO calculations. 109 236 Figure IV-l2. Best fits to the U data for the D80 and SSO calculations. 110 _TII I IIIIIIII I IIIIIIII I IIIII>TII I>lq O 0 " + x ID x wN 9 0143, mm I'D .. Ibo-4 I hy—j II-o—I II-o—I ..r' -e ” 0—0—4 -* PF, I—o—Ag 0—-0—1 d H.“ I fi—JP—‘Q H—fi \\ ‘0 I In I I I f d I IIII I I IIIIIII I I IIIIIII I I IIIIIII I I IIIIIII I L__LI_I ° '2 - I' ‘2' fl 9 o c: F. r-t [JS/QUJ] asp/op [lIIIIII I [IIII'IIT'I_"[IITIIII I [IIIIIII IglITWIIT I IIIIIIII I IITIIIII'I 4. *- cm 0 o 00-0 . "‘ID ONWQ v-Qco I. .—0 (00100 (\IO 0 I . I . r' ’—‘ .. D. C O. H e :3 ‘3 LO "‘ m 1 (m y I— do In " -I quIII 1 Mn“. I I|IIllll I IIIIIIII I [1111111 I hm“. I IIIIIIII I . O O Q (3 .—¢ (3. 0-0 u-Q 0" Figure IV-l2 9c,m,[degrees) GCJnIdegrees] 111 Figure IV—13. Best fits to the 23“ SSO calculations. U data for the D80 and 112 Hmoocmonacsoo maI>Hmr:aae Homoemooacso¢ IDMMI ea. on an. ea. . eMII nu _ . d . qr . duced a _ . >3. 3.. H +m [WIN/rm w I II. I . , I u m Imm MI... Ks. (III m .II>... .3 m m IN-.. ... .90 .h M MW 1 ”>3. n... H o. m .. m m/ I?) II... DI nu moo. I I .II .... I.. n H w .8. IN. u u fl omw II--. II m. 9 N... I... “N. I I [IIIIII I 1'1 TI I- 1 [MLJJ I I 1 I114 I 3 .... I.. m.N. IN. cma.III. ...... 3.1mm m C) d .3 no. [.Is/quI] ap/pp 113 Table IV-5. Best fit parameters resulting from fits to 2360 data with deformed spin orbit (D80) and spherical spin orbit (SSO) calculations. RESULTS OF FIT Parameter D80 (error) SSO (error) V (MeV) 52.716 (970) 52.890 (390) W (MeV) 5.000 5.000 WD (MeV) 5.369 (980) 5.123 (660) vSO (MeV) 5.88M (600) 6.006 (700) a (fm) 0.795 ( 22) 0.738 ( “0) a1 (fm) 0.776 ( 22) 0.780 ( M5) aSO (fm) 0.750 0.750 r (fm) 1.170 1.170 ri (fm) 1.320 1.320 PSO (fm) 1.010 1.010 82 0.220 ( 2) 0.218 ( 2) Bu 0.063 ( 2) 0.060 ( 2) 86 -0.003 ( 5) -0.003 ( 5) 119 Table IV-6. Best fit parameters resulting from fits to 239U data with deformed spin orbit (DSO) and spheri- cal spin orbit (SSO) calculations. RESULTS OF FIT Parameter DSO (error) SSO (error) V (MeV) 59.792 (700) 59.938 (600) w (MeV) 5 000 5.000 WD (MeV) 5.319 (970) 9.885 (560) VSO (MeV) 6.769 (920) 6.893 (550) a (fm) 0.768 ( 22) 0.799 ( 12) a1 (fm) 0.722 ( 32) 0.729 ( 16) 330 (fm) 0 750 0 750 r (fm) 1.170 1.170 ri (fm) 1.320 1.320 rSO (fm) 1.010 1.010 82 0.21M ( 2) 0.210 ( 2) Bu 0.072 ( 2) 0.072 ( 2) 86 0.007 ( A) 0.007 ( 3) CHAPTER V RESULTS AND DISCUSSION The multipole moments are calculated using the best fit parameters from the data analysis within the coupled channels formalism. Figure V-l compares the results of the deformed spin-orbit (DSO) and the spherical spin-orbit cal- culations. The results of this work are also compared with the microscopic calculation [Ne76]. These microsc0pic cal- culations [Ne76] involve finding the minimum of the nuclear potential energy treated as a function of the deformations. The wave functions of the nucleus at the equilibrium point are found and the moments are calculated using the multi- pole moment operators. In this calculation the average single-particle potential is expressed in terms of a har— monic oscillator potential. Overall, the trends of the moments resulting from the two analyses are similar, but not in complete agreement. For the uranium nuclei, the moments found using the SSO results are systematically lower. How- 232Th calculated using the 830 param- ever, the moments for eters agree quite well with the moments calculated from the DSO results. The SSO calculations do not fit the ground state data as well as the DSO calculations for angles 115 116 when m o>wm Lowcz whochmLmo ecu mcwm: xgoz mmN wmw rmw wa I _ a J . 3 f. 86 v. z / smog I 1’11 I LO . .... I I I I m ,,m II II mo I 19.6 .Icoaeeasoaeo on. es. own so. I... or. o. 8.. mQCOEOE popmH30Hmo was. so. wa mmw . wmw . rmm . .Hl> ogsmwu < mmm mmm rmm wa d _ _ _ I 3 LIP JOT.N ... I I do I\\\. 38 III“... N. I OHIIIWIIII IfiWm I ......ooz I I omm ....M . owe .... o 117 beyond 120 degrees. Another major difference between the SSO and DSO calculations (Figures IV—5, 11, 12 and 13) is the phase of the cross sections. The diffusenesses and deformation parameters (Tables IV-2, 9, 5, and 6) are in good agreement for 232Th for the 830 and DSO calculations. The same parameters show considerable deviations for the uranium isotopes with the DSO and SSO calculations. Since the DSO calculation leads to a better overall fit to the data, these results will be used in further comparisons. The moments follow the trends predicted by the model of Bertsch [Be68], including the extension of the formalism t0 the Q6 moment (Figure I—9a). Although B6 changes sign the moment does not but the trend indicates a change in sign for the q6 moment in this region. Since this moment follows a predicted trend the 86 value extracted appears to be physically significant not simply an artifact of the fitting procedure. The previously illustrated sensitivity of the fit to the data of the B6 parameter, Figure IV-2, where the effect of using a non-zero 86 value improves the fit, adds confidence to the extracted value. The quadru- pole and hexadecapole moments also follow the trends pre- dicted by this shell filling argument. Figure V—2 compares the moments calculated using the DSO parameters with the moments from Coulomb excitation [Be73], electron scattering (e,e') [C076], q-particle scatter- ing [He731, and microscopic calculations [Ne79]. The Q2 . ”.../Q ...:,.n~r.w I.;; LC. .xL. com .mccmpcezofid; oHLCcmCLCWE T2: x.r:mc; adgczachu Ixo m30fi>ogd Spas xgozz was» Eogm wcfipHSmop mucoEoE och mo COmHLoQEoo .ml> mpswfim 118 < < < mmm wmw ..mm ~m~ ‘ mmw mmm ..mw mmw mmw wmm ..mm mmm d _ _ H d d _ q Atom... _ _ d d 3 £I_I H OH I _I_ LIP Ifiorfl. s... I LN. 3. o no. I I ..o / .... .... I ... .... III I. LO LON.“ m\\\ \- NO I A DOB I I. I I I I I \\ . mil/I \\\\* mwa .I 1* \\.\\ IfiONm WI 12.... I III-II I 3.89..— I - ...... I .. I . 8.x. 9 I Iflcm u aha-n: . _ . e . _ . e e I _ . xw _ So... I 8 .. 119 moments for this work agree in trend with both the Coulomb excitation and theory although the Coulomb excitation re- sults are between 5% and 8% higher and the theory consist- ently lower than the moments from this work. The on moments agree in trend with the Coulomb excitation results for the three lighter nuclei although the magnitudes of the Coulomb excitation are between 2U% to 28% higher. The trends of these two on studies are in disagreement when 238U is in— cluded. The qu moments from this work are 10% less than the (e,e') moments for 232Th and 20% less for 238U. Both trend and magnitude with the microscopic calculations are closely followed. The a-particle scattering q2 and on moments for 238U using parameters from Reference [He73] disagree with the moments from this work. The Hendrie et al. [He73] results moments also disagree with the results of the systematic study by David et al. [Da76] (Figure V-3). The two studies use the same beam energy so that the Hendrie result should agree with the David result. This discrep- ancy may be in part due to the data analysis. A strong cor- relation was found between the charge and potential deforma- tions and the charge deformation was fixed to yield the proper quadrupole moment. In this way the potential deformation is linked with the charge quadrupole moment. Since the d-particle scattering results are not repro- ducable, this indicates some problem or ambiguity in the analysis. There are two sets of values plotted for the 120 Figure V—3. Comparison of the momentsobtained using a-particle scattering at 50 MeV. me rmN NmN oM'KJV rVPHR—VWWPL J . _ l omd 1 cm.“ mmN me rmN NmN T A a d a oo.+_ 122 David et al. study. The double values in the moments are the result of maintaining the same deformation parameters for different values of the optical model parameters includ- ing the volume term radius. Since the moments depend on a product of R and B, the doubled value situation exists. The (a,a') results appear to agree, within uncertainties, to the microscopic calculations, but the lack of any defi- nite trend for the Q2 moment may indicate some inconsistency or model breakdown in the analysis. The results of this work show agreement with the trends and, in part, magnitudes with the microscopic calculations for both the q2 and qu moments. Neglecting the qu moment 238U of , the Coulomb excitation measurements and this work show very similar trends, but with the above mentioned discrepancies in the magnitudes. This discrepancy, if sig— nificant, would indicate a smaller moment for the neutron distribution than for the proton distribution. This was 15M 176Yb, also observed for the rare earth nuclei Sm and 238 as well in the preliminary analyses of 232Th and U by King et al. This difference is opposite the difference predicted by Hartree-Fock calculations [NR77] which indi- cate that the charge moment is smaller than the nuclear moment. These calculations predict the neutron quadrupole moment to be 5% larger than the proton quadrupole moment for 232Th and 3% larger for 238U. The neutron hexadecapole moment is predicted to be 7% larger than the proton 123 238U. The hexadecapole moment for 232Th and 1% larger for Hartree-Fock calculations differ from the above mentioned microscopic calculations. For each nucleon in this calcula- tion,tflu3potential used is the average potential generated by the other nucleons, with additional rearrangement terms used for density dependent interactions. The wave func— tions are found in a self—consistent method by iterating the potential and the wave functions until a solution is obtained. Typically, the starting wave functions are an expansion of the oscillator potential. The experimental results are in line with the findings of Mackintosh [Ma76] in work involving Satchler's theorem. His findings indicate that either the neutron density for certain heavy nuclei is much less deformed than the proton density or the fold- ing model breaks down in an unexpected manner, inconsistent with the form of the density dependence most likely to occur, or with exchange effects, at least as they may be included at the present time. Thus there is an indication that the charge and matter distributions are different, but this issue is clouded by the necessary use of a model de- pendent analysis. Improvements to the analysis may in- clude the use of independent deformation parameters for the real and imaginary terms in the DOMP, as is the case for the radii and diffusenesses. The addition of the 8+ state to the DSO calculation would require considerably larger and more time consuming calculations, but would 12M allow a better determination of the value and the addition of an additional state may be used to evaluate 38 if the data supports a non-zero value for 88. APPENDICES APPENDIX A INTRODUCTION The ability to obtain very narrow (50 um) [No7u] lines for charged particles using nuclear emulsions in the focal plane of the Enge split—pole spectrograph [Sp68] at the Michigan State University Cyclotron Laboratory makes it an excellent device to measure the ultimate position resolu- tion obtainable with position sensitive detectors. Mark— ham and Robertson [Mk75] were able to measure a position resolution of 220 um FWHM for 35 MeV protons, using the in— clined cathode delay line counter. From this measurement, they were able to determine a contribution of luO um FWHM due to residual effects in the counter. The residual width is caused by effects associated with charge collection in the counter and secondary ionization of the proportional counter gas. A program was undertaken to develop position sensitive detectors in order to study the resolution at- tainable with thin proportional counters. The goal of the program was the development and use of small position sensitive gas proportional counters. The counters were built for particles at normal incidence to minimize energy loss straggling effects in the counter 125 126 gas which usually dominate resolution at “5 degrees [Mk75]. At normal incidence there are still contributions to the observed line width from the line width of the beam, multiple scattering in detector window and gas, and electronic noise. The contribution of the beam has been measured independently using photographic emulsions [No7A]. Multiple scattering effects are minimized by normal incidence and the residual contributions can be calculated, for both the window and the counter gas. An analysis of the contributions to line width by the gas and window appear in TableArl; The electronic noise for resistive division counters was estimated by in- jecting test pulses into the preamplifiers. To obtain normal particle incidence, the counter is placed at an angle of 45 degrees to the focal plane. Since the detector is not parallel to the focal plane, the par- ticle groups cannot be focussed at all points along the detector, resulting in the need to stabilize the position of the peak on the detector. A computer feedback system is used to control the spectrographic magnet power supply while maintaining the position peak within a fixed window. The computer also outputs the peak width by using a digital to analog convertor (DAC) and a meter to give a visual readout of the peak width during the beamline tuning pro- cess [No7U]. A difficulty with using a thin detector for lightly ionizing particles such as 35 MeV protons is that the energy loss of the particle in the detector is small, 127 .xmmo 0 mo wcme300mop oHmeocHx mch: mzchz xmoo UmLSmmoE Soap UmpmHSQHmoo H w .LOpmHSOmom cqu szcmpchoch ompzmmwzp .AEpm Hv mcwoopmo .LmHmz ooNHcHESHm E: on .hm>mm E: mm 5: mm m: em: I- m em mafia sdeo as m H: mm om mm: om m om COHmH>HQ o>HpmHmom EE m mm om m: pmm om H mmH conH>HQ m>HpmHmmm ES H HmspHmmm UmpSmmoz popwHSOHmo Emom mOHcoppomHm ommo sochz Lopcsoo Hmuoe .mLSpwpomSU CH cocoa opp E: CH mcoHpanppcoo HH< .mgmpcsoo HmcoHuLooopo chp pom chHz mcHH on mCOHuanLucoo no coHmeHumm .HI< mHomB 128 requiring high gains in the counter. With appropriate choice of gas filling and some attention to construction details to permit operation at high voltages, adequate gas gains can be obtained. In this work, two techniques for position readout were used, charge division with a resistive wire and delay-line readout of induced signals from a low resistance wire. CONSTRUCTION AND PERFORMANCE Two resistive wire counters were built using 25 Um carbon coated quartz wire [ZvOl]. The first detector was l-mm thick and used a sandwich type construction as shown in Figure A-l. Its active area was lO mm long and 2.5 mm in height. The sandwich consisted of a pair of 0.5 mm thick spacers glued to either side of the wire, with 6.25 um Havar windows glued to the outsides. The wire leads out of the sandwich were made using Havar strips. The wire was held in place with a conductive adhesive, which also limited the resistive portion of the wire to the active region (resistance = 80 k9). This module was placed in a frame which made the gas and electrical connections to the spectrograph. The operational bias was 1850 volts on the wire for a propane gas filling at 1 atmosphere pres— sure. A position resolution of 50 um FWHM (full width at half maximum) along the detector (70 pm FWHM along the EXPLODED VIEW THIN PROPORTIONAL COUNTER TOTAL THICKNESS = 1th"! GAS PORTS O 9 X / 0.00825 mm HAVAR FOIL / °c:7 7 0.25 mm MYLAR SPACER / '3\___/"/ 0.25 mm MYLAR SPACER 0.025 mm CARBON COATED F14: QUARTZ FIBER 5 EXTERNAL CONDUCTORS /4=7 ‘ / 0.50 mm MYLAR SPACER /(dH )/ 0.00825 mm HAVAR FOIL k-10 mm [R = 80 k9] u.-- ---- --- ---d ------ Figure A—l. Exploded view of 1 mm thick resistivo division counter. 130 focal plane) was observed (Figure A-2) for 35 MeV protons 2 carbon foil. The elastically scattered from a 20 ug/cm position spectrum represents an energy loss selection com- promising about UO percent of the total events. It was found that selecting particles with a particular energy loss signal yielded resolution about 20 percent better than thepositicmiresolution resulting from the acceptance of all events. Electrical breakdowns occurred often because of the small spacings in this counter. These damaged the resistive coating on the wire resulting in the need for frequent wire replacement. In order to improve the reliab- ility, a 2-mm thick resistive counter was built using the same wire and active area as the first design. The new design used l-mm thick G-lO fiberglass laminate spacers to support the wire in a groove cut into the aluminum body of the detector as in Figure A-3. The quartz wire was held in place using a conductive adhesive which also made electrical contact with larger wires connected to the feed- throughs. A line width of 65 pm (FWHM) along the detector was measured with this detector. This counter was more reliable than the first as the bias required was similar but the breakdown paths were longer. However, the carbon coating on the quartz fiber deteriorated for high counting rates (10 Khz) in a localized area (.1 mm) during the tuning process. This deterioration takes the form of a resistance change which results in position nonlinearities. To further Figure A-2. 131 Position spectrum for 35 MeV elastically scattered protons. .EE. woz8. _ u 882% 5 30. 6.95 on- u 92% >22 on I am 05.28% 2.3.0 88.1 328.6: 22:3 E385 2 5.36593 .6828 x25 EE _ x 93. Eu _ .2500 38:83:. as; «28.81 14 / Ewan. I .213... 13NNVH3 83d SanOD Figure A-2. Figure A-3. Photographs of 2 mm thick resistive division counter. Lower (closeup) photograph is about twice the actual size). l3“ improve the reliability, a readout mechanism not requiring the fragile carbon-coated quartz filament is needed. The highest resistivity metal alloy wires currently available in small diameters (<10 um) are much too low in resistance for such short detectors. A second type of detector was built utilizing tapped delay-line position encoding as shown in Figure A-A. The active region was 2 mm thick, 10 mm long and 2.5 mm high. The anode was a 25.“ pm diameter tungsten wire attached to a Delrin bridge. The delay-line is a commercially available lA-pin dual-in—line package [DaOl] having 10 taps with a total time delay of 500 nsec and a 500 Ohm imped- ance. The pickup stripes are 0.90 mm wide with 0.10 mm spacing between each. The stripes are made by vacuum deposition of copper using a mask onto a circuit board which connects the stripes with a standard 1“ pin IC socket. The mask is made by stretching 0.10 mm diameter wires between 2 screws with a pitch of 10 turns per cm, allowing the production of very uniformly spaced stripes with well defined edges. Techniques such as chemical etching and machining leave rough edges and etched stripes are subject to some undercutting. To produce a smooth surface for deposition of the stripes, the board was coated with lacquer and sanded smooth. This fills the slight irregularities in the G-lO circuit board. The delay line pickup board attached to the wire bridge, defining the lower surface of Figure A-u. Photographs of 2 mm thick delay line counter. Lower (close-up) photograph is about twice the actual size. 136 the active area. An aluminum block secured the 6 pm thick Havar back plane which defined the upper surface of the active area. The entire assembly was installed in a gas tight box with a 6.25 pm aluminized Mylar window. Elec- trical connections were made to the ends of the delay line and to the anode wire through a Kovar feedthrough. When biased to 2200 volts with propane at 1 atmosphere pressure, a position resolution of 65 pm FWHM along the detector was obtained for 35 MeV protons at normal incidence, scattered from a carbon foil. Figures A-5 and A-6 show comparable spectra for the 2 mm thick resistive wire counter and for the 2 mm thick delay line counter. This detector was quite reliable since the components are much less sensitive to damage from localized high counting rates, and the design allowed breakdown free operation at higher voltages. ELECTRONICS The charge division counters used charge sensitive preamplifiers, one at each end of the wire to obtain energy loss signals. The output signals were sent to amplifiers for shaping and further amplification with the analog sig- nals summed to give the total energy loss. The ratio of the signal from one end and the sum signal yielded the position. The ratio was calculated by converting the two analog signals to digital values and dividing using the 137 Figure A—5. Position spectra using 2 mm thick resistive division counter. 138 0.0. REE. woz<...m.o o.» .0. "new . >2). on I am onto. .3» 2.3.0 c205 3233: 0.3.5.. 2.3.2.. 2 8.36582. .2023 .II :35 56 N x 9:: Eu. .2530 33:33:. 3.3 2.3.3". 613 1. o H 12 T E: on_ SE .6 3... 1.8. .I 2:3... . m2 WBNNVHO 83d SiNnOO A-S. "(guru I“ 139 Figure A—6. Position spectra using 2 mm thick delay line counter. 1140 HES. moz22 on new I 053.33. 37.20 c230 . E: on. 3200...... 0.2.3.. 2320:. L .1:on ..o 3“. 3 3.3.2.3.: 3323 .2... EEN x 93. E0. .2500 2.... >23 I Elmo If :13... l as .1 man :2 TIBNNVHO 83d SlNFIOO A-(». Figure 1U1 computer. Figure A-7a illustrates the electronics setup used for signal processing. The bias network consisted of a current limiting resistor and isolation capacitors between the wire and preamplifiers. The delay-line counter electronics differ from the resistive division electronics as timing signals were necessary. A schematic is shown in Figure A-7b. The bias network contains a current limitation resistor with the provision to obtain a signal from the wire through an isola- tion capacitor. The delay line was resistively terminated to match the input impedance of the preamplifiers. The signals from each end of the delay line were preamplified and the output signal were processed by timing filter ampli- fiers (integration time constant = 200 nsec, differentiation time constant = 100 nsec). A constant-fraction discrimina- tor was used to derive timing signals from the timing filter amplifier output. The position was extracted by using the signal from one end to start a time-to—amplitude converter (TAC), and the signal from the opposite end, delayed in time by the total delay of the delay line, to stop the TAC. The TAC output is the position and was analyzed using a com— puter. Both types of counters could be backed by a silicon detector for particle identification. For the tuning pro- cedure this was not necessary since the elastically scat- tered protons dominated count rates. Figure A—7. 1U2 Schematic of electronics used with a) resistive division and b) delay line position encoding. PREAMP ARM) a) HV 1143 ——J\/\/\/\/VV\r- ._{ PREAMP AhflP SCA SUM SCA {—7 x v T -t 1 E ! . ‘ LINEAR COINC 4. GATE 325,2“ E AE ADCI ADCZ Pi gurc A- b ) IIV ANOOE 1| Woooicmocmo DELAY LINE PREAMP PREAMP "Em" TFA TFA AMP CFD CFD SC“ . ”0' sum I POSITION LINEAR 0‘7: DELAY TAC snout POSITION 'AE ADC I ADC 2 r7 {. 1AA RESULTS New upper limits were obtained for the optimal posi— tion resolution available with gas-filled proportional counter for charged particles. Muller et al. [Mu7l] have achieved a spacial resolution of A0 um FWHM with a zenon filled multiwire ionization chamber. Table A-1 lists the position resolution obtained and the contributions to the width. The residual contributions to the line width in- clude a number of line broadening effects which are dif- ficult to isolate. They may include spreading of the ava- lanche, photon or electron propagation along the wire, dif- fusion of primary electrons, and variations or fluctuations of the multiplication along the wire. The improved resolu— tion achieved by selecting a narrow range of particle energy loss allows further analysis of the resolution de- grading effects. Spectra corresponding to both high and low energy loss selection show poorer resolution. The former indicates that secondary ionization producing events such as scattered electrons or photon prOpagation in the gas cause a spreading of the line. Since the resolution improves with bias the gain-dependent effect of photon propagation can be judged to be less dominant. The low energy loss signal could result from either incomplete charge collec— tion or a smaller energy loss in the gas. Incomplete charge collection could result in excessive spreading of the 1145 avalanche due to diffusion of the primary electrons. An event with a small energy loss would result in a greater uncertainty in the position measurement. Since the resolu— tion improved with bias, the effects of charge collection appear to dominate and can be controlled. In addition to tuning of the beam line elements for narrow lines for a variety of particles, the study of closely spaced states in scattering experiments is feas— able. APPENDIX B The limitations of the detectors used for taking the data in this thesis pointed to the need for a more sophis— ticated position readout. The design, construction, and testing of a multiwire proportional counter (MWPC) was undertaken. The MWPC is a position sensitive detector which has found considerable use in high energy physics [Ch70] and in electron scattering [Be77]. It was recently a subject of a review article for nuclear physics [Ba79]. This type of readout uses an array of wires and the drift time of electrons in the proportional gas to determine the position of a particle track. An advantage of the multiwire readout is high spacial resolution (<1 mm) can be obtained for A sec-l). large detectors (>1 m) for high count rates (10 Figure 8—1 illustrates the wire plane which is the basic component of this device. The wire plane consists of smaller diameter active wires and large diameter guard wires. The active wires obtain this designation in that charge multiplication occurs at only these wires producing measurable signals. The guard wires are for field shaping and also isolate the active wires from each other. A particle passing through the gas filled region surrounding the wire plane leaves a track of electron-ion pairs in the 1U6 1147 \ Foil Planes 00.00.000.00. Active Wires Guard Wires Particle Figure B-l. Schematic view of wire plane for MWPC. Tapped Delay Line 390090 00 0 o 00 oo oo ocoiai Guard Wires Active Wires .1: Readout ; TO PULSE Lines g TRANSFORMERS Figure B-2. Schematic of Active and guard wire connec- tions. 1&8 gas. The fields produced by the wire plane collect the electrons. Charge which is collected by the active wires is multiplied by the high field surrounding the active wires. The active wires collect only a portion of the total number of electrons created since the charge is also being col- lected by the guard wires. A number of active wires will produce signals for each particle. This is an advantage of the multiwire readout in that the position of a track can be found by measuring its location at several points. This type of readout is less sensitive to resolution de- grading mechanisms and background caused by collecting charge from a large volume. Measuring the position at a number of locations reduces the errors caused by the skewing of the centroid as a result of energy loss fluctuations over a large region. This effect was found to be a major con- tribution to resolution [Mk75]. POSITION READOUT The time required for the electrons to drift from their origin on the track to the wire is related to the distance travelled. The electrons, under the influence of the electric fields produced by the wires, quickly attain terminal velocity due to collisions with the electrons in the gas. The only appreciable charge multiplication oc- curs in the region roughly equal to twice the collection 1&9 wire diameter. To measure the position relative to a wire requires only the measurement of the drift time. Finding the position of a track relative to two or more wires allows the calculation of the trajectory of the particle through the detector. By knowing the angle of incidence Of the particle at the detector, corrections can be made for use of a larger defining aperture, aberrations in the spectro- graph, or for a subdivision of the scattering angle within the angular range of the defining aperture when this is important. One application might be to measure the fine structure in an angular distribution using a large solid angle defining aperture, or a slotted aperture, where a number of closely spaced angles can be measured simultan- eously. The measurement of the trajectory with this type of MWPC readout is possible only if the particle trajectory is at an oblique angle to the wire plane, so that the par— ticle track is projected onto the wire plane. If the angle is small such that only one wire collects charge the tra- jectory information could be obtained by using two position sensitive detectors separated spacially along the trajec- tory. In the multiwire counter the position is measured relative to each individual wire. This is advantageous in that the integral linearity is limited by the accuracy of the wire placement. The position resolution is nearly 150 independent of the length of the counter, unlike position readouts which utilize resistive division or delay-line en— coded position readout. This MWPC readout differs from the standard digital readout [Ba79] which uses a separate preamplifier and dis- criminator for each active wire and uses digital electronics to find the particle track position. The present design is similar to the Bates device [Be77], using analog position encoding. Every fifth active wire is interconnected as in Figure 8-2 and the five signals processed through preampli— fiers. Thus for 90 active wires only 5 preamplifiers and discriminators are required. The determination of the group of wires involved is accomplished by coupling the guard wires to a delay line. The avalanche at the active wires induces a signal on the guard wires. The signal, using the delay line, can be used to locate the group of wires in- volved. The wire in the group nearest to the particle track produces a signal first and can be readily identified. By adding two additional preamplifiers and discriminators to accommodate the delay line readout, and by utilizing a CAMAC multistop time digitizer the drift time measurements become simple. The position and angle of the particle track and the aberration corrections can be calculated by using software to decode the timing information and display the results. An advantage of using software is that diag— nostics can be implemented in addition to display and gating. 151 The position relative to the wires, or fine position, is calculated using one of two methods, first-wire-timing or fiducial timing. The first—wire-timing scheme involves three active wires as in Figure B-3. By using the first wire to produce a pulse as a start signal, the relative times (B—l) can be measured. These two times are used to calculate the position by T = T T T > T X = %[1 — ¥:] where 2 + T (B-2) > T) = T_ T > T < + where d is the active wire spacing. The tangent of the angle of incidence, found using geometrical relationships is T (8-3) tan0= o.|<: V where V is the electron drift velocity which is a constant value. 152 O O O f O O o 9 9 : I 7+ I I meoswe: T_ = T_’ To T+ : T+ - To Figure B—3. Illustration of the times measured to derive position. '— K_ s_,‘ -)IK-d WIRE PLANE GROUND PLANE Figure B-u. Geometry of the counter showing dimensions im— portant to the electrical characteristics of the counter. The fiducial timing scheme involves using an external start such as the anode signal from a photomultiplier and scintillator. Similar to the first wire method, the two relative drift times are measured, with some time offset tz, - - z (B-U) T+ = T+"tZ The position relative to a wire is T - T _ + X = (B’S) T_ - T+ - 2tz and the angle can be determined from the relation, t - —V— 6 The term tZ represents an offset in time as the result of derivation of the time with two separate devices. The fiducial timing scheme involves only two time derivations in the MWPC where the first wire mode involves derivations (of two relative times using three wires. The fiducial tximing mode is more accurate since the error introduced b37 photomultiplier (dt x 1 ns) should be negligible com- FEired to the timing error of the multiwire counter wire 152b (dt 2 5 nsec). The active wires give the fine position, that being relative to the first wire in the group to pro— duce a signal. The wire location (coarse position) can be found by determining the wire group with the delay—line position encoding and by knowing which wire produced a signal first. The actual position is found by adding the fine position to the wire position, which is equal to its location times the wire spacing. The delay-line position resolution needs to be accurate enough that the base width of a peak be less than 5 active wire spacings (30 mm). In the case of delay fluctuations a calibration of the delay line readout can be done relative to the nearest active wire to prevent misidentification of the active wire group involved. Diagnostics which may be built in include testing for coarse and fine position linearity, and correct wire identification. Another diagnostic is the calculation of the sum of the two delay line signals which can be used to reject simultaneous events. The sum signal is propor— tional to the delay line length which is well defined. Variations from the true length could be used to reject an event. DESIGN The design problems to be overcome in the MWPC include higher operating voltages caused by the closely spaced 152C wires, the requirement of highly uniform fields and stable gains, and the accurate mechanical placement and tension- ing of the wires. Also, the effects of energy loss fluc- tuations for minimum ionizing particles are enhanced because relatively small segments of the particle track are used to derive the position. An additional and important considera- tion is the electronics and signal processing aspects of this type of device. TIMING CALCULATIONS Energy loss fluctuations were studied by performing a series of Monte Carlo calculations modeling the pulse development at a single wire in the counter. The Monte Carlo calculations were started by modeling the field lines for the geometry involved as in Figure B—U (page 152). An expression [Er72] for the potential produced by an array of wires with diameter d, spacing s, and distance L from the grounded surfaces is V = q £n[sin2(%§) + sin2h(%¥)] (B-6) The coordinate system is centered on a wire with the x direction along the wire plane and the y direction perpen- dicular to it. The charge per unit length q is, 153 q = vO/(2Tin sinh.> 165 Figure B—9. Potentials resulting from the relaxation calculation with the addition of field shap— ing planes. 166 224m... ...monEDm .01... erH ~FWW ....rL wZ> 167 capacitor in Figure B-lOa. The field in the gap is well known and it is also known that if a dielectric is inserted filling a portion of the gap as in Figure B-10b, the elec- tric field in the gap is increased. This increase in the field can be enough to cause an electric breakdown in the gap even if the dielectric has a breakdown field strength higher than that of the field of the gap before the di- electric was inserted. One method of preventing a discharge in the gap is to completely fill the gap with dielectric material. For the construction of the counter, it was important to eliminate gaps between dielectrics and con- ductors which would be prone to discharges. Joints between dielectrics should be normal to the electric field lines rather than parallel with them, and there should be no penetrations through the dielectric materials which could provide paths for surface discharges. Surface discharges may be limited by increasing the path length that the discharge must follow or to use materials which inhibit discharges. The susceptibility of various materials to surface discharge was determined. Different material was placed between parallel plates, with the plates allowed to extend beyond the material so that the edge of the material is parallel to the electric field. To measure surface discharge rate a charge sensitive pre- amplifier is connected to one of the plates. Charge flow- ing along the surface creates current pulses which can be 168 ' ':f:g:4.‘¢. . . . . ' \:‘.~¥¥'-- ........ 3&5“. \\ \ :: 5.5%". _: . . \ x \. .‘._-‘\‘ n‘I‘. - W ‘.‘ ‘ . \é‘ '. \\\I‘\.:b$§ fi?’ (M (W Parallel plate capacitor, a) without and b) with the dielectric material inserted. The electric field in the air-gap increases with the dielectric slab. Figure B—lO. HV TO DISC WIRE Figure B-ll. Schematic of preamplifier used in the‘MWPC. 169 detected and amplified. By scaling the amplified pulses in a multichannel analyzer, results could be obtained which allow the comparison of various materials. The materials G—lO (resin impregnated fiberglass) and teflon had the best resistance to surface discharge. The G—10 has an interesting characteristic of producing a considerable dis- charge rate when the potentials are changed. The dis- charge rate drops to minimal values when the potentials are fixed. It is believed that a surface charging process takes place with the surface charge flowing and establishing uniform fields along the surface of the material. The G-10 was chosen as a principal construction material because it is dimensionally stable and it is relatively easy to fabricate. The adhesive used for construction was a high quality epoxy which could be vacuum-pumped to remove en- trapped gas before use so that the adhesive layers are relatively free of gaps. ELECTRONICS The electronic instrumentation for the MWPC include the active wire readouts, the delay line and termination, high voltage isolation, and the bias network. The timing measurements require the handling of fast pulses. The degradation of the time resolution ultimately results in poorer position resolution. The preamplifier was a 733 170 differential video amplifier whose configuration is de- picted in Figure B-ll (page 168). This device has a DO MHz bandwidth and is designed to have excellent gain stability and low phase shifts. Results of the pulse modeling calculation show that the timing resolution strongly depends on the level at which a discriminator is set relative to the total peak height. This necessitates a stable gain to prevent timing slew and resolution degrada- tion. The wide bandwidth assures that the high frequency portions such as the sharp leading edge of the pulse are not lost. The preamplifier is also compact which leads to simple implementation in the space available. To couple the active wires and delay line to the pre— amplifier requires a device which allows isolation of the high voltage of the wire plane from the preamplifier cir- cuitry. An isolation capacitor is precluded in this device because the high operating voltages used require capacitors to be physically large. The large capacitance values (500 pf) would result in a considerable amount of energy stored in the capacitor bank of 7 capacitors. This stored energy would be detrimental to the preamplifiers and delay line components in the event of electrical breakdowns. Another approach is to use pulse transformers to achieve high voltage isolation. By adequately insulating the primary windings it is possible to use the pulse transformer to obtain very good signal transmission. The 171 turn ratio of the transformer can be adjusted to achieve impedance matching to the delay line. Two types of trans- former geometries were tested, a ferrite pot-core with isolated windings and a toroidal ferrite with the primary windings encased in Teflon tubing. The pot-core geometry illustrated in Figure B—l2 is simple to fabricate. It has reliable voltage isolation since the primary windings are isolated on a bobbin and encapsulated in an insulating material. A disadvantage of the pot-core is its relatively poor frequency response as illustrated in Figure B-l3. The phase portion of the figure shows that the transformer is highly inductive since the voltage-current phase is positive. The frequency response curve is generated by using a network analyzer to measure the ratio and phase dif- ference between the current and voltage. The toroidal geometry illustrated in Figure B—lh has better frequency response characteristics, Figure B-15 because the windings are closely spaced and the ferrite has no gaps. However, the fabrication is more difficult and the high voltage isolation depends on the integrity of the insulating sleeving used to isolate the primary windings. The impedance of a pulse transformer and its load re- sistance are, 2 = N R (B-13) 172 \.l .0 Photograph of a) bobbin and b) pot—core Figure B—12. used to make an isolation pulse trans- former. 173 POT CORE 5:20 Info 780 Q 8 r- .I '71; O ' .I O L Q 8 _ 0.. .. LIJ (I) < I - u 0. -80— 1 1 1l1111l 1 1 1l1111l 1 11111 1 I 111111' 1 1 1|1111| 1 1 111 ..Ifle P a E - : .C - 3 - . - -I 8 mo 2 E 1: < Z .. D - - Lu .. - O. . . 5 1°: ‘2 1 1 1l1111l 1 I 111111I 1 1 11 T 0.1 In 1 FREQUENCY [MHZ] Figure B—l3. Frequency and phase response for pot-core transformer Figure B-lu. Photograph of toroidal pulse transformer used in high voltage isolation. 1714 .oaomo Hmcofip napom mo uoommo on» wcfizocm m>pzo mmcoamou ommco pom mocosoohm .oHIm ohzmfim .mOfipmp coop LmEpommcmpp msoflpm> Low meLoumcmpp mmaso Hmofiomou w you m>p30 mmcoamop mocmsvmnm .mHIm mpsmflm ANIZU >sznowmu GB 2 u ”d dud-j . q 1:.- - q a dud—«d -. . c m4msz30wmu V OS on .— “.9 «Nu ....1q q q _.u.._. a . _...q-4JJ O 3 W a 68. comm 22 mum w I I pbppr b » —:-pb . . r...» p p . .l J I - \ Ow % .2... ‘ 1:1. . 4 1:... . . 6mm. am: 25 Nm 0 .. w4mUzm30mmu 00mm OhZH mfim OHomO 175 where BL is the load impedance and N is the transformer turns ratio. When considering the frequency response of a transformer, the inductance and capacitance introduced by the transformer leads must be considered. The capaci- tance dominates at higher frequencies and changes the load impedance. The delay line impedance was chosen to be 50 Q to avoid the differential non—linearities characteristic of higher impedance delay lines. To terminate the delay line a preamplifier impedance of 8OOS2and a turns ratio of 1:“ was used. This ratio also gives a four-fold voltage step-up and has a predicted impedance of about 50 Ohms. The impedance of the cable joining the preamp to the trans- former becomes approximately 100 Q at high freouencies which results in a very low net impedance (<10 Ohms) at high fre- quencies. The effect of the coupling cable is readily seen in Figure B—l6 showing the impedance and phase for a resistively terminated transformer with and without the coupling cable. Resistive termination has a phase which remains nearly zero. When the coupling cable is added, the termination circuit consists of the reactive impedance due to the cable, and the 780 ohm resistor. The dip in the phase curve above 8 Mhz corresponds to a drop in the impedance. The capacitive impedance of the cable is dominant at this frequency. When the impedance of the cable becomes smaller than that of the resistor the lower im- pedance dominates, creating a net load impedance which is 176 much lower than the expected value. The relation for the impedance was used to estimate the turns ratio with the final turns ratio being determined empirically satisfying the criterion of suitable voltage step-up and a relatively flat frequency response curve over the frequency range of in— terest (Figure B-lS). The pulse transformers used have a turns ratio of 5:7 with a preamp impedance of 110 Q. The pulse transformer windings are wound on the toroid following the winding of a 25 um Teflon film onto the toroid. This film adds some high voltage isolation but its main purpose is to protect the 0.5 mm I.D.,l.OImn O.D. Teflon tubing which encases theCLESmm diameter primary windings. The transformers are vacuum encapsulated using silicone rubber. The resultant transformer network has reliable high voltage isolation and good signal transmission in a compact package. The delay—line consists of nine 1U—pin DIP delay—lines [DaOl] connected sequentially. Each chip has 10 taps with a total delay of 50 nsec and a 50 R impedance. The DIP package is compact and allows considerable flexibility in construction or replacing portions of the delay-line. The high voltage bias supply network is illustrated in Figure B—l7. The 5.6 M9 resistors are for current limita- tion and the two other resistors serve as a divider network to supply the high voltage to the field shaping planes at the top and bottom of the vacuum box. The capacitor Figure B-l7. 177 Schematic of high voltage supply network. 178 .i t didwma O... fillmuw KwLfi—menw mm_>> OH In” meGJQ oziqrm GAME OF! _ J t. dzom 7 m N KEN. mmmzs 0... 2w >I mwhzaoo 104m 520 >I EMHZDOU NEST—.432 179 supplies a signal coupling to ground and must be able to withstand the high voltages used. Its value is chosen by measuring the other coupling capacitances and using a capacitance large enough to ensure good signal collec— tion. Using the expression for the gain of a proportional counter (Equation B-lu), the amplification of the counter for various geometries and wire diameters can be deter- mined. o = - U A [neokpd (B 1 ) where q is the charge per unit length; K is a mobility constant; AV is a gain constant; p is the gas pressure; and d is the wire diameter. The gain is calculated for a single wire in an infinite plane of wires between two grounded conductors. These calcula- tions were done to evaluate the ideal combination of wires to have a low operating voltage with wires that are rela— tively simple to obtain, install and maintain. This calcula- tion is also necessary to determine the operating voltage required to get suitable gains on the active wires with no appreciable gain on the guard wires. Results of the 180 calculations for various wire diameters were found in Table B-2. Smaller diameter wires yield comparable gains at lower operating voltages. The tensile strength and durability decrease with the wire diameter. In addition, the cost increases and availability decreases with decreas- ing size. Problems such as surface non-uniformities and size uniformity become a major consideration for smaller diameter wires. An additional consideration for the wire diameter choices include the transparency of the counter. Table B-2 lists transparencies which are related to the surface area oc- cupied by the wires in relation to the total active area of the counter. This is important when considering the effects on efficiency as particles which strike the wires would be lost. The guard wires are 50 um diameter nickel and the active wires were originally 25 um diameter tung— sten but later replaced by 13 pm diameter double—drawn stainless steel. The smaller diameter stainless steel wire was substituted to obtain lower operating voltages and because the tungsten wire surface tends to have irregul- arities. Rough portions on the wires will produce high field regions resulting in nonuniform gas gains. 181 ca x m mo cfimw opfiz m>Hpow pom popfiscmp mwwpfio>* mam. N-OH x m.m Has H Hmc. :icH x ~.m mHHE m mum. mica x s.m made m cmc. mica x m.m mHHE m mpao> cmmm HHS m. mam. N-OH x 0.: Has H cmm. Mica x c.H mHHE m Hem. :icH x ».m mHHE m 2mm. mica x c.H mHHE m mpHo> mmaw HHE w. mum. mica x c.H mHHE m cwc. mica x N.m mHHE m mmc. mica x m.H mHfiE m mpao> comm Hes H mocohmdwcmpe oapmm :Hmc mpfiz poumEmfio *mwmpao> popoEMaa o>flpo<\caw:c opfi3 cpwzc mpfiz o>apo< mpaz o>fiuo< .mpopoemwc opflz cpmsw ccm o>Hpom m30ahd> pom mofiocopmdwcmpp cam .mOflpmh :Hmw .wommpao> wcflpmpmco mum; m>fipow copmfizoamc .mim magma 182 CONSTRUCTION A side view of the counter is illustrated in Figure B-18. The wire support frame is made of aluminum with G—lO insulation epoxied into place. The circuit boards for the active wire and delay-line connections are epoxied to the top and bottom of the wire support frame. The active wire board contains the matrix network for the connection of every fifth active wire together. The delay-line board contains the sockets for the 1U pin DIP delay—line chips [DaOl] with the necessary interconnections to produce an operating delay line. The wire plane is attached by soldering the wires into place onto pins in the circuit boards. The wire location is maintained by grooves cut into the face of the wire plane support. To insure that the wire plane would be flat and that the wires would be vertical and parallel, the wire plane surface was machined flat and the grooves out following the final assembly of the wire plane support. The active wires are installed individually by soldering while tensioned using weights. The guard wires are installed as pairs, tensioned with weights to insure uniform tension. The front ground plane is produced by mounting a 6 Um aluminized Mylar film onto a G-lO support frame. The frame is held in place against the wire plane support with screws to make disassembly simple. The middle ground plane Figure B-18. 183 /. \\\\\ xi *—-5cm—i Schematic cross section of MWPC. Labeled parts are: A) gas windows, B) ground foil, C) wire plane, D) wire support insulation, E) covers F) active wire matrix circuit board, G) energy loss counter, H) separator foil, I) delay line circuit board, and J) field shaping planes. 18U which separates the multiwire active region from the energy—loss proportional counter is 12 mm aluminum foil. The foil is glued to the frame of the energy-loss portion which is removable to improve the serviceability of the counter. The energy—loss detector is a single wire pro- portional counter using a 25 pm stainless steel wire. This section gives a particle energy-loss signal for particle identification. The outer support and vacuum box is made of aluminum with 12.5 mm aluminum front and back covers with 500 mm by 1“ mm entrance and exit ports. The entrance and exit ports are positioned to allow particles with incident angles of U5 degrees to pass through the detector. The gas windows are 6 pm Mylar held in place on O—rings between the covers and gas box frame. The vacuum box has alignment grooves on its lower surface allowing simple and accurate place- ment in the spectrograph focal plane. Mounting brackets on the back cover allow the attachment of a 50 cm plastic scintillator with light pipe and photomultiplier. Figure B-l9 shows the frontal View of the counter. For maximum utilization of space and to allow the detector to have the active region at the highest possible radius to (ietect maximum rigidity particles, the electronics are installed at one end of the detector vacuum box. The rmeed to minimize the signal degradation requires the pre- anualifiers to be installed as near as possible to the 185 Figure B-19. Photograph showing a portion of the wire plane and the electronics housed in the vacuum box. 186 isolation transformers. The transformer board is attach— ed to the end of the wire plane frame and the high voltage regions were well separated from the grounded surfaces. The fields at the end of the wire plane are shaped by installing successively larger diameter wires near the ends. The preamplifiers are installed on the upper surface of the vacuum box with the lower region containing the high voltage voltage distribution and current limiting circuitry. The high voltage feedthroughs are made of Teflon and use 0- rings to produce a vacuum seal. The preamplifier power and outputs are brought out of the counter using a multi- pin Kovar feedthrough. A schematic of the electronics used, Figure B-20, shows a relatively simple setup. The amplified timing pulses are discriminated and delayed before processing with the time digitizer. The delay is added to guarantee that the sum (fiducial) start signal arrives first to start the time digitizer. The analog signals are processed using standard coincidence electronics and sent to the computer ADC's. The strobe delay module allows the rejection of a trigger event which produces timing pulses but which does not satisfy the coincidence requirements. The strobe delay module clears the time digitizer and the ADC's if a re- quired coincidence signal does not arrive within a fixed time interval following the time digitizer start signal. This decreases deadtimes caused by the computer processing invalid events. 187 Figure B-20. Schematic of electronics used with MWPC. The time digitizer and ADC's are part of a CAMAC system connected to a PDP ll/US com- puter. ax ZOKVOJU>U H n11 CPS—m h 02.2; .35.. 9:26. ”23 >_hu< 188 00¢ ¢332“. .. \ 99 .\ .... IA} 382.; ll mmnhmwad ‘1 $0 3002.? ‘ vowv zoE\ qu>m co \ 20mm kzw>w k Im 50 52 55 60 62 65 67 70 72 75 77 80 82 85 87 90 92 95 97 100 102 105 107 110 112 115 117 120 125 130 135. 1&0. .65 1M” .20 .71 .21 .72 .23 .73 .2" .7“ .2“ .75 .25 .75 .26 .76 .26 .76 .26 .76 .26 .76 .26 .75 .25 .75 .2“ .7“ .2“ .73 .23 .21 .20 18 17 8+ dO/d0 (mb/str) .20758-01 .2616E-01 .1373E-01 .1799E-01 .1u7uE-01 .1369E-01 .73023-02 .82978-02 .h666E-02 .56928-02 .36u1E-02 .7100E-02 .5712E-02 .8750E-02 .56HZE-02 .55828-02 .u837E-02 .NZBHE-OZ .2967E-02 .31H88-02 .3198E-02 .31188-02 .3258E-02 .36008-02 .33798-02 .3359E-02 .2715E-02 .251NE-02 .1871E-02 .246UE-02 .3379E-02 .25758-02 .21u25-02 .17HOE-02 20“ Error (mb/str) .351OE-02 .2856E-02 .32983-02 .1790E-02 .16098-02 .1951E-02 .26255-02 .1267E-02 .2172E-02 .7090E-03 .17u0E-02 .603uE-03 .1358E-02 .9252E-03 .12u7E-02 .73u28-03 .11fl6E-02 .u626E-03 .78qu-03 .3621E-03 .6638E-03 .35208-03 .5632E-03 .31193-03 .3017E-03 .3118E-03 .33193-03 .30178-03 .1911E-03 .2uqu-o3 .2917E-03 .251HE-03 .2213E-03 .2011E-03 205 23"U(p.p) 0+ 0 c.m. do/dQ (mb/str) Error (mb/str) 20.09 .7686E 0“ .231ZE 03 25.11 .2032E OH .6119E 02 30.13 .7291E 03 .2207E 02 35.15 .39u3E 03 .1038E 02 37.66 .26OHE 03 .7879E 01 “0.16 .1859E 03 .5606E 01 "2.67 .1589E 03 .N813E 01 “5.18 .1227E 03 .3712E 01 ”7.69 .7591E 02 .23225 01 50.20 .93855 02 .1BHBE 01 55.21 .191OE 02 .5980E 00 60.22 .23ZBE 02 .7097E 00 65.23 .1971E 02 .60713 00 70.2” .8120E 01 .2577E 00 75.25 .3OH1E 01 .1099E 00 80.25 .91135 01 .1335E 00 85.26 .43985 01 .1u29E 00 90.26 .2567E 01 .82HUE-01 95.26 .89355 00 .9211E-01 100.25 .5918E 00 .2338E-01 105.25 .8193E 00 .3019E-01 110.2“ .7055E 00 .25225-01 115.23 .3788E 00 .15075-01 120.22 .21368 00 .13918-01 125.21 .19738 00 .9717E-02 135.18 .13H6E 00 .6u17E-02 199.65 .6176E-01 ."0008-02 206 23"U(p,p') 2+ 0 c.m. d0/d0 (mb/str) Error (mb/str) 20.09 .909SE 02 .1191E 02 25.11 .2708E 02 .27978 01 30.13 .1576E 02 .1853E 01 35.15 .2HHOE 02 .1106E 01 37.66 .2101E 02 .8966E 00 ”0.16 .11833 02 .511OE 00 92.67 .837HE 01 .99928 00 ”5.18 .5782E 01 ."117E 00 ”7.69 .52788 01 .3229E 00 50.20 .6708E 01 .32808 00 55.21 .6708E 01 .2638E 00 60.22 .39323 01 .15138 00 65.23 .23893 01 .1219E 00 70.2” .313NE 01 .1183E 00 75.25 .2951E 01 .1086E 00 80.25 .19585 01 .57508-01 85.26 .9BOHE 00 .99588-01 90.26 .109BE 01 .91503-01 95.26 .1030E 01 .9725E-01 100.25 .6892E 00 .25593-01 105.25 .“1SHE 00 .2130E-01 110.2” .36598 00 .1568E-01 115.23 .3766E 00 .1511E-01 120.22 .35968 00 .16555-01 125.21 .2356E 00 .98893-02 135.18 .1586E 00 .72198-02 1flfl.65 .1566E 00 .71632-02 23H 30. 35. 37 “0. H2 “5 “7 50. 55 65 70 75 80 85 90 95 100 105 110 115 120 125 135. 1“" U(p.p') .m. 13 15 .66 16 .67 .18 .69 20 .21 .22 .23 .2u .25 .25 .26 .26 .26 .25 .25 .2“ .23 .22 .21 18 .65 ”4' do/dO (mb/str) .1626E 01 .1283E 01 .95528 00 .5833E 00 .8779E 00 .1097E 01 .1118E 01 .1028E 01 .u851E 00 .42695 00 .5505E 00 .N66ZE 00 .2590E 00 .23N9E 00 .2916E 00 .ZOSBE 00 .1H22E 00 .1263E 00 .1296E 00 .109SE 00 .81u0E-01 .7u6flE-01 .58788-01 .5937E-01 .51S6E-01 207 Error (mb/str) .2988E 00 .8989E-01 .87305-01 .55973-01 .65385-01 .59H6E-01 .6560E-01 .52238-01 .32213-01 .2H258-01 .2978E-01 .27955-01 .20563-01 .1H36E-01 .1688E-01 .10215-01 .99228-02 .79633-02 .7993E-02 .6u07E-02 .5290E-02 .17823-02 .3909E-02 .3807E-02 .3706E-02 23"U(p.p') “5. .20 .21 .22 .23 .2“ .25 .25 .26 .26 .26 .25 .25 .2“ .23 .22 .21 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 135. .65 1H“ 18 18 23"U(p 50 60 65 80 85 90 95 100 105 110 115 125 135 11111 .20 55. .22 .23 70. .25 .26 .26 .26 .25 .25 .2” .23 120. .21 .18 .65 21 2h 22 up.) dO/dQ (mb/str) /d 6+ .21135 00 .1003E 00 .8522E-01 .63u9E-01 .59888-01 .9955E-01 .7095E-01 .957uE-01 .3966E-01 .3182E-01 .97378-01 .3786E-01 .28125-01 .2703E-01 .2453E-01 .25868-01 .21515-01 .1998E-01 .1718E-01 8+ (mb/str) .8336E—01 .29153-01 .261uE-01 .1Su6E-01 .20398—01 .1317E-O1 .1863E-01 .1089E-01 .6366E-02 .85698-02 .6559E-02 .6559E-02 .32298-02 .53525-02 .HN78E-02 .28538-02 .3300E-02 208 Error (mb/str) .2315E-01 .1959E-01 .1157E-01 .80725-02 .8915E-02 .7Squ-02 .8397E-02 .5889E-02 .5U02E-02 .3320E-02 .5096E-02 .3706E-02 .3097E-02 .2853E-02 .2660E-02 .2620E-02 .2366E-02 .2031E-02 .2010E-02 Error (mb/str) .1011E-01 .7980E-02 .5N83E-02 .53008-02 .5300E-02 .3372E-02 .u1535-02 .21833—02 .1787E-02 .12188-02 .19723-02 .1371E-02 .91135-03 .11688-02 .98N9E-03 .7513E-03 .8630E-03 236u(p.p) 20 27 37 A2 A7 52 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 1““ .m. .09 25. .62 30. 32. 35. .65 “0. 11 13 6h 15 16 .67 45. .69 50. 18 19 .70 .21 .22 .23 .2“ .2” .25 .25 .25 .25 .25 .2“ .2“ .23 .22 .21 130. 135. 1H0. .65 19 18 16 0+ do/d§2(mb/str) .7291E 0H .1983E 0" .12u5E OH .709OE 03 .8283E 03 .2857E 03 .2333E 03 .192OE 03 .1630E 03 .1127E 03 .7720E 02 .fl180E 02 .2H37E 02 .1758E 02 .217OE 02 .1926E 02 .7803E 01 .2591E 01 .BHOSE 01 .3831E 01 .1993E O1 .6377E 00 .59583 00 .6862E 00 .5986E 00 .3u08E 00 .1560E 00 .1186E 00 .1315E 00 .1195E 00 .597flE-01 .3911E-01 209 Error (mb/str) .2189E 03 .6005E 02 .37988 02 .21803 02 .1292E 02 .8609E 01 .7031E 01 .5770E 01 .u906E 01 .39075 01 .2329E 01 .127OE 01 .79568 00 .SN7BE 00 .668SE 00 .6007E 00 .2H36E 00 .9233E-01 .1089E 00 .12008 00 .6356E-01 .ZUHSE-01 .2072E-01 .2337E-01 .2030E-01 .1289E-01 .6610E-02 .7615E-02 .5863E-02 .5097E-02 .3395E-02 .2369E-02 210 236U(p,p') 2+ 0 c.m do/dQ (mb/str) Error (mb/str) 20.09 .9979E 02 .1291E 02 25.11 .2996E 02 .6565E 01 27.62 .1187E 02 .29523 01 30.13 .1259E 02 .9373E 01 32.69 .1SOOE 02 .8082E 00 35.15 .17528 02 .8919E 00 37.65 .1756E 02 .69923 00 90.16 .1367E 02 .98958 00 92.67 .8911E 01 .3829E 00 95.18 .68928 01 .3663E 00 97.69 .5825E 01 .2996E 00 50.20 .5923E 01 .2619E 00 52.70 .799SE 01 .2623E 00 55.21 .687SE 01 .2993E 00 60.22 .3786E 01 .1863E 00 65.23 .2139E 01 .1938E 00 70.29 .2797E 01 .1092E 00 75.29 .2656E 01 .9592E-01 80.25 .1379E 01 .55325-01 85.25 .87823 00 .3725E-01 90.25 .979SE 00 .3509E-01 95.25 .8936E 00 .31268-01 100.25 .6597E 00 .2903E-01 105.29 .3756E 00 .1962E-01 110.29 .3599E 00 .19218-01 115.23 .3720E 00 .1337E-01 120.22 .29SZE 00 .1092E—01 125.21 .ZOOOE 00 .90993-02 130.19 .1535E 00 .6083E-02 135.18 .1299E 00 .52963-02 190.16 .91913-01 .9002E-02 199.65 .9528E-01 .3932E-02 211 236 U(p.p') 9* 0 c.m. dO/dQ (mb/str) Error (mb/str) 35.15 .9698E 00 .78088-01 37.65 .536ZE 00 .92258-01 90.16 .5659E 00 .3851E-01 92.67 .809OE 00 .9216E-01 95.18 .7856E 00 .6998E-01 97.69 .911OE 00 .9079E-01 50.20 .6263E 00 .9927E-01 52.70 .9557E 00 .29915-01 55.21 .3509E 00 .29158-01 60.22 .3962E 00 .19875-01 65.23 .9926E 00 .2722E-01 70.29 .3397E 00 .18713-01 75.29 .1920E 00 .11618-01 80.25 .1659E 00 .1097E-01 85.25 .2173E 00 .12925-01 90.25 .1603E 00 .7996E-02 95.25 .9089E-01 .63318-02 100.25 .99533-01 .6182E-02 105.29 .1013£ 00 .5077E-02 110.29 .95998-01 .9221E-02 115.23 .77928-01 .38635-02 120.22 .58228—01 .2997E-02 125.21 .91898-01 .23593-02 130.20 .97508-01 .2959E-02 135.18 .9763E-01 .2959E-02 190.16 .33353-01 .1881E-02 199.65 .3131E-01 .18228-02 236 is. u? so 55 60 65 70 75 so 85 9o 95 100 105 110 115 120 125 130 135. 110. 199 236U 55 60 70 75 80 85 90. 95 100 105 110 115 120 125 130 135. 190. 199 U(p,p') 18 .69 .20 .21 .22 .23 .29 .25 .25 .25 .26 .25 .25 .25 .29 .23 .22 .21 .20 18 16 .65 (pt .21 .22 .29 .25 .25 .25 26 .25 .25 .25 .29 .23 .22 .21 .20 18 16 .65 p') do/dQ (mb/str) 6+ .1111E 00 .9836E-01 .8052E-01 .6586E-01 .9079E-01 .28538-01 .9503E-01 .9712E-01 .3098E-01 .1790E-01 .2801E-01 .26358-01 .28538-01 .1561E-01 .2059E-01 .1826E-01 .2132E-01 .1690E-01 .1077E-01 .1318E-01 .10608-01 .76958-02 8+ (mb/str) .1062E-01 .5286E-02 .22908-02 .9938E-02 .5903E-02 .12908-01 .5799E—02 .1692E-02 .36398-02 .2598E-02 .2827E-02 .29773-02 .2280E-02 .2051E-02 .12398-02 .2320E-02 .1593E-02 .5575E-03 Error (mb/str) .1699E-01 .1257E-01 .11528-01 .9109E-02 .7118E-02 .7138E-02 .6560E-02 .5709E-02 .9131E-02 .3006E-02 .2797E-02 .23898-02 .2698E-02 .1662E-02 .15933-02 .1513E-02 .16238-02 .1359E-02 .10158-02 .11358-02 .9656E-03 .92588-03 Error (mb/str) .9500E-02 .3915E-02 .1921E-02 .22905-02 .23795-02 .27183-02 .1339E-02 .62723-03 .92583-03 .6869E-03 .5973E-03 .6172E-03 .5276E-03 .9679E-03 .9181E-03 .9679E-03 .37833-03 .2989E-03 213 2380(p,p) 0+ 6 c.m. do/dO (mb/str) Error (mb/str) 20.09 .6701E 09 .2031E 03 22.60 .3557E 09 .1068E 03 25.11 .1875E 09 .5669E 02 27.62 .1103E 09 .3315E 02 30.13 .6606E 03 .1990E 02 32.63 .9181E 03 .1259E 02 35.19 .2890E 03 .867SE 01 37.65 .226BE 03 .6836E 01 90.16 .1859E 03 .55BOE 01 92.67 .193ZE 03 .9321E 01 95.18 .1078E 03 .3238E 01 97.69 .6890E 02 .2067E 01 50.19 .3751E 02 .113OE 01 52.70 .2336E 02 .71OZE 00 55.21 .1791E 02 .5259E 00 57.71 .1908E 02 .5815E 00 60.22 .2119E 02 .6371E 00 62.72 .1921E 02 .5811E 00 65.2 .159SE 02 .9816E 00 67.73 .11133 02 .3356E 00 70.29 .5860E 01 .178SE 00 72.79 .3268E O1 .1026E 00 75.29 .2108E 01 .6569E-01 77.75 .25OOE 01 .78075-01 80.25 .3083E 01 .9986E-01 82.75 .3988E 01 .1062E 00 85.25 .3157E 01 .9706E-01 87.75 .2996E 01 .76158-01 90.25 .1538E 01 .98988-01 92.75 .9535E 00 .2997E-01 95.25 .5079E 00 .1716E-01 97.75 .9082E 00 .13508-01 100.25 .9353E 00 .19693-01 102.75 .5380E 00 .1783E-01 105.29 .5959E 00 .1953E-01 107.79 .5931E 00 .19085-01 110.29 .9835E 00 .1529E-C1 112.73 .3658E 00 .12076-01 115.23 .2903? 00 .79808-02 117.72 .1711fi 00 . 250t-02 120.22 .1173E 00 .3810E-02 125.21 .1119E 00 .9610E-02 130.19 .1091E 00 .9780E-02 135.18 .9938E-01 .3990E-02 190.16 .63895-01 .37508-02 199.65 .90758—01 .21508-02 219 2380(p,p') 2+ 0 c.m dI/dO (mb/str) Error (mb/str) 20.09 .6059E 02 .63223 01 22.60 .99308 02 .2573E 01 25.11 .2939E 02 .1883E 01 27.62 .1667E 02 .1835E 01 30.13 .1521E 02 .699ZE 00 32.63 .1691E 02 .91ZZE 00 35.19 .2197E 02 .65278 00 37.65 .1787E 02 .6886E 00 90.16 .1509E 02 .95588 00 92.67 .8529E 01 .5281E 00 95.18 .6677E 01 .2092E 00 97.69 .5602E 01 .2970E 00 50.19 .6882E 01 .2109E 00 52.70 .8023E 01 .2513E 00 55.21 .699ZE 01 .2129E 00 57.71 .5559E 01 .19583 00 60.22 .3782E 01 .1169E 00 62.72 .2362E 01 .1009E 00 65.23 .22SOE 01 .7098E-01 67.73 .2529E 01 .8109E-01 70.29 .2865E 01 .8862E-01 72.79 .2888E 01 .9176E-01 75.29 .2905E O1 .7959E-01 77.75 .19728 01 .63058-01 80.25 .1270E 01 .90973-01 82.75 .97638 00 .39508-01 85.25 .8599E 00 .2797E-01 87.75 .899ZE 00 .2888E-01 90.25 .9776E 00 .3096E-01 92.75 .1002E 01 .31383—01 95.25 .887OE 00 .28578-01 97.75 .779OE 00 .23973-01 100.25 .57358 00 .18868-01 102.75 .95828 00 .15708-01 105.29 .369SE 00 .1259E-01 107.79 .3198E 00 .1189E-01 110.29 .3328E 00 .1093E-01 112.73 .3959E 00 .1131E-01 115.23 .3918E 00 .1097E-01 117.72 .3138E 00 .1029E-01 120.22 .27OOE 00 .8360E-02 125.21 .1959E 00 .6800E-02 130.19 .156SE 00 .5990E—02 135.18 .1289E 00 .9630E-02 190.16 .1218E 00 .9860E-02 199.65 .1189E 00 .9290E-02 215 238U(p,p') u+ 0 c.m. do/dQ (mb/str) Error (mb/str) 30.13 .1997E 01 .1593E 00 32.63 .7517E 00 .1153E 00 35.15 .623OE 00 .5119E-01 37.65 .3691E 00 .5276E-01 90.16 .5299E 00 .25288-(1 92.67 .6766E 00 .3858E-01 95.18 .7070E 00 .27073-01 97.69 .676ZE 00 .33888-01 50.19 .5006E 00 .19908-01 52.70 .9011E 00 .20308-01 55.21 .2992E 00 .1016E-01 57.71 .229SE 00 .1950E-01 60.22 .3101E 00 .11968-01 62.72 .3561E 00 .18563-01 65.23 .9075E 00 .19968-01 67.73 .3953E 00 .11938-01 70.29 .2602E 00 .1017E-01 72.79 .1732E 00 .7170E-02 75.29 .1939E 00 .63008-02 77.75 .191OE 00 .5850E-02 80.25 .1679E 00 .70603-02 82.75 .1765E 00 .65908-02 85.25 .1873E 00 .76908-02 87.75 .1717E 00 .63703-02 90.25 .19OSE 00 .50308-02 92.75 .1119E 00 .909OE-02 95.25 .7790E-01 .3870E-02 97.75 .7836E-01 .29808-02 100.25 .77853-01 .36808-02 102.75 .89733-01 .37203-02 105.29 .8921E-01 .38903-02 107.79 .88255-01 .36508-02 110.29 .82208-01 .3290E-02 112.73 .7397E-01 .31203-02 115.23 .5910E-01 .29005-02 117.72 .5019E-01 .20503-02 120.22 .9973E-01 .1590E-02 125.21 .9799E-01 .2090E-02 130.19 .98315-01 .2120E-02 135.18 .9909E-01 .19908-02 190.16 .9039E-01 .18108-02 199.65 .35923-01 .16508-02 216 2380(p.p') 6* 0 c.m. dO/dQ (mb/str) Error (mb/str) 90.16 .9201E-01 .88305-02 92.67 .86895-01 .75008-02 95.18 .92758-01 .1711E-01 97.69 .1153E 00 .88208-02 50.19 .8691E-01 .6620E-02 52.70 .7515E-01 .7000E-02 55.21 .9616E-01 .3270E-02 57.71 .33095-01 .3250E-02 60.22 .3116E-01 .2390E-02 62.72 .27998-01 .3010E-02 65.23 .9396E-01 .3120E-02 67.73 .37908-01 .2120E-02 70.29 .51653-01 .3290E-02 72.79 .9868E-01 .2670E-02 75.29 .5035E-01 .3120E-02 77.75 .36858-01 .2350E-02 80.25 .33765-01 .2950E-02 82.75 .2315E-01 .15103-02 85.25 .23388-01 .19805-02 87.75 .26128-01 .1630E-02 90.25 .2685E-01 .12905-02 92.75 .30705-01 .15103-02 95.25 .29878-01 .2110E-02 97.75 .26813-01 .13003-02 100.25 .1967E-01 .15508-02 102.75 .1821E-01 .1160E-02 105.29 .1651E-01 .1900E-02 107.79 .15253-01 .119OE-02 110.29 .1923E-01 .91008-03 112.73 .15558-01 .92008-03 115.23 .1537E-01 .95003—03 117.72 .1797E-01 .9300E-03 120.22 .1575E-01 .6800E-03 125.21 .1379E-01 .9300E-03 130.19 .1161E-01 .89008-03 135.18 .1119E-01 .8200E-03 190.16 .13293-01 .87008-03 199.65 .12323-01 .82003-03 238 95. 97 50. 52 55. 57 60 62 65 67 70 72 75. 77 80 82 85 87 90 92 95 97 100 102 105 107 110 112 115 117 120 125 130. 135. 190. 199 U(p.p') .01. 18 .69 19 .70 21 .71 .22 .73 .23 .73 .29 .79 21 .75 .25 .75 .25 .75 .25 .75 .25 .75 .25 .75 .29 .79 .29 .73 .23 .73 .22 .21 19 18 16 .65 8+ do/dQ (mb/str) .2075E-01 .1796E-01 .2699E-01 .1293E-01 .13903-01 .8970E-02 .6290E-02 .9910E-02 .7990E-02 .61003-02 .8160E-02 .6510E-02 .1079E-01 .71003-02 .9260E-02 .7520E-02 .59908-02 .3900E-02 .35908-02 .29308-02 .27203-02 .32705-02 .2250E-02 .35103-02 .2720E-02 .2990E-02 .2290E-02 .2160E-02 .2910E-02 .29708-02 .1870E-02 .221OE-02 .2980E-02 .1870E-02 .20008-02 .1980E-02 217 Error (mb/str) .9320E-02 .3690E-02 .9570E-02 .3060E-02 .16508-02 .1780E-02 .1090E-02 .17808-02 .1190E-02 .8300E-03 .1180E-02 .8900E-03 .1300E-02 .98008-03 .1200E-02 .81005-03 .9100E-03 .62008-03 .73003-03 .37008-03 .58008-03 .39008-03 .99008-03 .97005-03 .59008-03 .9800E-03 .33008-03 .3100E-03 .3900E—03 .3100E-03 .18008-03 .3900E-03 .3600E-03 .3200E-03 .3100E-03 .2600E-03 REFERENCES [Ba79] [Bc792 [Be68] [Be69] [Be73] [Be77] [Bk76] [B171] [Br79] [Ch70] [00591 [C076] [DaOl] [Da76] [Dv78] REFERENCES G. 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