ENELASTEC PROTON SCATTERENG F ROM 48CA THESIS FOR THE DEGREE OF PHD. MICHIGAN STATE UNIVERSITY CARL JEROME MAGGIORE 1971 This is to certify that the thesis entitled INELASTIC PROTON SCATTERING FROM 48CA presented by Carl Jerome Maggiore has been accepted towards fulfillment of the requirements for Ph. D degree in Phxsics (59%sz “(/ijEW Major profes( Date ”73/37, /¥/ / . 0-169 LIBRARY Michigan State University ABSTRACT INELASTIC PROTON SCATTERING FROM 48m By Carl Jerome Maggiore Inelastic proton scattering from the nucleus 48Ca has been per- formed at four energies: 25.11, 29.83, 35.00, and 40.21 MBV, using the proton beam from the MSU sector-focused cyclotron. Cross sections were taken every five degrees from 130 to 1000 with Ge(Li) counters fabricated at this laboratory.. The overall resolution obtained was less than 30 Rev at all energies. The elastic scattering from 48Ca was compared with the elastic scattering from 4003 using the optical model. It was found that the relative matter distributions are in agreement with the predictions of the A1/3 law The inelastic scattering revealed several previously unreported excited states in 48Ca. Angular momentum transfers for most of the states were obtained by comparison of the shapes of the angular dis- tributions to those of known L. Where possible, spin assignments are inferred on the basis of this and other data. The experimental angular distributions are compared with calcu- lated distributions using the collective model distorted wave Born approximation. The nuclear deformations obtained are used to calcu- late the vibrational model parameters and the reduced transition probabilities. The results are compared with previous inelastic alpha scattering experiments and inelastic electron scattering results. The energy dependence of the results and the sensitivity of the deformations to the optical model parameters were studied. INELASTIC PROTON SCATTERING FROM 48CA By Carl Jerome Maggiore A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1971 For Jan 11 ACKNOWLEDGEMENTS I would like to give special thanks to Charles Gruhn, my advisor, for his patient and unlimited willingness to help throughout the last four years. I am unable to adequetely express the debt of gratitude that I owe him. Special thanks are also due to Barry Freedom for help with the calculations, the data taking, and being there when needed. To Thomas Kuo who worked closely with me throughout the experiment many thanks are due. Without him the work could not have been done. And for help and understanding in the non-technical aspects of this work my deepest thanks to my parents and my wife, Jan. iii TABLE OF CONTENTS Acknowledgments List of Tables List of Figures 1. Introduction 2. Experimental Procedures 2.1 2.2 2.3 2.4 2.5 2.6 3. Data 3.1 3.2 3.3 3.4 Modifications to the Goniometer Target Storage System Cyclotron and Beam Transport Detectors Electronics Data Acquisition Analysis Angle Calibration Normalization Excitation Energies Cross Sections 4. Optical Model Studies 4.1 4.2 Optical Model for DWBA Calculations Optical Model Difference between 40Ca and 48C3 5. Theoretical Analysis 5.1 5.2 DWBA Theory Collective Model iv iii vi vii iii iii iv vi ix xi xviii xviii xix xxii XXV xxvi xxvi xxxi xlvi xlvi xlix 5.3 Vibrational MOdel 5.4 Calculations Results 030305030505 05¢".th 6. .l 7 States below 5 MeV States between 5 and 6 MeV States between 6 and 7 MEV States between 7 and 8 MeV States between 8 and 9 MeV Summary Comparison with Theory Bibliography Appendices I. II. Detector Fabrication and Testing HHHHHH 0|.wa .1 .6 Choice of Ge(Li) Fabrication Packaging Testing Radiation Damage Other Ge(Li) Detectors Experimental Data II.1 Theoretical Angular Distributions II II. II II. .2 3 .4 5 Plotted Angular Distributions Tabulated Angular Distributions Tabulated Nuclear Deformations Quantities Calculated from the Nuclear Deformations liii 1x 1x 1xvi 1xviii lxxiii lxxiv lxxviii lxxxii lxxxiv lxxxvii lxxxvii lxxxviii xcii xcv xcvii ciii cviii cviii cxiii cxliv clxxvi clxxxi o: N #9903 (ONO-'60 LIST OF TABLES Contributions to the energy resolution Isotopic analysis of the target Contributions to the uncertainty in absolute normalization Excitation energies of 48Ca Fricke's average optical parameters Potential well depths using Fricke geometry Potential well depths with equal real and imaginary geometries Differences in the optical model parameters for 480a and 400a Upper limits on the 0+ cross sections Comparison of the nuclear deformations Contributions to the energy resolution vi xiii xxi xxi xxiv xxvii xxviii xxviii xxxviii 1xvii lxxxi C .b 05650505030501010101 pnhhpaopopwwmwmw COQQOSU'AODNHOSUIkWNI-J caansEoEoLisbioi—a H O .11 LIST OF FIGURES Cyclotron and beam layout Ge(Li) electronics Typical 25 mev spectrum Typical 30 mev spectrum Typical 35 MeV spectrum Typical 40 MéV spectrum Optical model fit with R = I geometry Optical model fit with Fricke geometry 40 MeV X‘surface 35 MeV 1 :surface 30 MeV 2' surface 25 MeV Xturface Ratio of elastic angular distributions Optical model radii with Usym=o Optical model radii with Usym= 4.4 MeV Optical model radii with "syn: o and unequal geometries Optical model radii wirh Usym= 4.4 MeV and unequal geometries DWBA calculations for L = 2 states DWBA calculations for L = 3 states DWBA calculations for L = 4 states DWVA calculations for L = 5 states Comparison of 48Ca and 50Ti Comparison of 48Ca and 52Cr L = 3 states L = 5 states L = 4 states Comparison with other experiments vii vii xii xiv xv xvi xvii xxix xxxiv xxxx xxxvi xxxvii xl xli xlii xliii xliv lv lvi lvii lviii 1xi lxii lxv lxix lxxi lxxix 2. Experimentally determined F3 lxxx Surface barrier geometry xc Detector mount xciii Slit scattering xciv 137Cs spectrum xcvi Alpha particle spectra xxviii Proton resolution at 40 MeV xcix Proton radiation damage cii Relative efficiency curve cvi viii l. INTRUJUCTION 48Ca is a doubly closed shell nucleus and is used as the core for a large number of nuclei in the f region of the periodic 48 7/2 table. {elatively little work has been done on Ca because of the difficulty obtaining targets.* Inelastic alpha scattering performed at 42 MeV (Pe 65) and 31.5 MeV (Li 67) has identified the spins and parities of the strongly excited states, but the resolu— tion of ”"100 keV is not able to resolve many of the weak or high lying states. The 46Ca (t,p)48Ca reaction has been used to study the level structure of 48Ca (Bj 67) and detects a large number of levels, but the experiment was only able to positively identify the 0+ levels in 48C3. Inelastic proton scattering is able to identify angular momentum transfer reasonably well if the data are clean, and has the advantage of being a useful probe of the microscopic struc— ture (Cl 66). Therefore the present experiment involving inelastic proton scattering was undertaken. The ability of the (p,p') reaction to identify angular momentum transfer increases as the incident beam energy increases, also the direct reaction theory is expected to be more correct at higher energies where compound nuclear effects are small. The experiment was performed at four energies to check the consistency of the DWBA * 48Ca is a stable nucleus, but constitutes only 0.18% of the natural abundance of Ca. method of analysis and the collective model calculations. The experiment was performed with Ge(Li) counters because these detectors are able to give 30 keV resolution at 40 MeV, and they have the dynamic range needed to obtain the data in a reasonable period of time. A magnet spectrograph can yield better resolution, but at the time was not available. Stacks of Si(Li) counters, while able to detect 40 MeV protons, cannot do so with 30 keV resolution and clean valleys. The experiment was performed with the goniometer of Ken Thompson (Th 69), which was designed specifically for use with Ge(Li) detectors. The detectors were fabricated in this laboratory. A discussion of the fabrication techniques is presented in Appendix I. 2. EXPERIMENTAL PROCEDURE 2.1 Modifications to the Coniometer In order to obtain the data for this experiment in a ”reasonable” period of time it was decided that a detection system that would allow simultaneous data taking at two angles was needed. Other requirements were that small angle data into 15° be taken, and that the only windows the scattered protons traverse be the 1/4 mil aluminized mylar windows on the detector cryostats. Therefore it was necessary to design a new- 16" larget chamber with a sliding seal for use with the goniometer (Th 69). The modular design of the goniometer makes it particularly con- venient for modification to particular experimental requirements. The details of the 16” target chamber are shown on MSUCL drawing HA—llO— 901—H. The basic design calls for input and exit ports compatible with the taped beam pipe and slip-fit O—ring seals used previously. The data taking window extends from 10° to 110°. There are two view- ing ports opposite the data taking window that extend from 20° to 70° and from 110° to 160°. There is also a fixed Leybold fitting at 90° on this side of the chamber. 0n the data taking side of the chamber, there are two BNC feed throughs at 145° and 155°, and another Leybold fitting at 135°. This particular design allows data to be taken from about 12° to 110°. If one wants to take data at scattering angles larger than 110° the chamber may be rotated 180° and data taken from 70° to 170°. The monitor counter may be set on the secondary arm at any angle to view the beam through the monitor ports or at either of the fixed Leybold fittings. The sliding seal is composed of a 1/8” O—ring inset in the chamber and a sliding steel strap made of 9 mil shimstock. Pressure sensitive teflon tape was applied to the chamber and the clamping ring to provide a smooth non~stick surface for the steel strap. In practice it was necessary to glue the O—ring into the groove in the chamber to prevent movement of the O-ring when the steel strap was moved. In addition the strap and Owring were well lubricated with Dow Corning silicone high vacuum grease. No particular problems were encountered with the sliding seal in use as long as it was kept clean and lubricated. The vacuum feed throughs to the detector cryostat caps were short sections of 3/4" copper tubing. The tubing was soldered into a brass block which was in turn soldered to the steel strap. The cryostat caps were coupled to the copper tubing using a simple O-ring slip fitting. To provide the counter torque needed when the sliding seal is in motion, the target chamber was rigidly attached to a quadrapole support stand with a l" X 5” aluminum arm. This same quadrapole support stand, which was bolted to the floor, was used to support the vacuum diffusion pump for the goniometer. 2.2 Target Storage System The target used in this experiment was relatively expensive and it would oxidize completely if exposed to the atmosphere for a few hours. Therefore, it was necessary to design and build a vacuum storage system for the target. The goniometer was initially designed with a target transfer lock which could be used to transfer a target into the target chamber without breaking vacuum (Th 69), therefore the target storage system was designed to be compatible with the transfer unit of the goniometer. A modular design consisting of three basic units was used. A cryogenic pumping system with three ports, a transfer valve, and a storage chamber are the three basic units. The details for the target storage system are shown on MSUCL drawings HA—ll4—lOO-F to HA—114—106-F. The cryogenic pumping system is based on a Linde LD—lO cryosorption pump attached to three NRC 1253-1 1/8” valves which are coupled to the standard 4" Marmon flanges. A cryosorption pump was used because a system was needed which was independent of probable university—wide power failures. While it is true that the pump must always be kept at liquid nitrogen temperature, it was not felt that this was a particular disadvantage, since the detectors also had to be stored at liquid nitrogen temperature and could be kept at the same dewar. The second unit in the storage system is the storage-transfer valve. This is a vacuum valve which has 4” Harmon flanges on both sides, can hold a vacuum on either side, and is wide enough to allow passage of a 1 1/4" target frame in the open position. The third unit is the storage chamber itself which is merely an aluminum chamber with a lucite window and a target holder. To make a target transfer from the storage system to the gonioneter the portable storage system is moved out to the experimental area near the goniometer. The storage valve is closed and the storage chamber and valve removed from the cryosorption pump. The transfer unit (Th 69) is attached to the storage valve and then evacuated. The valve is Opened and the target moved into the transfer unit. The valve is closed and the storage chamber is removed from the valve. The trans- fer unit with the target is now attached to the goniometer. When the goniometer is evacuated, the transfer valve is Opened and the target is transferred to the target ladder of the goniometer. The complete transfer in vacuum requires about 45 minutes. 2.3 Cyclotron and Beam Transport The Michigan State University sector—focused cyclotron (Bl 66) was used to produce the proton beams used in this experiment. The machine is a variable energy, isochronous cyclotron utilizing an electrostatic deflector and magnetic channel for single turn extrac— tion. The experiment was performed with an internal beam of l to 5 microamps. The extraction efficiency varied from 70% to 100%. The beam current on target was varied from 3 to 90 nanoamps depending on the scattering angle. The extracted beam is focused and energy analysed by the beam transport system shown in Figure 2.1. The two horizontal bending magnets, M1 and H2, are used to center the beam on the object slit, 31, and to align the beam parallel to the beam pipe axis. The quadra- pole doublets, 01 and Q2, are used to focus the beam on slit 81. The divergence of the beam is defined by slits 51 and 82 which are separated Y\\\\\\\l oumim oz< nine 2 m o .534) zomkouo>o \\\\\\\\\: x x 3 \ \ \ \ \ \ 3.. no -Qfitt-‘ r—ri , i *7" Cyclotron and bean layout. Figure 2.1 by 48 inches. M3 and M4 are two 45° bending magnets which are the primary elements of the analysis system. The quadrapole doublet Q3 focuses the beam on slit S3. M5 is another 45° bending magnet which deflects the beam into the goniometer. The quadrapole doublets Q4 and Q5 focus the beam onto the target. More complete descriptions of the properties of the energy analysis system have been published elsewhere (Ma 67) (Sn 67). During this experiment the slits 81 and S3 were set at 15 mils for energy resolution of 10 keV. 82 was set at 100 mils to yield a beam divergence oftt2 mrad. For the final beam preparation a scintillator with a 1/8 inch hole in the center was inserted in the target ladder of the gonio— meter. The beam spot was viewed with a television camera to check for proper focus and centering. In addition a tantalum ring, R1, with a 1/2 inch hole was located 16 inches in front of the target on the beam axis. The beam current on this ring was monitored through- out the experiment. The criteria used to insure prOper alignment of the beam were: a well focused and centered beam on the scintillator, minimum current on the ring, maximum current in the Faraday cup, and minimum neutron background in the experimental room. During the experiment the beam spot on target was approximately 1/16 inch wide and 3/8 inches high. The current on the ring was always less than 1% of the beam dumped in the Faraday cup and was usually 0.1% or less. The current on the ring was probably due to slit scattering from S3. The neutron background in the experimental area provided a very sensitive test of the alignment of the beam into the goniometer. If the beam scraped the beam pipe, the input snout, or the exit snout it would increase the neutron background by 2 or 3 orders of magnitude. The Faraday cup used in this experiment is actually only a shielded beam dump and as such was not intended to measure absolute charge accurately. A 12 foot section of beam pipe, insulated from the goniometer by a Delrin spacer, with a 1/2 inch thick aluminum cap was used. It was surrounded by concrete and parrafin shielding described elsewhere (Th 69a) to reduce the neutron background seen by the detectors. The Faraday cup was in contact with the parrafin and concrete shielding blocks and was probably subject to some leakage current to ground. The Faraday cup was connected to an Ortec model 439 current digitizer used with an Ortec model 430 sealer to integrate the charge. The current digitizer outputs a logic pulse for every 10"10 Coulomb of integrated charge. This logic pulse is then fed into the scaler to record the total integrated charge. This arrangement provided relative numbers for the total incident charge for each run; these numbers were used as a check on the monitor counter which was used for the actual normalization. 2.4 Detectors The detectors used in this experiment were lithium drifted germa- nium counters of the surface barrier geometry designed specifically for this experiment. (See Appendix I) The two detectors were 10 separated by l4.6°. The small angle counter was 13.25 inches from the target and had a final 30 mil Ta collimator that was 6.6 mm high and 2.2 mm wide. The large angle counter was 11.25 inches from the target and had a final 30 mil Ta collimator that was 6.2 mm high and 2.2 mm wide. The two detectors were operated at 1500 V and 1200 V bias respectively with leakage currents of less than 0.1 na. The monitor counter used in this experiment was also of the Ge (Li) type, but since Optimum resolution was not required, it was used in the side entry geometry. The detector was mounted in a Harshaw cryostat of the "sausage" type (Model 15). The monitor counter was mounted at a fixed angle on the secondary arm of the goniometer. The protons scattered into the monitor counter traversed an air space of about 1/2 inch between the 1/2 mil Kapton window on the target chamber of the goniometer and the 1/4 mil aluminized mylar window on the cryostat. 2.5 Electronics The electronic equipment used in this experiment is shown in Figure 2.2. At the time the experiment was performed, it was neces— sary to use rather unconventional arrangement of the electronics to obtain acceptable resolution. It was our experience that with commercially available electronics, after amplification to the required 5 to 10 volt output signal, the rms noise level would be 3 to 4 mV, thus yielding a precision of 0.04% to 0.06% in the voltage measurement. At 40 MeV this corresponds to a contribution of 16 to 24 keV to the overall resolution. This was not acceptable. 11 It was found that by using a modified Ortec 109A preamplifier and the second stage of the Tennelec TC200 amplifier, the total electronic noise as measured with a Canberra stabilized pulser (Model 1501) was less than 6 keV at 40 MeV. The outputs of the amplifiers were fed into two Northern Scientific NS 629 analog-to— digital converters. The ADCs were interfaced to a Sigma 7 computer which was used to store the data. The ADCs were set to provide 8192 channel conversion gain. Only the upper 4096 channels of information were stored by using the 4096 channel digital offset. Using this configuration spectra were Obtained with about 5 keV per channel. Conventional electronics were used with the monitor counter: Ortec 109A preamplifier, Ortec 410 linear amplifier, Ortec biased amplifier and into a Nuclear Data 160 multichannel analyser. To make the dead time corrections two Ortec 420 single channel analysers were used. A window was set on the elastic peak from the monitor counter; the output of the single channel analyser was used to feed an Ortec 430 scaler and the channel zero of each NS 629 ADC. The Ortec 416 gate and delay generator was used to provide proper pulse shaping for the ADCs. The dead time correction was made by comparing the number of counts in the scaler with the number of counts in channel zero. A similar arrangment was used to make the dead time corrections for the monitor counter. The dead times through- out the experiment were always less than 5%. 2.6 Data quuisition The data were acquired during two three day runs. Data for >3... ow .6 $90.0 ”3.5.626 .6 8.3095 .83»... 83x a...» Son Ema .<.I.n. omkmo .wo.;< .m .02. an uoEuoEt. Figure 2.2 Ge(Li) electronics. on? a 022....» omEo 053 com o» woe <8. H *au...:ooa on? : QE< .— dE< 9:8 . _ a...» a... 885 . a 8.62% 2460. to. onSBmE 15 each energy were taken at 20 angles in 5° steps from about 13° to 100°. The data at 28° and 73° were taken twice, once with each put in position for aligning the beam at the next energy. The counters were removed during the alignment procedure to prevent radiation damage from the neutron background. The resolution obtained during this experiment was between 25 and 30 keV (FWHM). The contributions to this energy resolution are listed in Table 2.1. Notice that the straggling contributions from the windows add directly rather than an quadrature, and they are the largest contribution to the energy resolution. Table 2.1 Contributions to the energy resolution Source A E (keV) A 122 (keV2 ) Electronics 6.0 36 Ion pair statistics 6.2 39 Nuclear collisions 0.7 Straggling Target 5 Package window 5.3 18.3 337 Detector window 8 _j; Beam 10 100 Kinematics 10 100 Total 2475 602 Representative spectra at each energy are shown in Figures 2.2 — 2.5. +2 OEB’E . (9) 693'? (a) sea 9 _£ 299-; -9 cats 9 “0‘9 +9 99C? +932 299'9 v . (9)999'9 .( )gets (9 3,6007. (9) now. °z° '1 a“ m m z. Illll llll I I 'U a Q v (9) 99's ‘ , , mean (t t) 899 8 g sore (VS) ass-e 05 04 .22 “g '92 ‘5? I ‘IHNNVHQ 33d 8m...) ._—__~# ’ - V K -i - .-_._—.____~ .~._— MSU CYC 3000 2500 CHANNEL NUMBER l000 500 15 'F" OZ 2 (tr) '9 (9) (2) 962's -9 '9 9 *9 ’17"? m '9 (9) 999 (we) ( E ) IOVL IZQ'L v) (9‘; ) (E) O..— OEB'E 2000 |||||||| l | NIH NH | 03" M 3m- ‘1 I1“- hum! l1 I1 2500 “NI Dam-L CHANNEL NUMBER 0 3 l | I500 89'3 — 1 l0 9 lNOO — 1 IDOL—1.. - l N 9 WBNNVHO 83d SlNflOO ..__.___.—___ __._._ __ _ 7 --__..._._.-‘__F_ ..______.__._.. _ 3000 I000 50 RGU CYC F igure 2.4 Typical 30 Mev spectrum. l6 (.0155— O..- Y 3000 I III I - I I I I II IIIIIIII III III 03 oz 029's — ”1 'E 209'? —— (1711.091? —— 3m- 13) 33%? —_ ._ x (Z) 862'9 -g 3991; —— b -9 cars — 9 8609 —— ‘b 922'9 —-— '17"Z 3’9'9 —— (”981.9 — (V ' Z) 6001 — (9) 9889 H. '- 89'2 — l0° IO..- “I 9 IO‘ - IO° - '1 bl 1/ H_Q_§EIEi__§J-.NDO9_._ _ —_,_._. m _-._. - ._ 2500 2000 I500 I000 3 00 MSU CYC CHANNEL NUMBER Figure 2.5 Typical 35 Mev spectrum. (.0159— (9) Itl‘S ' (Z) 862‘9 l7 O..- ‘Z 098'2 — '9 209$.— It) [.0917 --- (9) 6???— '€ 3929—- “9 £223 — S 960'9 -— 99 9229— .952 3’9'9— (91981'9 — (s) 9999 (V2) 6007. : J i 3000 IIII _ -,, _ . ou— btuvz “”Egéaas 4; even.— ‘I 9 war— tmm— T (9 ma ' = . . mecca: (vs 8998 -9 99m_ wunmme-' I 1- :r o o.- %) O 03» 89.2 — e 2 s 8 N ‘3’ O 8 v“’ In I 1 I l V n N '- 9 <3 o C) S _ IIBNNVHO 83d SlNIIOO IO" l500 2000 2500 CHANNEL NUMBER |000 5’10 MSU CYC Figyre 2.6 Typical 40 Mev spectrum. 3. DATA ANALYSIS In this experiment the relative cross sections were measured using a monitor counter for normalization. The absolute cross 40 sections were obtained by normalizing the Ca elastic scattering, Observed at large angles, to previous work and using the ratio of isotopic abundances in the target (c.f. Sec. 3.2). The use of a monitor counter at a fixed angle to provide the relative normalization for each run eliminated the need to know the exact areal density of the target, solid angles of the detectors, target angle, and total incident charge. The relative normalization between the two detectors used in this experiment was determined by taking data at a number of overlap angles. Dead time corrections were made for both detector ADC's as well as the monitor counter ADC. 3.1 Angle Calibration The program, PEAKSTRIP, written by R. A. Paddock, was used to Obtain the centroid, net counts, and statistical error in the counts for each peak in the spectrum. The input consisted of the two channel numbers, defining the edges of each peak, and the backgrounds at these boundary channels. A linear background is assumed under the peak. If there were more than 30 counts in the peak, the centroid was determined using the top two-thirds of the peak; otherwise the total peak was used. 18 19 The fractional standard error for the counts in each peak was determined by the formula where N is the total number of counts and B is the total background count. To determine the scattering angle for each spectrum the computer program, ANGCAL, was written. The program input consists of the centroids of three uncontaminated peaks, one of which is moving kine— matically faster than the other two. The two slowly moving peaks are used for energy calibration, the third peak is used to determine the angle. An initial guess is made for the angle, and then, through an iterative procedure, the actual scattering angle is determined. The process usually converges within four iterations. Relativistic kine- matics, calculated by the program KIND, written by P. J. Plauger, are 120 was used used throughout. Typically elastic scattering from H or for the fast moving peak, and the ground state and known excited states of 480a (Ma 66) (Bj 67) were used for the kinematically slow moving peaks. The angle calibration determined by the above procedure is believed accurate to t0.l°; the major limitations are the accuracy with which the centroid can be determined, the uncertainty in the energy calibration curve, and the uncertainty of the incident beam energy. 3.2 Normalization The relative normalization for each run was obtained by 20 normalizing to the total counts in the elastic peak observed by the monitor counter. In each monitor spectrum the edges of the elastic peak were chosen at a constant fraction Of the total peak height. The ratio of monitor counts to the integrated current for each run was calculated and found to be constant to within 5%. It is believed that the monitor counter yields the better relative normalization since the current digitizer and Faraday cup were subject to some leakage current. Since data were taken simultaneously at two angles during the experiment it was necessary to determine the relative normalization between counters. This normalization is determined by the difference in solid angle subtended by the two counters and any difference in the detection efficiency of the two counters. The relative normal- ization between counters for this experiment was determined by taking data over the same angular range with each counter and then normal~ izing one angular distribution to the other. This was done at each energy and found to be constant within 2%. If a large error were made in the relative normalization between counters, the error would show up as systematic discontinuities in the angular distributions of all states at the overlap angles where one counter started taking data and the other stopped. No such discontinuities in the angular disr tributions were observed. At scattering angles greater than 65° this experiment was able to completely resolve the elastic scattering from 4003 and 48Ca. Table 3.1 lists the composition of the target used in this eXperiment. 21 a Table 3.1 Isotopic analysis of the target. Isotope Atomic % Precision 40 3.58 10.05 42 0.05 10.01 43 0.01 44 0.11 :0.02 46 (0.01 48 96.25 10.05 * Determined by the Stable IsotOpes Division Of the Oak Ridge National Laboratory where the target was made. Table 3.2 Contributions to the uncertainty in absolute normalization. Source % Target composition 2 Normalization of 400a 5 . 40. Statistics. Ca peak 7 Monitor peak 3 —-—-—— Total ’r'lOZ 22 43 It can be seen that Ca is the major contaminant and the relative amount is determined to within 5%. Accurate elastic scattering data for 4OCa already exists (Fr 67); therefore it was decided to normalize 480a data using the ratio of isotOpic abundances in the the present target. As can be seen from Table 3.2, the absolute cross sections determined in this manner are accurate tott10%. The principal contri- butions to the uncertainty are the statistics of the 4OCa elastic 4 peak and the absolute normalization of the 0Ca elastic scattering. 3.3 Excitation Energies To determine the excitation energies of the various states observed, the program FOILTARCAL, written by R. A. Paddock, was used. The input was the output of PEAKSTRIP plus information concerning target composition, target orientation, the reaction involved, the detector angle, and a set of standard reference peaks. The program uses the reference peaks to determine a calibration curve of given order, which is then used to find the excitation energies of the unknown peaks. The program accounts for target thickness and uses relativistic kinematics throughout. The reference peaks used for calibration purposes were the ground states of 4803, 16O, 12C, the 4.44 MeV state of 12C, the excited states of Z‘8(.‘a listed in Table 3.3, and the (p,d) ground state. Only reference peaks that were free of contaminants were used. In order to use the deuteron peak as a calibration point in 23 the proton spectrum it was necessary to make a correction for the window in front of the detector. Since the deuteron loses more energy than a proton of the same energy in traversing the 1/4 mil aluminized mylar window, it was necessary to calculate the difference in energy loss between a proton and deuteron of the same energy and add this correction factor to the excitation energy of the deuteron. This correction factor varied from 20 to 60 kilovolts depending on the energy and angle of the scattered deuteron. Both linear and quadratic energy calibration curves were tried. It was found that both linear and quadratic calibration curves yield— ed excitation energies for known states that agreed with those of Marinov and Erskine (ha 66) to within the calculated uncertainties. As might be expected the quadratic curve yielded a better absolute fit to the known excited states up to 7 MeV in excitation energy. As a check on the calibration curve above 7 MeV, the deuteron peak corresponding to the 2.580 - 2.600 doublet in 470a was used. Again the necessary corrections to make the deuteron look like an equivalent energy proton were made. The linear calibration curve predicted the position of the deuteron doublet to within 7 keV with an uncertainty ofj:ll keV. The quadratic calibration curve predicted an excitation energy for the doublet that was approximately 50 keV high. Without strong evidence to indicate that a quadratic or higher order calibration curve was needed, it was decided that the linear energy calibration curve would be used. These results indicate that 24 Table 3.3 Excitation Energies of 480a. 8*(neV) 1*(neV) E*(neV) t*(16V) Present Data Ma 66 La 66 Bj 66 (p,p') (p,p') (p.t) 3.830i0.005 3.833* 3.818 3.827”r 4.284 4.272 4.281 4.50210.004 4.506+ 4.498 4.496* 4.60710.006 4.613 4.604 5.14210.004 5.146 5.13 5.249t0.008 5.266 5.298:0.007 5.362i0.005 5.368T 5.37 5.459 5.72310.004 5.728 5.724 6.098:0.008 6.106 6.096 6.335i0.005 6.338* 6.34 6.329* 6.642:0.009 6.61 6.645 6.786i0.008 6.79 6.793 6.885i0.008 7.009i0.008 7.320i0.025 7.401:0.025 7.471¢0.025 7.521:0.025 7.643:0.006 7.650 7.786:0.007 7.940:0.006 7.97 8.03710.009 8.018 8.25010.008 8.237 8.364i0.010 8.268 8.473 8.501:0.008 8.513 8.543¢0.008 8.538 8.589:0.007 8.604 8.658i0.010 8.697 8.786:0.008 8.782 8.868i0.008 1. Points used to determine the energy calibration curve. 25 the detectors and electronics used in this experiment yielded a data taking system which was linear to within 0.1% over a 10 MeV range of excitation energy. 3.4 Cross Sections The program RELTOMOM, written by R. A. Paddock, was used to convert the PEAKSTRIP output and the monitor counts into the center— of—mass cross section for each peak. It was at this point that spurious data points were reanalyzed. Whenever possible, corrections were made for contaminated peaks. 120, 160’ In particular and 400a were subtracted from the forward angle elastic scattering. To make these corrections the cross sec- 12 d 16 tions of the elastic scattering from C an 0 were used, where kinematically separated, to determine the relative amounts of carbon and oxygen on the target at each energy. Using the known 12C and 160 cross sections (Ca 67), the background subtraction could be made at d 16O on the target was smaller angles. The total amount of 12C an approximately constant throughout the experiment. The same technique was used to subtract the excited states of 40Ca from the 480a excited states when they were not kinematically separated. 4. OPTICAL MODEL STUDIES In order to perform the distorted wave Born approximation cal— culations, it is necessary to obtain the optical potential which describes the elastic scattering at each energy, because it is used to define part of the wave function in the entrance and exit channels. The optical potential is also of interest in itself because the para— meterization used to describe the optical potential defines a radius which is usually associated with the matter distribution. Since good proton elastic scattering data exist for 400a (Ru 70) (Fr 67) the study of the difference between elastic scattering from 40Ca 48 and Ca and its relation to the Optical model was undertaken. 4.1 Optical Model for DWBA Calculations A commonly used optical potential, which has been found adequate to describe cross section and polarization data throughout the peri- odic table (Fr 67), is of the form mantel) + (II/1711,02 v99 _c_1_>f(xs>;.§_ de ° r dr V(r) = Vc(r) - Vo f(xo) - i(WO - 4WD VC is the Coulomb potential for a uniformly charged sphere of radius 1.25 A1/3. The geometry is of the Woods-Saxon form, that is f(xi) = [l + exp (Xi)]-1 where 26 27 Fricke gt, 31. found a set of average Optical potential parameters which fit a large number of targets. These parameters are listed in Table 4.1. Table 4.1 Fricke's average Optical parameters. r = 1.16F A a = 0.75F O o rI = 1.37F aI = 0.63F IS = 1.06F a = 0.738F 3 VS = 6.04 MeV _..- “—— “MD- It was found that by using these average geometry parameters a reasonable fit to the elastic scattering data could be found by search~ ing on the potential well depths V0, W0, and WD. The optical model search code, GIBELUHP, was used to minimize 7L2 by varying the potential well depths. The quantityl252 is a measure of the goodness of fit of the theory to the data. 2 N 2 X = 1 [Ho-Tbsp Juxein/Avmein zlb‘l where II is the number of points, 01;X(61) and 6.1.1.1(61) are the experi~ mental and theoretical cross sections at the angle 91, andAOi'Jx(ei) is the experimental error associated with the it“ data point. The final parameters used at each energy are listed in Table 4.2. 28 Table 4.2 Potential well depths using Fricke geometry. Energy (Mev Vo(neV) WO(HeV) WU(HeV) ;[2/N 25.11 50.98 0.60 6.04 11 29.33 49.93 3.96 3.61 11 35.00 48.80 5.24 2.34 7 40.21 47.67 5.24 2.35 4 The fits provided by these parameters to the data are shown in Figure 4.1. In extracting a deformation parameterlg’for the inelastic scatter- ing (see Section 5.) there is a possible ambiguity due to the fact that the real and imaginary geometries are not equal. Therefore, a set Of Optical parameters were found with the additional constraint that the real and imaginary geometries be equal. In this analysis r0 = r = 1.20F I and a0 = aI = 0.68F. The Optical strength parameters are listed in Table 4.3. Table 4.3 Potential well depths with equal real and imaginary geometries. . . . . . 2 " Lnergy (deV) vo(neV) wo(neV) wu(deV) ‘Jf /L. 25.11 51.72 0.36 6.95 13 29.83 45.93 0.15 6.57 6.4 35.00 46.50 3.49 4.62 3.6 40.21 46.58 4.13 4.57 2.0 The fits to the data are shown in Figure 4.2. 29 Basso 3.33... ¢b\b ON_ 00. 00 OO O¢ ON O ON. OO. OO 8 O¢ ON 0 A _ _ _ _ _ 3 _ a _ a _ _ ._ m m fil O o .l r O O O O C O G .g I O 1 Moduzxx m.nuz\x u n N o N 1 >02 O¢ >02 on W + o . s 1 O a - fismuzmx . 2.29 H m >0: on >22 mm m P. :1. O_ _..- ___.__.._. .— Figure 4.1 Optical Mbdel fit with R=I geometry. 50 28330 32230 ON. 8. om 8 0.. 8 0 ON. 8. om cm 9 8 O J _ q _ _ _ er a q _ _ u T 4 . r 1 o T r o m Oo¢flZ\Nx 00FNZ\NX . >22 9. . >22 on I . 2 2 . 2 2 l - 2 . 1 v o 1 m __u—‘A%A O o __u_‘AWA 2.0 O.- m m >22 on >22 mm . 1 2.3880 9.2.... 3.3 8 b _ _ b _ w¢ _ _ _ h _ b .b li‘\ mb\b Figure 4.2 Optical model fit with Fricke geometry. 51 40 4.2 Optical Model Difference Between Ca and 48 Ca Electromagnetic studies of the relative charge distributions of . . . . 48. . 40. the calc1um isotopes indicate that for Ca relative to La, the half density point of the charge distribution (R ) increases by 0P 0.15F and the surface diffusivity decreases by 12%. (Fr 68) Recent optical model analyses of 30 MeV elastic alpha scattering from these nuclei by Bernstein,_g£..§1. indicate thatzfiRo = R0p(40Ca) = 0.15F P and the surface diffusivity is essentially unchanged (Be 69). Fernandez and Blair have calculated a strong absorption radius for 42 MeV elastic alpha scattering and also find ARtOJSF with the diffusivity being a constant. (Fe 70) If one assumes that the matter distribution is related to the geometry of the optical potential used to fit the elastic scattering, then one may be able to determine differences in the matter distri- bution by looking at differences in the Optical potential. We have 40 therefore used the optical model to fit the Ca data and fix the potential well depths at each energy. The 48Ca data are then fit by using the potential strengths obtained from the 40Ca analysis and performing a search which grids the parameters determining the geom- etry of the Optical model. Such a grid search was performed so that the sensitivity of the fit to the radius and diffusivity would be determined. The Optical model with its large number of parameters presents a problem in itself since many of the parameters are known to be coupled. It was therefore decided to simplify the potential as much 32 as possible. The spin-orbit potential did not improve the fit to the data, particularly since polarization and large angle data were not being fit. Therefore, the spin orbit terms were eliminated entirely with no effect on the results presented here. One possible optical potential would have a Coulomb term and either a surface or a volume imaginary term along with the real volume term. In this potential the real and imaginary terms have the same geometry. As a first try, therefore, a potential of the following form was used: U(r) = UC(r)-[VR~i4wfid_]f(x) Ddx . _ _ ~l 3 f(x) = (1+ek) 1 where x = (r to“ / ) a This is essentially the same potential used by Bernstein 3&3 31, in their alpha particle analysis except that a surface absorption rather than volume absorption term is used. The procedure was to fix the geometry for the 40Ca analysis (r0 = 1.25 fm, and a = 0.65 fm) and search on VR and NO to Obtain the best fit at each energy. Then a “geometric” analysis of the 48Ca data was made by holding VR and ”D the same for both isoteopes and performing a grid search on ro and a. An immediate objection to the procedure of holding VR the same for both nuclei can be made since there is a symmetry term in the real central potential of the form V .(§:§)- (SI 68) This is SYA A particularly important if one is trying to describe differences in the elastic scattering by differences in the geometry because of the Vr2 ambiguity in the optical model. (Pe 62) Therefore a grid search 55 was also performed for the 4baa data where VR(48Ca) = VR(4OCa) + Vsm( §:§). The value of VSY,I used was 26.4 MeV (Fr 67) which added A L 4.4 MeV to the real well depth of 4OCa. The results of a grid search on ro and a are most easily visualized using an iso—Z2 plot as in Figure 4.3. It can be seen that the radius has a more well defined minimum in 22 Space than the diffusivity and that the two parameters are slightly coupled. Plots at the other energies are shown in Figures 4.4, 4.5, and 4.6. Notice that the minimum in 22 for the 25 MeV data is not well defined as a function of diffusivity. To investigate the sensitivity of the results to the form of the imaginary potential, the same calculations were performed using volume absorption only and a combination of volume and surface absorp— tion. The quality of the fit at any given energy varied depending on the form of the imaginary potential. The higher energy data was fitted better with more volume absorption and the lower energy data was fitted better with more surface absorption. The geometry parameters yielding a best fit in each case were, however, approximately independent of the form of the imaginary potential at each energy. Elastic proton scattering is often fit with an Optical model having a different real and imaginary geometry. The sensitivity of the results to the requirement that the real and imaginary geometries be equal was investigated by using the geometry parameters of Fricke, gt, El: (Fr 67) for the 40 Ca data. The results at each energy are listed in Table 4.4 and are in reasonable agreement with the results obtained by holding the real and imaginary geometries equal. The E 5 . .. . o_.,.,,.._,,_.mo...,..mo.,...._.wo. No. 0 0.1.0.- 8.- mo... d _ _ _ .toom 290 < .28.... 82.88 x . - . E 83580 . >22. 0v ”mmozmmmta ME mouNX mom om>mmmmo >22 mm muozmmmta ME 28.x mofimam X 8 - - . u 2.. Q I. co 0. I V LO 0. O. ' I N Q ' 3. <1 2’ O NO. surface.- Figure 4.4 35 Mev y 56 o< 0.. m0. m0. v0. NO. O NO.- .zoom 2904/ .toom 5520 x >m ow>mmwmo .mmozwmmuua MI... mo“. «X #0.. $0.. mo.- _ 1 _ >22 Om mofimsmNX 8.. O..- Q' Q I NT O..- mo.- OO. I h N 9 O NO. 51 30 Mdv Isurface. Figure 4 .5 57 o< O_. OO. OO. v0. NO. O NO.- ¢O.- 00.- mo.- ///0 .zoom 22o a .288 8.82m x .>m Qw>mwmm0 >22 ON mmozwmmun—E MI... mop. «X m002 «.0 u :20: >02 0.0 u :20: >0: «.0 n :20: >0: 0.0 n 2200 no v no . u M o u 22 q N\2AN 00 q N\2A22v O O mo.o n Hm .m2.o u m mo.o u H n m H . o H o NM.H N .H ©H.H l .H ”mooq mN.H " n H “mooq wuoq paw mowq How mumumemumm Hmpoe Hauaumo msu CH mmocmuowwaa m.¢ manme 59 cases where the radii and diffusivities were changed by the same absolute amounts and by the same percentage amounts were found to differ negligibly. Figure 4.7 shows the ratioCT(48Ca)/c7(400a) versus the center— of—mass scattering angle for each energy. It is indicative of how well the ratio of cross-sections is fit with the geometric search procedure and the optical model having equal real and imaginary geometries. The results one would Obtain if one used the differences in the proton distributions determined by electron scattering are also shown. The electromagnetic differences do not fit the data, particularly at higher energies. Greenlees, Pyle, and Tang (Ge 68) (Ge 68a) have pointed out that the geometric quantity which is best determined by the optical model is the root mean square radius. Our results, listed in Table 4.4 are in good agreement with this fact if one neglects the results for the 25 MeV data. One can justify neglecting this 25 Rev data because the minimum inZ2 space for r and a is not well defined at this energy, but consists of a broad trough, the minimum Of which does not corre~ spond to a line of constant rms radius. The results shown in Figures 4.8 ~ 4.11 indicate that the half density point of the radius and the diffusivity are not uniquely determined by the present optical model analysis. The sign and the magnitude of the differences depend on the energy of the incident protons and whether or not a symmetry term is added to the real potential. The average difference in the rms radii of 48Ca and 400a observed by this Optical model analysis is 0.15F which equals the v ~ni IO ‘3 I j I I *1 T r s I I I I I _ , I EXPERIMENT g 5 _ E-M . - m)! MINIMIZED -. 2002+: ‘ E'p = 25 MeV ‘ I _ AR" 003 F 2 : A0 = * 00' F ‘ 0.5 _ _ l0 : ~ ~ - ~ ~— 0 0 — 4 5 _ . I I l 1 5f 30 MeV A“: " 0.08 F 1 A0 =+ 0.07 F : 1 Ep '= 35 Mev Afo="o.05 F 1 A0 =+0.03 F 1 Ep - 40 MeV : AfiF" 0.05 F A0 8+ 0.03F ——“' 1111 O I 1 1 l 1 1 L _L 1 i __ L 1 1 __ .1 O 0 I0 20 30 4O 50 60 70 80 90 K10 "0 123 I30 ”.0 [50 8cm Figure 4.7 Ratio of elastic angular distributions. r,(F) L30 |.25 |.20 41 Figure 4.8 Optical model radii with USym .65 0° "3):: 0 0 40 MeV A 35 MeV r, = r1 x SOMeV 0g= 0I E] 25 MeV USYM = O 21—- 25% chzange m X :\RMSR= 4.26F : ‘ékx - 2J1...- - - 1 1 1 I l I 1 1 l\ 1 l L l L 1 J -60 .75 00 2h: 0.. ) _ I25 I20 I.l5 42 Figure 4.9 Optical model radii with US 0 40 MeV A 35 MeV x 3OM0V r = r U 25 Mev o I 25% change .. + m. USYM= 4.4 Mev W RMSR = 4.26 F \ \ \\\\ : \ ‘\.._ ’-——4\ \ -\ |——x———I l \ I I I I l 1 l l l l J 1 l J l .65 .70 .75 0.,(F) = 4.4 Mev. ym 45 0 40 MeV r0 1: rI A 35 MeV X 30 MeV El 25 MeV USYM = O + 25% change a.=|= aI _ RMSR= 4.29F .. \ 5 T l.l5 :- .__)I(__.\ I.|() 1 I l L l 1 l l l I 1 i1 1 l\\ l I 1 065 I 070 0°(F) 075 080 Figure 4.10 Optical model radii with USym = 0 and unequal geometries. |.|5 - l.l0 - |.05 1 .70 44 r, 4: r1 0 40 MeV 0° 4. 01 A 35 MeV x 30 MeV U SYM = 4.4 MeV D 25 MeV +25% change in X2 RMSR = 4.29 F .75 .80 .85 a.(F[ _._—_Y __—_ Y 7.-- ._._—___._ Figure 4.11 Optical model radii with Usymz 4.4 Mev and unequal geometries. 45 difference in the rms radii predicted by the A1/3 law. This result is not in agreement with the elastic alpha particle scattering data. If one assumes that the rms radius of the matter distribution is related to the rms radius of the optical potential via a constant interaction distance; then the difference in the optical model radii equals the difference in the rms matter radii. If one further assumes that the rms radius of the proton distribution is given by the rms radius of the charge distribution determined by electron scattering, X then our results, in conjunction with the electron scattering results, 48 indicate that the Ca nucleus has an excess neutron density in the surface region. This agrees with the conclusions based on Coulomb energy differences, (No 68) shell model calculations, (El 67) and hartee-Fock calculations. (Ta 68) .- >'€ o Frosch 35, El! found that the rms charge radius of 40Ca is 0.01 fm smaller than 40Ca.l 5. THEORETICAL ANALYSIS The data were compared to the predictions of the collective model using the formalism of the distorted wave Born approximation. Details of the theory are described elsewhere (Ba 62) (R0 61) (Sa 64). An outline of the theory is presented below. 5.1 DWBA Thquy For inelastic scattering the form of the reaction is 1 i: A(a,a ) A where a is the projectile and A is the target nucleus. The total Hamiltonian for the system is H=H+T +U(r)+V(r,§) o o o where'E represents the internal coordinates of the projectile and target. To is the relative kinetic energy for the two parts of the system. U(ro) is the optical potential describing the elastic scattering ro is the separation vector between the projectile and the target. V(ro,§) is the potential producing the inelastic scattering. 46 47 The eigenfuctions of the total Hamiltonian,9’, are solutions of the Schrfiedinger equation (E—n)V=0 5.1 Similarly, the eigenfunctions, v(§), of the hamiltonian, h(g), are solutions to the equation [En - H1 vn (g) = o and represent the internal states of the target and projectile. The subscript, n, represents either the initial states, 1, or the final states, f. The solution to equation 5.1 has the following asymptotic form '1’" ————-> .1105) exp €15]: . r) *zAif vf (g) expékfrJ/ro (r—+ ~) It is composed of an incident plane wave and an outgoing spherical wave. The cross section for the final state, f, is given by The usual procedure is to define a transition amplitude such that tif = FL (r0) 5.4 The term, P (re), is the radially dependent form factor which L depends on the model used for its explicit form. Now the cross section is 2 k (2.1 + 1) 2 ’ '2 dcr= /) f f B. 5.5 ——- ——-—— m ‘y 5%— (Ln. (21m? ki (231 + 1) 1*” (2L + 1) where 5.2 Collective Model The collective model assumes that the excited states of the nucleus are due to deformations from a Spherical ground state. The deformed nucleus is described by a deformed Optical potential. tk multipole expansion of the nuclear surface is made ,, _ 0 .49) - R01} +29% Y L (3)]. AJCial symmetry is assumed. Next the total potential is expanded 50 in a Taylor series about the Spherical radius, R . 0 2R ') P\=l\o The term U(r~R ) is the optical potential which describes the o elastic scattering. The second term is assumed to describe the inelastic scattering, i.e. it is the interaction potential 0 r=— R}; a . V(§o,,) 2% O . L §g_Y ( ) 5 7 / ar This form factor is used to calculate the cross sections for in- elastic scattering using equations 5.5 and 5.6. The calculated angular distribution is normalized to the experimental angular distributions by the deformation parameter,d(L =/§9LRO. 5.3 Vibrational Model The vibrational model yields the same formal results as the rotational collective model. This model relates the deformation, 31.8 f5: R0, to a mass transport parameter, DL’ and the surface tension parameter, CL. The Hamiltonian describing the multipole deformation,JL =/6lRo in the ”vibrational” picture is given by (La 60): =Z —M ' Jr a HL n ( ) 1/2[DL am L,—:~i+ CL L21 dL,-M] where 2 £1, =24 I am! ”'5 Auk-v 51 and BL is the ”mass transport” parameter and CL is the ”force constant” of the vibrator. These parameters are either calculated by more specific models or are determined by experiment. As an example, in the classical incompressible, irrotational hydrodynamical model, is given by (La 60): D ( L)hvd ')_ (D )g = (2L+l) AM L) =(_2.1:..t.l) e2 <9“) 2 SP Afl‘ L 2 . . . . . . where {r > is calculated uSing a uniform charge distribution. The value GPp of the ratio B(EL, O-—*L)/BSp EL; 0 a>L) meas~ urea in some sense the ”collective strength" of the state. Along the same vein it is of general interest to compare the reduced transition probabilities with two sum rules. The first is the non~ energy—weighted sum rule, NEWSR (La 60) based on the shell model. NEWSR = X Bn(EL; 0 —-r L) = e22 (r213 n 40 where the sum is over all states with spin L. The second sum rule is an energy—weighted sum rule, (Na 65) awsx =% (E - roman; L ~90) = 22(2th2 (2L+1)2 n ___.__._ SfiAM This sum rule is model independent in as much as the nuclear Hamiltonian does not contain velocity dependent potentials. 5.6 Calcglations “ u”-— The computer code JULIE (Ba 62) was used to make all DWBA calculations using the XUS Sigma-7 computer. Coulomb excitation was included for L = 2 and L = 3 cases, and the deformation of both the real and imaginary potential was used. The calculations were done with the two different sets of Optical model parameters listed in Tables 4.2 and 4.3. Calculations were made at each energy for 54 L = 2, 3, 4, 5, and 6. The results of the calculations are shown in appendix II, Figures II.1 — 11.4. The angular distributions appear to be relatively insensitive to the Optical model used. The theoretical angular distributions,CTDwBA, are related to the experimental angular distributions by the expression, A 2 5131pr) = *1 ’91. 2J3” J DwBA cm (2L+i)’ 2.1 A+1 L is the transferred orbital angular momentum, JA = O for even— even nucleii, and JB = L; therefore the expression above reduces to 9.0:(EXP) 35:2 JDWBA dn /7 The deformation parameter,lfi7L, was found for each state by com— parison of the theoretical and experimental angular distributions using the computer program, SIGTOTE, written by K. M. Thompson (Th 69a). The program normalizes the integrated cross sections for the experimental and theoretical angular distributions. The extraction of a meaningful deformation parameter depends on a knowledge of the L transfer for the observed state. When the state has been Observed previously and a definite L assignment has been made there is no problem, but for a weak or previously unob- served states there may be some ambiguity concerning the L transfer of the state. The general features of the data as a function of energy and L transfer are shown in Figures 5.1 - 5.4. he states are of known L (Li 67) and the collective model fits to the data are shown. 55 1 48(3c1(p.p') 1 2’,1-:"=3.830Mev ' 25.11 Me —— 1 35.00MeV -------- f : 40121 MeV —— 3 P .1 l0.0 1 1 1 \ . 10.0 1 ’1: I .o 8=.70 F - E 1: . '3 I0.0 :' '1 \ p ' b . 1 “O . 35.00 MeV . ; 8=.72F " 4, .. I0.0 r ‘- ; 29.83 MeV : t I I 8::73F: : D . .I .. W 25.” MeV I.0 :- 8=.8I F ‘3 1: I I ' : 0 I 1 1 1 1 1 1 1 1 1 1 1 1 1 O 20 4O 60 80 100 IZO I40 ‘ , 0cm (deg) i 1 Figure 5.1 DWBA calculations for L=2 states.. 56 48000.19) 3', 15": 4502Mev 1 '0-0 g' 25.11 MeV —— a ‘ : 29.83 MeV —--— : 1 35.00 MeV -------- j 1 . 40.2l MeV . 1 . . l0.0 -: i 40 2| MeV I0.0 . ' 1 : 8=.8| F : t I 2 (I) ‘s b . JED . 1 10.0 1 .g : \- I g 35.00Mev- .89F ' 10.0 : 29.83 MeV ‘3 . , , 8=.86F : .. I I I .. L . 25.11 MeV LO 1',- 83..94F -: E - i b I d O" l I l l l l l I l l l l l 0 20 40 60 80H|00 120 14g____ H. , ._fi _ ‘— Figure 5.2 DWBA calculations for L=3 States. dO/dn (mb/sr) 57 4800 (p,p') 4’, E'=6.335 MeV 25.1! MeV —— . - \.\ 29.83 MeV -—-—- 1.0 :- \ 35.00 Mev ------ “z E 40.2l MeV :- r- d J; 4 j .1 E __l 35.00Mev - * 8=.39F - a . ' 29.83 MeV ‘ 10 1 8=.391= I 25.11 MeV ~ . . 8=.4.41= I O" l l l l l l l j l I l l l 0 20 40 60 80 100 120 140 am (deg) Figure 5.3 DWBA calculations for L=4 states. '1 I0.0 I r! IIIT' w—‘H |.O l U rUTIIl 58, . 4800 (p. P') 5'.E‘= 5.723 MeV 25.ll MeV -—-—— ' 29.83 Me 35.00 MeV ----- -—- 40.2l MeV \ 1 1 1 111111 1 171 11111 40.21 MeV r; 8=.46F U) \ .— 1 n : g : g I 1 B . ‘ 13 1 1.0 _. 25.11Mev 3 3:.49F‘ ().l 1 1 1 1 l I l l 1 1, 1 1 0 20 40 60 80 100 120 141 9cm(deg.) Figure 5.4 DWBA calculations for L=5 states. 59 It can be seen that as the L value increases the angular distribution peaks at successively larger angles. Also notice that the structure of the angular distribution is more pronounced for the higher energy data. For making L assignments the 35 and 40 MeV data are more useful than the 25 and 30 MeV data. The lower energy data tend to be relatively flat and structureless. The tentative L assignments made for the states Observed in this exper— iment are shown in Figure 5.5 along with previous results for 48Ca. The individual states are discussed in more detail in the following chapter. When no L assignment could be made several different L values were tried. It was found that the/é?L Obtained was almost inde- pendent Of the choice Of L. 'his is because the theoretical angular distributions have approximately the same average cross section for various L values, but they peak at different angles. 6. R‘SULTS In this chapter the individual states observed in this experi— ment are discussed and compared with the results Obtained from other experiments. When nuclear deformations are compared the deformation,(j:L = fiQLRO, for 40 Rev with real and imaginary geom— etries equal is used. The energy dependence of the CgL's is discussed later. 6.1 States below 5 MeV 3.830 —-. . . 48- . . . The first exCited state of Ca 15 the strongly exc1ted 2+ state at 3.830 MeV. The angular distribution is compared with L = 2 collective model calculations in Figure 5.1. The L = 2 . . . 48. aSSignment agrees with all the preVious experiments on Ca (Pe 65) (Li 67) (La 66) (Bj 67) (Te 68). It is interesting to compare the . . . . 1 . . 50 angular distribution with that of tne first 2+ state in Ti and 52Cr. Figures 6.1 and 6.2 show that the two angular distributions are virtually the same. The figures also show the results of a microsc0pic calculation (Pr 70) involving the Kallio Kolltveit interaction plus exchange with core polarization. The calculation assumes excitations within the (1f )2 configuration and is seen to 7/2 provide a reasonable fit to the data for tne 48Ca core. The core 60 :._.8v>os_mmm.~ «1m +¢ .. 1 - :._.Sv>o.2mmm._ u m ..N .. so...>§mm.m...u .... 30.2%: mod... n .m. A #338 $8 .36 $3. 1 1 >22 9. a 33:0... 25 as 8.. 00. on 00 cc ON oo. oo om 0* ON .1 _ 14 . . . - q - . _Av. um. . . q . Iq . . q q . I l o O I j / II. J o x ’1 I I /O 4 I o o w , . H n ... I. ... H / n p n / .1. H u 0 W o u/ ..I. u x 1 . .. / \. 1 O O/KOIPO .0 W in! fl 01” x./ . _I no J ) l / I ,r. u/ I I w.- l on / I I I o/ \ \ I / .l I / I ... .7 \ ... m u . . x“ m c on I ._m m 0.. m a on m _ _ x I _ I‘ll , ..II: I. . 1. .II-... .I II 1, I III. |.. I .I.. .. . llullll r'lIIIIII i 'l 1 III: 11... 1 1 .l .1 .I-' I. ...O 0.. .0. (IS/qw1vpx-op Figure 6.1 Comparison of 480a and 50Ti. .—-—- .--- . ... ___._..___. ._.._..___ _._.___- .-- “Comm AND “01mm AT 40 MeV —— IMPULSE APPROX.+ Ex. \11 CORE POL. FOR ”c1. 1.1.): A11v=2>+ 811v=4 > 1.1;» 81 |V=2>- A] 1v=4 > A1, we.) AND 1112+sz . 1 -2* 5*: 3.83 MeVC‘Ca) -4* 6*: 6.33 Mev1‘°Ca1 x 27 5": 1.434 M0V(52Cr) x4; 1:": 2.37 MeVIszcr) A2, . 0.98 A: . 0.53 | o. E- 0“. l '00 L i . .. _:: E\ ".2. 3 E x ' I Z \x. i i /" "It I - \x ’2“ 1 r— / :5 « Lo.— \0 x q1:0.I r 0*... 1 5 'V : g E \ s : 0“].X. : E 1: K 2 E N \ ° " 3’ I . ‘ \. ‘ 3 ' ' 1 5 \ \2; 832.985 MeV( Cr) 5 v E x 4; E=2.767 1111M$2 Cr): : 82 =0.02 ; : )1: 83=0.47 ; ' 91le ‘ P , N ‘ . 1. . . , \x . : \ f : r '3 : \ : i \ : .. \ .. I x . I: -1 r \ -1 t \ . . . . L \ 1 L l l I I l I I I l I I I I I I I I #1 0 20 4O 60 80 IOO 0 20 4O 60 80 1’30 90M (deg) GCM (deg? Figure 6.2 Comparison of 4803 and 52Cr. 63 strength for each multipole and valence configuration is determined from the bound state matrix elements of Kuo and Brown (Fe 70) (Pe 69). Since the microscopic model with realistic forces contains no free parameters, the comparison of the calculations based on this model with experiment provides a direct test Of the theory. The nuclear deformation observed in this experiment of 0.65 fm is slightly higher than that Observed in the inelastic alpha scat— tering experiments Of 0.53 fm for 42 MeV (1's (Pe 65) anddrL = 0.71 fm for 31.5 MeV experiment (Li 66). The 12 MeV (p,p'f) (Te 62) experi— ment finds 3 J1. = 1.0 fm. The reduced transition probability in WeisskOpf single particle units is 4.1 for the uniform Fermi equiva- lent charge distribution compared with 1.7 for inelastic electron scattering (Ei 69), 5.4 for the 31.5 MeV alpha work (Be 69), and 7.70 for the 12 MeV proton work (Te 68). In general it is found that the 12 MeV (p,p'l) experiment Observes larger nuclear deforma— tions and reduced transition probabilities. This could be due to compound nuclear effects and or two step processes. The first 0+ excited state in 48Ca is not observed in the present experiment. Upper limits for the cross section at each energy are shown in Table 6.1, and are about 1.5%, the strength of the first 2+ state. The (t,p) experiment observes the state with a strength Of about 60% of the ground state or 150% the strength of the first 2+ state. The fact that this first 0+ is so weak 64 40 , , compared to the 0+ state in Ca Observed with the same (p,p') reaction has been used as evidence for the existence of deformed . 40 admixture in the Ca ground state, (Gr 70) and conversely the 48 , , ground state of Ca contains less deformed admixture. 4.502 48 The first 3 — state in Ca occurs at 4.502 MeV and is strongly excited by the (p,p') reaction. A comparison with L = 3 collective model calculations is shown in Figure 5.2. Figure 6.3 shows the comparison of the experimental angular distribution with the known experimental angular distributions for known L = 3 transfers in 40Ca (Ru 70). It shows that the p,p' reaction is able to make L transfer assignments based on the shape of the angular distribution, and the shape Of the angular distribution is approximately independ- ent of the target nucleus. The reduced transition probability in agreement with the (e,e') result. The deformation parameter Observed here is 0.89 fm and somewhat larger than the alpha results of 0.56 fm (Pe 65) and 0.76 fm (Li 67). Again the 12 MeV proton results Observe a deformation larger than our results (1.15 fm). i607 Analysis Of the 4.607 state is complicated by the fact that f C‘ . J. H . the strong Ca J — state at 4.48 heV contaminates a large part of the angular distribution. The data seem to favor an L = 4 transfer, but L = 3 cannot be ruled out on the basis of these data alone. 65 40 Mev I I 48Co (p. p’) T f L=3 i r l I States. 35 MeV I lIIIIl IIII I I IIIIIIJ I Figureg6r3 L = 3. states. OCM(deg) ‘ l 1 l l l A l l L l L I _I 0 20 4O 60 80 IOO l20 0 20 4O 60 80 IOO |20 Guided) 66 However, the 10 MeV proton experiment (La 66) Observes an angular distribution which peaks beyond the 3 - state and is compatible with an L = 4 DWBA calculation. The alpha experiments were not able to resolve the state from the stronger 4.502 state, but the angular distribution Obtained (Li 67) is not inconsistent with an L = 4 transfer. The state is not Observed in the (t,p) experiment. 6.2 Stgtes between 5 and 6 MeV 5.141 In this experiment a total Of 5 states are Observed between 5 and 6 MeV in excitation energy. The weakly excited state at 5.141 is assigned an L = 5 transfer. This is not in agreement with the 42 MeV alpha work (Pe 65) which makes a tentative L = 3 assignment or the 31 MeV alpha work (Li 66) which is most consistent with an L transfer of 4. Lippincott's data do not rule out a possible L = 5 though. The present results are in agreement with the L = 5 assignment made in the (p,p'J) work of Tellez gg. 31. It is interesting to note that at 25 MeV the state is more strongly excited than at the higher energies (J; = .31 fm at 25 MeV versus grL::.22 fm at the other energies). The 12 MeV proton experiment Observes a strength of A; = .87 fm. The alpha results Of Peterson agree with ours, J; = 0.17 fm at 42 MeV. 5.249,5.298 The 31 MeV alpha experiment (Li 66) was not able to resolve a 67 weakly excited state at 5.31 from the strong 3 - at 5.37. With our resolution it was possible to see that there are two weakly excited states in this region at 5.249 and 5.298 MeV. The 5.249 state appears to be L = 5 transfer but could also be L 4. The 5.298 state is consistent with L = 2. 5.362 The 5.362 state is a strongly excited L = 3 state in agreement with all the previous L assignments except one (Te 68) which makes a tentative L = 4 assignment. The nuclear deformation Observed in this eXperiment is about twice that observed in the alpha experiments. The state is not Observed in the (t,p) experiment. A state at 5.37 MeV is Observed in electron scattering, but has not been analysed (Li 69). The 5.48 0+ state Observed in the (t,p) work (hi 66) is not observed in this experiment. An upper limit* on the cross section at each energy is given below. Table 6.1 Upper Limits on the 0+ Cross Sections .. Incident 4.28 State 5.48 State Energy z of 2+ (3.83) z of 2+ (3.83) (MeV) 25 2.3 1 30 1.5 1.2 35 1.2 1.1 40 1.1 1.0 * The upper limits were obtained by taking the ratio of the background to the 2+ cross section at 3 angles. 68 5.723 The state at 5.723 MeV is excited with an L = 5 transfer in agreement with the 31 MeV alpha experiment. The comparison with L = 5 collective model calculation is shown in Figure 5.4, and the comparison with the shape of a known L = 5 angular distribution from AOCa is shown in Figure 6.4. Peterson observed the state as a 2+ and Tellez 9E: g1, tentatively assign L = 3, but the present evidence for L = 5 seems conclusive. The deformation of 0.46 fm is again larger than that observed with alphas (0.32 fm (Li 66)). Tellez £33.31. obtain a deformation of 0.44 fm in agreement with the present value, but it is not known if this is due to their different L assignment. In any case, it is the only deformation which they observe that is not substantially larger than that Observed in the present experiment. The state is not observed in (t,p) or (e,e') experiments, which is also consistant with the Jfl. = 5 — , assignment. 6.3 States between 6 and 7 MeV 6:098 The state at 6.098 MeV is believed to correspond to the 6.11 Mev state observed in the d—eXperiments. The state is only weakly excited and the statistics on the angular distribution are not good enough to make a positive L assignment, but the data appear to be most consistent with L = 5. dc/dn (mb/sr) I A —I .Ol 69 l I T I ITTII 15*: 5.723 Mev j l IIIIIII E‘= 5.141 MeV 1'1 1111”] 15*: 6.885 MeV 'TijIIIII v lllelll l r I I 1 48Ca (p,p’) L= 5 States 35 MeV E*=8.384 MeV it H i Q . 1 + E*=8.543Mev f? r t— E 1, > E ,1?’ , E‘=8.786Mev L I E"=8.868 MeV k l l I l I Lgflv 1 P4 1 l l o 20 40 60 80 100 120 0 20 40 60 8 100120 ammo) Cameo) 11s «w Figure 6.4 L = 5 states.. 1 JLII 1 1 1 11111 L 11_LJJ_L I 1 111114 1 1 1 14111] 70 6.335 The 6.335 state angular distribution is consistent with L = 4 assignment made in the dexperiment (Li 67). The fits to the collective model DWBA calculations are shown in Figure 5.3. Figures 50 52 6.1 and 6.2 compare the L = 4 states observed in Ti and Cr (Pr 70) with this L = 4 state and the overlap is seen to be almost * 1 O I exact. The same theoretical calculation as used for the 2+ states is also shown (sec 6.1). The comparison with the shape of a known L = 4 state in 4OCa is shown in Figure 6.5 and overlap is not as 50 52 good as in the case of the comparison with Ti and Cr. But this may be due to the different configurations giving rise to the 4+ 40 48 states in Ca and Ca. In 48Ca the 4+ state arises via the (f )—1 p3/2 configuration while in 40Ca the configuration giving 7/2 rise to 4+ states would be(2h92p) & (4h—4p).The core configurations giving rise to 4+ states in 50Ti and 52Cr would be the same as for 48Ca. The deformation of 0.37 fm is comparable to that observed in the 31 MeV experiment (0.38 fm). The (t,p) experiment assigns L = 2 for this state based on the position of the first maximum, but a second maximum at 70° as observed for the 3.83 MeV state is missing. 6.642 The state at 6.642 MeV is actually a close multiplet. It is at least a triplet of states. The resolution in this experiment was * _ The two L = 4 states in 52Cr must be added together to compare the strengths observed since the strength is divided between seniority l and seniority 2 states. def/d0 (mb/sr) 71 48 , , CO (9.9) L=4 States ‘ 35 MeV h h E*=6.335 MeV + O E‘ =4.607 MeV ? E"=7.788 MeV . +++ * + ?+ . 9 I E*= 8.250 Mev H W O 20 4o 80 80 ICC 120 20 4o 60 80 IOO I20 3914339 . mum 72 not able to resolve the individual components of the multiplet but it was able to reveal that the state was in fact a multiplet by the broadened peak shape. This is in agreement with the 12 MeV (p,p'J) experiment which observes a triplet at 6.618, 6.654, and 6.687 MeV. The 31 MeV alpha data for this state (Li 67) are con— sistent with a 4+ assignment beyond 40 degrees, but the first maximum appears to be washed out. This is what one would expect if the state were a combination of L = 2 and L = 4. The angular distribution observed in this experiment has the slope associated with a 2+ state, but the valleys are missing. his is also what one would expect if the state were a combination of L = 2 and L = 4. By combining the known L = 2 and L = 4 shapes in ratio of l to l, a reasonable fit to the data could be obtained at each energy. For purposes of calculations the strength of this 6.642 state is assumed to be 50% L = 2 and 50% L = 4, and the total strength of the multiplet is the sum of the two strengths. The deformation observed in the (1 experiment of 0.36 fm (Li 67) is comparable to the total observed strength of the multiplet of 0.35 fm. The (t,p) experiment observes a single state at 6.645 MeV. 6.786, 6.885 The two weakly excited states at 6.786 and 6.885 MeV are tentatively assumed to be L = 4 and L = 5 respectively. These L assignments are suspicious at best, considering the poor statistics. The (t,p) tentatively assigns 2+ to the 6.793 state, but this seems 73 to be based on a single data point. Except for that single point the (t,p) angular distribution is the same as that for the 6.329 state which probably corresponds to the known L = 4 state at 6.335 HeV. 6.4 States between 7 and 8 MeV 7.009 The first state above 7 MeV is a doublet at 7.009 MeV. The angular distribution is consistent with a combination of L = 2 and L = 4 in the ratio of l to l. The calculations for this state assume that 50% of the strength is L = 2 and 50% of the strength is L = 4. These L assignments should be considered very tentative at the present time. The total strength of 0.28 fm is almost twice the strength of 0.16 fm observed by Peterson with 42 MeV alphas, and who assumed an L = 3 state. Lippincott reports a weak state at 7.16 MeV. No state is observed at this energy in the present experiment or by any of the other experiments. 7.320, 7.401, 7.471, 7.521 Lippincott observed a weak state at 7.53 MeV at a few large angles. Tellez_e£..al. observed a quartet of states in this region at 7.305, 7.402, 7.444, and 7.589 MeV. In this experiment a quartet of weakly excited states is observed in this region. Of the four states observed at 7.320, 7.401, 7.471, and 7.521 MeV, 74 only the strongest state at 7.401 had angular distributions at each energy consistent with a single L value. This state is tentatively assigned L = 3. 7.643 The strong L = 3 state at 7.643 MeV agrees with the L assign- ment obtained previously in the alpha experiments. The state is only weakly observed in the (t,p) eXperiment. It is observed in the electron scattering experiment, but not analysed. The nuclear deformation of 0.49 fm is comparable to that observed in the 31 MeV alpha eXperiment of 0.54 fm. The only state observed by Peterson in this region is a 3 — state at 7.76 with a deformation of 0.33 fm. It is probably the same state. 7.786, 7.940 The state at 7.786 has angular distributions which are con- sistent with an assignment of L = 4. Analysis of the 7.940 state is complicated by the fact that it is contaminated by the much larger deuteron peak over most of the angular range and could only be observed at large angles beyond 70°. No L assignment could be made. 6.5 States between 8 and 9 MeV 8.037 The analysis of the first observed state above 8 MeV is also 75 complicated by the deuteron peak and data could be obtained at only a few angles. No L assignment is possible from the data obtained. At these higher excitation energies the density of states increases and it becomes difficult to make positive L assignments because most of the states are only weakly excited and often they are members of close lying multiplets which are not well resolved. The 30 keV resolution enables one to identify many of the states as multiplets by looking for broadened peak shapes. 3312.52 There is a doublet observed at 8.250 MeV. This probably corresponds to the 8.263, 8.237 doublet observed in the (t,p) work (Bj 67). The angular distributions are not definitely L = 4 or L = 5, but appear to peak midway between the ”classic” L = 4 and L = 5 distributions observed at 6.335 and 5.723 MeV. The analysis is again complicated by the fact that the large angle data at 40 and 35 MeV is contaminated by the much larger deuteron peak. This is the data that would allow one to determine if the doublet is L = 4 or L = 5 or a combination. A combination of 50% L = 4 and 50% L = 5 is able to fit the limited data, but there is not enough data to determine if this is the correct composition of the doublet. The (t,p) eXperiment observes a strength of 50% of the ground state for the 8.268 MeV state, and indicates that the 8.268 MeV state is probably a 4+ state. 76 8.364 The multiplet at 8.364 MeV can be fit using a combination of 20% L = 3 and 80% L = 5. These states have not been previously reported. The state has a strong L = 5 character as illustrated in Figure 6.4. A state at 8.473 MeV is reported by Bjerregaard 35, g}. in their (t,p) work, but the state is not seen in this experiment. 8.501, 8.543, 8.589 The next three states are each separated from one another by about 40 keV and are just able to be resolved by the present experi— ment. The 8.501 and 8.589 MeV states have L = 3 angular distribu- tions. The middle state at 8.543 has an apparent L = 5 angular distribution. The (t,p) experiment also observes 3 states in this region at 8.513, 8.538, and 8.604 MeV which are strongly excited at 52%, 68%, and 31% of the ground state respectively. Inelastic electron scattering observes a broad bump in this energy region. 8.658 The 8.658 state is another state whose peak shape indicates that it is not a single state. A reasonable fit can be obtained using 67% L = 3 and 33% L = 4, but the evidence is not conclusive for these assignments. 77 8.786 The state at 8.786 MeV is a strongly excited state with an apparent L = 5 angular distribution. The state is well resolved with no close contaminants and the angular distribution agrees almost point for point with the L = 5 angular distribution at 5.723 MeV. The (t,p) eXperiment observes a state 8.782 MeV with a strength of 42% of the ground state indicating a sizeable 2 n particle component in the excitation. 8.868 The last strong state observed in this experiment is a very close lying doublet at 8.868 MeV. The evidence that this state is a doublet is the fact that the state consistently has a resolu~ tion about 5 to 10 keV broader than the 8.786 MeV state just below it. Also the shape of the angular distribution, while strongly L = 5 in character does rise at the forward angles. It is possible to fit the angular distributions at each energy assuming 20% L = 4 and 80% L = 5. The inelastic electron scattering observes a state close to 9 MeV; but it is not analysed. With regard to the L = 5 assignments for the states that appear to be doublets (8.868, 8.364, and 8.250 MeV) it should be pointed out that there is no possible combination of lower L transfers which can give rise to an angular distribution which peaks around 60° as the L = 5 angular distribution does. It would however be possible to construct combinations with states of even higher angular momen- tum transfer which would peak as observed. 78 6 . 6 Summary The p,p' reaction is able to differentiate between L transfers to a given state by the position of the first maximum in the angular distribution. In making the L assignments associated with the states observed in this experiment, consistency of L assignment at each energy was required. It was not always possible to make definite L assignments, particularly in the cases of weak states having large errors associated with the data. The distinction between L = 3 and L = 4 was often difficult to make because a 20% change in normalization would make an L = 3 distribution overlap an L = 4 distribution. The L assignments determined in this experiment are compared with previous work in Figure 6.6. The relative strengths of the states at 40 deV are shown in Figure 6.7. The fact which stands out is the large amount of apparent L = 5 strength at excitation energy above 8 MeV. These high lying apparent L = 5 states are not understood at the present time. If the states between 8 and 9 MeV observed in the electron scattering are the same as these apparent L = 5 transfer states, then it is unlikely that the Jfl‘is greater than 3 -, because of the lack of angular momentum transfer avail~ able. Furthermore, it is difficult to produce a nuclear model which would predict such a cluster of 5 - states. It is for these reasons that one is led to one possible conclusion that the members of the multiplet have undetermined Jfl‘and are excited via a 5 — 79 n>2}. a. «>5 3 an... $6.3 5.6 I! .~ 36 .0 .ON.Q I ON.’ I ”0's. I I" can. I -¢.' l m .n I n b u“ I .o Sex... I - o n I ——uw l and I .v and II 0".“ I 9' no-c l mafia III «0.0 I ”00$ I o_-u | no.“ I once. I -n 3.» II ”—0.. I hnN.O OON.. III“ FGO.O '00.0 III N05... | .mpzesfismnxe sonpo spas acmwuaaeoo n>£ 9 ““>22 0. 28.3 rad. .~ 8.» II E ......n I QN‘ I NhN.' l . In... a. DOV. l 1n .0? QO¢.Q n . II 2.» II ... v o. n DON.» I.” “n.“ I ”no” I ”F.“ I 'Nfiln ' :6 I 83.» I Al—v 'n-. l 'n.@ I as... I $5.0 I ”at” | In .5.” I ”’85 I "no. I 5.. 02¢ mufimmzm gratuxu m6 ehswflm .>02 0.: :34: ”no." I '.~.' I 8“.' I ”...? I .'—on I .Nb.0 ll 0°_co I anu‘ I 3. An. .Q. .0. atom. .093 83 .0'.» Eng 005.5 nvo‘ 08.. 08.. ton .v. :93 ‘3 3+0. n 5.03 hzumwmn Ono.» :53 1 D t I a. .9 8. 2: 2: 2: 1 Oh (MN) A983N3 NOILVJJXB 80 n N n 0” E I, 5 3 S .4 ' E n E 5 a a I III I . . - m 0 l5 ‘9 0 V In N '- (AGIN),3 2. Figure 6.7 Experimentally determined {3. 4o 55 25 20 IS IO 82 (10") 81 doorway state. An alternate explanation would be that the multiplet is based on the coupling between quadrapole and octupole states with parentage in the anti—analog configuration. This interpretation could be verified by studying thez’~ decay of the states. The deformation observed in this experiment are compared with the results of previous experiments in Table 6.2 This experiment usually observes a deformation larger than that for the alpha experiments. The deformations observed in the 12 MeV (p,p'l) experiment are always larger except for the 5 - state at 5.723 MeV. Table 6.2 Comparison of Huclear Jeformations ’ 12* of (L) ”Li. (L) J (L) JL <1.) L L Present exp (Pe 65) (Li 67)* (Te 68) 3.830 0.65(2) 0.53(2) 0.7l(2) 1.0(2) 4.502 0.89(3) 0.56(3) 0.76(3) l.15(3) 4.607 0.24(4) ,0.10(2) 5.141 0.22(5) 0.l7(3) 0.87(5) 5.362 0.458(3) 0.26(3) 0.15(4) 5.723 0.46(5) (2) 0.32(4) 0.44(3) 6.335 0.37(4) 0.38(4) 6.642 0.35(2 and 4) 0.36(4) 7.643 0.49(3) 0.54(3) * 4 , Calculated from the /éL using R = 5.62 fm. o 82 This may be due to compound nuclear effects, exchange effects, or 2 step processes enhancing the cross section at lower energies. The reduced transition probabilities are compared to the electron scattering results in Table 6.3.The values are in agree- ment for the 3 — state but differ by a factor of two for the 2+ state. A possible explanation might be that the electron interacts with the nucleus through the charge form factor by exciting protons while the proton can interact through both protons and neutrons, and the large number of excess neutrons in 48Ca may cause some discrepancies. It is observed that some of the 4+ states rise at forward angles. This same effect has been observed with other nuclei in this region (Ku 70) (Pr 70) (Th 69a) and is not understood at the present time. 6.7 Comparison with Theory Jaffrin and Ripka have calculated the single particle-hole excitations giving rise to the odd parity levels in 480a. (Ja 68). They predict two groupings of negative parity states. The lower group consists of two 3 - states, one 5 - state, two 4 — unnatural parity states, and a 2 — unnatural parity state. In the same region of excitation energy (4 to 6.5 MeV) we observe two 3 - states and four states with L = 5 angular momentum transfer. The L = 5 transfer implies that the states are negative parity, perhaps two of the L = 5 states are associated with the predicted 4 - states. 83 The reaction would occur through L = 5 transfer with spin flip. The same process may be occurring in the higher grouping of negative parity states between 8 and 10 MeV. The theory predicts a 5 - state, two 3 - states, two 2 - and two 4 — states. We observe several L = 3 and L = 5 states in this region which may be associated with the predicted unnatural parity states. It would be useful to have the results of a (p,p'I) angular correlation experiment to help determine the spins of these states. Ba Be 33 B1 B1 Ca Ch E1 E1 Fe Fr Fr 61 Gr 62 69 67 66 66a 67 65 69 67 7O 67 68 66 70 67 BIBLIOGRAPHY Bassel, R. H., R. M. Drisko, and G. R. Satchler. Oak Ridge National Laboratory Report ORNL-3240 (unpublished, 1962). Bernstein, A. M., M. Duffy, E. P. Lippincott. Phys. Letters 303, 20 (1969). Bjerregaard, J. H., Ole Hansen, 0. Nathan, R. Chapman, S. 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APPENDI CES APPENDIX 1 Detector Fabrication and Testing In this section a detailed description of the fabrication and testing of the Ge(Li) proton detectors is presented. 1. Choice of Ge(Li) The choice of Ge(Li) rather than Si(Li) for making counters capable of detecting protons of energy greater than 30 MeV was made for the following reasons: 1. The range of a proton in Ge is about one half of that in Si. This allows one to use a single 5 mm drifted detectors for 40 MeV protons rather than a 9 mm stack of Si(Li) detectors. The resolution of Ge(Li) detectors should ulti— mately be better than Si(Li) detectors because the cost to form an ion pair in Ge is 20% less than in Si(2.98 vs 3.66 eV), (Pe 69a) and the maximum transfer of energy in nuclear collisions in Ge is less (X2.5) than in Si. The reaction contribution to the tails should be less structured in energy and therefore more easily accounted for as a source of background. This is because Ge has a higher density of states 87 88 of lower excitation energy and a relatively uniform Spread of isotOpic abundance. 4. Ge detectors appear to be less susceptible to proton radiation damage effects than Si(Li). 2. Fabrication The starting material is horizontally grown, gallium doped germanium having a resistivity of 10 — 20 ohm - cm, an etch pit density of less than 1000 per cm2, and a carrier lifetime greater than 400 microseconds. A parallel slab of suitable thickness is cut from the ingot using a diamond saw or a wire abrasive cutter. The surfaces are lapped with 600 grit and then 1000 grit to remove the saw cut damage. After taping the surfaces not to be exposed to lithium the slab is coated with lithium in a vacuum and let up to an argon atmosphere. The lithium surface is immediately coated with mineral oil and then put in a furnace being purged with argon. Diffuse at 400° for about 10 minutes and allow to cool to room temperature in about 20 minutes. After lightly lapping the diffused surface the resistance measured with an ohmmeter across 1 cm of surface should be less than 30 ohms. After lapping the sides, the n—type and p-type surfaces are taped in preparation for the etches. The first etch is in 2:1(90Z HNO : 50% HF) for 2 minutes. After rinsing with at least 3 1500 ml of deionized water the crystal is etched for one minute in 89 1:1(50% HF : 30% H202) and rinsed well with deionized water or methyl alcohol. The sides are blown dry with dry nitrogen and the tape is removed. The diode characteristics of the crystal are then measured at room temperature. If the saturation portion of the curve has a lepe of less than 0.4 mA/lOO V at 400 V bias it is suitable for drifting. The diode is placed under reverse bias (400 V,’“25 mA/cm2 of diffused surface in a freon bath and drifted until the desired drift depth is achieved as observed by the c0pper stain test. The solution used for the c0pper stain test is a saturated solution of CuSO4 in H20 and 10% by volume HF(50%). This stock solution is diluted 1:1 with H20 for use. By wiping the solution on a freshly lapped surface with a cotton swab while the diode is under reverse bias a c0pper stain will form at the P-I junction. The drift depth W may be calculated as follows: W2 = 2/4 Vt where //qis the lithium mobilityIVA.5 X lo—10 cmZ/V—sec at 23°C. V is reverse bias of the diode during the drift in volts. t is the time in seconds. The thin window geometry shown in Figure I.l is used for 90 E: is ...... _,II 3.: a mmOE anthem 385m :4 56?. 223:. m me: : MW >FWEomo-eo_tom 825m 2de f m Figure 1.1 Surface barrier geometry. 91 detecting protons in the 25 ~ 50 MeV range. The thin window is achieved by fabrication of a p+ contact on the intrinsic region. The procedure is as follows: A drifted piece of Ge crystal is cut to the desired geometry. A l-cm diameter flat ended quartz rod is chucked in a mill and is used with 600 grit abrasive and water to bore just into the intrinsic region through the p—type region. A p~type rim is thus left free to use for mechanical mounting minimizing injection of charge. The same rim has the added advantage of providing a simple means of incapsulating the p+ contact during subsequent etching of the outer surfaces. Crystal damage in the bored hole is removed by lapping with finer grits and then etching. The etching of the bored hole is rinsed and dried carefully prior to evaporation of a thin Au film onto the Ge surfaces of the hole and the exposed intrinsic region. The hole and p+ contact are then incapsulated by placing a piece of tape across the p- type rim sealing off the gold p+ contact. he n-type surface is also covered with tape before final etching with the HF : H202 etch. The diode is then mounted in the cryostat, evacuated, and cooled. When cooLed to LN2 temperature the finished detector must have a leakage current of less than 1 na at bias greater than lOOV/mm drafted depth. If this low leakage current is not 92 obtained the diode must be recycled through the final etch procedure until it is obtained. 3. Packaging The requirement that the Ge(Li) detector be stored in vacuum and at liquid nitrogen temperature at all times does present a packaging problem. The goniometer (Th 69) was designed to be com— patible with cryostats of the Chasman design (Ch 65); therefore, this package was used. Figure 1.2 shows the mounting and collimation used with the proton detectors. The use of the thin slit in front of the colli— mator was found to minimize the slit scattering contribution to the ”tails” of the peaks. Figure I.3 summarizes the results of a study of the slit scattering problem. The response of the detector and slits to the 12 C(p,p') reaction at 40 MeV was measured at a labora— tory angle of 40 degrees. The top spectrum shows the response to what was thought to be an ”ideal” slit geometry. A broad satellite peak was observed to be associated with each of the excited states of 12C. This satellite peak was then shown to be due to slit scattering by degrading the energy of the scattered particles which are in the region of the thick slit and using the thin slit as the effective collimator. The result is seen in the middle spectrum. The “thin” collimator was then made of Pilot B scintillator and the signal from a phototube viewing the scintillator was used to turn off the Ge(Li) detector when protons passed through it. This 93 55.. mw Erma; oz< 58m 232 NEE @2205 $55 #73 o... 4.2 On N.H ensues ,,,,,,, man—>2 .3 1:2 v\_._ Side Entry Ge (Li) Detector 030 V I? Bias). 94 Slit Scattering Study, Cl2 (p,p') 40 MeV 45 Degrees Detector Response Figure I.3 Slit scattering. 7.66} MeV 4.44l MeV Grounld State | 1 l ‘ i 1 ml + + 2500 3750 3000 3250 _ Channel ..., __ , l e 7.7,, - _ ,LF1__ .-._ K __ 33$) Slit Geometry Brass C apperature rnm 64mm Brass 3 ~l.0cm - 3 2,5 mmx6.0 mm ~25.0cm from ~30 mm dia. beam spot "Pilot 8" Scintillator l.6 mm x 4.0mm apperature -l.6mm Same as above but with Anticoincidence gate from Scintillator 95 technique greatly reduced the Slit scattering contribution to the tail as seen in the bottom spectrum of Figure 1.3. This technique also allows use of relatively narrow collimation in order to reduce kinematic broadening effects and at the same time minimize the problem of slit scattering from the thick slits. 4- 12.55.2193 Once the detector is mounted there are a number of preliminary tests which the counter must pass if it is to be successful proton counter. All of these tests are necessary but not sufficient condi- tions to have a good proton counter. The final worth of the counter can only be determined by use with the beam. The first test is to check the counter as a J — detector and monitor its charge collection and resolution as a function of bias voltage. As the voltage is increased the peak height increases and the resolution improves. For a good proton counter both of these effects should show saturation at bias leVels of’”100 V/mm drifted depth. If the peak height continues to increase as the bias is increased up to the point at which breakdown occurs, it is indica— tive of charge collection problems in the detector. Figure 1.4 shows the complete spectrum of 137Cs obtained with one of the proton counters. An evaporated source was placed in front of the 1/4 mil aluminized mylar window; therefore, the K and L con- version electron peaks appear in the spectrum. The fact that these peaks have a resolution compatible with the straggling through the 96 .ESM comm m . one» u bmH v H am mum—2:2 1522410 OOON Ont com. Com. 08. 00h 00m fl —— — 4‘ id #1 4 d I .99. 313$ T - saw zikfi 68. l mmW€E mnw¢x Aizse 2&00749 ;0\>9_ $.00 «2855 5.5% moEmam 38 208% Is; 8s. no zambmem 205.84“ zo_mmm>zoo 024. >9. :1. 3.3 a I see - o. a , sens ems 8.3 m En? em.» a _ rec. , N mmPZDOO _ _ _ _ _ _ _ L Do— E. 2 _ _;_i;___,_ 1 . 1 _ so. 1 .0. 1 1N0. _ been when __ I lg momma . Inc. . 588 62.9 chem ,. me. 1 o. _ c _, I . mso. _ mmpzaoo _. . .o fi 024 0 fi to Home be: some so. mmJOrEflu (In—1.4 It; Emu... mmmzxoi... 3002.3 [ill-III 99 80¢ nhwm 0N3 000m obnn Dawn 83 08W. 1 1 _Onn_1_ __ 1; a _1 _ ,o 1 11 1 _ 1 T Sea... - .0: >920. - 2.522%1 -~o_ - 3.1;. 599.8. ..E. 91o -moe mmeDa >9.N._N >§O¢ 593.21 _ _ _ - p o— 1 OOON _ 009 0rd. OOO. or.» .. OnN 0v 141.11 1 ,1 111, a 1 , 1 1 es, 1 _o_ 1 u 1N0— - .....z: 5E8.» L.N.efio 1%., has . >228 3.3.2a p _ . _ p _ _ Avo— ,_ fl , 1 , 1 1 1 , , 1 1 1 o— _1_ 11.1; __ 11 , 1: 1 :11 _ 1_ _ 1 1,1 1 1 1:1 _1__ ,_ _,__1,__E1___1=__i o I .01 A212,“: >918 . l EdvI SV ow. 1N0— , as: 58$.» League 1 0. $98 >918: . m us >019.» Ah 3 01m_ _ _ — o— IOPUMHMO mm=mm xva 38213 850.812 .159 8.1an 24mm .0 468585 1.1.18 .925 0.205 oz_u_oo22 ow 2015.188 Gauze m1: oe mzofiametzoo , .SOawSHOmoa museum was Op maofiusnfihpaoo H.H panah 101 detectors in the side entry geometry. Protons at 42 nev were scat— tering from a 13 mil tantalum foil. All protons were counted above 160 keV. After each bombardment the response of the detector was measured with 137C3 lf—rays, 6OCO Y'mrays, and the elastic scattering of protons from Ta. Conventional electronics were used for these experiments. The detector was operated at a bias of 100 V/mm. The response to the Tlrays was made with 7 keV (FWHH) initial limiting resolution in the electronics. The integration and differentiation time constants were set for 1.6 K 10’6 sec. The resolution was measured as a function of total proton flux presented to the detector. A significant deterioration ('12 keV FWHM) in the resolution after about 1010 protons/cm2 total flux was observed. There was no noticeable increase in reverse current after the bombard~ ment, although during the bombardment the reverse current was propor— tional to the beam current presented to the target and was as large as 500 namp. In Figure 1.7 a charge collection efficiency is shown as a function of total proton flux presented to the detector. It is interesting to note the charge collection efficiency response was the same for both.‘Y—rays and protons. The charge collection efficiency vs. total flux was observed to fit the follow- ing functional form: £=1—1<¢ where {is the pulse height normalized to its prebombarded value ¢is the integrated proton flux in protons/cm -12 12 K = 3.2 X 10 3:0.8 X 10_ cmz/proton 102 .ewwEaU aofipwwpws cowonm 8A muswfim - —--- b h —-hh-- - - —-Fp- - b . Eo mcwaocav 9 20. «9 o0. ...O_ 4.1.. a u - —¢-q-qd q u quadudd I d —qqu-dd - 1 x2... coeoen. m> £32. 8.3.... 8.8.8. j I. 9.2850 2.380 c. 32:60 8.8.81 seen. W AUHVAXU O I. w won: 4 I // coeocn. o. wd 0. mm v. x a x . .u cw Eu «T a... .. 1 /N u 0v. I _ u 0 /\££/ I m/ml . I ON .0 00.0 00.0 00.. ,_ --.—.W-— wr—h (q 1‘) 103 The previous functional form can be understood using the Hall (Ma 52) and Shockley-Read (Sh 52) single-level recombination theory. Their theory predicts the changes in free carrier lifetime, (lip - lfico), is a linear function of the number of defects introduced, the capture- cross—section of the defect for minority holes or electrons, the position of the Fermi level and the position of the recombination level in the forbidden gap. The charge collection efficiency, 5 , is related to the free carrier lifetime. £=1 - cu m.- - llro) and (1/1: - lleo) ’-‘-' (ZR/t) 4’ where t is the charge collection time 15 is the carrier lifetime before bombardment ‘Tis the carrier lifetime after bombardment of Q protons/cm2 . y. ..r 6. Other Ge(Li)'Detectors ‘ . The use of lithium drifted germanium is not restricted to making detectors of the thin window surface barrier geometry. The side entry geometry offers the possibilities as detecting higher energy particles (Gr 67) and making special purpose debaters with structured electrodes to measure the denSity of ionization along the path of the particle (Gr 68b). The chief disadvantage of the side entry geometry is the nonuniform window on the side through which the particles pass. The 104 best resolution measured for this geometry is 60 keV (FWHM) for 40 MeV protons scattered from Au. A contribution of about 40 keV is attrib— uted to this nonuniform window. The relative importance of this non- uniform window decreases as the range of the particle being detected increases. We have also explored the feasibility of using a small side entry Ge(Li) detector in a thin-windowed mount to measure T'—ray and electron intensities simultaneously and consequently serve as a single crystal conversion-coefficient spectrometer (Gr 69a). There are several advantages to such a system, principally in the fact that it uses fewer electronics and only one analyzer, the Ge(Li)-Si(Li) system usually used can use one analyzer by measuring Y‘-rays and electrons sequentially, but then live—time and half-life corrections become more cumbersome. Also, a single efficiency curve can be made for the single—crystal Ge(Li) spectrometer, one that contains information about both 1’-ray and electron intensities. (This is possible because the electron efficiency curve is a slowly varying function of energy.) Finally, the single—crystal spectrometer is potentially a powerful tool for coincidence experiments involving another detector because it would often mean the difference between a double and triple coincidence or, again, sequential experiments. For short-lived, difficult-to"mahe nuclides, this can be important. Disadvantages of such a device are source strength, i.e., the detectors are necessarily small, so strong sources are required, and the straggling experienced by the electrons in passing through the 105 window, which must be accounted for in stripping out the data and which affects the background of the spectra as a whole. In particular, the straggling makes it very difficult to separate the L and H electron peaks because of their small energy difference and large overlap. There also appears to be no single optimum size of detector to cover all energy regions, so one would be compelled to have an assortment of sizes. The efficiency curve for such a detector is shown in Figure 1.8. It takes the form of the relative efficiencies for 1’—rays and elec— trons, i.e., vs. the T'-ray energy, By. [For purposes of illustration, the data has been compressed onto a single graph. In actual practice, one has to account for the differences in binding energy for different elements.] To obtain the conversion coefficient of a transition, one merely obtains an experimental intensity ratio for the‘Y —rays and electrons and multiplies this by the corresponding ordinate from Figure 1.8 i.e., “cf: Ar Because the efficiency for electrons varies very slowly, the above efficiency curve is very nearly the same as the efficiency curve for ‘r—rays alone. he latter curve is presented in Figure 1.8 with an offset scale for comparison. 106 IO. I \0 g \ \ \ \\ \ \ ?\ \\ g ’n‘ \ \ 3 \ a D \\ \ ’\~ -2 \e 3 IO — \\ “ i c:) \ 1R\\ f u \3 « 0 \ \ \ \ 0 \ \ \ 0 \ \\ 10'3 '3 A. IO IO IO ENERGY (keV) Figure 1.8 Relative efficiency curve. 107 To determine conversion coefficients most precisely, the efficiencies for detecting electrons and ‘r-rays should be comparable, at least within several orders of magnitude. This means that a small detector is required, particularly for lower energies, where the Compton backgrounds from the ‘Y-rays can easily obscure the electron peaks, especially when the latter have been broadened by straggling in passing through the window. At higher energies the Y’-ray effi— ciency becomes very small and so do most conversion coefficients, so this becomes the limitation. A larger detector would be more useful for higher energies, and a smaller (thinner, to lower the ‘r-ray efficiency) at lower energies. In addition, the window thick— ness could be reduced to 0.1 mil or less, and, in fact, straggling could be essentially eliminated by using a vacuum interlock to allow one to place the source inside the can with the detector and by using a Ge(Li) detector of the surface barrier geometry. APPENDIX 11 II.1 Theoretical Angular Distributions 0n the following pages are plotted the results of DWBA calculations at each energy. 108 do'lda (mb/sr) I u utrnl / / \ / I'— u b 1 1111111 1 / IO IO IO IO IO L 6N 1 l '11""$" 109 T I 'UUU‘ T IT'I'U' \ I IIIIIIII “Co (pm’) 25 Mev _ R g I - - Fricke (Beam. 1 lllll l lllllll \ I A \ . L33 1 rj UVIIT l \ / / '1.- m 1 . 11.111 1 l / 00 0| 1 141411] 1 l 4O 60 80 IOO IZO ecu (dfiq) do/da (mb/sr) no . “Ca (p.p') so MeV I _ R=l __ Fricke Geom I I LJIJII 60 80 IOO IZO Io2 da-ldn (mb/sr) Io° 1.1]. I 111111 A l l l jllllll l Lilllljl O 20 40 6'0 8'0 ch‘M’ IOO Iéo da/dn (mb/ sr) IO IO 112 “Ca (p,p') 40 MeV _ R = I _ _ Fricke Geom. . \. G q 2.0 4.0 6.0 8.0 9“ (deg) I00 IZO 11.2 Plotted Angular Distributions On the following pages are plotted the experimental center-of- mass angular distributions of each observed state at each of the incident beam energies. 113 IO IO -.--.114_.._-_,_- - T I I V'I'l .11'4‘1—r-1-rfl11T-flr-l—l-T-I-mrr‘fw o 4800 “LP” - 5": 3.830 MeV f o 0 T .... 0 40 MeV . O '. ' .35 MeV " ‘. . ' 30 MeV "-,,.,25 MeV l l J l J I 20 40 so 80 I00 120‘ ecm(deg) 115 ‘IO : . 48 I : 0.... CE (p,p') , _ o { . . E =4.502 MeV ', LP 0. \IO:- 0 . : o 40 MeV ; - . O O . . ' o .o : ' .o . - ’0 ho: '- E . 35 MeV : *....o. .Oooh ‘ ‘: ..o ID:- i : ’ 30 MeV L : ’00.... . l I -. I ' |_ o 25 Mev I : o i i ' I o -20 4o 60 80 I00 I29". l l l l llll 1 1 111111 [4, l l l 1111' .L l I l [1111 llml 116 .1-____~—____+_—_._. 3 4s , 5 : C0 (pop) : 1- 8 .. - E = 4.607 MeV .. - § § 1’ ".I :- ‘9 -: : M¢ '5 if ’ 40 MW 1 . +’+¢¢ ? - ¢ 1, . o + f s w _ “1’”. ’35Mev : .‘ 1. ‘ - ¢ .l :- ‘¢ _ : 30 MeV : J? 1' ¢ : - i ‘. 25 MeV - 0 alone 4° 60 39 '00 _ __'_2_9___ a 117 \ E Ca(p.p’) 3 g : E"'=5.I4I MeV _ g ' fi+++ - ‘.|L_ 1|» * _ a E . ’ ¢‘ 3 : +4» I .f s" + i ;.I :_ ii 4. -: F E +‘ E I : l+ ‘ <, _ " ‘H 35 Mev " .. ?§¢ ... , 1 g i 1 30 Mev f _ 9§¢¢¢.. a 6 _29_559169____§9 I00 I20 1. __ _____, r. ‘7— _'_=,_ Ca (p. p’) i : i , * 5* = 5.249 MeV: g-Ol :- + H 40 Mev 1 s : i : ++ ++ +¢ * : _ * + - .O|L_ 35 MeV ‘— ‘g 1 1’ i l 3 ++ + i : - + + + +1 1 - i ’0' b- * 30 MeV _: ‘5 ++ + + i '5 Z 1 §* _ 1 : + H 25 Mev .0l 1 l l ' t l o #20 _ 4O 60 80 IOO lag __ 119 E ‘°Co '1'.» ¢ IIIUIII I ljjTl W ' H1111, 4s 11 fi? 00 (p.p’) E” = 6.098 MeV 40 Mev +111 11111$1 L411: 11111PL 4 11¢1111 | 100' 1‘ fi__. da-lda(mb/sr) " 123 '.=.' 1* +-~ "Cow '3 I ' E’=s.335 MeV 1 1— . 1-1 p s . e .‘1 0H0. 40 MeV '17 #0 j. E '. 1 3 1- ' g _ . 7 ¢ . ‘1 T t H I'- +. o A 3 o 35 Mev : 3 ". 1 I I 0 s I 4 '. 1 "s . + '1 _, O I'E- * + 30 MeV Ti I ‘--. 1 : C .‘O Q. g '1 . 25 MeV _ O " O — 5 3 o g 20 , 40 so so 100 120 I0 124 4% Ida (mb/sr) 1163- 5 4s , : : C0 (Pap) : - 5‘: 6.641 MeV - - + 1 — + — - g o 40 MeV " .- ‘1, '. -. .3- "o. . ' . 35 MeV -. Z ‘ Q E I H j t , . 1 , 30 Mev . *1 .1 E ’1 3 _ o. 25 MeV ‘ .0 C 1 4 1 1 .4 1 20 40 so so _IOO 120 125 " E + “Ca(p,p') E : + ++ E‘=s.7ssMev .. *1 + +1.. +’ :J E- +++ +++ 40 MeV _ 1 E +++ .I 1- + +1 .‘F ”+35 MeV fl .|:- +1 I ': 5 f *+ ‘ , : + ' L 4? + f + 30 MeV ‘1? "a" + T: i E i : i ?+ * 25 MeV 1 T + 1"°'o 20 4'0 so so 150 120 126 ."5 1+ 1, c..1p,p'1 -: 1 - +q E =s.sss MeV 1 1+ 1 I ‘r + 40 MeV 27 '.I _. 1 ‘ E +*+ i’1, 1+1 1 I 11 : 5. 1 M v 1 i +.. +? 35 e 1 1 * ~ ' 5 +_ a <: 1’ T + 30 MeV _ I * ,1 1 .l - ': E i 111 ’ Z s 25 MeV : 1 J i 4 5 ‘0' 2b 43 so so loo E0 w 4—-h ~._.“ . -" '——-— - ...u 4 \o n 127 lj rl'lil - ll 4¢—I Jj IIUUn T IfIUIll I .l1 *1 4"Ca (p,p') + u 25 MeV J E ‘= 7.009 MeV 1 4,1 LJJJIL $4 [11111]] W 4 jllLlll $4 1 1 llllj IlLl 20 40 so 80 IOO ”ng 128 d : “Co (p.9’) - I E*=7.320 Mev: DJ E“ ‘ _ E + . : + + <1 + “ OJ 7 + —: E + + 4OMeV _ 'dcr/da (mb/sr)” W OJ? +++ +t++ 35MeV : E ‘ g L + “H + 30Mev : a? :- + ++ ? 1 + + .4 ..J +++ +* 25Mev ‘ 2 .0I n L L 4 I Q -20 40 so; 80 I00 IZQWM #— —- 129 5 4e 3 ; Ca (p,p’) 3 : E"‘=7.4OI MeV : _ § .. .I __ 1’ _ E E : H I 4% + *H 1 E ' §§ $ 40 MeV q EAJ _ ‘F + + _. s. C § 2 £ :- + H -‘- .a ' + §+ : E 4E ? - g - + + 1’ * 35Mev ~ 3 " :— ’ ¢ +‘ ? 4 *+ + : L «p .. ... ¢ * .- ' 9 $ * 30Mev " .I ? N :1— §¢ .5 : § 25Mev 1 F- -+ .OI 1 1 1 1 1 n 0 a 20 _40 60 #§9_,_.LQ_Q____|_§9_,___ e da/dn (mb/sr) .Ol 130 llllll I'll ...74.L . 4L” '9 I IIIIII — l'l 48ca(p’pl) ‘ E*=7.47I MeV : T +++ H +++ ++ ++*¢ ++ ++ 4OMeV VJ hf N +35 MeV T 30 MeV 3 1+? *? 25MeV O 20 40 60 80 IOO '20 96M (“2’ __ e . 131 E “cum l : E*= 7.52: MeV .I :_ f E + 4 +++ ‘ | + ++ 40 MeV 1 - Z 1’ ‘6, W ++ l -' + +++ 35 MeV . [T'rlllll' —.— + —o— dc/da (mb/sr) 9. I [I'll] ___._ _+ T 30 MeV 1 T 1 [UTIIII '41 g N ? 25 Mev ‘ + L L1111 ”I “1‘ o 20 4o 60 80 IOO l20 9cm (deg) 1* da-ldh (mb/sr) '0 = 4a ‘ E Co (p.p’)' E x - C E = 7.643 MeV 1 . '0 . '0 O 7- . 40 MeV j ‘7 ' ‘ - ‘ O. - .. , .. . O... .1 I — ' ’ - : o : I 1 b . «II . o - lt , 35 MeV 4 .— +¢ . .0 ¢ . O. W I .- . ' 1 ‘5 " ' so Mev .1 ' ,*,. . - | h . .- i ;- I I 'o . 25 Mev : .| I 1 .l l l L 0 20 4O 60 80 I00 I20 #132 9m(deg.) 133 48cc (p’pl) + * E' = 7.786 MeV ++ 1 -'.r +H++ 'g E +25 MeV: 0' I I L I I I . 20 4O 60 80 I00 I 20 .....__———— ._.———" 134 IIIII .....,+. .. ' 4L . . I IIIIII 48 : Ca (p.p’) .. E‘= 7.940 MeV : 1 + h 40 MeV -o- I :1 141:] t + 1taswlev .. H 3 f w 130Mev ‘ H ¢ 5 IZSMeV '_' so __ so I60 Iéo 135 * Co(p p) . + E =8.037 I I MeV‘ I:- 40 MeV 1 i r- i 3 _ 1+} . § H + ‘ 5' EH . -__- H, 35MeV ;_ w : ’+ : <; + ' _ 4f _. E 30Mev z“: : + 1 i H ' I “+9 25MeV o _ 2g 5 40 so do I60 Iéo f 136 I“- 9 9 ‘ 4a , E CO (9,9) 2 5": 8.250 MeV . 40 MeV - I. f f‘ - 35 MeV _ ”I I 30 Mev ‘ “a I," 'I 25 MeV : ,_ _ \\\-r——— _’ I" 0 2'0 40 6'0 80 I60 Iéo I! 137 If I 486°(p’p') HI” E’=8.364 MeV I 1 111114; 40 MeV 1111' {H ”H.“ 6? 35 MeV I . * . i _ _ 20 4O 60 80 IOO IZO —'~ 138 Jr IIIIIII I IIIITTI da/dd“(7n”b7sr) I IIIIIIWI lillilwl I TIIIIII .Ol M”, 4300 (p.p’) i I E*=8.50I MeV ; I" d I + + 1- 9 ¢ I I +’ 6 + ‘¢ 4OMeV : I : IIII+ I‘+ +’ i I. I 35Mev : I § -I I II I ” ‘2‘ ”I + 30Mev I N, i I? ‘ I II‘ .3 + 25Mev 4 O [P’- 20 40 60 80 529K420 \ 139 I : «bafihpq 3 a 0 _ $ 6+ '3 I E . “I. I” 40 Mev , : _ IIII,H - 7 I ' 5' I 'E : I 35 MeV E , .. I ,1 IIII d I II - I fig- I 30 MeV ': I ‘ : I I I - *II+ - I . I .- I? :.I _ I 25 MeV 1 s I 3 ‘ 0 e 20 40 60 80 I00 I20 \ I fl 140 II I ++I I § 48Ca (p,p’) . E‘=8.589 MeV . fl? *III _ E “If ”I I 4OMeV E I I - I‘' 1 II ‘ I» II? _ I 35M v 5 I*Q I e 5 II, q i; I § - I.— . I I 30 MW .1 I E I I - / * *IIQ’ j ; I, .. El __ I 25 Mev _= I= ¢ I 0 22 4O 60 80 IOO IZO m 141 «Ca (p,p’) II 1 E’=8.658 MeV II? JE- II ‘5 I +I I 40 MeV ; II I “*II -'E' I ‘: 5 * I - 4% II 35 MeV I “H. ? l:- + I+§ '5 : I : “T + 30MeV ' I‘II _- “HI I.25Mev 3 __0__ 26 4'0 60 80 I60 I20 *- - .. “...-— -.- .. ...“..- ...-.....-3 a. , , Hf? “ _ — «T I ITIUIII v T V II II III1II'$ 142 I UIWIUI O r I II I” I II I I +I ’ §§o¢ 4e , Cg(p.p) I E = 8.786 MeV I§§ ’I I 25 May L 39 1 40 60 80 I60 T20 I LIIIIJII I lillljll J I [III] I I 111111 143 48 Ca (p.p') E*=8.868 MeV I 30‘ MeV I 25 Mev I I J I 1 l IIIIII I l llLIIlI I IIIIIII E II” + .. f? r r I ”(E E I I _ f+II”I, '5' fi. I ++ I _ I III“ .I I00 I20 II.3 Tabulated Angular Distributions The following pages contain listings of the differential cross section versus center of mass scattering angle for the excited states of 48Ca at each energy. The error shown is the total relative standard error . 144 ZAqa CA 48 (P;P) 25 “EV 12036 27025 17046 32034 22056 37043 42052 48000 53007 67083 58013 72086 73027 87092 78029 83031 97092 12077 27066 17057 32076 22097 37085 28007 42093 48041 63019 53048 63024 53054 73028 73068 88034 78.71 93034 83073 98033 000000 0065507E+O4 0016857E+O3 0022079E+Q4 0024346E+02 O073801£+O3 00908025+02 O015168€+O3 0015075E+C3 0097593E+02 0095748E+01 O044355E+02 00157365+02 0016888E+02 00170155+02 0022883E+02 002243ZE+02 0050529E+31 (P19) 35 V‘ELV 000300 0046846E+O4 O044213E+C2 C019897E+O4 0055059E+02 0.48968E+03 O014934E+O3 0034817E+02 0015526E+03 O094435E+02 0013525E+02 0037824E+32 0020865E+32 O014S49E+02 0017799E+02 O017164E+02 00350316+01 0012056E+02 0025536E+01 0065410E+01 O027S72E+01 000931 004078 001245 009927 001356 00286R 001957 C023§R 002241 005393 003034 003856 004198 003173 003346 002856 004559 000933 007235 901197 005469 001636 00?131 004990 001734 002535 145 005093 703873 004290 005668 003899 905305 0099C? 005431 C0895? 005616 006537 CA 48 12077 27066 17087 32075 22097 37084 28007 42093 48041 63019 53048 68023 58054 73067 '78070 93033 CAQB 12036 27026 17047 32035 22047 37044 27057 42053 47091 62050 52098 67084 58004 72075 73018 87094 78021 92094 83023 97094 (P00) (‘ ‘A— 2:03 a; COQQUV 0054151E+Q4 0060661E+GP 00198CIF+O4 O02362??+02 0050941E+C3 00122PCF+C3 0042551E+02 0016318E+O3 00120405+33 0011072E+CE 0064341E+CE 0014841E+CE 0019577C+02 0019401E+02 0013736E+C2 00363C6E+01 (P0P) #3 ”EV G'OOOO 0053055E+34 004827OE+02 0020531E+O4 O090656E+02 O047874E+O3 0016777E+O3 0041752E+32 0013973E+33 O064996E+32 O015553E+02 0021657E+32 O015949E+02 0012864E+02 001157SE+02 O011753E+CE 0022659E+01 0059843E+C1 00235515+01 0030191E+01 0022598E+01 “.0953 C05577 501131 00689? 001595 002400 004482 001636 C0?564 F06257 C0309? 004827 005046 004623 305063 c.953a 001143 008735 001490 C06167 C01647 C020R5 304418 001788 003132 3047C? 004726 704159 005099 004864 005373 009273 0.7185 003696 007449 006524 * CA 48 * CA48 12038 27030 17049 32040 22060 37050 27071 42059 48007 62087 53015 67092 58022 72096 .73037 58003 78040 93003 83042 98002 12078 27070 17089 32080 23000 37089 28011 42098 48047 63026 53054 68031 58060 73035 73075 88041 78078 93041 83080 98040 (pip) (Plp) 25 MEV 3083C 0060832E+C1 O058992E+31 0053753E+O1 0.58799E+o1 0051857E+01 O049C995+01 O052931E+01 003524CE+01 002333OE+01 '0012149E+01 .o.180655+01 O010029E+01 001447OE+01 0082955E+OO O085638E+OO O066280Ef00 O07O638E+00 O066762£+00 0064932E*00 O061102E+OO 35 MEV 30830 0095647E+01 0050447E+01 0077559E+01 0037970E+01 O058169E+01 0020184E+01 0050372E+01 O013292£+01 00146O4E+01 O071334E+OO O014993E+01 0040344E+OO 0011576E+01 O028844E+00 O028912E+OO O046165€+00 O040327E+00 0033848E+OO O050213E+00 0019955E+OO 409168 .201696 303149 108070 108154 .102808 105150 '1.3537 201188 201274 107937 107871 108516 108670 200674 106303 201616 1(5130 109344 103355 209325 200866 203239 20CC94 105245 200493 102501 201786 202941 201990 200602 301020 201532 300991 402433 203702 300424 204913 200587 204814 146 ‘I' 0 CA 48 (PIP) 29083 MEV 30830 12079 O088269E+C1 403556 27070 O057345E+31 209661 17090 00693E9E+01 207992 32080 004619PF+31 106883 23000 00568025+31 105538 37089 0'3394IE+21 105102 28011 0.53069E+01 10P638 42098 0019756E+Q1 107025 48047 0015553F+01 204714 63026 0086BCOE+OO 205190 53055 0014367E+31 202597 68031 0059963E+QC 203471 58061 0012283E+31 Eoouug 73076 0038056E+00 303833 78079 0027224E+00 306907 93042 0046182E+OO 204425 CA48 (P191'40 MEV 30830 112037 001083OE+02 309997 17048 O083O91£+01 207754 32039 C025703E+01 304304 22049 O069651E+01 10490? 37'“8 0014142E+01 206854 27059 0051058E+01 102390 42057 O010648E+01 205510 47096 O'151C4E+01 202313 62085 O043134E+00 209281 53003 0013524F+O1 200323 67090 O025359E+00 304783 58010 0090897E+00 205000 72084 0030975E+00 300168 88000 0027129E+00 207707 78027 0.41259E+00 2080C9 93001 0015836E+00 304732 83029 00384BCE+00 201140 98000 00102655+00 301771 i ‘I CAQB CA 48 (PIP) 12038 27031 17050 320Q1 22061 37051 27072 42060 48009 62089 53017 67094 58024 72098 73039 88005 78042 93005 830#4 98004 12079 27070 17090 32080 23001 37090 28011 42099 48048 63027 53055 63032 58062 73036 73076 880“2 78079 93042 83081 98041 (PIP) 25 MEV 4.502 0.48215E+01 0°43834E+01 O0#82#3F+010 O041406E+01 O049267E+01 0039669E+01 00‘0332E+01 0034893E+31 O033462E+01 0019981E+01 O028665E+01 0017O7IE+OI 002357IE+01 0015428E+01 O016184E+01 O085368€+00 0014120E+01 0066116E+OO 001114OE+01 0053459E+OO 35 MEV 40502 0054412E+01 0.54047E+Ol 0059864E+01 005374EF+CI 005991HE+01 00#0672E+01 0056369E+01 O033578F+01 0025189E+31 0016632E+01 001877OE+01 001257BE+01 001638#E+Ol O097977E+30 0094626E+OO O045450F+OO 00é8464E+00 0041858€+OO O05“273E+00 O0#1916E+00 600392 '2.5544 304537 201533 109011 103806 107721 103109 106302 105371 103333 1023695 103Q94 10?505 103707 104398 103617 105249 103073 147 104289» #03537 ?00063 2068”? 106879 105207 102450 101795 102003 106253 710954“ 1.75?3 109836 1070“9 106656 9029?R 204946 203137 202365 109711 107002 \ i I 12079 27071 17090 32081 23001 37091 23012 42099 480“8 63028 53056 68033 73077 78080 93043 CAQS 12038 27029 17049 32039 22049 37049 27060 42058 47096 62086 53004 67091 58011 72085 73025 88002 78028 93002 83030 (PIP) 3 CA 48 (PIP) 29'? “EV #050? O052454E+01 0051851F+31 0054966E+Cl O049630E+01 0053713E+01 0042935E+01 O05335€E+Cl O036151E+31 O02780?E+Ql 0015659F+01 0021901E+01 0014967E+01 0012047E+01 0070684E+00 O043953E+OO MEV #0502 0063832F+Ol 00701?2E+01 006836OE+01 0058020E+01 0069739E+01 0045674E+01 0066909E+01 0030066E+Ol O019757E+01 O012156E+01 O015347E+31 0097894E+00 0013958F+01 0067113E+OO 0068662E+OQ 0036050E+OO O0“85#3E+JO O031613E+OO 00“2580E+OO 403226 P0P745 907063 106353 106996 1 027951 101837 101463 106913 106730 1070C? 105231 108714 2.2596 205012 500179 20?“?6 301050 20C9C2 104561 109759 100763 103513 1-9IFQ 1072CC 108069 107126 109915 200791 P03O3D 204708 2057C3 204171 900053 i CA 48.1P09) 25 MEV ' 27031 * CAQR 32041 37051 27072 42060 62089 53017 67095 58024 72099 73039 88005 78042 93005 830““ 98005 32080 23001 37090 28011 42099 “8048 53055 68032 58062 73036 73076 88042 78079 93042 83081 (PIP) “0607 0026150E+00 0034972E+00 003501SF+00 0024091E+00 0038729E+00 00271505+00 0031409E+30 0026190E+00 0029130E+00 O024296£+00 0.?3039E000 0018149E+OO 0023236E+00 0015160E+00 0018837E+00 0012598E+00 35 “EV “0637 0033190E+QO 0035172E+OO 0028940E+33 0035735E+00 0.29946E+03 0020019E+CO 0015508E+0 001002RE+00 0013066E+00 00961325'01 00910585'01 0049737E'01 0068035E'01 00292745'31 0055831E'01 1201658 '800645 502605, 1001078 “05395 408878 408698 309611 “06685 306760 402129 306321 306549 304922 30726? 300017 9-6OC9 1304433 50667“ 1100022 409218 30921? 6025°9 600970 705607 509000 709307 902426 707853 901597 148 6-“243 ’ i CA 48 ‘I 27071 32081 23001 37091 43000 43049 63028 53056 68033 73078 78081 9304# CA48 (PIP) 37049 27060 “7097 62086 5300# 67091 58011 72085 73026 88002 78029 93002 83031 (Pip) 40607 003934CE+CC 0031393E+03 003364QE+OO 0031811E+CC 0032279E+00 0.27063E+CO 0015011E+00 0021238E+OO 0013299E+00 0010493E+00 00698052'01 0063966C'01 #0 ”EV 40607 0021239E+OO Oo23450E+OO 0013836E+03 00709555'01 0012082E+00 0066hl9E'31 0010182E+OO 0052803E-01 00557658'01 0025353E'01 0050333E’01 001“7“9E'01 00339905'01 2908 MEV 2.7224 700458 90770? 800601 hoEOCO 604551 607596 701314 601839 9.0008 705377 700290 708182 805367 10007“2 909466 80h841 806722 1001542 1009435 903659 907308 806564 1204578 705517 _cA 48 cAua 32042 37052 48011 62091 53018 67096 58025 73000 73041 88007 93007 98006 32081 37091 23012 43000 48049 53056 68033 58063 73037 88044 78081 93044 83083 98043 (P0?) (PIP) 25 MEV 50141 0011087E+00 O014852E+OO 0023225E+00 0018250E+00 0022232E+00 0016674E+00 0021382E+00 0015392E+00 0015426E+00 00991315'01 00877266'01 O097408E'01 35 VEV 5.141 3.12052E+OO 0014498E+00 0011260E+OO 0015351E+OO O-20536E+03 0017823E+OO OolOuOOE+OO 0-13233E+OO 0071823E001 0.43141E-01 0061262E'01 00278526-31 0.53198E-01 0025816E'01 ~1509830 801040 800035 507374 602960 405060 Soflllu 405797 409383 406943 407634 305200 1500741 006227 1103310 707135 699339 509904 604748 6.4276 605762 Q08471 804244 904891 608692 703790 149 cA 48 32082 28012 43001 48050 63029 53057 68035 58064 73079 78082 93045 CA48 32040 37049 27060 42058 47097 62087 53005 67092 58012 72086 73026 88003 78030 93003 83032 “98002 (P;P) (pip) 50141 0-10704C+OO 00948335-01 0017125E+00 0019834E+QO 0013326F+00 0018563E+OO 0011781F+OO 00137a8E+OO 0010120E+OO 00543655-01 0045653E'01 40 ”EV 50141 0'14204E000 0'17957E+00 0099617E'01 0016158E+00 0015520E+00 0088508E‘01 0016058E+OO 0070819E'31 0012416E+OO 00538922'01 0066955E'01 0022233E'01 0050947E‘OL 00181265’01 00324825'01 00142405'31 2908 rEv 1101341 130?479 1301579 708621 601489 609771 509333 605539 609633 807742 804651 290C833 709762 12033C8 804328 800430 704747 603940 704747 702797 805685 808071 1100263 809697 1106863 709175 909324 CA #8 (P0P) 25 ”EV 32042 37052 42062 62091 53019 67097 58026 73001 73041 88008 93008 83046 ‘98007 ‘ CAMS 32081 28012 43000 48049 63028 53056 68033 58063 83044 73081 93044 83083 98043 (PIP) 50249 - 00526115“01 0.705766201 O089976E’C1 0047542E'01 0069085E'01 00429916901 0065567E‘01 O032465E‘01 00359625’01 00267095'01 00223732'01 00199332'01 00127155'01 35 VEV 5.249 . 0044632E'01 O045037E'01 00400545'01 0054804E'01 00278245‘01 00556215'01 0024690E-01 0038720E'01 0085183E'O2 0°20302E'01 00528585'02 O074228E'02 0031828E'O2 1908928 1?01458 1006164 1203981 1209592 90P638 1008447 1008417 1104793 1003333 1008487 1301376 1009917 2409333 1704133 1706629 1606292 1209875 1103673 1604545 1205783 1709677 1509824 1906154 2007778 2402963 150 , Q CA 48 32082 23002 37092 28013 43001 148050 63030 53058 68035 "58064 73079 93045 6 CA48 (P,p) 42059 62087 53005 67092 58012 72086 73027 83032 (PIP) 50249 0.543225-31 0061137E-01 00539CBE'31 0041560E'01 O069395E’Q1 O074468E'31 00271685'01 0950346E‘31 0026178E'01 .00396755-01 0019000E'01 00716665'02 4C MEV 50249 O048644E‘01 00137755'01 00349905'01 00132265-01 0032346E'01 00128575‘01 (00169935'01 00502296’02 29 0% MEV 2002143 4501600 1505570 2004151 1203896 1307653 1406349 1900000 1301579 1209875 2105217 2609630 1700357 2P03503 1500685 1306250 1508332 2002979 1605000 2206000 CA 48 27032 32042 37052 42062 48011 62091 53019 67097 58026 73001 780#4 93008 830“7 98007 CA45 27071 32081 23001 28012 #3000 48049 53056 58063 .73078 88044 78081 930#4 83083 98043 (P)P) (P0P) 25 MEV 50295 O020415f+00 0013716F+30 0014556E+OO 0076957F-Ol 0076325F-01 O0309ESE'01 0059214F'01 00241325'01 004#389F'01 00259255'01 00245615’01 0020313E'01 00228585'01 00166035-01 35 MEV” 50295 0080910E'Ol 0095212E'OI 001007BE+OO ‘O010094E+OO 0039966E‘01 00277095-01 C'“C864E-01 00279905’31 00163785'01 00851825'02 001353QE'01 00813205'02 00109288-01‘ 00412595'02 1400533 1309055 706616 1105309 1407447 1501492 130469? 2P0RZPZ 14006“? 1107838 16010“1 1006957 130“800 90430“ 160?105 1404844 260023? 1105615 1Q09298 2509232 1300278 IS'IOCO 1701473 1709677 1906842 1508000 17079?“ 2098000 151 CA 48 (p,p) 2908 VEV 27072 32082 23002 37092 28013 48050 63030 53058 68035 73079 CA48 22050 37050 ‘27061 42059 #7097 _62087 53005 67092 58012 83032 (P09) 50235 0012135E+03 0014227E+CO 0094148E'01 0011667E+00 0012546E+OO 00585095'01 00245505'01 00630&3E'01 00168785'01 00115655'01 “O MEV 50295 0012570E+OO 0077793E‘01 0012507E+OO O0Q6472E'01 00Q12225'01 00137755'01 0025882E'01 00126755'01 00209295'31 0061948E'02 16062CC IOOSQQ6 BE'COCC QOOOCC 1000000 1505325 1505965 1207596 160Q493 2106785 200323? 1307660 909641 1508318 1703973 BIOFOCO 1907037 1901956 1908182 1906757 § CA 48 i CARS 27032 32043 29062 37053 27073 42062 69092 53019 67097 58026 73001 730“1 88008 78045 93008 83047 98007 12079 27071 17090 32081 23001 28012 43000 48049 63029 53057 53063 73038 73078 83044 9304“ 83083 98043 (Pip) (P0P) 25 "Ev 5.362 0085737E+DO 1809746 0-61248F+OO o.8#172E+OO 00643215+OO 0084349E+00 00625245+OO 00547865+OO 00540425+00 0052071E+03 O0“8459F+00 0051053E+OO 0055398E+OO' 0034293E+00 O048788Ef00 O025135E+00 0042699E+00 0019493E¥00 35 MEV 50362 0011156E+01 00113065+01 00112515+01 O-IO#QBE+01 O010183E+01 0011169E+01 O065134E+30 0064899€+OO O04643OE+OO 0053008E+OO 0048858E+OO 0035376E+OO 0034394E+00 0012365E+OO 0011242E+OO 00130415+00 001081OE+OO 507883 1204946 70Q343 701123 305891 301356 30h191 20“216 703420 R029CC P045C1 203894 P0392? P06896 P01859 20‘534 1308723 406008 901547 4000“3 6097?“ ?07384 209185 30C896 207940 ?03651 301765 208166 308655 “09973 #04702 3055“3 304362 152 I CA 48 (Flo) 2908 MEV 50362 18079 0085275E+00 1901309 27.72 0095862E+OO 502810~ 32082 O080268E+OO “01431 23002 0084973E+OO 500463 37092 O07Q503E+OO 3018C“ 28013 0086877E+00 302239 “8050 0056957E+CO 309Q67 63030 0.46011E+00 3.1265 53058 0008520E+00 3.q535 68035 O0Q8939E+CO 207056 73080 O'“0726E+OO 30?677 78083 O027953E+OO 306650 93046 001“227E+OO 406007 CAQB (P1P) #0 MEV 50362 12038 0016196E+01 1h03725 27030 O01QQ75E+O1 502209 17069 0019559E+31 802556 32040 O013255€+01 #04821 22050 O013865E+01 309643 37-50 0012853£+01 205096 27061 0019439E+01 204238 “2059 0073049E+OO 209245 47098 0060861E+00 306135 62087 0045697E+00 P09HFC 53005 0054639E+00 301675 67093 O03“085E+00 300218 58012 O0Q7EBOE+OO 303732 72087 0022513E+00 307631 73027 0022091E+00 403354 88003 00881505'01 5006“? 78030 00137095+OO 500653 93003 008938#E‘01 #0767“ 83032 00109SOE+00 “0125“ 98002 00722585'01 30957“ 8 * CA48 .27033 17051 32043 22062 37053 . 42063 48012 62093 53020 73002 73043 88009 78046 93009 83048 98008 12079 27072 17091 32082 23002 37092 28012 43001 63029 53057 68034 58064 73039 73079 88045 78082 93045 83084 98044 (P1P) CA #8 (P0P) 25 MEV 50723 0071285E+00 0085853E+00 0068738E+00 0067913E+00 Oo63490€+00. ‘o.53115€+oo 0052678F+00 0042246E+00 0047920E+00- 0034841E+00 0037888E+00 0025501E+00 00337935+OO O022197E+OO O028690E+OO 0021879E+00 35 MEV 50723 00498355+00 00534285+30 0053010E+00 0062615E+00 0055880E+00 0063968E+00 0062722E+00 0064311E+00 0048024E+00 O065653E+00 0048177E+OO O056950E+00 0032116E+OO 0029045E+00 O018355E+OO 0.27387E+00 0015736E+00 O022701E+00 0012154E+00 701794 1302895 505191 705087 307176 400394 .501402 ?.6756 153’ 309941‘ 208606 300792 6209359 300288 209390 208082 203655 3002699 608446 901173 504014 701069 306365 307946 302169 207524 300078 208672 2.9476 209694 402371 400449 307490 307483 3011.5 302211 Q CA 48 (P1P) 29.8 ”EV 50723 12080 00754IOE+OO 2909880 27072 17091 32053 23002 37093 43002 48051 63031 53059 68036 73080 78084 93047 0071087E+OO 0065631E+30 O0729395+OO 00616C1E+CO 00698455+00 O064868E+00 O062444E+00 0043892E+00 0060642E+00 0041361E+OO 0032833E+00 0018763E+00 00173865000 CA48 (Pip) 40 MEV 50723 27030 0053851E+OO 17049 0053449E+OO 32040 22050 37050 27061 42059 47098 62088 53006 67093 58012 72087 73027 88004 78031 93004 83033 98003 0.57982E+oo 0050141E+OO O071569E+OO 0061996E+OO 0074657E+OO 0070004E+OO 0045333E+OO o-6#254E+oo 0034247E+OO 0056454E+OO 0027681E+00 0030517E+OO O013534E+00 0021612E+00 0010360E+OO 0018550E+00 0079861E'O1 5.4471 1205424 b.4365 606836 903975 300507 308504 302043 600150 209500. 306566 405047 400595 900563 230577? 704490 1309468 306700 309915 20776? 304139 20°287 209650 300265 301238 304061 306292 400086 309743 403825 300948 307446 8 CA 48 (PIP) 32044 37054 27074 42064 48013 62094 53021 58028 73044 88011 78047 93011 83049 98010 i CA48 (POP) 25 N‘EV 60098 001239CE+00 00152055+00 0013702E+00 00904725'01 0011035E+00 00811988‘01 00101455+00 0087917E'01 00558585'01 00352675'01 00491125'01 00284095‘01 00446145'01 0029847E'01 35 MEV 1709727 1803333 1606403 1308375 1309485 1004148 1106759 1003935 1004787 1105485 1103177 1800518 901271 709824 27072 32082 23002 37092 43001 48050 63030 53058 68035 58065 73039 73080 88046 78083 93046 83085 98045 60098 0010427E+00 0092188E'01 0910072E+OO 00885855'01 O090438E'31 00898635'01 00479835'01 007262CE'01 00482465'01 0051298E-01 00290975'01 00269715'01 00181355'01 0021367E'01 0014435E‘01 0025772E'01 00134405'01 3008367 1809516 240337? 1500111 1107861 1300342 907754 908233 100255? 10'50C0 1009725 1703214 1503030 1409000 1307324 10.4000 1005965 154 Q CA 48 17091 32083 37093 28014 43002 48052 .63032 53059 68037 58066 78085 93048 O CA48 (P0P) (PIP) 32041 37051 27061 48060 47099 62089 53006 67094 58013 73028 88005 78031 93005 83033 98004 60098 0010168E+00 0010174E+00 0010365E+OO 009089OE’01 O0117C9F+OO 0013822F+OO 00676505'01 0011641E+00 00492415'01 00694016'01 0023145E'01 00180505'01 4O MEV 60098 00780515'01 001063OE+00 0088333E‘01 0010723E+OO 0068477E'O1 00371835'01 00531865-01 00297535'01 00337538-01 00248365-01 00115065'01 00228465'01 00124395‘01 0013393E'01 00114505'01 2908 MEV 7207380 1609102 1008487 1802085 808192 907363 900764 909635 903566 904214 1503030 1407059 3100636 2701275 1306102 1105020 1501504 1209629 1503694 1300926 1608450 1701644 1603390 1404324 1501143 1506125 1202101 155 ‘I 0 CA «a (2.0) 25 MEV CA 48 (2.2) 29.8 MEV 60335 V 60335 12040 0015424E+01 1503297 12.80 0.12155E+01 1305889 17.52 0096514E+OO 1005675 27.73 O096753E+OO 5.1779 32.04 o.75388€+00 503317 17.92 0011182E+01 901991 37.55 0065948E+OO 306559 32084 O081118€+OO 404614 42.64 0055515E+00 307800 37.94 0.67494E+oo 305657 48014 0058330E+00 “-4826 43.03 0062138E+Oo 300623 62095 003669SE+00 “'0855 48052 0053686E+OO 0.1400 53.22 0.51232£+oo 3.7379 63032 0022586E+OO 405878 58029 0044684E+OO 3064“? 53.60 0042556E+OO 401866 73005 O033747E+OO P09741 68038 0013903E+OO 4.5412 73045 0038354E+00 300782 58067 0025279E+00 406235 88011 0016195E+oo 307135 73.82 0017632E+OO 501265 78048 OO327395+00 303860 78085 0011782E+OO 509673 83050 0020862E+OO 305241 93048 0057866E-01 704816 98011 0098215E-01 307881 4 I’ CA#8 (2.2; 35 MEV. CA48 (P0P) 00 MEV 60335 60335 27072 0085321E+00 50?369 12038 0092674E+00 2305890 17091 0-14949E001 704973 27031 0078392E+OO 707382 32083 0082659E+OO 406349 17050 0099906E+OO 1206522 23002 00129285+01 307482 32041 00809105+OO 602836 37092 00702655*00 3'7479 / 37051 0084029E+00 304312 28013 0082792E+OO 303149 27061 0094758E+OO 302141 43002 0060599E+OO 30P9PS «2060 00579O9E+00 3032Q1 48051 0045788F+00 4039?? “7.99 00386585000 Q.0500 61.1\ 0.1«aunr.ga H.07PL 69089 0.19000F003 L016Hfl 51.52 0.3193Hr+ou «.7337 53.07 0.217995000 5.77Po 63036 0016754E+OO 500112 67094 001314OE+OO F05178 58065 0024341E+OO 906198 58013 0012506E+OO 702433 73.40 0015375E+OO 403576 72.88 00115142000 5.6152 7308C 0014689E+00 601443 73029 0013082E+00 503831 88046 0058527E-01 704366 88005 0030032E-01 903636 78083 0014387E+00 S0?97O 78032 0011176E+00 507017 93046 0038628E-01 800842 93.05 0023813E-01 9.9030 83085 00102675000 407169 83034 00530705-01 603470 98045 0024994E-o1 706368 93000 0019148E-01 806884 f CA 48 § CA48 (P1P) 25 MEV, 60641 A 27034 0010301E+01 17052 0013886E+01 32045 O0788OOE+OO 22064 0010797E+01 37055 O075837E+00 27075 O088957E+OO 48015 007437EE+00 62096 0046581E+OO 53023 O063988€+OO 68001 00359585+OO 58030 0055741E+00 73006 00299O3E+OO 73096 O031191E+OO 88013 00175825+00 93013 0012821E+00 83052 00201485+00 98012 0010836E000 (PIP) 35 MEV 60641 12080 0015493E+31 27073 O079771E+30 17091 0012757E+01 32083 0072831E+00 23003 0010946E+01 28013 0080218E+OO 4700? 0061937F+00 «H051 0046641F+00 63031 00838QQE+00 53059 0038853E+30 68036 0021090E+00 73041 0016281E+CO 73081 0016277E*OO 88047 O063747E‘01 7808“ 0012855E+00 93087 00581845'01 83086 O0952“7E'01 98046 00“7632E'01 508707 909736 503667 600242 305‘099~ 403101 309575 306248 303243 301568 302774 30?326 30512“ 307575 #01447 305073 3069“5 1603188 506373 9076C6 “0922“ 506989 305638 703“]? “061Q7 “00854 309839 “04858 “0P6E3 509911 703664 506842 70?489 #09585 504579 156 Q i CA 48 (P19) 27074 17092 32084 23003 37094 43004 “8053 63033 53061 68038 73083 78086 930#9 CA#8 (p,P) 12038 27031 17050 22051 37051 27062 “2060 “7099 62090 53007 67095 72089 73029 88006 78032 93006 83035 98005 908 MEV 60641 0010327E+01 0013369E+01 0078749E*OO 0010673E+01 0077087E+OO O071126E+OO 0066277E+OO 00316335+OO 0051335E+OO 0025510E+OO 0019117E+OO 0012693E+OO 0078838E'01 40 MEV 60641 0023IOCE+01 0067950E+OO 0.12768E+01 0092929E+00 0065472E+00 0078052E+00 005PSISE+OO 003QQ7EE+OO 0016971F+OO 0025198E+OO 0014379E+OO 001129SE+03 001213CE+OO O0#3488E'01 00938465‘01 0032699E‘01 006OQ3SE'01 00298305'01 502277 804996 408801 502826 303095 208481 307904 306907 308383 400594 409870 5066C2 603973 1905659 807723 1302789 601106 308388 307267 30807“ R0969? “01988 506331 509261 509855 603193 706233 603092 805598 601496 6087“? CA 48 (P,P) 27034 37056 27075 42065 68002 58030 73006 73047 88013 93013 98012 cAus 32083 37093 28014 48051 63032 53059 58066 73041 73081 85047 78084 93047 83086 98046 (P1P) 25 MEV 60786 0019022E+00 0011524E+OO 0013494E+OO O064418E'O1 00292665'31 00386492'01 00375512'01 0'“1734E'01 00166062'01 00200205'01 00179212'01 35 MEV 60786 0011147E+OO 0011258E+00 0012488E+OO 0062758E-01 00316332'01 0044835F'01 0051283E'31 00330952'01 00274482'01 00189595'01 00284862'01 00166725‘01 00275222‘01 00150925'31 1702571 1206560 1605620 2000438 1502660 2105684 1208323 1208825 1706495 1507720 1106657 1601600 1204210 1102981 2001862 1203846 1205949 1009364 10.3661 1601754 1505362 1302250 1300244 1006592 1000625 157 CA-48 (P1p) .27074 32084 37094 28015 43004 48053 68039 58068 78087 93050 60786 2908 KEV 00993792'01 0012254E+00 00933662-01 0099456E'01 00792212'01 0071357C'01 0026851E'01 0040634E'01 00210385'01 00164585'01 CA 48 (P1P) 40 MEV 32042 22051 42061 48000 62090 53007 67095 58014 72089 73029 88006 78033 93006 83035 98005 60786 00946072'01 0011544E+00 00637982'01 00405892‘01 00371752'01 00311362'01 00261672'01 O’46591E'O1 0'194162'01 0028540E‘01 00107262'01 0.206832'01 00906322'02 00205915'01 00914168'02 2008293 1500425 1?09927 1500094 1109205 1509255 1408461 1301341 1605000 1702258 2604500 2802967 1506735 2600597 1209629 22-2961 1407789 1400612 1904648 1506071 2101273 1408507 1800784 1201382 1309263 5A 48 27035 37056 27076 42066 48015 62097 68002 58031 73006 73047 88014 93014 83052 98013 cA48 32083 37093 28014 48052 63032 53059 58066 73041 73081 88048 78084 93048 83087 98047 (P12) (pip) 25 MEV 60885 002486BE+OO 00176155+OO O016447E+OO 0012315E+OO 00153252+OO 0071014E'01 00700745'01 008909OE'01 00637225’01 00686135'01 00340675'01 00218602'01 00539325'01 00266982'01 35 MEV 60885 00921405'01 00822875'01 00841565'01 00793672‘01 0053878E'01 0090741C'31 0065267E‘01 0033495E'01 0.443025'01 0.152115’01 0035964E'01 0.17078E‘01 00212345'01 00120262'01 1400983 901083 1107186 1100275 1109841 1202143 809119 1006027 806154 907489 1003367 1406195 708407 901654 1606129 1502400 1309631 1405659 200065 Q07500 906857 1002231 1201956 1603390 11.3416 1300357 1206990 1105196 158 CA 48 (P0P) 27074 32084 37095 28015 43004 63034 53061 58068 73084 78087 93050 60865 0017693E+OO 00146005+00 00146515+OO 001393BE+OO 001044RE+OO 00486952'01 00866585'01. 00584715'01 0042525E'01 00354132'01 0014334E’O1 CA48 (P09) 40 MEV 32042 22051 37051 27062 48000 53007 67095 58014 72089 73030 ' 88006 78033 93006 83035 98005 60835 00922375'01 0010021E+00 0080552E'O1 00763205'01 00605782'01 0058917E'01 00369092'01 00503935'01 0022151E'O1 00278602'01 0066304E'O2 00203742'01 00101305'01 00180605'01 0058699E'02 2908 MEV 1304931 1205000 900047 1201292 1306983 1209734 1005385 10072C3 110?815 1107525 1609815 2404615 3107975 1502035 1905588 1908500 1407856 1903060 1203019 1800123 1405366 2901176 1405303 1607368 1303518 1800328 (A 48 cAafl 27035 17052 32046 22064 37056 27076 “2066 48016 53024 68002 73007 73047 88014 93014 83053 98013 12080 32083 23003 37093 28014 “3003 63032 53060 63037 58066 73041 73082 88048 78085 93048 83087 98047 (P0P) (92”) 25 “CV 70009 O0657“7E+00 O078466F+OO O060109E+OO 0058795E+OO 0061976E+OO O0697192+OO O0Q6948E+OO O0h3296F+OO 0035576E+00 0018551E+OO 0013607E+OO O01693OE+OO 0014671E+OO 0089133E'O1 001“516E+00 00103QBE#00 35 ”EV 70009 706653 1600336 1903268 1101822 309799 408277 405487 507659 407309 406064 5015““ 502105 403676 502337 #09005 401727 0073889E+OO 2406524 O-“1311E+OO O072916E+OO 0039594E+OO O049O16E+OO 0031839E+OO O018665E+30 0°25236E+OO 0017349E+OO 0019066E+OO 0098460E'01 0010497E+OO O0#7260F'01 0097206E’01 00559115'01 O06#733E'01 00443325'01 609928 701621 505046 #09225 503489 Q0510R 500“0Q 907026 502“?“ 507669 705367 805058 60604# 605745 606656 505160 159 cA #8 27074 17092 2300“ 37095 28015 43004 “805“ 6303# 68039 58068 93050 CA48 (P1P) 17050 32042 22051 37052 27062 42061 #8000 62090 53008 67095 58015 72090 73030 88006 78033 93006 83035 98006 (Pip) 2908 MEV 70039 0059132E+OO 0093612E+33 005860CE+OQ 0042792E+OO O051598€+OO 0033664E+OO O029298E+OO 001650#E+OO 0015593E+OO‘ O018135E+OO 006“239E'31 4O MEV 70009 0.58616E+00 0035947E+OO 0.3735#E+OO 0034513E+OO 0.48707E+OO 0029162E+00 0017506E+OO 0.161435+00 0.18153E+OO 0080425E'01 o.17779E+OO 0.66998E'01 00778025'01 00269125-01 0066676E'01 0020615E-01 00‘70415'01 0020689E-01 6O°OS7 190098? 7009F8 503392 #08634 4 06845 602176 509243 502472 508999 7.1074 2209852 1002763 1201562 600165 500276 503050 90R635 1006780 60q549 606918 601096 803551 801572 1100870 706343 1007672 70053“ 802558 CA 48 (P,D) 32047 42067 48017 62098 53025 58032 73049 78052 93016 83054 98015 CA48 43003 48052 53060 68038 73082 88049 78086 93049 83088 98048 (PIP) 25 MEV 70320 00824585'01 00672C7E“01 00842952'01 00433345'01 0046451E-01 0066287E‘01 0021382E-01 00212235-01 0.16046E-01 0016453E’01 00152425'01 35 MEV 70320 00301245301 00252195?01 0019278E'01 O020562F'01 0025037E'01 00107165'01 00181585'01 00109715-01 0076275E'02 00100225°01 2C03182 2002941 1801442 1401915 1908687 1200675 1701250 1803855 1509174 1906888 1108483 2502836 3400488 3305204 1°°°000 1308654 2601539 1706470 1906505 2701622 1405529 160 CA 48 (PIP) 27074 23004 37095 43005 48054 63035 53062 68040 73085 78088 93051 CA48 27032 37052 27062 42061 48000 62091 58015 72090 73030 ' 88007 78034 93007 83036 98006 (P1P) 7032C 001187IE+00 0016354E+00 00769762'01 0076489E-Ol 00462892'01 00305592'01 0034532E'01 00254692'01 00268325'01 0.245415'01 0024422E'01 40 VEV 70320 00164765+00 0058461E'01 0015634E+OO O078966E'01 00337625'01 0016519E‘01 00251925'01 0090235E'02 00139295'01 0078004E'02 0077168E'02 00373205’02 00435245'02 0028869E‘02 2908 VEV 1704286 2203134 1606283 1505412 2200432 2008873 2202631 2003108 2206154 2103286 1201956 2103061 2003292 907703 1307253 2101875 2500000 2004101 27093°4 1900488 2304500 2704400 3004762 2600769 2904333 cA 48 22065 37057 27077 48017 62099 53025 58033 78052 93016 83055 CA48 (Pa 32084 37094 43003 48053 53060 68038 58067 73042 88049 78086 93049 83088 98048 (P19) 25 MEV 70401 0039436E+00 0018778E+00 0025294E+00 O016776F+00 0010833E+OO. 0.1158EE+00 0013378E+00 00805432'01 0040777E'01 00733042'01 P) 35 MEV 70401 00210952+OO 0015793E+00 0011779E+00 00879535'01 00827788'01 O056825E'01 0048939E‘01 00488345'01 0026133E'01 0041657E'01 00103695'01 00230852'01 0010022E‘01 1004801 809258 901323 10.5507 706723 905709 801611 608444 708195 603042 1001056 800667 904580 1208741 1009178 906711 1203810 907268 1002632 1003590 1607451 1107054 1401647 161 CA 48 (P191 27075 32085 23004 28016 43005 48055 63035 53063 58070 73085 78088 93052 CA48 (P,p) 37052 27062 42061 48001 62091 53008 67096 73031 88007 78034 93007 83036 98006 2908 70401 0026647E+00 0019283E+00 0021416E+00 0027863E+00 0010843E+OO 0012823E+OO 0065052E-01 00938975901 00643978'01 00598542'01 00252425'01 00175205'01 40 MEV 70401 0011763E+00 0016905E+00 00551005‘01 00563232‘01 00440505'01 00416632'01 00349755'01 0039067E-o1 00994555'02 00219152'01 00639772'02 00165725'01 00654382'02 MEV 1201273 1090203 1408832 708848 1105975 1007337 2700993 1005419 1007154 2103103 1606666 1805606 1008242 903850 1704488 1609677 12.0000 1609310 1200709 1004696 1607451 1308732 2202222 1104747 1703970 W CA 48 32047 62099 68004 58033 93016 83055 cA48 27073 32084 43003 48053 53061 68038 58068 73043 73083 88049 93049 83088 98048 (p19) (P1P) 25 MEV 70471 00656015'01 0025352E‘01 0.297915'01 0031716E'01 00290015‘01 00305285'01 35 MEV 7.071 O085035E'O1 0056448E'01 0066984E'O1 0074418E'01 0052159E-01 00441135’01 0065928E'01 00312215'01 0039480E'01 0023355E'01 00178925'01 00173165-01 0075464E'02 2206857 1809818 1309649 1905256 908020 1004910 1903500 2308421 1302684 1400496 1401739 1101780 1002750 1009829 1100488 1008471 1903409 1400833 1602344 162 CA 48 (PIP) 27075 32086 37096 28016 48055 63036 53063 73086 78089 CA48 (PID) 27032 37052 27062 42062 48001 62091 67096 72091 73031 88007 78034 93007 83036 98007 70471 00823575'01 00625355'01 0061960E‘01 0046173E'01 0073597E'01 00176635‘01 0057547E’01 0099067E'02 00455745'02 4O MEV 70471 0084052E'01 0.10265E+00 0014510E+OO 0073753E'01 0076911E'01 00285635'01 00289165'01 00235155'01 0031253E'01 00975045'02 00179035'01 00728635'02 0013392E'O1 00279085'03 2908 MEV 2709118 2801042 2304725 8509830 1E08660 2606098 1504316 3900834 4104615 3401600 1208055 1005412 508941 1403228 1404096 1302952 1300465 1106087 1702000 1601724 2109512 1207500 3100345 CA 48 (Pip1‘25 ”EV 32047 22065 62099 68005 .58033 73049 93016 83055 CA48 27074 43003 48053 53061 68038 58068 73043 88049 93049 83088 (PIP) 70521 - ' 0088088E'01 0010575E+CO 0042405E'01 00206659‘01 00467588'01 00249435'01 0013543E'01 00210225'01 35 MEV 70521 0015093E+00 0040009E'01 0033826E'01 0030047E“01 00287855'01 0025633E’01 00250845'01 00109915'01 00101665'01 0012575E'01 163 01903833 2700741 1309239 190740? 1409826 1700000 1601195 1308869 1108732 1907528 2h04545 1905094 1402857 1503273 1208510 1508000 1607400 1803279 CA 48 (PIP) 27075 ‘32086 43005 48055 63036 _53063 73086 78089 70521 0072664E-01 0070349E'01 0010437E+OO 0056144E‘01 00904645'02 00424025'01 00990655'02 '00490798‘02 CA48 (P,p) 40 MEV 27063 48001 62091 67096 72091 73031 88007 78034 83036 70521 001189EE+00 0047841E'01 0031660E'01 0'223065'01 0015038E'01 00275168'01 00877545'02 0015742E'01 0011048E'01 8908 MEV 2904333 2206852 1100043 1803243 4509048 1808428 3909583 5005000 1200503 1808987 1501413 1601481 1707272 1207654 1802000 1704314 1403788 cA48 cA «a (P,p) 25 MEV ‘ 12041 27036 17053 22065 37058 27077 42068 48018 62099 53026 68005 58033 73010 '73050 88017 93017 98016 12080 27074 17092 32084 23003 37094 28015 43004 48053 63033 53061 58068 73043 73083 88049 78086 93050 83088 98049 (PIP) 70643 o.22318£+o1 10-8270 O019952£+01 0017161E+OL O023981E+01 0311331E+01 00171SCE+O1 O01007PE+O1 00103388+01 003724OF+00 0081806E+00 0.34056E+OO O048909E+00 002996CE+00 0029634E+00 O025387F+00 0022376E+OO O023905E+00 35 MEV 70643 0020259E+O1 001624OE+01 00235088+O1 001467SE*01 0020097E+O1 0.12u09E+01 0.16725E+01 0084397E+00 O059898E+00 O038659E+30 O052382E+00 0040824E+CO 0026604E+OO 0028068E+00 0019014E+00 0023O7OE+OO 0018380E+OO 0019583E+00 00277105’02 309918 807562 300729 209233 2.2032 207416 303659 401856 208979 303010 304805 301924 307896 300418 300967 203909 1u.7953 400720 1104934 305466 508463 207662 204014 207111 308932 301622 304361 305810 305446 403087 309783 402546 305055 305011 3502341 164 CA 48 (P,p) 2908 MEV 12081 0023548E+01 1304947 27075 17093 32086 23005 37096 28016 '43006 48055 63036 "53063 68041 58070 93052 CA48 (P1P) 27032 17051 32042 22052 37052 27063 42062 48001 62091 53009 67097 58016 72091 88008 78034 93008 83037 98007 0019787E+01 O022481E+01 00154495+01 0020228E+O1 0012095E+01 00159O4E+01 001049CE+010 0092479E+00 0033944E+00 0055603E+00 'O036409E+00 0036503E+00 O017069E+OO 40 MEV 70643 0019566E+01 0023827E001 0017210E001 00207O4E+01 0012524E+01 0018884E+01 0080254E+00 0050867E+OO o.38335£+oo 0040223E+OO 0030292E+OO 004553CE+00 0028050E+OO 0018526E+OO 0021637E+OO 00157815+OO 0019819E+OO 0011452E+00 307552 1306710 300287 301285 206267 204221 204151 301870 308236 306427 805784 400000 402613 405653 702605 400838 304317 206238 202182 209789 404060 302065 309345 303573 305209 304411 304947 309501 304786 300498 300412 it CA 48 i CA48 48018 63000 68005 58034 73010 73050 .93017 83056 98016 37094 43004 “8053 63034 53061 58068 73043 73083 83050 73057 93050 83089 98049 (P,P) (P1P) 25 MEV 70766 O015880E+OO 0.907928-01 0.88558F-o1 00121565+00 0010826E+00 0095608E'01 00678655'01, 00945046'01 0.56452E-01 35 MEV 70756 002151“E+00 0025397E+OO 0026750E+OO 0011502E+OO 0017517E+OO 0014074E+OO 00707115'01 0089548F'01 0041901E'01 O07QObEE'Ol 00216535'01 0074829E‘01 00179235‘01 11.1326 1006091 709606 907793 601875 80158“ 609341 600464 604432 15.5443 11.6920 605149 60459? 603819 605728 708717 309333 907574 709856 13065P6 1308209 1001053 165 ‘I * “3006 48055 63036 68042 58070 78089 93053 CA 48 (P19) 2908 MEV 70786 0015793E+OO 0017979E+OO 00908375'01 001163lE+OO 0010896E+OO 0010517E+00 00655695'01 CA48 (P1P) 40 MEV 70786 1701428 801941 805450 1200355 801318 802600 708178 32063 O028367E*00 1103000 22052 0033723E+OO 37053 O033999E+OO 27063 0035224E+00 #2062 0018436E+OO 48001 0017743E+00 53009 00134O7E+OO 67097 58016 72091 88008 7803“ 93008 83037 98007 00856QIE'01 0011311E+00 0067534E'01 00195015'01 0060fi965'01 00152835'01 0036659E'01 0010778E'01 1108045 600000 906369 701835 807201 705750 70213? Q0O8’OO 709826 1307100 805816 1302552 801050 1203750“ 0 CA 48 (P.P)'25 MEV 70940 78055 00616115'01 93018 O05#76QE‘01 83057 O06233CE'01 98017 0042893E'01 * CA#8 (PIP) 35 MEV 70940 0059057E'01 00624905’01 0033109E‘01 0020332E'01 00175215'01 0012971E'01 68039 58068 78087 93050 83089 98049 806722 708468 706627 60703# 1000886 1003955 1308172 1104000 1500235 1206636 166 * CA 48 (Pap) ‘I 70940 680#2 O0h8172E-31 73087 0045399E-01 78090 00294458-31 .93053 00185835-01 CA48 (P1P) 40 MEV‘ 70940 72091 00235135-01 73032 0029552E-o1 93008 0097744E-02 33037 00185805-01 98007 00808#OE-02 908 MEV 1004000 1104273 1600833 1605“28 1501628 1305517 18.3000 1109139 1k00833 W * VCA 48 (P0P) 25 MEV * CA48 (P0P) 32048 37059 27078 42069 48019 53028 27074 17092 32085 23004 37095 28015 53062 73044 73084 78087 93051 83090 98050 80037 0022268E+OO 0017810E+OO 0022813E+OO 0015292E+OO 0015955F+OO 0018146E+OO 35 MEV 80037 0.33361E+OO 0042652E+OO 0017966E+00 0031807E+00 0018483E+00 0.19993E+OO 0017116E+00 O069370E'01 0070283E'01 00697755'01 0045138E'01 0055243E'01 00321925'01 1308319 1105144 1101897 1003137 1306700 704754 7098C9 2305316 1205041 1204779 009822 1002403 701159 708461 907329 805969 704009 706828 707619 137 i CA 48 (P0P) G 27076 37097 28017 43007 78091 93054 CA48 (P1P) 72092 73032 88009 93009 83037 98008 80037 0022756F+00 00104155+00 00165035+00 0012635E+00 0056785E'01 00557485‘01 «O MEV 80037 0.470206-01 00692926-01 0036661E-01 00319898'01 0050383E-01 0021269E-01 2908 MEV 1307021 1301503 1107156 1100534 903642 804905 904128 802598 808351 900944 605515 709547 168 CA 48 (P1P) 25 MEV cA 48 (P,P) 2908 MEV , 80250 80250 27037 0055871E+OO 306019 27.76 00660765+OO 6.9963 17054 00490345000 2203490 23005 0060960E+00 706580 32049 004699SE+00 706733 37097 0060507E+00 400889 22066 0066647E+00 707319 23.17 0058101E+00 4.9950 37060 0043233E+OO 5f7729 43007 O053454E+OO 309579 27078 0050628E+OO 604019 48.57 0.52928E+00 407120 42070 0046825E+OO 407337 63.38 0.4267QE+OO 3.4591 “8020 0050285E+00 507359 53065 0049161E+00 401724 63002 0038836F+00 409491 68043 0036777E+00 305585 53028 0043504E+00 402123 73088 0032230E+OO 402791 68008 0037879E+00 302132 73.91 0.2411SE+00 402078 58036 0046649E+00 305148 - 73012 0038769E+OO 208538 73053 O038352E+00 302817 78056 0040848E+OO 209656 83058 00343615000 207537 CA48 (P0P) 35 MEV CA48 (P0P) 40 MEV 80250 80250 17051 0050756E+00 2908034 27.74 0.80096E+00 501512 32043 0084597E+00 601844 17093 0060459E+00 1507455 22052 O068434E+OO 801148 32085 0075120E+00 500158 37053 00835095+oo 307116 23004 0074594E+00 600251 ' 42063 0069645E+00 302391 37095 0066555E+00- 309478 48002 0056662E+00 309914 28015 O0657CBE+OO 403302 53010 00479665+00 308932 43005 0068388E+00 3015?4 58017 0038202E+00 400187 48054 0061904E+00 308550 93009 0048517E-01 608028 63035 0033594E+00 3.7332 98008 0044174E-01 500959 53062 0051854E+00 307301 68040 0034645E+00 307411 58069 0039042E+OO 308998 O C A 42 27038 17054 320“9 22067 37060 27078 42070 '48020 CA 63002 53029 68008 58036 73013 ’73053 78056 93020 43 27075 17093 23004 37095 28015 43005 48054 63035 53062 68040 58069 730Q5 73085 78088 (P;P) (P0P) 25 MEV 8030“ _'. 0041491E+OO .005692#F+OO O0“1553E+00 ‘O0632“7E+OO O027Q75€+OO 00h7967F+OO 0033225E+OO 0032062F+OO 0022987E¥OO 0029953E+00 0017758E+OO 0025517E+OO 0021226E+00 0026180E+00' 0016359E+OO 0091717E'01 35 “EV 80364 0030591E+OO 0037784E+OO 00339CQE+00 0025844£+OO 002727IE+OO 0026104E+00 0031657E+00 O020426E+OO 0031904E+OO O0201“4€+OO o.27999£+oo 00129125+00 0018725E+OO 00105015+00 706732 170?717 806171 7.53QQ 705200 $06721 50966C 705758 508737 504413 30095? #07978 #00494 “01565 500578 508170. 803333 2603929 1703138 609““0 705795 506850 509379 40969“ 500337 501373 407388 505124 507301 700373 169 G CA 48 27076 23006 37098 _ 28017 43007 48057 63038 53065 ‘680Q4 73088 78092 (P19) 230% 8036“ 0036544E+CO 00QOQ73E+33 0031442E+30 00QOSOEE+DO 0026972F+OO 0027372E+30 0019506C+OO o.23365£+oo 00203665+OO 70018116E+OO 0.932325-01 CA48 (P09) 40.MEV 17051 32043- 22052 37053 42063 48002 62093 53010 58017 VLV 30F2°€ 90:946 40P7F7 L.0915 609317 703130 503929 603990 500676 601913 703872 80364 ‘ 00#3378E+00 310110 00“135IE+OO 1000114 0038523E+OO 1202368 003OEIOE+OO 702075 O028056E+00 601762 003117SE+OO 509379 0016582E+00 6.0207 0023456E+00 600204 O023899E+00 503459 cAuB :A 48 (P19) 25 "EV 27038 17054 32049 22067 37060 27079 42070 -48021 53029 68009 53037 73013 73054 ' 78057 93021 83060 27075 17093 32085 23004 37096 28016 43005 48055 63036 53063 68041 58070 73045 73085 78089 83091 (P1P) '80531 , O069678E+30 0085859F+OO 0057277E+00 O068317E+30 O035381E+DO 0062599F+30 0034516E+OO O029142E+30 0917523E+OO 00120435+OO 0013566€+OO 001103ZE+30 001113OE+OO 0010249E+OO 00435775'01 00840715'01 35 MEV 80501 0056SOPE+30 0010416E+01 O061747E+OO 0070136E+00 0045699E+OO 0057013E+OO 00261465*OO 0015305E+OO Q0134OSE+OO O014166E+00 0012332E+OO 0014301E+OO 0076831E'01 00876025'01 00619385'01 00395755'01 4.99PP' 1200000 605573 609533 50793? ““0011 5004C8 603023 607861 602561 506023 508013 606240 .603429 902905 500717 601316 1505881 504062 803467 406072 402446 501890 809795 609119 1401360 1202515 607296 701146 80258? 901609 809010 170 cA 48 32087 23006 37098 28017 43008 43057 63039 53066 68044 73089 78092 CA48 ‘PIP) 17051 32043 22052 37054 27063 42063 48002 62093 53010 67098 72093 73033 88010 83038 (P19) 290? 30551 0049057E+03 0053630E+33 O035724E+CO 00598065003 O023807E+OO 0019151F+CQ 0013033F+30 0015678E+00 0013209E+00 00101105000 00581505-01 40 MEV 80501 0076336E+OO 0054577E+OO 00712105+OO .0035194E+00 0068765E+OO 0020379E+OO 0015011E+OO 0098387E'01 0013259E+OO 00677265'01 00475665'01 00587565'01 00415355'01 0035150E'01 KEV 903369 1306750 701219 709346 =-°223 301859 600C66 707143 5096C9 706694 900542 16023?9 704589 603719 507045 309728 609596 807218 800175 802094 803902 906494 903410 709249 808048 171 * 0 :A 48 (9,2) 25 MEV CA 43 (P00) 2908 MEV 3.543 3.503 27.38 0.50425E+oo 803280 27076 0036052E+OO 900268 17054 0040459E+oo 19.9675 - 32.87 o.37742£+oo 6.2276 22067 0054363E+00 700599 23.06 0.25595E+oo 10.9857 37.60 o.41678€+00 409982 37098 0.31435€+oo 5.0069 27.79 0036751F+OO 5.4492 28.17 o.30175E+oo 601632 “3'71 0.30878E+30 501225 43008 0029349E+oo «.9219 “8'21 0028493E+OO 696850 48057 0028049E+OO 602216 53029 0028447E+OO 4.8781 63039 0021699E+OO 4.8274 68009 0020411E+OO n.2917 53066 0027360E+00 5.4469 58.37 00230006+oo «.7743 68044 0019848E+OO «.7295 73014 0018285E+oo 4-1059 73089 0012791E+OO 606903 73.54 0.13712E000 5.4675 73.92 0086919E-01 700766 78057 0014339E+QO 500446 93.21 0066839E-01 604890 83060 0.11331E+oo 0.8597 7 4 CA48 (P0P) 35 Mev CA48 (PIP) 4O MEV 80593 80543 17.93 00323oOE+OO 19.1500 17.51 0.251555+oo 46.5517 3;.86 0036087E+00 7°2206 32.44 0024571E+OO 11.3753 .34 0-407 #E+00 7--304 22.52 0026101E+OO 1304369 .37' 6 0'?38515*00 6'“396 37.50 0023438E+OO 7.0577 28016 0030519E+00 509746 27064 0018984E+OO 904331 43005 0024663E+OO 502131 42.63 00221135+OO 508294 «3.55 0.23356E003 6.3368 48002 0027661E+00 506937 63.35 0.19139E+oo 407713 62093 0015480E+00 F05778 53063 00229485+OO 596085 53.10 0024794E+OO 5.2g52 68.;1 001§o§§E+oo g-3216 67098 0012389E+00 506578 580 o 0.1 7 6 +00 . 02 58017 0.23374E+00 4.9451 9 73°45 0-122185+00 5'3489 , 72.93 0081462E-01 607617 73086 0010926E+OO 7.1050 73,33 0.913605.01 5.9042 78-89 008~719E'01 7'4916 88010 0036855E-01 2.5503 83.91 0'601375’01 6'366“ 78036 0045366E-01 904966 83039 0034815E-01 805481 ;A 48 17055 32050 22067 37061 27079 92071 48021 53030 68009 58037 73014 73054 78058 93021 CAQB 27075 17093 32086 23004 37096 28016 43005 “3055 63036 53063 68041 58070 730“5 78089 83091 (PIP) (P09) 25 MEV 80589 0052625E+00 00510925+OO 0.62009E+OO 003999OE+OO 0044903E+OO 00357525+OO O036505€+OO 003369uE+OO O01609EE+OO O02807OE+OO O01“063E*00 0015700E+OO 001127IE+OO 0067281E'01 35'Mev 80539 00652055+00 00728525+00 005209SE+00 0067091E+00 00395155+00 00542205+00 00232115+00 OOBIEJQE+OO 001389#E+00 0018301E+00 00133C35+OO 00172815+00 0010351E+00 00743955'01 00570955'01 1702312 700366 608907 50“21? 601707 500079 600266 406940 “06450 404631 40SQ91 '502495 509184 606573 507068 1108195 600238 508659 408935 404257 4095C3 fioRHQP 1002100 605170 600506 509110 507397 801340 701011 172~ CA 48 (Pap) 27077 32088 23006 37098 28017 43008 48058 63039 53066 68044 78092 CA48 (P1P) 17051 32044 22052 3705“ 27064 42063 48002 62093 53010 67099 58017 72093 73033 88010 78036 83039 80589 O0SSQCSE+OO 0051013E+OO 0056427E+OO 00353126+00 0.42602E+OO O03173OE+00 0.27366E+OO 0015413E+00 0020337E+00 O011282E+00 0011040E+00 ‘ “O MEV E0539 0069825E+00 0062370E+00 0061956E+00 0042173E+00 00544856+00 O028139E+00 0014647E+OO O013332€+00 0012923E+00 O077359E'01 0014062E+00 00694335-01 00804915'01 00553805'01 0067894E'01 0039334E'01 2908 WEV 704236 504235 703348 5009““ 502055 409864 606066 50866“ 606815 606921 602931 1802671 701856 702842 502939 406420 504453 804876 609391 709556 703391 607230 704921 7051C5 609366 706045 708808 cAus ;A as 17055 32050 22067 27079 42071 48021 63004 53030 68009 58038 73014 73054 78058 93022 83060 98021 27075 17093 32086 23005 37096 28016 43006 48055 63036 530ffi3 58070 88052 78089 93052 83091 (Pip) (P1P) 25 MEV 80658 O013038E+CO 0017778E+DO 0025677F+OO 0020926E+OO 001246IE+OO 00165115+30 0092107E-01 00126OSE+OO 0094940E'01 ‘00134#5E+OO 00113586+OO 0012257E+OO 0010504E+OO 00100268+30 00102168+OO 0063614E-01 35 MEV 80658 0026972E+OO O02806CE+OO 00173645+30 0022236E+00 001709QE+OO O02176“E+00 0017653E+00 0013582E+OO 0089“03E'01 0013258E+OO 0072663E'01 0038740E‘01 00637165'01 0'17486E'31 0051636E'01 4H03#55 1501474 1801878 1132770 1100362 1108873" 100P450 905428 707966 7034““ 600883 508862 606#96 308752 306762 509702 808740 2700355 2208632 2606474 1505338 908683 705191 1009C50 808930 803761 1008397 902199 909162 160360# 901535 173 CA “8 (P,P) 27077 32088 23006 37098 28018 43008 #8058 63039 53066 68045 73089 78093 93056 80658 001379CE+OO 002017OE+OO' 0022545E+OC 0016124E+OO 001649BE+OO 0016179E+OO 0016O7OE+OO 0010203E+00 0011863E+OO 0084271E'01 0091599E'01 0061682E‘01 00382295'01 CA48 (P0P) 40 MEV 32044 82053 37054 27064 “2063 “8003 53010 58018 73033 88010 78037 93010 80658 0022206E+OO 002419EE+00 00166695+OO 0.21897E+OO 0014004E+OO 0011681E+OO 00909365’01 0088837E'01 00523015'01 0037440E‘01 00398105'01 0024526E'01 2308 MEV 1709824 907226 1501243 906667 100?844 707639 1000283 708819 1902806 807061 807568 905739 1004861 1309468 16031“1 1006752 902901 904056 1105026 1108842 905187 10.0286 809583 1101550 1007971 )P) 25 MEV ' 174 2A 48 (P cA 48 (P.P) 29.8 VEV 80786 80786 37°38 0'7”99E+OO 7'101“ 12.82 009#SISE+DO 39.3381 17'55 0'637?QE*30 16.0876 . 27077 006507CE+OO 6078““ 32.50 0.630955+00 6-5074 " 17.94 0.72424E+00 23.5433 22'67 0°565°95+00 7‘5853 32.88 0.66358E+00 4.7627 27079 006473QE+OO S'Ogai 23.06 0.55929€+OO 795316 48.22 0.54301E+00 #09493 28.18 0.61663E+00 4.3333 63-0“ O-“1553E+00 3'“??6 43.08 o.53654£+00 3.7379 53'30 0'531“9E*0° 3'6532 38-58 005063IE+OO «.5808 68010 0037142E+00 3.1993 63.00 0.38400E+OO 3.6502 58.38 0.#9105E+OO 3.2341 53.66 c.5356os+oo 3.8565 73.15 0.369§6E+OO 2.8827 68.05 0037181E+00 3.#126 73-55 0-3“9=>9F+0o 3'3913 73.90 o.28469£.oo #03913 78°59 0°3095°E*90 3'3“68 78-93 0.2691sz.oo 3.9193 93.22 0o16577E+00 3.7842 93.56 0-100355000 5.8333 83.61 o.24361E+00 3.3053 cAQS (PIP) 35 MEV ' CA#8 (PIP) 40 MEV 8.786 _ 8.786 27.75 0.63496E+OO 5-78?6 17.51 0v35992£+00 36-5301 17.93 0.51258E+oo 2106316 32.#4 o.6354«£+00 7.2193 32.86 0.58765E+00 5.5010 22053 0.4953BE+00 8.9280 23.05 0066379E+OO 602801 3705# 0066387E+OO 401170 37.96 0.59626E+oo «.0132 27.64 0.56795E+OO 4.6934 28.16 0-535155+00 406020 42.63 o.5423«£+00 3.6643 «3.06 O.62119E+OO 3.2921 48.03 0.62940E+00 3.6740 63.55 0.58811E+Oo 3.7921 62.94 o.357css+oo 3.6021 63.36 0.4105«E+00 3.2039 53.11 0.48050E+00 3.6783 . .- 97E+ 0 3.4655 58.18 0050069E*OO 303463 53.63 0 565 o _ 3.3153 72-93 0019462E+00 0.1952 680#2 0081365F+OO : .2967 73-34 0021226E+00 #.4368 58.70 0.60396E+00 3 E+ 3.2500 88.10 0-682506-01 6.1943 73.46 0.30090 00 “.3554 78037 0016263E+00 #o7818 73.86 0-283OOE+OO 5.0935- 93-10 0.663235-01 5.8138 33.53 0.11457E+OO «.7195 83039 0011114E+00 6.4367 78.89 0-20#31E+OO 98 83.92 0.15149E+oo 6.1156 '09 0059865E-01 6.4502 98;52 0.39507E-01 706388 jA 48 (P 27039 17055 32050 22068 27080 42072 48022 63005 53031 68010 58038 73015 73055 78059 83061 CA48 (P 27075 17093 32086 23005 37096 28016 43006 48056 63036 53064 68042 58071 73046 73086 88053 78090 83092 ,p) 25 MEV 80868' 0040375E+OO 005326OE+OO O031617E+CO 0043260E+CO 0033786E+oo 0031456E+OO O033SOOE+OO 0026016E+OO O0326O7E+OO 0023678E+OO 0030013E+00 O019681E+OO 0.21633E+oo 00165355000 O013487E+OO IP) 35 MEV 80868 0065402E+OO O051253E+OO 907047 117.6975 ‘906331 1105452 708750 506667 606159 501451 409267 403794 403193 400699 405556 5.0201 406030 1301656 1801263 O055496E+OO 0063920E+OO 0041939E+OO 0049019E+00 0.39479E+oo O045780E+OO 0032543E+OO 0049003E+OO 00211495+OO 0039029E+00 00176595000 0019251E+00 0013435E+00 O014380E+OO 0011274E+Oo 508690 600883 904765 9055QE 401479 405812 307449 307907 408643 308449 404758 504550 406953 507525 408958 175 I CA 48 (p19) 12082 27477 17094 32088 23006 37099 28018 43009 ,48058 63040 53067 68045 73090 78093 80868 2908 MEV 0090907E+00 3907475 004136OE+OO 0053829E+OO 0042152E+OO O047394E+OO O036867E+OO O042746E+OO 0033654E+00 0038804E+OO 0029831E+OO 0035820E+OO 00242825+OO O016256E+OO 0010408E+OO CA48 (9,0) 40 MEV 17051 32044 22053 37054 27064 42064 48003 62094 53011 58018 72093 73034 78037 93011 83039 98010 80868 0.737135000 0.55036E+oo 0064350E+00 0044018E+oo 00573£9E+00 00473385000 0044177E+00 00203285000 0.39577E+oo 0037384E+oo 0011808E+oo 0013312E+oo 0011511E+oo 00590046-01 0010913E+oo 0038306E-o1 308129 17.0089. 600802 804447 504299 505667 501869 505801 401544 408780 .403839 603909 607273 2105823 707854 802480 502136 406003 401383 403534 501066 401657 309720 507834 509490 508418 602319 405813 507186 11.4 Tabulated Nuclear Deformations The following pages contain the tabulated nuclear deformations, JL gflLRo’ for the states observed in this experiment. For the analysis labeled R = I, the value of Ro is 1.20A1/3. For the analysis labeled Fricke Geometry, R0 = 1.16A1/3. 176 Ca48 30830 4050? 40607 50141 50249 50295 50362 50723 60098 60335 60641 60641 60786 60885 70009 7ICO9 70320 70320 70401 70471 70471 70471 70521 70521 70643 70786 70940 80037 80037 80037 80250 80250 80364 80364 80501 80543 80589 80658 80658 80786 80868 80868 25 Mev mrmwtwmwmwmtwmcm:wcwwrwwmmrmmr:mrmmwNmerum R=I 00784 00912 00345 00295 00160 00129 00432 00479 00201 00430 00210 00210 00145 00217 00164 00164 00119 00124 00211 00115 00127 00138 00124 00137 00499 00228 00221 0024? 00180 00215 0235 0235 0074 0301 00282 00351 00296 0074 0148 00470 0074 0305 177 30830 40502 40607 50141 50249 50295 50362 50723 60098 60335 60641 60641 60786 60885 70009 70009 70320 70320 70401 70471 70471 .70471 70521 70521 70643 70786 70940 80037 80037 80037 80250 80250 80364 80364 80501 80543 80589 30658 80658 80786 80868 80868 Fricke F mcmw¢wmwmwm¢wmrwtw:wm:wwwm:mm4~rm¢mmwmmw¢wna 00790 00910 C0343 00296 00160 00133 00434 00480 00201 00430 00210 00210 00144 00217 00165 00165 00120 00126 00212 00116 00128 00139 00124 C0138 00498 00230 00226 00236 00185 00214 0229 0229 0072 0292 00281 00352 00296 0072 0144 00470 0072 0296 ca48 30830 40502 40607 50141 5-209 50295 50362 50723 60098 60335 60641 60641 60641 60786 60885 7.009 70009 70320 70320 70401 70471 70471 7.071 70521 70521 70786 70940 80037 80037 80037 80250 80250 80364 80364 80501 80543 80589 80658 80658 80786 80868 80868 30.00 E .Lfl{(flh%#h)mpuUHJU"¢(JRJ¢LP#P#LJUL¢UJwLUR)#FVUW#J?¢FU¢rm£flhHVL8U1#UJN R=I 00703 00833 00268 00233 00125 00126 00393 00453 00175 00382 00190 00190 00407 00133 00173 00137 00137 ' 00122 00121 00166 00106 00119 00124 00103 00120 00243 00167 00182 00185 00172 0213 0218 0065 0253 00244 00307 00257 0070 0140 -00431 -0074 0292 178 30830 40502 40607 50141 50249 50295 50362 50723 60098 60335 60641 60641 60786 60885 70009 70009 70320 70320 70401 70471 70471 70471 70521 70521 70786 70940 8.037 8.037 80037 80250 80250 80364 80364 80501 80543 80589 80658 80658 80786 80868 80868 Fricke F LJUNJLfl#WJh)#Lfl#‘#LUUW¢LDUJNFU#’NLN#'#fU‘fU1mtdn)m(fl£‘wfu m V (”#Wflthtd S L 00737 00921 00284 00246 00134 00130 00431 00485 00187 00407 00200 00200 00146 00185 00150 00150 00126 00134 00184 00117 00126 00133 00119 00127 00253 00174 00191 00191 00192 0229 0229 0068 0263 00270 00331 00284 0072 0144 00461 0076 0309 ca48 30533 40502 1+0607 50141 50?#9 50295 50362 50723 60C93 60335 60641 60641 60755 60885 7-009 70009 70320 70320 70401 70471 70471 70471 70521 70521 706k3 70786 70940 80037 80037 80037 80?50 50250 80364 80364 80501 80543 80589 80658 50658 80786 80868 80868 35Ihv m¢mw+~wmwmwm:wn;rm¢w¢ww¢wwwm¢mm¢rm¢mmwmmm¢wm R=I % L C0733 00965 00?53 00222 C0116 00107 00“2? 00457 00156 00377 00180 00180 O01Q8 0.15% 00142 00142 C0097 00101 00168 00135 00142 O01#4 00118 00122 00473 01243 00171 00230 00209 00218 0233 0223 0065 0253 00270 00291 00273 0070 01#O O0“26 0079 0314 179 30830 40502 “0607 501Q1 50249 50295 50362 50723 60098 60335 60641 60641 60786 60885 70009 70009 70320 70320 70Q01 70471 70471 70471 70521 70521 70643 70786 70940 80037 80037 80037 80250 80250 8036“ 80364 80501 805Q3 80589 80658 80658 80786 80868 80868 Fricke ‘ mcwm mtmwcwmwmwmtwmrwtw¢wm¢wwwm¢mm+rmcwmwmm 00729 00893 00265 00237 00124 00111 00Q38 00487 00167 00395 00190 00190 00154 00168 00147 00147 00101 00106 00175 00140 001QS 0015“ 00122 00128 00k87 00260 00181 00242 00216 00227 0229 0229 0068 0263 00230 00311 00282 0072 0144 00454 0080 0326 48 30830 40502 40607 5.141 50249 50295 50362 50723 60093 60335 60641 60641 60786 60885 70009 70009 70320 70320 70401 7.471 70471 70471 70521 70521 70643 70786 70943 80037 80037 80037 80250 80253 80364 80364. 80501 80543 80589 80653 80658 80786 80868 80868 4OIhv mcmw:wmwmwmrmw:m¢w¢wm¢wwwm4~mmcrmrwmwmmmtwm R=I 00677 00857 00208 00208 C0106 C0110 00443 00444 00143 00354 00170 00170 00132 00142 00121 00121 00113 00113 00142 00139 00141‘ 00145 00125 00130 0.471 00234 00146 00239 00248 00222 0210 0210 0061 0244 00253 00265 00262 0065 0130 00402 0074 0296 180 30830 40502 40607 50141 50249 50295 50362 50723 60098 60335 60641 60641 60786 60885 70009 70009 70320 70320 70401 70471 70471 70471 70521 70521 70643 70786 70940 80037 80037 80037 80250 80250 80364 80364 80501 80543 80589 80658 80658 80786 80868 80868 Fnuma F [DUTU'lS-‘wm mcmwawwwmwwcwmtm:wtwm¢wwwm+~mm¢+~mtmmw 00702' 00884 00216 00220 00112 00113 00458 00469 00151 00369 00180 00180 00133 00150 00127 00127 00117 00117 00147 00144 00146 00153 00129 00135 00486 00243 00155 00258 00244 00277 0216 0216 0063 0250 00261 00279 00270 0068 0136 00424 0076 0305 II.5 Quantities calculated from nuclear deformations. On the following pages are tabulated the parameters calculated from the nuclear deformations. The L is normalized to an inter- action radius of 1.25A1/3. 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