THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING GAMMA-GAMMA DIRECTIONAL CORRELATION MEASUREMENTS IN Se76 AND CdllO..,: *... --.,''.....'.. Emerson G. F nk Jr. i A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1958 March, 1958 IP-272

/D l Doctoral Committee: Professor Marcellus L. Wiedenbeck, Chairman Professor H. Richard Crane Assistant Professor Karl T. Hecht Professor Wilfred Kaplan Associate Professor Robert W. Pidd ii

ACKNOWLEDGMENTS The author wishes to express his sincere thanks to: Professor M. L. Wiedenbeck for making this experiment possible and for his guidance and encouragement throughout the coarse of the work. R. G. Arns and G. D. Hickman for their assistance in recording the data and for many helpful discussions. Dr. M. K. Brice for her translation of the Russian references. The College of Engineering Industry Program for the printing of this thesis. My wife, Irene, for her assistance in the preparation of this manuscript. The author also wishes to express his appreciation to the Office of Naval Research for the partial support of this work under Contract Nonr - 1224 (13). iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS.............................................. iii LIST OF TABLES............................................... vi LIST OF FIGURES.......................................... vii I. INTRODUCTION AND THEORY................................ 1 Angular Correlation................................. 1 Simplified Theory of Gamma-Gamma Directional Correlation..................................... 4 Theoretical Results for Gamma-Gamma Directional Correlations......................................... 8 Pure Gamma-Gamma Cascade........................ 8 Gamma-Gamma Cascade with Mixtures............... 9 The 1 -- 3 Directional Correlation.............. 11 II. EXPERIMENTAL PROBLEMS................................... 13 Method............................................... 13 Stability............................................ 14 Complex Decay Schemes................................ 14 Accidental Coincidences and Background............... 15 Resolving Time and Source Strength................... 16 Efficiency and Solid Angle Variations................ 18 Decaying Source...................................... 18 Effect of Finite Solid Angle and Source Extension.... 18 Extranuclear Field Effects........................... 20 Scattering Effects................................... 21 III. EXPERIMENTAL PROCEDURE.................................. 23 Apparatus............................................ 23 General Description............................ 23 Source Mounting........................... 25 Detectors....................................... 25 Fast Channels................................ 26 Slow Channels................................ 28 Scalers........................................ 29 Stability.................................... 29 iv

TABLE OF CONTENTS CONT'D Page Procedure in Typical Correlation Measurement......... 30 Alignment of Apparatus......................... 30 Correlation Measurement......................... 31 Data Analysis................................... 31 IV. RESULTS OF GAMMA-GAMA DIRECTIONAL CORRELATION MEASUREMENTS IN Se.................................... 33 Introduction......................................... 33 Results and Interpretation.......................... 36 0.65 Mev - 0.55 Mev Correlation................. 36 2.05 Mev - 0.55 Mev Correlation................. 4 41 1.40 Mev - 1.20 Mev Correlation................. 41 Summary and Discussion............................... 44 V. RESULTS OF GAMMA-GAMMA DIRECTIONAL CORRELATION MEASUREMENTS IN Cdl10................................... 55 Introduction......................................... 55 Results.............................................. 60 1.389 Mev - 0.885 Mev Directional Correlation... 60 0.935 Mev - 0.885 Mev Directional Correlation... 60 0.885 Mev - 0.656 Mev Directional Correlation... 63 1.516 Mev - 0.656 Mev and 1.516 Mev - 0.759 Mev Directional Correlations........................ 63 1.389 Mev - 0.656 Mev Directional Correlation... 6 Interpretation of Results............................ 7 Interpretation of 1.389 Mev - 0.885 Mev, 0.885 Mev - 0.656 Mev, and 1.389 Mev - 0.656 Mev Correlations.................................... 71 Interpretation of the 0.935 Mev - 0.885 Mev Correlation..................................... Interpretation of 1.516 Mev - 0.759 Mev and 1.516 Mev - 0.656 Mev Correlations.............. 90 Summary and Discussion............................... BIBLIOGRAPHY......................... 93 v

LIST OF TABLES Table Page 1 As7 Beta Decay Data.................................... 33 2 Properties of Even-Even Nuclei Having Assignments of 2+ for Both the First and Second Excited States............. 47 3 Directional Correlation Results for Cd.............. 70 vi

LIST OF FIGURES Figure Page I Detector Arrangement................................. 13 2 Finite Solid Angle Subtended by Detectors............ 19 3 Block Diagram of Apparatus........................... 24 4 Cross-Section of Source Holder....................... 25 5 Decay Scheme of As76.............................. 34 6 Se7 Gamma Ray Spectrum.............................. 37 7 0.65 Mev - 0.55 Mev Directional Correlation in Se76.. 39 8 A2 and A4 vs. Q for a 2(D,Q)2(Q)0 Sequence........... 40 9 2.05 Mev - 0.55 Mev Directional Correlation in Se76.. 42 10 A2 and A4 vs. Q for a 3(DQ)2(Q)O Sequence.......... 43 11 1.40 Mev - 1.20 Mev Directional Correlation in Se76. 45 12 Vibrational Spectra in Even-Even Nuclei.............. 51 13 Decay Scheme of Ag1m.............................. 56 14 Scintillation Spectrum of Gamma Rays of Cd........ 59 110 15 1.389 Mev - 0.885 Mev Correlation in Cd........... 61 16 0.935 Mev - 0.885 Mev Correlation in Cd6......... 64 17 0.885 Mev - 0.656 Mev Correlation in Cd......... 65 18 1.516 Mev - 0.759 Mev and 1.516 Mev - 0.656 Mev Correlations in Cd0................................ 67 19 Main Portion of Cd10 Level Scheme................... 71 20 A2 and A4 vs. Q for a 5(D,Q)4(Q)2 Sequence........... 72 21 A2 and A4 vs. Q for a 6(0)3(D,Q)2 Sequence........... 74 22 A2 and A4 vs. Q for a 3(DQ)2(Q)0 Sequence........... 75 vii

LIST OF FIGURES CONT'D Figure Page 23 A2 and A4 vs. Q for a 5(D,Q)4(Q)2 Sequence........... 80 24 A2 and A4 vs. Q for a 4(D,Q)4(Q)2 Sequence........... 31 25 A2 and A4 vs. Q for a 3(D,Q)2(Q)0 Sequence........... 86 26 A2 and A4 vs. Q for a 5(Q)3(D,Q)2 Sequence.......... 87 27 Revised Level Scheme for Cd0................9...... 89 viii

CHAPTER I INTRODUCTION AND THEORY Angular Correlation The main concern of low energy nuclear physics is the determination of the properties of nuclear energy levels and the interpretation of these properties on the basis of nuclear models. Nuclear levels are characterized by their energy, angular momentum (spin), parity, magnetic moment, electric quadrupole moment, and lifetime. The angular correlation of successive nuclear radiations is a very useful method for determining the spin and parity of excited levels and the angular momentum of the emitted radiation. In some cases one can also use angular correlation methods to determine some of the electric and magnetic properties of the nucleus by studying the electric and magnetic interactions of the nucleus with its surrounding fields. In general the probability of emission of a particle or quantum by a radioactive nucleus depends on the angle between the direction of emission and the nuclear spin axis. Normally, however, the radiation pattern from a radioactive sample is isotropic because the nuclei are randomly oriented in space. Only if the nuclei are aligned by external fields can an anisotropic pattern be expected. In the case where the nuclei emit two successive radiations an effective alignment can be obtained. This comes about in the following manner. The observation of the first radiation in a given direction selects an ensemble of nuclei that has an anisotropic distribution of spin orientations. The direction of the succeeding radiation then shows -1

-2a definite angular correlation with respect to the direction of the first radiation (except in rare cases where isotropy results as an accident(l)). An angular correlation measurement thus consists of measuring the number of coincidences between the two radiations as a function of the angle subtended by the axes of the two detectors. Actually the term angular correlation comprises both directional correlation and polarization correlation. In a directional correlation, only the directions of the two radiations are observed while in a polarization correlation, the polarization of one or both of the radiations is also measured. There are many types of correlation processes. The most widely measured types are gamma-gamma, beta-gamma(3) alpha-gamma(4) and internal conversion electron-gamma(5) correlations. The information which can be obtained from the correlation depends on the radiations observed and the properties which are singled out by the experiment. Alpha-gamma and gamma-gamma directional correlations yield the spins of the nuclear levels but not the parities. However, the relative parities can be determined if one also observes the polarization of the gamma rays or if one measures the directional correlation between conversion electrons. The directional correlation of a beta-gamma cascade depends on the nuclear spins, the beta energy, the atomic number Z, and the type of interaction involved in the beta decay. It was first suggested by Pryce in a private communication to Dunworth (6) in 1940 that two successive nuclear radiations will in general be correlated in their relative propagation directions. Independently, Hamilton(7) in 1940 carried out calculations for the gamma-gamma

-3directional correlation in pure-multipole cascades. Many unsuccessful experimental attempts were made to verify Hamiltonts theory in the succeeding years. In 1946, Goertzel(8) investigated the effect of extranuclear fields on a directional correlation. His results explained why some of the experiments disagreed with Hamilton's theory. However, the disagreement of theory and experiment actually was the result of inadequate experimental techniques. In 1947, Brady and Deutsch(9) carried out the first successful correlation measurements using Geiger counters as gamma detectors. The introduction of the scintillation counter as a gamma detector in 1948(10) started a rapid development in the field of angular correlation, and today angular correlation is an important tool in nuclear spectroscopy. This investigation is concerned with the application of gammagamma directional correlation techniques in studying the gamma ray cascades following the beta decay of As76 and Ag110m thus providing information on the spins of the excited states of Se76 and Cd110. Three gamma-gamma directional correlations are measured in Se76 with the result that unique spin assignments can be made to all of the Se76 energy levels. An interpretation of the level scheme in terms of vibrational levels is also made. Six correlations are measured in the complex scheme of Cd110 and assignments made to six levels. The results indicate that the sequence of emission of two of the transitions should be the reverse of the order previously reported, thereby changing the level scheme of Cd 10 A new level scheme is proposed.

Simplified Theory of Gamma-Gamma Directional Correlation The general theory of angular correlation has been treated from several different approaches and by numerous authors(718'1120). The approach which will be presented here is a simplified theory of gammagamma directional correlation which provides some physical insight into the problem(21-23) Consider first a single gamma transition of angular momentum tV occurring between two nuclear states B and C whose spins are denoted by Jb and Jc respectively. Let Lz be the projection of L on the quantization axis (z-axis). The gamma ray is then characterized by the angular momentum quantum number or multipolarity L and the magnetic quantum number M where L i LL+1) and LZ-M-. The states B and C are described by the quantum numbers Jb, mb and Jc, mc where M = mb - m. Each component between two specific magnetic substates has a characteristic directional distribution FL () where - denotes the angle between the emitted gamma ray and the z-axis. The angular distribution function L( can be found by calculating the Poynting vector as a function of angle for multipole radiation of order L and magnetic quantum number M. It is impossible to separate the individual components mb - mc, and thus the unresolved line B - C is always observed. To calculate the total directional distribution TL(&) for the transition B - C one must also know the relative population P (mb) for each substate mb and the relative transition probability G (mb mc) for each component mb -mrc. The expression for the directional distribution is

-5then then L( P (mb) G (7 lc) FJ(o) (1) The relative transition probability G (mb me) depends only on mb and mc and not on the specific nuclear properties. It does not depend on the wave functions describing the nuclear states. It can be shown by group theoretical methods(25'26) that G (mb mc) is equal to the square of the Clebsch-Gordan coefficient for the vector addition Jb = Jc + L, mb = m + M. G(mb c)= (cT L-TlMI Jb b) (2) The relative populations P (mb) depend on the energies of the various mb states and on the way in which level B was created. Consider now a nucleus decaying through the cascade A ->B - C by successive emission of two gamma rays. The directional correlation function WV ) is the relative probability JA, A that " is emitted at an angle & with L the direction of. If the quantization J6 B axis z is made to coincide with the direction i L L of emission of 71 the directional' correlation between the two gamma rays becomes the same as _LL t(), the directional distribution of Z with respect to the z-axis. If the relative populations P(mb) are known, W(e) can be calculated from equations (1) and (2r. The relative population P(mb) is given by the sum of all transitions ma -4mb leading into the state mb. If all ma states are assumed to be equally populated, then P(7n,)-E G(rn) FZ() (~)

-6The special choice of the z-axis makes possible another simplification since a photon moving in a definite direction can have only the angular momentum +f along its propagation direction(27). Therefore M1 is restricted to the values + 1 and only the functions L,(O) and FL, (O) appear in equation (3). The directional correlation function is obtained from equations (1), (2), and (3) and the fact that W(O-fLLZ (OG) giving VVVK)-z (JbL. lil F _-m (o)with (Jc LZ7n M1 JbI) F=2 Lwith M2 = mb - m. The directional distribution functions FLM() can be expressed in powers of cos ~. Therefore W(o) is a function of powers of cos2. From equation (4) it is seen that the gamma-gamma directional correlation function depends on five parameters, the spins of the three levels and the multipolarity of the two gamma transitions. Therefore information can be gained about these quantities in a directional correlation measurement. However, additional information must be known about some of these quantities if an unambiguous assignment is to be made from a directional correlation measurement. The directional correlation function does not depend on the parities of the states. This can be understood classically. Electric and magnetic radiations of the same multipole order are related by the < < _- - (28) transformation E -H, H - -E. Since the Poynting vector is unaffected by this transformation the directional distributions F

-7are not changed and W() is left unaltered. Thus electric and magnetic radiation cannot be distinguished in a gamma-gamma directional correlation measurement, and no information can be gained concerning the parity of the nuclear states. Two important assumptions were made in the derivation of the correlation function. First, the magnetic sublevels of the initial and final nuclear states were assumed to be uniformly populated. In practice this condition is satisfied except when the source is in a strong magnetic field at very low temperatures, in which case the substates are populated according to a Maxwell-Boltzmann distribution. Second, the intermediate state was assumed not to be disturbed by extranuclear fields (2932) that is, the sublevels of the intermediate state should not be repopulated during the lifetime of the state. When the first gamma ray is detected some knowledge is gained about the orientation of the nucleus from which it came. If the nucleus is affected by extranuclear fields, it may precess and change magnetic sublevels before the second gamma ray is emitted. The information gained by the first detector will then be partially lost and the correlation will be attenuated. If the maximum correlation is to be attained, the lifetime of the intermediate state must be short enough so that the fields will not affect the nucleus before the second gamma ray is emitted. In general, a lifetime less than 10-1 sec. is sufficient to insure this. For states with longer lifetimes, perturbations are possible, and in order to observe the maximum correlation one must find a nuclear environment where the

-8extranuclear fields are small (e.g., a regular lattice site in a cubic crystal) or where their time average vanishes (e.g., certain liquids). The evaluation of equation (4) for various spins and multipole orders is difficult due to the tedious sums over magnetic quantum numbers. This difficulty was overcome in the general development of the theory. The theory was also extended to include mixed multipole gamma transitions, radiations other than gamma rays, and cases where the intermediate state is perturbed. Theoretical Results for Gamna-Gamma Directional Correlations The results of the general theory of angular correlation as applied to gamma-gamma directional correlations will be presented in this section. The results will be put in the notation of Ferentz and Rosenzweig (33). Pure Gamma-Gamma Cascade L1 L2 Consider a cascade jl -4 j J2. The directional correlation fun-ction can be written in the form Anax W(e)-Z AA&(4e (5) where Pk is the Legendre polynomial of order k. The sum extends only over the Legendre polynomials of even k, and the value of kmax is given by the minimum of the set of numbers (2L1, 2L2, 2j). Normally one never encounters a kmax greater than 4 so that the maximum number of terms needed in the expansion is three. The coefficients Ak can be broken up into two factors, each of which depends on only one step of the cascade.

-9A A 1). A (2) (6) Ak-Ak Ak k where Ak( = Fk(L1 L1 jl ) A(2)^ - ( L 2 j) (7) Ak = Fk(L2 L2 J2 J) The F coefficients have been tabulated by Ferentz and Rosenzweig(33) for all conceivable values of the parameters J l j 2 j, L1, and L2. Gamnia-Gamma Cascade with Mixtures A gamma transition is said to be of mixed multipolarity when it must be described by more than one value of angular momentum L. Generally the transition probability for magnetic radiation of order L is greater than that for electric radiation of order L + 1, but depending on the energy of the transition, M-L and E-L+1 radiation can compete with each other. A few cases of mixtures between E-L and M-L+l radiation have also been reported. These are unusual because the transition probability for magnetic radiation of order L+1 is generally much smaller than that for electric radiation of order L. When either or both transitions of a cascade are mixed, the correlation function becomes a coherent sum and cross terms appear. For a mixed transition, the mixing parameter; is defined by Biedenharn and Rose(34) as the ratio of the reduced matrix elements for L+1 and L radiation respectively, and it is a real quantity. is then the ratio of the total intensity of the L+l1 radiation to that of the L

-10radiation. ~ can be either positive or negative depending on the relative phase of the reduced matrix elements. Lloyd(18) has shown that only the relative phases 0 and T1 are of physical significance. For the case where both transitions of the cascade are mixed and described by mixing ratios l and z respectively, the correlation function is given by equations (5) and (6) but with Ak() and Ak(2) defined as A~ =F(iL, L,t. ) + 2, FA (LL,+I,.)+ FJ(L,+IL,+l,, L) (8) As)= FA(LzLZ+, ZF (LLZ+/ z)+F^ ML, (9) In even-even nuclei double mixtures are not encountered very frequently, but in odd A nuclei they occur quite frequently. Since the correlation function contains two additional parameters in the case of a double mixture the interpretation of correlations is further complicated. Any experimental correlation function can be explained by many different spin sequences if double mixtures are considered. If a mixture occurs in the first transition only,, can be set equal to zero, or if a mixture occurs in the second transition only, ~ can be set equal to zero in equations (8) and (9). Consider the case of a mixture of dipole (L = 1) and quadrupole (L = 2) radiation occurring in the first transition of a gamma-gamma cascade. Making use of equations (8) and (9) and some of the properties of the F coefficients, the expansion coefficients Ak can be written as Ao -1,A....+ A- -.. (10) Ao-l A - =.,.l

-11where a,b,c, and d are products of the appropriate F functions for the cascade. To compare the experimental values of A2 and A4 with theory one normally plots the quadratic functions given by equations (10) versus, but to cover the entire range of b one must plot 6 from 0 to. For dipole-quadrupole mixtures and especially for large values of S it is more convenient to introduce the quantity Q where Q is defined as Q = &/+ &2). It is easily seen that Q is the quadrupole content of the radiation while l-Q is the dipole content. In terms of Q, equations (10) become AO =1, A2 = a(l-Q) + b Q(Q)' + cQ, A4 = dQ (11) The equation for A2 is then an ellipse when plotted as a function of Q, and the equation for A4 is a straight line. Now one need only plot A2 and A4 versus Q for values of Q between 0 and 1 to compare the experimental coefficients with the theoretical coefficients. The 1 -- 3 Directional Correlation In many nuclear decay schemes more than two gamma rays are in cascade. For example, for a triple cascade one can observe the correlation functions W( Y1 E ), W( Wz 3 ), ___ and W( H b3 ) with the unmentioned L radiation being unobserved in each case. - L. The cases of W( A ) ) and WW( 63 ) LI are covered by the previous discussion for a simple double cascade. Biedenharn, 3 L2 Arfken, and Rose(34'35) have extended P the theory of angular correlation to the case of the 1 - 3 correlation with the intermediate radiation unobserved.

-12For pure transitions the 1-3 directional correlation function. w(e L + &*w-,(, 13), where W n (12) The it e rferene where W(ji jl j2 j2; k L1) is a Rbcah W-function(l5) and ka is given by the minimum of the set of numbers (2Lo, 2 2L2; 2jl, 2j2). If the unobserved transition is mixed, the expression for the correlation function becomes W( ) = W(L1) + + W(L1') (13) where W(L1) and W(L1') are given by equation (12). The interference term is not present in this case because the mixed radiation is unobserved. If a mixture occurs in the first transition, the correlation function. is given by W(e) - W(Lo) - ( W(Lo'/) + 2 g W(LoLo/) (14) where W(LO), W(LO'), and W(LO Lot) are obtained from equation (12).

CHAPTER II EXPERIMENTAL PROBLEMS Method Before going into the experimental problems involved in a directional correlation measurement the method of making the measurement will be briefly described. One detector is fixed in position while the other is free to rotate about the centrally mounted source. (Figure 1) 1800 /f~ ~ SOURCE 2 70~ 1 - I g o.90 6 MOVABLE DETECTOR FIXED DETECTOR Figure 1. Detector Arrangement -13

-14The correlation function is measured experimentally by observing the number of coincidences per unit time between the two detectors as a function of the angle — between them. Since the correlation function involves powers of cos2, all the information about the correlation can be gained by taking data in a single quadrant, for example from e = 90~ to 180~. However, to insure against any possible source misalignment and false asymmetries due to scattering from nearby objects, data are taken not only in the quadrant from 900 to 180~ but also in the quadrant from 180~ to 270~. The data from the two quadrants are then combined. Stability Since a correlation measurement involves a comparison between coincidence rates at various angles it is extremely important that the equipment be stable. Because some instability is always present (generally a steady drift), data should be taken for only a short period of time at each angle. By running back and forth through the doable quadrant sequence many times the necessary number of coincidences can then be accumulated, and a steady drift does not cause any difficulty. In addition, any short term instabilities tend to be averaged out by this method. Complex Decay Schemes If the nucleus being investigated has more than one gammagamma cascade, the interpretation of a single correlation measurement is complicated by the interference from the other cascades. Since scintillation counters(36) have energy selective properties the utilization of them as detecto can partially overcome this difficulty. However, even with energy selection the effect of interference due to unresolved peaks or Compton background from other gamma rays allows

-15only a partially effective selection of any one gamma ray. Of course, one important exception to this is the highest energy gamma ray present in the decay. Accidental Coincidences and Background In addition to the real coincidences which are due to the simultaneous detection of two gamma rays from the same nucleus there will be accidental coincidences arising from the simultaneous detection of two gamma rays originating in two different nuclei. The term simultaneous is used in the sense that if two counts arrive at the coincidence circuit within the time interval Z, where t is the resolving time of the coincidence circuit, they will be recorded as being in coincidence. The total coincidence rate NT is what is actually measured. The real coincidence rate NR is then given by NR = NT - NA (15) where NA is the accidental coincidence rate. For counts occurring in a random time sequence the accidental coincidence rate can be expressed as (37) NA = 2tN1 N2 (16) where N1 and N2 are the single counting rates. It is desirable that the accidental rate be small compared to the real coincidence rate since an error in the determination of NA will be reflected as an error in NR. There are two methods of determining the resolving time using equation (16). One method consists of measuring the coincidence rate from two independent sources while the other method involves using a single source and a delay in one channel much longer than the resolving time t. In either case, all the coincidences recorded are then accidental coinci

-16dences. Knowing NA and the single rates N1 and N2, t can be calculated from equation (16). No correction need be made for the background counting rate since energy selection is employed and the single rates are much greater than the background. In addition, any coincidences which are due to the constant background will be corrected for by the process of determining the accidental coincidences. Resolving Time and Source Strength In the case of selective counters the real coincidence rate is given by NR= N W E, 0 2 (17) where N is the source strength, C7, and C( are the solid angles subtended by the two detectors, and E, and E are the detection efficiencies for the counters. The single rates are N, = Nc,, Nz- N c E, (18) Inserting equations (18) into the expression for the accidental coincidence rate, one obtains NA' Z " NZ, cz E (19) Dividing equation (19) by equation (17) an expression for the real to accidental ratio is obtained. MzNR^~~ - |__^~~ 1(20) NA 2'u N This ratio should be kept as large as possible in order to reduce the correction to the observed coincidence rate. Since NR is proportional to N, a lower limit on the source strength N is imposed by the minimum

-17tolerable real coincidence rate NR. The maximum value of N is limited in many cases by other factors such as single counting rates. Thus 2I, the resolving time, is the prime factor in determining the ratio of real to accidental coincidences, and one would like to make 2: as small as possible to give the maximum real to accidental ratio. A lower limit on t is imposed by the properties of the scintillator which is used for detection. It can be shown that the resolving time It should not be less than the scintillation crystal decay constant Cd if energy selection is to be maintained and all real coincidence events are to be registered by the coincidence circuit(38). The crystal decay constant determines the rise time of the photomultiplier output pulse. For sodium iodide crystals, which are normally used for gamma ray detection because of their good energy resolution, the crystal -7 decay constant is 2.5 x 107 sec. This sets a lower limit of approximately 2.5 x 10-7 sec. on the resolving time of the coincidence circuit if the above conditions are to be maintained. It is possible to obtain a shorter resolving time by utilizing the initial portion of the output pulse to trigger the coincidence circuit. However, this method destroys the energy selection properties of the circuit. The technique of doing this will be described in the following chapter. In practicea compromise must be made between the real to accidental ratio and the time needed to obtain the necessary data. The real to accidental ratio should be kept greater than five to one, but if the decay scheme is complex and the branching ratios are low, one must sometimes make it as great as one to one.

-18Efficiency a-:J! Solid Angle Variations If the source is not cea:-rdc. exactly, the solid angle subtended by one detector will vary with the angular position. In addition, the efficiencies E, and Ez for the detection of gamma rays may vary. These effects may produce false asymmetries. A first order correction for these variations is obtained by dividing the real coincidence rate by the two single counting rates N1 and N2. Using equations (17) and (18) one obtains N/ r NTZ N NF- = N^ - N,~ - N (21) The corrected real coincidence rate NR' then depends only on the source strength N and is independent of variations in the solid angles and efficiencies. Decaying Source If the half-life of the source is much longer than the time necessary to take the data in one quadrant, no correction need be made for the source decay. For a short half-life source, taking the data in the order 90~ - (90~ + ) - (270~ -e-) — 270~ provides a first order correction for the decay. The data from 90~ and 270 areadded together, the data from 120~ and 150 are added together, etc. Effect of Finite Solid Angle and Source Extension Since each detector subtends a finite solid angle, the two detectors do not define a single angle -.but instead a range of angles from 4,- to 0z. (Figure 2) It has been shown by Frankel(39) that this effect merely attenuates the correlation.

-1i Figure 2. Finite Solid Angle Subtended by Detectors (39- 2) The measured correlation function can be written (39 W\(&) = V G A P (cos ) (22) ( even) where Ak are the expansion coefficients which depend only on the parameters of the cascade and Gk are the attenuation coefficients. The Gk are functions of the efficiency of the detectors, the dimensions of the scintillation crystal, and the distance from source to crystal. The efficiency is a function of the gamma ray energies and the angle between the counter axis and the propagation direction of the gamma rays. Several methods can be used to determine Gk. 1. The most accurate method of determining the Gk is to measure the angular efficiencies of each detector for each energy by means of a collimated beam of gamma rays. The Gk can then be found by a numerical integration(42'43) 2. If the energies are not too different from 511 kev, annihilation radiation can be used to determine the counter resolution. The attenuation coefficients are then found by

-20a numerical integration over the resolution curve. The expressions for Gk have been tabulated up to G4 for the case where the resolution curve can be approximated by a triangular or Gaussian distribution. () 3. The Gk can be calculated for a given geometry as a function of the absorption coefficient/C of the crystal. Rose(41) has tabulated the attenuation coefficients G2 and G4 for 1-1/2" by 1" cylindrical NaI crystals for source distances of 7 and 10 cm. and for values of A from 0.12 cm-1 to 40 cm-1. For.the geometry used in this experiment, namely 2" by 2" NaI (T1) crystals at a distance of 10 cm. from the source, it was found that methods 1 and 2 yield results for Gk which are equal within experimental error for gamma energies between 500 kev and 2 Mev(43). The only correction for source size that has been rigorously treated is that for an axially extended cylindrical source. It was found that for the above geometry the correction for axial extension was negligible for sources less than 1 cm. in length. Extranuclear Field Effects It was mentioned in Chapter I that the correlation function can be attenuated by extranuclear fields. However, if a source is in the form of a dilute solution, the theoretical correlation can be completely restored, or if the interaction is very large, it can be partially restored(3'03). This is due to the fact that in a liquid there are continual rearrangements of the perturbing fields because of molecular collisions. The extranuclear field may be reoriented many times during

-21the lifetime of the intermediate state, and the net effect will not cause the nucleus to undergo a large precession. Usually the intermediate state lifetimes are short enough so that the effects of extranuclear fields are not serious. Scattering Effects Another problem which must be considered in angular correlation is scattering. Effects due to scattering can mask the true correlation. The scattering of gamma radiation in the source, the scattering from one crystal to the other, and the scattering of radiation from nearby objects can all produce false asymmetries in the measured correlation. The correction for scattering in the source is complicated and (21) difficult to apply(21) However, it is usually negligible for high energy gamma rays (greater than 500 kev) and for sources with low atomic number Z. The source should be made as narrow as possible and contained in a holder constructed of a material with a low Z and with as thin a wall as possible to minimize scattering effects. In addition, the use of energy selection helps to reduce the effect of scattering in the source. Crystal to crystal scattering can cause false asymmetries since a photon can enter one crystal and be partially absorbed and partially scattered. The scattered photon can then enter the other detector and be absorbed, with this event being registered as a coincidence(45). One method of avoiding coincidences due to this effect is to shield the crystals with lead. Then a scattered photon must traverse two thicknesses of lead while the primary photon must only pass through a single thickness. A second method makes use of energy selection with the scattered photon not being counted since it necessarily has a lower energy than

-22the primary photon. In some cases both methods must be used simultaneously. The effect of scattering from nearby objects is likewise cornbatted by the use of lead shielding and energy selection.

CHAPTER III EXPERIMENTAL PROCEDURE Apparatus General Description In Chapter II it was pointed out that a coincidence circuit with both a short resolving time and pulse height selection is needed to investigate directional correlations of cascades occurring in nuclei with complex decay schemes. The so-called method of parallel channels provides a means for achieving this. Two parallel channels are utilized, one of which provides the short resolving time and the other, the energy selective properties. A coincidence circuit employing this method is called a fast-slow coincidence spectrometer. The reason for this nomenclature will be seen later. A block diagram of the fast-slow coincidence spectrometer used in this experiment is shown in Figure 3. The apparatus was designed and built by R. Scharenberg and M. Stewart(46,47). Scintillation counters were used as gamma ray detectors, and each counter fed both a fast and a slow channel which were in parallel. The fast channels led to a fast coincidence circuit with a resolving time of about 8 x 109 sec. The fast coincidence circuit recorded a count when any pair of gamma rays were in coincidence. The output of this was fed into a slow triple coincidence circuit (- - 2 x 10-7 sec.) along with the energy selected pulses from the slow channels. If the discriminator in slow channel 1 selects only a single gamma energy N and the discriminator in slow channel 2 selects only A, then the gate circuit (triple coincidence circuit) will give a count only when the fast coincidence is between -23

S)'OURCE DETECTOR I DETECTOR SLOW CATHIDE I FAST CATHODE AST CATHODE SLCW CATHODE FOLLOWER j FOLLOWER FOLLOWER FOLLOWER 2-STAGE 2-STAGE WIDEBAND WIDEBAND AMPLIFIER AMPLIFIER IAMPLFIER MPL FIim P -STAGE A-1 1-STAGE WDBN AMPLIFIER WIDEBAND AMPLIFIER AMLE AN~PLIFFIER PULSE P PULSE AMPLIFIER AMPLIFIER DIFFERENTIAL LITMTER LIMITER DISCRIMINATOR DISCRIMINATOR 2 -STAGEI IFAST BLOC KINGi FAST F IEAST BLOCKINGIl 2-STAGE WIDE BAN D OSILTR COINCI IDENCCE OSILTR WIDEBAND AMPL~IF IER CIRCUIT AMPLIFI {~VARIABLE I ISCALERI A-1 AMPLIFIESR SCALER VARIABLE I DELAY I I ~ 1 AND DISCRIMINATOR SLCW BLOCKING I SCALER ^ OSCILLATOR SLOW BLOCKING SLOW BLOCKING INVERTER - GATE IVRE AMPLIFIER OSCI LATOR ~IRC ~ OSCILLATOR A-i AMPLIFIER AND SCALER SCALR IDISCRIMINATOR SCALER Figure 3. Block Diagram of Apparatus

-25-, and Y. The effective resolving time of this fast-slow coincidence circuit is determined principally by the fast coincidence circuit resolving time and is approximately 1 x 10 sec. Since the details of the electronic circuits have been thoroughly described by Scharenberg and Stewart(46,47), only a brief description of the apparatus will be presented here. Source Mounting The sources used in this experiment were liquids. The source material was contained in a cylindrical cavity 1/8" in diameter and 3/8" in length drilled in a lucite holder (Figure 4). The wall was approximately 1/32" thick. The source holder was held at a height of about 5" above the table by a brass rod, and in all correlation measurements the source to crystal distance was 10 cm. LUCITE CAP SOURCE LUCITE HOLDER Figure 4o Cross-Section of Source Holder Detectors The gamma ray detectors consisted of commercial NaI (Tl) crystals mounted on RCA 6342 photomultiplier tubes. The crystals were cylindrical in shape, 2" in diameter and 2" thick, and were coupled to the end of the phototubes using Dow-Corning 200 Silicone oil (viscosity = 10 poise). The phototubes were magnetically shielded with mu-metal

-26shields. Each phototube was mounted inside a 2-1/2" iron pipe with the crystal projecting through the front cap. Aluminum shields 3/16" thick were placed between the crystals and the source to stop beta particles from entering the crystals. Lateral lead shielding was used in some of the correlation measurements to prevent counter to counter scattering when it could not be eliminated by energy selection. Fast Channels Since the resolving time of a coincidence circuit is of the order of the width of the input pulses it is necessary to produce pulses of about 10 millimicroseconds duration if a resolving time of 1 x 10-8 sec. is desired, and if each pulse is to produce the same effect on the coincidence circuit, they should be uniform in shape and size. In addition, the pulses should have a fast rise if no jitter is to occur in firing the coincidence circuit (due to the fact that scintillation counter pulses with different amplitudes are delayed by different amounts). Thus the slow-rising, long-duration, non-uniform pulses from the scintillation counter must be converted to uniform pulses with a fast rise and short duration. This is accomplished at the expense of losing all information about the amplitude of the pulse (and therefore the energy of the incident radiation). The negative output pulse (0.5-5 v.) from the scintillation counter is fed first into a fast cathode follower which has a gain of about about 0.5. From here the pulse is sent through 200 ohm coaxial cable into a series of three 100 megacycle transmission line amplifiers (Hewlett-Packard types 460A and 460B) each of which has a maximum gain

-27of about eight. Fast amplifiers must be used since the high frequency components of the pulse must be amplified to produce a fast rising pulse. The first amplifier is a two-stage linear amplifier, and the second is a single-stage linear amplifier. Both of these saturate at about eight volts into a 200 ohm load. The third amplifier is a pulse amplifier which saturates at about sixty volts. The pulse amplifier will amplify only a positive signal. With the maximum gain available, all pulses corresponding to gamma ray energies of about 200 kev or higher saturate by the time they reach the pulse amplifier. The pulse amplifier adds no further saturation and produces a negative output pulse of about 60 volts. This large negative pulse is then fed into a limiter circuit consisting of a sharp cut-off pentode which cuts off with a one-volt signal on the grid. This produces a very fast rising pulse ( 5 x 10-9 sec.). Since the plate resistor in the limiter must be small to obtain a fast rise the gain of the limiter is small. Another two-stage wideband amplifier is used to amplify the small limiter pulse. As soon as saturation occurs in the fast amplifiers, all information about the original pulse height and gamma ray energy is lost. The amplified limiter pulse ( 15 v. positive) is fed into a fast blocking oscillator circuit(48) employing subminiature components. The blocking oscillator produces a uniform positive pulse of about 40 v. with a 10-8 sec. rise and 6 x 10-8 sec. duration. Since a negative pulse is needed for the coincidence circuit an inverting stage is used to convert the positive blocking oscillator pulse to.a negative pulse. The inverter tube saturates very quickly preserving the fast rise and gives a 7 v. flat-topped negative pulse. A

-28shorted delay line is then used to clip the pulse width to 2 x 10-" sec. -8 The final pulse is 7 v. negative with a rise time of about 1 x 10 sec. and a duration of about 2 x 10-8 sec. The pulses from the two fast channels are fed into a Garwin type coincidence circuit(4950). The Garwin coincidence circuit is used because of its fast resolving time and good discrimination ratio of coincidence pulses to singles pulses. The output of the fast coincidence circuit is sent to an amplifier and discriminator (Atomic model 204B) which passes the coincidence pulses but not the singles pulses. Since the electrical lengths of the two fast channels are dependent on the amplifier gain settings, blocking oscillator bias voltage, etc., the channel lengths must be aligned properly. This is accomplished by adjusting the coaxial cable lengths. Slow Channels The function of the slow channels is to amplify the scintillation counter pulses and select pulses which have amplitudes between some predeterm:ined limits. As mentioned previously,the energy selection channels (slow channels) are placed in parallel with the fast channels. The pulse from the scintillation counter is fed first into a slow cathode follower which has a gain of about 0.25, and from there into an A-1 amplifier (Atomic model 204B). The output of the A-1 amplifier is fed into a differential discriminator circ it which was designed by Lu(51). The discriminator output is sent through a variable delay and single-stage amplifier into the slow blocking oscillator circuit. The variable delays provide an adjustment to align the slow channels. The slow blocking oscillators are almost identical to thie fast blocking oscillators, the

-29main difference being the use of a pulse transformer that gives a 0.2 microsecond pulse width rather than the 0.06 microsecond width as in the fast channels. The outputs from the two energy channels together with the fast coincidence output are then put in triple coincidence. The gate circuit (triple coincidence circuit) is a Garwin type circuit, and the resolving time ( 2 x 10-7 sec.) is determined by the 0.2 microsecond width input pulses. The output of the gate circuit is sent to an amplifier and discriminator where the smaller singles and doubles pulses are rejected and the triple coincidence pulses are passed on to a scaler. Scalers Six scalers are connected so as to record the fast singles counting rates, the slow singles counting rates, the fast coincidence rate, and the gate coincidence rate. The scalers are the conventional binary type scalers. The fast singles rates and the fast coincidence rate are merely used as a check on the performance of the fast channels while the slow singles rates are used to correct the observed gate coincidence rate for solid angle variations, efficiency variations, and source decay. Stability It was mentioned in Chapter II that stability is very important if accurate correlation measurements are to be made. The problem of stability is reduced if the power and voltage sources are regulated properly. The 110 v. A.C. power was regulated to + 0.1% by means of Sorensen regulators, except for the scaler power which was not critical. The separate D.C. voltage supplies were also regulated to about + 0.2%,

-30with special care being exercised with the phototube supply which was regulated to within + 0.01%. The equipment was operated in an air-conditioned room which made all temperature effects negligible. With the precautions taken, the energy selected counting rates were stable to within + 2% and all other counting rates to within + 1%. Procedure in A Typical Correlation Measurement The procedure followed in making the angular correlation measurement was approximately the same for all the correlations which were run. Alignment of Apparatus First, the source was centered properly so that the solid angle remained constant as the movable detector was rotated from 90~ to 270~. Second, the fast and slow channels were aligned. Since different energies and counting rates could affect the electrical lengths, the same source and discriminator settings which were to be used in the correlation measurement were also used in the alignment. The gain of the fast amplifiers was adjusted so that the lowest energy of interest saturated the limiter. The alignment of the fast channels was accomplished by observing the fast coincidence rate as a function of the relative cable length in the two channels. Since the resolving time is about ten millimicroseconds and the delay in the cable is one millimicrosecond per foot, the alignment process can be done with a relatively small amount of cable. The energy channels would require several hundred feet of cable to align by this method, so they were aligned with the aid of a Tektronix 517 oscilloscope. Delay cable was added after the fast coincidence output until the fast coincidence pulses arrived at the gate circuit last. These

-31pulses were used to trigger the oscilloscope, and the slow channel singles pulses were applied to the vertical input. The variable delays in the slow channels were adjusted until the singles pulses appeared at the beginning of the sweep. Correlation Measurement The data was normally taken at 15~ intervals in the double quadrant sequence, running for 5 minutes at each angle. This procedure was continued until sufficient statistics were obtained. The total number of coincidences accumulated depended on the magnitude of the correlation asymmetry, the real to accidental ratio, and the coincidence counting rate. If the counting rate is very low, one must settle for poorer statistics since it is not advisable to run the correlation over too long a period of time because of stability problems. The accidental coincidence rate was measured by the double source method after every three or four sweeps through the double quadrant sequence. The counting rates and discriminator settings which were used in the accidental measurement were the same as those used in the actual correlation measurement. This allowed an accurate determination of the accidental rate. For the Cd110 measurements, the real to accidental ratio was always greater than ten to one, while for Se76 the ratio was always greater than five to one. Data Analysis After correcting for the accidental counting rate, the coincidence rate was normalized by dividing by the two energy channel singles rates N1 and N2. In the case of Se76 the coincidence rate was divided by N1 and N2 and multiplied by N (iO80) Nz (8ec). The reason for this was that the division by N1 N2 makes the normalized coincidence

-32rates at the end of the measurement much larger than those at the beginning of the measurement because of the source decay. In the process of making a weighted least-squares fit to the data this gives a false statistical weight to the later measurements. By multiplying by N1(180~) N2(180~) this difficulty is overcome. The method of taking data in the double quadrant sequence provided sufficient correction for the source decay here. After all the data for a given angle were added together, a leastsquares fit of the data was made to the function vW() - I + A2 P (C e) - /A (.cc.&) The procedure in making the least-squares fit has been extensively treated by Rose(52). The annihilation radiation from Na22 was used to correct for the effect of finite angular resolution. This correction was applied to the normalized expansion coefficients A2' and A4' giving the corrected coefficients A2 and A4. After the corrected coefficients A2 and A4 were obtainedthey were compared with the theoretical results for all possible values of the cascade parameters.

CHAPTER IV RESULTS OF GAMMA-GAMMA DIRECTIONAL CORRELATION MEASUREMENTS IN Se76 Introduction As76 decays by complex beta emission to Se76 with a half-life of 26.8 hours. The decay scheme of As76 has been the subject of many investigations(5357). The presently accepted scheme was first proposed by Kraushaar and Goldhaber(56) and later confirmed by Kurbatov, Murray, and Sakai(57). The decay scheme presented by Kurbatov, et al. (57) is shown in Figure 5. The numbers in parentheses are the relative gamma intensities. The log ft values for the beta transitions and their interpretation are given in Table 1. TABLE 1. As76 BETA DECAY DATA Beta Energy (Mev) Log ft Interpretation 2.97 8.8 Unique 1st Forbidden (AJ= 2, yes) 2.41 8.2 1st Forbidden (A J = 0, 1; yes) 1.76 7.9 1st Forbidden (AJ = 0, 1; yes) 0.36 6.1 1st Forbidden (AJ = O, t 1; yes) or Allowed (A J = 0, 1;, no) The ground state spin of As has been measured to be 2 by an atomic beam method(58). This agrees with the value of 2- predicted by Nordheim's rules (59) -33

34 A76 As 7.5 2.5% SE 1.76 16%,\ \ \ 1.40 2.05'~\ \ \ ~(0.02) (0.04) tI \ \2.41 1\ \ \ 2.965\ \' 1, 2+ 50.5 % 0.65 1.20 \ \ (0.20) (0.21) 2+ 0.,55 (1.00) Figure 5DOe+ Figure 5. Decay Scheme of As76

-35Directional correlation measurements have been made previously on the 0.65 Mev - 0.55 Mev and 1.40 Mev - 1.20 Mev cascades. Kraushaar and Goldhaber(56) measured the 0.65 - 0.55 correlation without using energy selection and assigned spin 2+ to both the 0.55 Mev and 1.20 Mev levels (assuming a 0+ ground state) with the 0.65 Mev gamma ray consisting of 34 to 80 percent E2 radiation and the remainder MI radiation. Metzger and Todd(60) repeated this correlation using pulse height selection and confirmed the 0+ - 2+ - 2+ assignment. Their results indicated that the 0.65 Mev gamma ray is almost pure electric quadrupole radiation (Q > 85%). Wiedling(61) recently reported a measurement of the 1.40 Mev - 1.20 Mev directional correlation. The results agreed very well with a 3(D)2(Q)0 sequence. Wiedling made an assignment of 3- to the 2.60 Mev level with the 1.40 Mev gamma transition being pure El radiation. This assignment of negative parity to the 2.60 Mev level was made on the basis of relative gamma intensities, the log ft value for the 0.36 Mev beta transition, and the fact that the lowest odd spin state in an even-even nucleus usually has odd parity. However, none of these allow a unique determination of the parity of the 2.60 Mev level. Kurbatov's log ft values (Table 1) are in good agreement with the assignment of 0+, 2+, 2+ to the three lowest levels in Se76, but the value of 6.1 for the 0.36 Mev beta lies on the borderline between an allowed and first forbidden transition. No definite assignment can be made to the 2.60 Mev level from this log ft value although Kurbatov preferred 3+ In the present investigation, correlation measurements were

-36made on the 2.05 Mev - 0.55 Mev cascade for the first time. In addition, the 1.40 Mev - 1.20 Miev and 0.65 M-ev - 0.55 Mev directional correlations were remeasured to provide a check on the previous investigations and to see whether a more accurate resLilt could be obtained for the mixture in the 0.65 Mev transition. The source material was obtained from Oak Ridge. It was in the form of arsenic dissolved in dilute hydrochloric acid. Small amounts of Sb122 and Sbl24 were present in the source material. The decay was carefully studied, and it was found that the effect of the contamination on the correlations was negligible. The observed gamma ray spectrum, Figure 6, was in agreement with the decay scheme reported by Kurbatov, et al.57 The mean lifetime of the first excited state has been measured to be (3.3 + 2.2) x 10-11 sec.(62), and the lifetime of the 1.20 Mev state is expected to be short. Because of this and the fact that the source was in a dilute solution the measured correlation functions should not be attenuated due to extranuclear field effects. For each correlation the discriminators were set in such a way that there was no interference from any of the other cascades. Thus the full correlation was measured in each case. Results and Interpretation 0.65 Mev - 0.55 Mev Correlation Both differential discriminators were set at position A as shown in Figure 6 so as to include both the 550 kev and 650 kev photopeaks. Lateral lead shielding was used for this correlation. The data

37 N(E) SCINTILLATION T SPECTRUM 1.20 0.55 X20 f O0,65 "1.40 A~ ~ ~ ~ ~ ~ ~ C ) 100 200 300 400 500 600 PULSE HEIGHT Figure 6. Se76 Gamma Ray Spectrum

-38are shown in Figure 7. The solid curve is the least squares curve corrected for finite geometry, and the error flags indicate the rootmean-square statistical errors of the experimental points. The broken curve is a plot of the theoretical correlation function for a pure 2(Q)2(Q)0 cascade. The experimental values of the expansion coefficients corrected for finite geometry are A2 = -0.042 + 0.015 and A4 0.319 + 0.023. The errors quoted are those defined by Rose in Equation 30 of reference (52). If one assumes a spin of 0+ for the ground state of Se76 (even-even nucleus), the experimental coefficients are not compatible with any combination of spins considering pure dipole or quadrupole radiation. If a mixture in the 650 kev transition is considered, only the 2(D,Q)2(Q)0 sequence will fit the data. In Figure 8 the values of A2 and A4 are plotted vs. Q, the quadrupole content, for a 2(D,Q)2(Q)0 sequence. The error flags represent the experimental values of A2 and A4. From Figure 8 it is seen that the data are consistent with a value of Q equal to 0.997 + 0.002. It can thus be concluded that the first and second excited states have spins of 2+ and that the 650 kev gamma transition is a mixture of (99.7 + 0.2)% electric quadrupole and (0.3 + 0.2)% magnetic dipole radiation. This result is in agreement with the value of Q > 0.85 found by Metzger and Todd(60). However, the results of the present investigation restrict the quadrupole content of the 0.65 Mev transition to much smaller limits than found in the previous measurements. Subsequent to the present investigation, Lindqvist(63) reported another measurement of the 0.65-0.55 correlation. He found a value of Q = 0.98 + 0.01. However, Lindqvist's data was taken at only three angles.

39 1.15 - W() 0.65 MEV- 0.55 MEV CORRELATION 1.10 - 1.05- // 0,95- / 0.85 \ // / 0.80 / 0175- / 0.70 90~ 1200 8 150" 180" Figure 7. 0.65 Mev - 0.55 Mev Directional Correlation in Se76

40 A2 AND A4 VS. Q FOR A A 2(D,Q)2(Q)O SEQUENCE _ -0.05 0.5 - _ ~ -0 10-1 ^^^^~^^^^^^ _______038 Q 1,00 (8>0) 0.4- ~ ~ ~ | l A4(EXP) 0.3 A2 (EXP) -0.2 -0.3 0 0.2 0.4 0.6 0.8 1.0 Q Figure 8. A2 and A4 vs. Q for a 2(D,Q)2(Q)0 Sequence

-412.05 Mev - 0.55 Mev Correlation For the 2.05 Mev - 0.55 Mev correlation one discriminator was set integrally at C and the other differentially at D as shown in Figure 6. Lateral lead shielding was used for this correlation. Because of the low coincidence rate, data were taken at only four angles. The experimental data and least squares curve corrected for finite geometry are shown in Figure 9. The corrected coefficients are A2 = -0.027 + 0.022 and A4 = -0.075 + 0.033. The negative value for A4 rules out the combinations 4(Q)2(Q)0 and 2(D,Q)2(Q)0 since both require a positive A4. The data can best be explained by the sequence 3(D,Q)2(Q)0. In Figure 10 the theoretical values of A2 and A4 are plotted vs. Q, the quadrupole content of the 3-2 transition. It is seen that the experimental values of A2 and'A4 are compatible with a value of Q = 0.948 + 0.014. Since an El-M2 mixture of this magnitude is very unlikely it is reasonable to conclude that the 2.05 Mev gamma ray consists of (94.8 + 1.4)% E2 and (5.2 + 1.4)% MI radiation. On the basis of this and the selection rules for gamma transitions, a value of 3+ can be assigned to the 2.60 Mev level. (57) This assignment agrees with that of Kurbatov, et al. (57), which was made on the basis of log ft values and relative intensities, but the + parity disagrees with Wiedlingts assignment(61). The data can almost be explained by a 1(D,Q)2(Q)O sequence. However, a spin of 1 for the upper level is very unlikely because of the absence of the 2.60 Mev crossover transition. 1.40 Mev - 1.20 Mev Correlation For this correlation the discriminators were both set integrally at position B (Figure 6) so as to include everything above the 1.20 Mev

42 W( ) 2.05MEV -0.55MEV CORRELATION 1.061.041.02 - 1.00 0.98 0,960,94 0.92 0.90 - 0.88 - l l I 90" 120" - 1500 1800 Figure 9. 2.05 Mev - 0.55 Mev Directional Correlation in Se76

43 0.3 (E X~P| eA(8<0) 0.2 0.1 -- A2 AA -0.1 -0.3 -0.4 0 -0.5 -0.6 _ _________,, 0 0.2 0.4 Q 0.6 0.8 1.0 Figure 10. A2 and A4 vs. Q for a 3(D,Q)2(Q)0 Sequence

-44photopeak. No lateral lead shielding was needed. The data are shown in Figure 11, the solid curve being the least squares curve corrected for finite geometry and the dotted carve the theoretical curve for a 3(D)2(Q)0 combination. The corrected experimental coefficients are A2 = -0.076 + 0.022 and A4 = -0.003 + 0.032. It is seen that the error in A4 is ten times larger than the coefficient itself. Thus the existence of any A4 is questionable. When only A2 is considered, a value of A2 = -0.077 + 0.019 is obtained. This is in good agreement with the theoretical value of A2 = -0.0714 for a 3(D)2(Q)0 cascade. Considering this sequence, the maximum amount of quadrupole admixture in the 3-2 transition consistent with the data is 0.05%. The data can also be explained by the sequence l(D,Q)2(Q)0. However, the possibility of spin 1 for the 2.60 level has already been ruled out. Therefore the results of the 1.40 - 1.20 correlation confirm the spin assignment of 3 to the 2.60 Mev level in Se76. Since a positive parity for this state is necessary to explain the 2.05 - 0.55 correlation it is concluded that the 1.40 Mev gamma ray must be MI radiation. Wiedling had assigned El radiation to the 1.40 Miev transition assuming a negative parity for the 2.60 level. Summary and Discussion The results of the correlations confirm the assignment of 0+, 2+, 2+, 3+ to the energy levels of Se76 in order of increasing energy. The 0.55 Mev and 1.20 Mev gamma rays are found to be pure E2 radiation, the 0.65 Mev gamma ray (99.7 + 0.2)% E2 and (0.3 + 0.2)% Ml, the 2.05 Mev gamma ray (94.8 + 1.4)% E2 and (5.2 + 1.4)% Ml, and the 1.40 Mev gamma ray almost pure ML (o0.05% E2).

W 0 ) 1.40 MEV - 1.20 MEV 1.02 CORRELATION 1.00 0.98 0.960.94 - J \1 0.92- \\ 0.90- 0.880.86- 90" 120~ 5 150~ 180~ Figure 11. 1.40 Mev - 1.20 Mev Directional Correlation in Se76

-46These results are difficult to explain in terms of an individual particle model. If one calculates the ratio of'E2 to M1 transition probabilities using Rose's theoretical estimate for the transition of a single proton(64), the following results are obtained for the gamma transitions in Se76. [I = oJ 00 LI(MI) Jio M1 L (E2) j = 0009 L I(Ml) 0.6 EV Therefore appreciable E2 admixtures are not expected in any of these gamma rays according to a strict individual particle model. Almost all even-even nuclei have a spin of 2+ for the first excited state, and in many cases the second excited state is also 2+. Table 2 lists several of these nuclei(65). The energies of the first and second excited states, E2 and E2, are given in columns two and three and their ratio E2/E2 in column four. There are some noticeable regularities here. As one goes farther from the closed shell values N = 28, 50, 82, and 126, the E2 and EI values become smaller. However, the ratio E2' /E2 is approximately constant for all cases listed, having a mean value of about 2.2. The fifth column gives the E2 transition probability from the ground state to the first excited state in units of the single particle estimate. This transition probability is obtained from Coulomb excitation results(65). In the Coulomb excitation process the target nuclei are bombarded with charged particles whose energy is low enough so that

-47TABLE 2. PROPERTIES OF EVEN-EVEN NUCLEI HAVING ASSIGNMENTS OF 2+ FOR BOTH THE FIRST AND SECOND EXCITED STATES E2 E2' B(E2; 02) B(E2; 2' 0) Nucleus (Mev) (Mev) E2'/E2 Bsp(E2) (M1/E2)21, 2 B(E2; 2'-2) 26Fe58 0.81 1.62 2.00 0.2 0.01 28Ni60 1.33 2.18 1.64 17 (3.10-3) 30Zn64 1.00 2.27 2.27 15 (0.1) Zn66 1.05 2.40 2.29 11 (0.04) 34Se76 0.55 1.19 2.17 45 -1 0.1 36Kr82 0.77 1.45 1.88 (0.01) Kr84 0.9 1.9 2.1 >0.1 40Zr92 0.93 1.83 1.97 (0.o6) 44Ru100 0.54 1.36 2.52 22 (0.02) Ru102 0.47 1.10 2.34 45 (0.15) 52Te122 0.57 1.26 2.21 26 0.1 0.01 Te126 O.65 1.40 2.16 17 (0.004) 54Xe126 0.39 o.86 2.20 (0.01) Xe128 o.46 0.98 2.13 (0.01) 78Pt192 0.32 0.61 1.90 0.025 0.008 Pt194 0.33 O.62 1.88 50 small 0.01 Pt196 0.35 0.69 1.97 38 0.05 < 4.10-4 80Hg198 0.41 1.09 2.66 29 0.7 0.03 84Po214 0.61 1.38 2.26 15 > 1

-48they will not penetrate the Coulomb barrier of the nucleus and cause a nuclear reaction. The electromagnetic field of the charged particle interacts with the nucleus and can cause a nuclear excitation. Coulomb excitation is mainly an electric quadrupole process. The yield function can be measured accurately and the cross section for E2 excitation calculated. From Table 2 it is seen that for all those nuclei whose first + 2 state has been excited by Coulomb excitation, the observed cross section is greater than that expected for a single particle excitation. The sixth column in Table 2 gives the ratio of Ml to E2 radiation in the 2+ ~22+ transition as determined from angular correlation or conversion coefficient data. It is seen that in almost all cases there is a large admixture of electric quadrupole radiation in the 2+ -2+ transition. The seventh column gives the ratio of the reduced E2 transition probabilities for the cross-over and cascade radiation from the second excited state. The reduced transition probability B(L; If -Ii ) is defined in terms of the total transition probability T by the expression(65) Tr (L~1) ( 7L+I ) T — (2 L+ 1)!!17Z ffi i;) where L is the multipolarity and Uo is the angular frequency of the radiation (WU- E/). It is seen from Table 2 that the reduced transition probability for the cross-over transition is considerably less than that for the cascade decay for all cases listed. On the basis of a single particle model they would be approximately equal. The results presented in Table 2 indicate that the excitations involved here are due mainly to a cooperative motion involving many

-49nucleons. It is known that nuclei with doubly closed shells have very high binding energies and are spherically symmetric. Nuclei which have many particles in unfilled shells exhibit large quadrupole moments and nuclear spectra which can be explained by a collective rotation of the nucleons about a non-spherical equilibrium shape, the so-called rotational spectra. In the intermediate regions between these extremes, excited states corresponding to quadrupole vibrations (ellipsoidal vibrations) about a spherical equilibrium shape might be expected (65'66) An enhancement of E2 transition probabilities would then be associated with these vibrational states. The characterization of excitation level spectra as vibrational is not expected to be as accurate as in the case of rotational spectra. The vibrational energies involved (several hundred kev to 1 Mev) are no longer very small compared to typical intrinsic particle excitation energies (1 or 2 Mev), and therefore interaction between the intrinsic motion and the vibrational motion may be significant. In the case of rotational spectra, the rotational energies are much smaller than the intrinsic excitation energies, and coupling between the two is insignificant for the low-lying levels. The shape oscillations of a spherical nucleus can be classified according to their multipole order (66). The excitation quanta are called phonons and have total angular momentum X and parity (-1 ) The vibrational motion is associated with an oscillating electric multipole moment. For small amplitudes of oscillation (e.g., harmonic deformation potential) the solution of the Schrodinger equation gives a harmonic energy spectrum with a uniform spacing between the levels. The lowest frequencies of collective vibration are expected to be of quad

-50rupole type ( X = 2) since a surface deformation with X = 1 merely represents a center-of-mass displacement. The vibrational excitation spectra are simplest for the groundstate configuration of even-even nuclei for which the intrinsic structure does not contribute to the nuclear angular momentum. The energy spectrum assuming harmonic vibrations is shown up to the 2 phonon state in Figure 12a66). A state of energy E(n) = (n + 5/2) W2z can be characterized as containing n phonons each of which carries an angular momentum of 2 and even parity. Therefore all the excited states have even parity. The second excited state is degenerate with spins 0+, 2+ and 4+ in the harmonic approximation. E2 transitions between the 2 ic2 state and the ground state are forbidden since the phonon number cannot change by more than one, and Ml transitions between any pair of levels are forbidden in this simple model for even-even nuclei. For the group of nuclei considered in Table 2 the ratios of the energies of the second and first excited states are rather close to 2 which suggests that the harmonic approximation has some validity. The large electric quadrupole admixture in the transition from the second to the first excited state and the fact that the crossover transition is inhibited in these nuclei give additional support to this model. Calculations have also been made assuming an anharmonic deformation potential (67). The potential is assumed to be a function only of a quantity (3 which measures the deviation from sphericity of the nucleus. The potential is not dependent on the specific shape of the nucleus (i.e., no favoring of prolate or oblate shapes). According to these calculations the degeneracy of the second excited state is partially lifted, but the 2+ and 4+ states remain at the same energy. This is shown in Figure 12b.

-51a. Harmonic b. Anharmonic Co Experimental 0+ 2Tihw 0,2,4+ 4+ 2,4+ _ - 42+ I1w ~ 2+ + 2+ 0h7w2 0 - 0+ - 0+ Figure 12. Vibrational Spectra in Even-Even Nuclei The E2 crossover transition between the second 2+ state and the ground state is still expected to remain forbidden. The ratio of the energies of the second and first excited states is now expected to be slightly larger than 2. The average value 2.2 of the empirical ratio implies that there is actually some anharmonicity but with the spherical shape at least on the borderline of being stable. Any favoring of prolate or oblate shapes will split the degeneracy between the 2+ and 4+ states but always so as to lower the 4+ state if there is no vibration-particle coupling. The frequent appearance of 2+ second excited states, Figure 12c, may be due to coupling between the vibrational motion and the intrinsic

-52particle motion. This effect could be important since the vibrational energies are not much smaller than the excitation energies of the individual nucleons. The theory of vibrational spectra has been somewhat successful in explaining the character of the first few excited states in several of the nuclei listed in Table 2. However, more theoretical work must be done, especially in the case of higher excited states where vibrationparticle coupling becomes important. An explanation of the Se76 level scheme in terms of vibrational levels presents some interesting problems. The Se76 nucleus contains 34 protons and 42 neutrons. Therefore Se76 has 6 protons outside of the partially closed proton shell at Z = 28 and 8 neutrons lacking from the closed neutron shell at N = 50, and it might be expected to exhibit a vibrational level structure. The first excited state in Se76 has been (68) reached by Coulomb excitation, and the cross-section for this was found to be much larger than the cross-section expected for a single particle excitation (Table 2). The Coulomb excitation result, the value of 2.17 for the ratio E2,/E2, the fact that the 0.65 Mev gamma transition is almost pure E2, and the inhibition of the 1.20 Mev crossover transition, (Table 2)all suggest that the first two excited states are mainly vibrational in character. Therefore it is concluded that the first excited state is mainly the result of a one-phonon vibrational excitation while the second excited state is mainly the result of a two-phonon vibrational excitation. Since the 0.65 Mev gamma transition contains some Ml radiation and the 1.20 Mev cross-over transition is not completely forbidden, it must be assumed that the second excited state is not a pure vibrational state but that some vibration-particle coupling exists.

-53The very different nature of the two transitions originating from the third excited state in Se76 is difficult to understand. One possibility is that the third excited state is due to a two-phonon vibrational excitation coupled with a single particle excitation of the ground state configuration. If this is true, then the 1.40 Mev gamma ray occurs between two states with the same number of phonons and is primarily a single particle transition. This could account for the fact that the 1.40 Mev gamma transition is almost pure magnetic dipole radiation. However, the 2.05 Mev transition would require both a change in vibrational excitation and particle excitation, and this might account for the large E2 component (-/95%) in the 2.05 Mev transition.

CHAPTER V RESULTS OF GAMMA-GAMMA DIRECTIONAL CORRELATION MEASUREMENTS IN Cdl0 Introduction Ag1lom decays by complex beta emission to excited states of Cd110 and by an isomeric gamma transition to the ground state of Agl10 with a half-life of 253 days(69). Agll in turn decays to Cd1lO by complex beta emission with a half-life of 24 seconds. The decay of AgO11 has been the subject of numerous investigations(776) The presently accepted decay scheme, which was first proposed by Siegbahn(70), is shown in Figure 13. The relative gamma intensities (in parentheses) and energy values are due to Siegbahn(70). The gamma rays for which no intensities are given are weak transitions. The position of the 656 kev, 885 kev, 935 kev and 1389 kev gamma rays in the scheme has (70,74) been well established by coincidence measurements'. The 1516 kev gamma is known to be in coincidence with the 759 kev and 656 kev gammas, but the order of the 1516 kev and 659 kev gamma transitions has not been definitely established. Siegbahn placed them in the order shown in Figure 13 on the basis of the estimated relative intensities and the fact that the three weak gammas with energies of 706 kev, 676 kev, and 814 kev could then be fitted in with the addition of only one more level. Four additional weak gamma rays have been found in conversion electron work. These are at 575 kev(76), 618 kev(7175'76)), 740 kev(71) and 1480 kev(7176). However, these cannot be fitted into the previous decay scheme. The K-shell internal conversion coefficient for the 656 kev transition has been measured by Siegbahn to be (2.5 + 0.4) x 10-3. The theoretical values obtained by interpolation from Sliv and Bands' tables -~5

Ag110 Cd 11 6+ 0.087(58%),+ T 10.5160 (3 5%) 0.447 0.706 1.389 2.12 0.935 (33) (17) 0.676 0.814 (31) 2.86 0.759 0.885 (22) (81) vii,!'r~'~ ~2+ 0.656 (100) 0+ ALL ENERGIES IN MEV Figure 13. Decay Scheme of Agliom

-57of C0(77) are 1.0 x 10-3 for El, 2.75 x 10-3 for E2 and 3.1 x 10-3 for MI radiation. The experimental value agrees best with an assignment of E2 for the 656 kev gamma ray. Assuming 0+ for the ground state of the even-even nucleus Cdl10 the first excited state is then 2+. The fact that the first excited state has been Coulomb excited(78J79) supports this assignment. Measurements of K/(L+M) ratios have been made for many of the gamma transitions(71). However, no information concerning multipolarities can be learned from these because the theoretical K/(L+M) ratios are very insensitive to multipole order in this region of Z and for the energy values involved. The beta spectrum of AgllOm has been investigated by several groups(70-76). Two high energy beta transitions of allowed type with endpoint energies of 2.86 Mev and 2.12 Mev have been found. These originate from the ground state of Ag and go to the ground state and first excited state of Cd110 Since both transitions are of allowed type(80) (AJ = 0 or + 1, no) the spin of the ground state of AgllO must be 1+. This agrees with the value predicted by Nordheim's rules(59). Antoneva(7l) has reported an additional weak group at about 1.4 Mev, but no confirmation of this has been made. Two soft beta transitions with endpoint energies of 87 kev and 530 kev originate from Agllom. The Fermi plot of the 530 kev beta has been reported to be curvilinear, and Siegbahn(70) suggested that another weak low energy group might be present (dotted line in Figure 13). It is possible, however, that the 530 kev beta transition is of forbidden type which would give a non-linear Fermi plot. Using the measured beta branching ratios(71), approximate log ft values for the low energy beta transitions can be found from Moszkowski's

-58graphs(81) This gives a log ft value of about 8.4 for the 530 kev beta and about 5.6 for the 87 kev beta. These values indicate that the 530 kev beta is a forbidden transition while the 87 kev beta is of allowed type. The spin of Ag11m has been measured recently by an atomic beam method, and a value of 6 was found(2). Since the ground state spin is 1+, the 116 kev isomeric transition must then be either M5 or E5 radiation. The K/(L+M) and K/L ratios for the highly converted 116 kev gamma transition have been measured by several groups(7'71'757 ) Siegbahn() reported a K/L value of 1.3 which is close to the theoretical value of 1.2 for an M5 transition. The theoretical value for an E5 transition is 0.24. All other measurements gave K/(L+M) values between 1.2 and 2.1. Thus it is concluded that the 116 kev gamma is an M5 transition, and consequently the Agllom level must have positive parity. Even though the decay scheme is quite complex, which makes correlation work difficult, any correlation measurements would be useful in determining the spins of the levels in Cd110. The following directional correlation measurements are proposed: 1.389 Mev - 0.885 Mev, 0.935 Mev - 0.885 Mev, 0.885 Mev - 0.656 Mev, 1.516 Mev - 0.759 Mev, 1.516 Mev - 0.656 Mev and 1.389 Mev - 0.656 Mev. The source material was obtained from Oak Ridge. It was in the form of AgNO3 in HNO3. No appreciable contamination was present in the source. The mean lifetime of the first excited state has been measured to be about 5.5 x 10-12 sec.(78,79) and the other intermediate state lifetimes are assumed to be small. Because of this and the fact that the source was in a dilute solution, the correlations should not be attenuated due to extranuclear fields. The observed scintillation spectrum is shown in Figure 14.

N(E) ARROWS AND LETTERS t REFER TO DISCRIMINATOR 0.656 SETTINGS USED IN THE \I;~~~~ ~~CORRELATION MEASUREMENTS 0.885 — IJ 35'0.935 0.759 C 1.389 lE 1.516 F 0 20 30 40 ENERGY 50 60 Figure 14. Scintillation Spectrum of Gamma Rays of CdllO

-60Results 1.389 Mev - 0.885 Mev Directional Correlation For the 1.389 Mev - 0.885 Mev correlation one discriminator was set integrally at position A and the other differentially at position B as shown in Figure 14. With these settings there is no interference from any other cascadesand the full correlation is expected. Lateral lead shielding was not needed for this correlation since coincidences due to scattering were eliminated by energy selection. The least squares curve corrected for finite geometry is shown in Figure 15. The error flags represent the root-mean-square statistical errors of the experimental points. The corrected correlation function shows an asymmetry of 39% negative. (Asymmetry is defined as A = W(180 ) - o (900)) The correlaW(90 ) tion function is given by w(Q) = 1 - (0.308 + 0.013) P2(Cos G) + (0.009 + 0.020) P4(Cos 0) 0.935 Mev - 0.885 Mev Directional Correlation Since the 1.389 Mev and 0.935 Mev gamma rays are of comparable intensity, the 0.935 Mev- - 0.885 Mev correlation cannot be done without interference from the 1.389 Mev - 0.885 Mev correlation. Because the 1.389 Mev - 0.885 Mev correlation has a large asymmetry, the interference can cause the observed 0.935 - 0.885 correlation to be quite different from the true correlation. In this case, however, a fairly accurate subtraction process can be carried out to eliminate the interference. This was done in the following manner. First, discriminator I was set differentially on the 885 kev peak and discriminator II differentially at the position where the 935 kev peak is expected (C and D in Figure 14). The correlation was then run at all angles and the total real coincidence

-,1 1.00 W (e) 0.90 0.85 0.80 0.75 0.70 0.65 0.60 900 1200 150~ 180~ Figure 15. 1.389 sv - 0.885 Mev Correlation in Cd

-62rates NR(gi) were found. For the second measurement, discriminator I was set differentially (with the same discriminator window as previously) on the Compton distribution of the 1.389 Mev gamma (position E in Figure 14) and discriminator II was left on the 935 kev peak (position D). Data were taken at just the 90~ and 180~ points and the total real coincidence rates N() (90~) and N( ) (180~) were found. For the third measurement, discriminator I was set back on the 885 kev peak as in the first measurement and discriminator II was set differentially (with the same window as previously) on the 1.389 Mev Compton distribution (position E). Data were taken at the 90~ and 180~ points, giving the total real coincidence rates N(3)(900) and N(3)(180~). As expected, the asymmetry observed in measurements 2 and 3 was approximately the same as that found in the measurement of the 1.389 Mev - 0.885 Mev correlation. In all three measurements lateral lead shielding was used to eliminate coincidences due to scattering. The coincidence rates N42)(900) and N(3)(90~) were added together giving the total background coincidence rate at 90~, NB(900). The background coincidence rate at each angle NB(Gi) was found by multiplying NB(90~) by the value of W(0i) for the 1.389 Mev - 0.885 Mev interfering correlation (after W(Gi)was normalized to 1 at 90~). The 0.935 Mev - 0.885 Mev coincidence rates were then found by subtracting NB(Qi) from the corresponding NR(Gi). Since some uncertainty was obviously introduced here, a + 10o error was assigned to the background coincidence rates before subtraction. One important assumption must be made in this process. That is, the Compton distribution of the 1.389 Mev gamma ray is assumed to be flat below the Compton peak. This is quite valid for the type of crystals and geometry employed in the measurements.

-63The 0.935 Mev - 0.885 Mev correlation function after correction for the background correlation and finite geometry is shown in Figure 16. The correlation function before correction for the background has an asymmetry of about 7% positive, while the corrected correlation function shows an asymmetry of about 23% positive and is given by w(G) = i + (0.150 + 0.027) P2(Cos G) - (0.006 + 0.036) P4(Cos G) 0.885 Mev - 0.656 Mev Directional Correlation For this correlation one discriminator was set differentially on the low energy side of the 0.885 Mev peak and the other differentially on the low energy side of the 0.656 Mev peak (positions F and G in Figure 14). Lateral lead shielding was used. Even though the 0.885 Mev and 0.656 Mev gamma rays are the most intense gammas in the decay, some interference will be present from the other cascades. Since some of the interfering correlations have positive asymmetries and some have negative asymmetries, the net effect is probably a fairly isotropic interference which will lower the whole correlation somewhat. With the discriminator settings used, it is estimated that about 10% of the total coincidence counts are due to interfering cascades. However, no correction for this was made because of the uncertainty involved. The least-squares curve corrected for finite geometry is shown in Figure 17. The correlation function shows a 12% positive asymmetry and is given by W(G) = 1 + (0.073 + 0.014) P2(Cos G) + (0.009 + 0.020) P4(Cos Q) If a 10% isotropic background were present, the asymmetry in the correlation function would be about 14. 1.516 Mev - 0.656 Mev and 1.516 Mev - 0.759 Mev Directional Correlations The 1.516 Mev - 0.656 Mev and 1.516 Mev - 0.759 Mev correlations

-041.32 W(&) I/ 4 (D) 4(Q) 2/ 1.28 1.24 1.20 1.16 // 1.12 6/(Q)4(Q)2 ^/ / 1. 08 1.04 - / 7 1.00 0.96 90~ 1200 1500 1800 Figure 16. 0.935 Mev - 0.885 Mev Correlation in CdllO

-'Il' - 1.16 1.14 4Q)4(Q)2(Q)0 / W(e) / 1.12 / / - 1.10 1.08 1.06 / O / 1.00 - 2 0.97 -1 ~ 1 ~ I ~ 1 ~ I ~ 1~ 90~ 120~ 150~ 180~ Figure 17. 0.885 Mev - 0.656 Mev Correlation in Cdl1.

-66are complicated by the fact that the 0.656 and 0.759 peaks are not resolved by the scintillation counters. In addition, the 1.516 and 1.389 peaks are only partially resolved. However, because the 1.516 peak lies above the 1.389 peak, an effective selection of the 1.516 gamma of about 80% can be attained. To circumvent the first problem, the following procedure was followed. (a) Discriminator I was set integrally on the high energy side of the 1.516 Mev peak (position H in Figure 14) and discriminator II was set differentially on the 0.759 Mev peak (position J). No lateral lead shielding was needed here. The correlation was run at all seven angles giving the corrected correlation function Wa(Q) where Wa(Q) = 1 - (0.202 + 0.021) P2(Cos Q) - (0.006 + 0.030) P4(Cos g) The correlation function Wa () is mainly composed of the 1.516 - 0.759 correlation but contains some interference from the 1.516 - 0.656 correlation. It is shown as curve a in Figure 18. (b) Discriminator I was left at the same setting while discriminator II was set differentially on the low energy side of the 0.656 peak (position G). For this case the corrected correlation function was given by Wb(0) = 1 - (0.328 + 0.023) P2(Cos Q) - (0.022 + 0.031) P4(Cos Q) The correlation function Wb () is mainly composed of the 1.516 - 0.656 correlation but contains some interference from the 1.516 - 0.759 correlation. It is shown as curve b in Figure 18. If W1(G) is the true 1.516 - 0.759 correlation function, and

-67 - 1.00 w(o) 1 o.90o 0.800.70\'0.50 a - 1.516 - 0.759 Before Interference Correction b - 1.516 -.656 Before Interference Correction c - 1.516 - 0.759 After Interference Correction d - 1.516 - 0.656 After Interference Correction l I - I I I I. l I 900 1200 150~ 1800 e Figure 18. 1.516 ev - 0.759 Mev and 1.516 Mev - o.656 Mev Correlations in CdllO

-68W2(9) is the true 1.516 - 0.656 correlation function, then the observed correlations Wa and Wb are given by Wa = XaW1 + (l-Xa)W2 (23) Wb = Xb Wl+ (1-Xb)W2 (24) where Xa and Xb are the fractions of Wa and Wb composed of the 1.516 - 0.759 correlation. Solving these equations for W1 and W2 one obtains (1-Xb)Wa - (1-Xa)Wb Wi - (25) 1 Xa-Xb XaWb - XbWa W2 = Xa-Xb To correct for the interference, the quantities Xa and Xb must be determined. Xa and Xb were found in the following manner. First, the scintillation spectrum of Cs137 was run using about the same source strength as the AgllOm source. Cs137 contains a single gamma ray at 662 kev. Using the Cs137 spectrum, the individual 656 kev and 759 kev Cd110 peaks were constructed graphically, assuming equal intensity for both peaks. The areas under the peaks corresponding to the discriminator settings in a and b were then determined. This gave approximate values for the quantities Xa and Xb. The values found were Xa = 0.85 and Xb = 0.32. Since some uncertainty is introduced here, it was considered reasonable to assign maximum errors of + 0.10 to Xa and Xb. Therefore values of Xa from 0.75 to 0.95 and values of Xb from 0.22 to 0.32 were considered in the calculation of the correlation functions W1 and W2 from Equations (25) and (26).

-69The result for the 1.516 Mev - 0.759 Mev correlation function was w,() = - (0.66.5)P2(Cos 9) - (0.002_0: 6)P4(Cos ) and the result for the 1.516 Mev - 0.656 Mev correlation function was w() 1 - (.404. o )P2(cos ) - (0.031+ )P4(os ) The coefficients in W1 and W2 are the values found for Xa = 0.85 and Xb = 0.32. The errors quoted for the coefficients correspond to the maximum errors assigned to Xa and Xb. These correlation functions are shown as curves c and d in Figure 18. 1.389 Mev - 0.656 Mev Directional Correlation For this correlation, one discriminator was set integrally below the 1.389 Mev and 1.516 Mev peaks (position A in Figure 14) and the other discriminator differentially on the low energy side of the 0.656 Mev peak (position G). This correlation consisted mainly of a composite of the 1.516 - 0.656 and 1.389 - 0.656 correlations and showed an asymmetry of 40% negative. A least squares analysis of the data was not made because of the difficulty involved in interpreting the coefficients due to the interfering cascades. It was estimated that about 45% of the coincidences were due to the 1.389 - 0.656 correlation and about 25% were due to the 1.516 - 0.656 cascade. Other interfering cascades were the 1.516 - 0.760 (10o%) and 1.389 - 0.885 ( 20%). Assuming these rough estimates for the interference, and the asymmetries measured previously for the interfering correlations, it was concluded that the 1.389 Mev - o.656 Mev correlation has an asymmetry of about 40% negative.

-70Interpretation of Results To facilitate the interpretation of the correlation results the experimental values of A2 and A4 are summarized in Table 3. TABLE 3. DIRECTIONAL CORRELATION RESULTS FOR Cd110 Correlation A2 A4 1.389-0.885 - 0.308+0.013 0.009+0.020 0.885-0.656 0.073+0.014 0.009+0.020 0.935-0.885 0.150+0.027 - 0.006+0.036 1.516-0.759 -(o.166+o050) -(0.002+o o0 ) -'' -0.100 -' 0.0 1.516-0.756 -(O*404+0-135) -(0.031+00 1: ) -0-070 -0.0 1.389-0.656 Asymmetry -0. 40 The portion of the decay scheme which is pertinent to the data taken is shown in Figure 19, and the possible spins which must be considered for each level are listed. The levels are designated by Roman numerals and henceforth will be referred to by these numbers. The possible spin values are arrived at by considering the beta decay data, the relative gamma intensities, and the known spin values for the Ag10 levels and the two lowest Cd110 levels. Because of the nature of the beta transitions to levels V and VI, the only spin values which must be considered for these two states are 4, 5 and 6. Since no cross-over transitions from states III and IV to the ground state have been observed and no beta transitions leading to levels III and IV have been found, no spin lower than 2 or higher than 4 need be considered for levels III and IV.

-71zai: - -4,7 - - - c4,5,6 1.389 1.516 0.935 1V L'' -, - 2,3,4 mIII.. -- 2,3,4 0.885 0.759 Ru 2+ 0.656 Figure 9 Main Portion of CdllO Level Scheme Figure 19o Main Portion of CdllO Level Scheme Interpretation of 1.389 Mev - 0.885 Mev, 0.885 Mev - 0.656 Mev, and 1.389 Mev - 0.656 Mev Correlations Since the 1.389 Mev - 0.885 Mev correlation is free of interference from other cascades it is the logical correlation with which to begin the interpretation. However, any spin value which is determined for level IV on the basis of the 1.389 - 0.885 correlation must also be consistent with the data from the 0.885 - 0.656, 0.935 - 0.885 and 1.389 - 0.656 correlations. These correlations provide a cross-check on the interpretation. Considering pure radiations only, no combination of the possible spins for levels II, IV and VI is consistent with the 1.389 Mev - 0.885 Mev data. If one considers dipole-quadrupole mixtures in one or both of the transitions, ohly three sequences are consistent with the data. These are 5(D,Q)4(Q)2, 6(0)3(D,Q)2 and 4(D,Q)3(D,Q)2. Since no sequence with a spin of 2 for level IV comes close to fitting the data, this spin value can be discarded. In Figure 20 the theoretical values for A2 and A4 are plotted

A, (8a<0) 0.2 - 04 A C ^2 A^^ ^ 4 r) 0.1 0 > / A4(EXP) 0 0 PI) ^:) -0.1 0 ^ -0.2-.0 AD (DI lo I= A (EX P.) (D2 -0.4 I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I 0 0.20 0.40 0.60 0 80.00

-73versus Q, the quadrupole content of the 5-4 transition, for the 5(D,Q)4(Q)2 sequence. It is determined from Figure 20 that the experimental values of A2 and A4 are consistent with a value of Q = 0.135 + 0.015 (S>0). In Figure 21 a similar curve is shown for a 6(0)3(D,Q)2 sequence where Q is the quadrupole content of the 3-2 transition. The data are consistent with a value of Q = 0.09 + 0.02 or 0.73 + 0.03 (6<0). The only spin values remaining for level IV are 3 and 4. Thus it should be possible to explain the 0.885 Mev - 0.656 Mev correlation by either a 4(Q)2(Q)0 or 3(D,Q)2(Q)0 sequence. In Figure 17, which shows the 0.885 Mev - 0.656 Mev correlation function, the theoretical curve for a 4(Q)2(Q)0 sequence is also plotted. The observed curve does not quite fit the theoretical 4(Q)2(Q)0 curve, but the expected presence of interference from the other cascades could explain the discrepancy. The theoretical values of A2 and A4 for a 4(Q)2(Q)0 sequence are A2 = 0.1020 and A4 = 0.0091 while the experimental values are A2 = 0.073 + 0.014 and A4 = 0.009 + 0.020. When the error in A2 is considered, the discrepancy is not too great. On this basis it is concluded that the 4(Q)2(Q)0 sequence is consistent with the data for the 0.885 - 0.656 correlation. Therefore spins of 5, 4, 2 and 0 for levels VI, IV, II and I respectively are in agreement with both the 1.389 Mev - 0.885 Mev and 0.885 Mev - 0.656 Mev correlations. The 0.885 Mev - 0.656 Mev correlation data can also be explained by a 3(D,Q)2(Q)0 sequence. From Figure 22 it is seen that the data for the 0.885 - 0.656 correlation are consistent with a value of Q = 0.04 + 0.01 (~<0). It was shown previously that a 6(0)3(D,Q)2 sequence will explain the 1.389 Mev - 0.885 Mev correlation. If the true sequence of spins is 6, 3, 2 and 0, the value of Q = 0.04 + 0.01 for the 0.885 Mev

-740.3 A2 (8>0) 0.2 0.,~ ~~~~/ ^^^~\~ -0.005 A2 - A4.0 A4 0.1 A4 (EXP.) COVERS ENTIRE RANGE OF Q 0 / 0 -0.i-0.2 -0."3 1A2 (EXP.) A2 (8<0) -0.4 ~ 0 0.20 0.40 0 0.60 0.80 1.00 Figure 21. A2 and A4 vs. Q for a 6(0)3(D,Q)2 Sequence.

-75-,2(8 <0) 0. 0.05 A2 A4 OJ - 0 A4 XP.) -0.2- \ A-0.3-0.4 -0.1 -0.5- ^"A2 (8 >0) L,,. i,, II 0 0.20 0.40 J60 080 1,00 Q Figure 22. A2 and A^4 vs. Q for a 3(D,Q)2(Q)0 Sequence.

-76gamma as found from the 0.885 - 0.656 data should agree with the value Q = 0.09 + 0.02 found from the 1.389 - 0.885 data. There is a slight discrepancy here. This can be explained easily if there is interference present in the 0.885 - 0.656 correlation as mentioned before. If this is considered, both correlations are then consistent with a value of Q 0.09 + 0.02 (6< 0) for the 0.885 Mev transition. It was stated previously that the 1.389 Mev - 0.885 Mev correlation can also be explained by a 4(D,Q)3(D,Q)2 sequence (double mixture). Assuming this sequence of spins, the mixing parameter for the 4-3 transition can be calculated using the value of Q = 0.04 + 0.01 (&< 0) for the 3-2 transition as found from the 0.885 - 0.656 correlation data. If this is done, a value of Q = 0.25 + 0.05 or 0.65 + 0.05 (< 0) is obtained for the 1.389 Mev gamma transition. In summary, the results of the 1.389 Mev - 0.885 Mev and 0.885 Mev - 0.656 Mev correlations are consistent with spin sequences of 5(D,Q)4(Q)2(Q)o, 6(0)3(D,Q)2(Q)o and 4(D,Q)3(D,Q)2(Q)0. A further check on the spins of levels IV and VI is provided by the data for the 1.389 Mev - 0.656 Mev correlation. The 1.389 - 0.656 correlation is a 1-3 correlation with the intermediate radiation unobserved. Even though the results of this correlation are ambiguous due to the interfering cascades, it is most certain that the 1.389 - 0.656 correlation possesses a fairly large negative asymmetry. The theoretical 1-3 correlation function can be calculated for the possible sequences using equations (12), (13) and (14) of Chapter I. For a 5(D,Q)4(Q)2(Q)0 sequence, the theoretical 1-3 correlation function is identical to the 5(D,Q)4(Q)2 correlation function. If this is the correct spin sequence, the 1.389 - 0.656 correlation should be identical to the 1.389 - 0.885 correlation. The experimental data tends to support

-77the 5(D,Q)4(Q)2(Q)0 sequence since the 1.389 - 0.885 correlation shows an asymmetry of 39% negative while the results of the 1.389 - 0.656 correlation indicate an asymmetry of about 40o negative. If the theoretical 1-3 correlation function for a 6(0)3(DQ)2(Q)0 sequence is calculated, the resulting coefficients are A2 = 0.179(1-Q) + 0.045 Q A4 = -0.0043(1-Q) + 0.0065 Q where Q is the quadrupole content of the unobserved radiation. Inserting the value of Q = 0.09 + 0.02 determined previously from the 1.389 - 0.885 and 0.885 - 0.656 correlation data, a value of A2 = 0.167 + 0.003 is found. (A4 is negligible). This corresponds to an asymmetry of about 25% positive. Since the asymmetry of the 1.389 - 0.656 correlation is certainly iegative, the 6(0)3(D,Q)2(Q)0 sequence for levels VI, IV, II and I can be ruled out. The theoretical 1-3 correlation function for a 4(D,Q)3(D,Q)2(Q)0 sequence can likewise be calculated. The resulting coefficients are A2 = [o.1443(l-Q1)+1.443 Q1 (-Q1)+0.30931] [-o.4949(l-Q2)-0.237Q2 A4 = 0.1489Q1 [-0.4467(1-Q2)+0.6701Q2 where Q1 is the quadrupole content of the 4-3 transition and Q2 is the quadrupole content of the 3-2 transition. Inserting the values of = 0.25 or 0.65 (<^0) and Q2 = 0.04 (S< 0) found previously from the 1.389 - 0.885 and 0.885 - 0.656 correlations, the results are A2 = 0.21, A4 = 0.015 for Q1 = 0.25, and A2 = 0.21, A4 = 0.039 for Q1 = 0.65. Both of these sets of coefficients correspond to an asymmetry of about 33^ positive, and since the 1.389 - 0.656 asymmetry is certainly negative,the 4(D,Q)3(D,Q)2(Q)0 spin sequence can be discarded.

-78Therefore the 5(D,Q)4(Q)2(Q)O sequence is the only sequence of spins for levels VI, IV, II and I which will simultaneously satisfy the results of the 1.389 Mev - 0.885 Mev, 0.885 Mev - 0.656 Mev, and 1.389 Mev - 0.656 Mev correlations. With this sequence, the correlation data requires the 1.389 Mev gamma transition to be a mixture of (13.5 + 1.5)% quadrupole and (86.5 + 1.5)% dipole radiation. Because directional correlation results alone cannot determine the parity of the states involved, one must turn to other considerations if parities are to be assigned to levels IV and V. Since the spin and parity of the Agilom level are 6 and + respectively and the experimental evidence indicates that the 87 kev beta transition is an allowed transition, level VI must have positive parity. Therefore an assignment of 5+ is made to level VI. The 1.389 Mev gamma transition consists of a mixture of 13% quadrupole and 87% dipole radiation according to the correlation results. An El-M2 mixture of this magnitude is very unlikely, but an M1-E2 mixture is quite probable. Therefore an M1-E2 mixture is assumed for the 1.389 Mev transition, and the parity of level IV must then be positive. This requires the 0.885 kev gamma to be E2 radiation. The assignment of 4+ to level IV is consistent with the fact that there is no observed beta transition from the AgOm level to this level. The beta transition would have to be second forbidden (AJ = 2, no; log ft - 12-15) and therefore the transition probability could be small compared to the transition probabilities for the two observed betas. The 4+ assignment is also consistent with the fact that in even-even nuclei, low-lying levels with even spin normally have even parity. Interpretation of the 0.935 Mev - 0.885 Mev Correlation Level V and the 0.935 Mev - 0.885 Mev correlation must now be

-79considered. The possible spins for level V are 4, 5,and 6. Since the spins of levels IV and II have already been established as 4 and 2 respectively, the combinations to be considered for the 0.935 Mev - 0.885 Mev correlation are 4-4-2, 5-4-2 and 6-4-2. In Figure 16 the theoretical curves for pure 6(Q)4(Q)2 and 4(D)4(Q)2 sequences are plotted together with the observed 0.935 Mev - 0.885 Mev correlation function. The theoretical coefficients for a 6(Q)4(Q)2 sequence are A2 = 0.1020 and A4 = 0.0091, and for a 4(D)4(Q)2 sequence they are A2 = 0.1965 and A4 = 0. The experimental values of the coefficients are A2 = 0.150 + 0.027 and A4 = -0.006 + 0.036. Neither of these sequences is quite consistent with the experimental data, but they are both close enough to warrant consideration as possibilities. They cannot be definitely discarded on the basis of the correlation data alone because the 0.935 - 0.885 correlation was obtained by a subtraction process which introduces uncertainties in the data. The other pure sequence which must be considered is 5(D)4(Q)2. This possibility can be ruled out, however, since it would require a negative value for A2. If dipole-quadrupole mixtures are considered for the 0.935 Mev transition, both the 5(D,Q)4(Q)2 and 4(D,Q)4(Q)2 sequences are consistent with the 0.935 - 0.885 correlation data. In Figure 23 the theoretical values of A2 and A4 are plotted versus the quadrupole content of the 5-4 transition for a 5(D,Q)4(Q)2 sequence. The experimental data are seen to be consistent with a value of Q = 0.14 + 0.o4 (6<0). A similar curve for the 4(D,Q)4(Q)2 sequence is shown in Figure 24. For this case, the data are compatible with a value of Q = 0.020 + 0.018 ( < 0). Since the background correlation determination was carefully done and a + 10% error assigned to the background before subtraction it

001 08'0 09'0 Ot'O O0 0. I I I -, I I I 80(- - ( O < 9) -' o o90'0- -'0- o'o - -- - - o I'(0>s) a d I______^dX3) t 0'0 o'0 I7' V~~...~.'

0.15 AD (a >0O 0. -0.05 A2 A( Ro AA40.10 0.2 0 0..05 p- 0.1 GDu 0.,-0.1 -0.05 I A2 (8(E0) cD 0.1 0 0.20 0.40 0.60 0 1.00 Q

-32is believed that the data for the 0.935 - 0.885 correlation are accurate. On this basis it is assumed that the 5(D,Q)4(Q)2 and 4,(D,Q)4(Q)2 sequences are more likely than the 4(D)4(Q)2 and 6(Q)4(Q)2 sequences, which were not in good agreement w th the experimental data. Thus the results of the 0.935 Mev - 0.885 Mev correlation support a spin of 4 or 5 for level V with the possibility of spin 6. If the spin is 4, the 935 kev transition consists of a mixture of (98.0 + 1.8)% dipole and (2.0 + 1.8)% quadrupole radiation. If the spin is 5, the 935 kev transition consists of a mixture of (86 + 4)% dipole and (14 T 4)% quadrupole radiation. Consider a spin of 5 for level V. Since an El-M2 mixture of the magnitude needed to explain the data is very unlikely it must be assumed that the mixture is of M1-E2 character. This requires an assignment of 5 for level V, and therefore the 530 kev beta transition would have to be of allowed type. However, this disagrees with the beta decay data which indicates that this is a forbidden transition (log ft - 8). On this basis it is concluded that a spin of 5 for level V is not very likely. Consider now a spin of 4. Since only a small admixture of quadrupole radiation is indicated by the data, the argument against El-M2 mixtures cannot be used here. A value of 4+ for level V would require the 530 kev beta to be a second forbidden transition (AJ = 2, no; log ft - 12-15) which disagrees with the experimental log ft value of about 8. An assignment of 4~ for level V seems to agree best with the beta decay data and correlation results. This requires a unique first forbidden beta transition (AJ = 2, yes; log ft 7.5 - 9.5) and almost pure El radiation for the 0.935 Mev gamma transition. The less likely possibility of spin 6 for level V would require an assignment of 6- and M2 radiation for the 0.935 Mev transition. Therefore the correlation data for the 0.935 Mev - 0.885 Mev

-83 - cascade considered together with the beta decay data indicate a preference for an assignment of 4- to level V with assignments of 5- and 6- being much less likely. The results up to this point are summarized in the level scheme shown below. M | 1 5+!Z.. ~ ~ 4-(5-,6-) 1.389 1.516 0.935 I- ~. ~ 4+.m'-. 2,3,4 0.885 0.759...........2+ 0.656 IT - 0+ Interpretation of 1.516 Mev - 0.759 Mev and 1.516 Mev - 0.656 Mev Correlations The 1.516 Mev - 0.759 Mev and 1.516 Mev - 0.656 Mev directional correlations will now be considered. These are not too accurate but could give some indication as to the spin of level III. According to the level scheme, the 1.516 - 0.656 correlation is a 1-3 correlation while the 1.516 Mev - 0.759 Mev correlation is a simple 1-2 correlation. The sequences which must be considered for the 1.516 Mev - o.656 Mev correlation are 5(0)2(D,Q)2(Q)0, 5(Q)3(D,Q)2(Q)0 and 5(D,Q)4(Q)2(Q)O. From the experimental data it is certain that the 1.516 Mev - 0.656 Mev correlation must have a large negative asymmetry. If the 1-3 correlation theoretical values for A2 and A4 are calculated for the sequences 5(0)2(D,Q)2(Q)0

-34and 5(Q)3(DQ)2(Q)0o it is found that neither sequence can give a negative asymmetry greater than 6%, no matter what the mixing parameter is. Therefore these sequences can be ruled out. If the spin sequence is 5(D,Q)4(Q)2(Q)0, the 1-3 correlation function is identical to the 1-2 correlation. Thus the 1.516 - 0.656 and 1.516 - 0.759 correlations would have to be equal. The data shown in Table 3 are not in agreement with this, and any interference which might be present due to the highly negative 1.389 - 0.885 and 1.389 - 0.656 correlations cannot possibly explain the discrepancy. Therefore the data for the 1.516 Mev - 0.656 Mev and 1.516 Mev - 0.759 Mev correlations are not in agreement with any of the possible spins 2, 3, or 4 for level III. It is of interest to consider the possibility of these two transitions occurring in the reverse order, thereby introducing a new Cd110 level at about 2.170 Mev and removing the level at 1.415 Mev (level III). If the 1.516 Mev and 0.759 Mev transitions are reversed, the sequences which must be considered for the 1.516 Mev - 0.656 Mev correlation are 4(Q)2(Q)0, 3(D,Q)2(Q)0, and 2(D,Q)2(Q)0. The 4(Q)2(Q)0 sequence can be ruled out since it gives a positive value for A2 and a positive asymmetry. The 2(D,Q)2(Q)0 sequence can have an A2 as large as -0.31 for a quadrupole content of 70%, but this mixture would require a large value for A4 (A4 = +0.22) which is inconsistent with the data. Furthermore, the 2(D,Q)2(Q)0 sequence would require;iragnetic octopole radiation for the 0.759 Mev transition. This is very unlikely if one considers the relative intensities of the 0.759 Mev and 1.389 Mev transitions and the fact that the 1.389 Mev transition is primarily M1 radiation. Thus the 2(D,Q)2(Q)0 sequence is discarded as a possibility. However, the 3(D,Q)2(Q)0 sequence

-85will explain the data for the 1.516 Mev - 0.656 Mev correlation. Figure 25 shows the mixture curve for this sequence along with the experimental values of A2 and A4. From Figure 25 it is determined that tLle data are consistent with a value of Q between 0.11 and 0.97 ( >0). Therefore one should be able to explain the 1.516 Mev - 0.759 Mev correlation data by a 5(Q)3(D,Q)2 sequence with a value of Q between 0.11 and 0.97 (6 0). In Figure 26 the mixing curve for a 5(Q)3(D,Q)2 sequence is shown. The experimental value of A2 for the 1.516 - 0.759 correlation is indicated by the error flag. The data is consistent with a value of Q = 0.07+015 or Q = 0.+0.17 but for ~< 0. Consequently, -0.07 -0.20 the 1.516 - 0.759 correlation does not verify the res ults of the 1.516 - 0.656 correlation. One can argue, however, that the interference from the highly negative 1.389 - 0.656 and 1.389 - 0.885 correlations and an inaccurate determination of the amount of 1.516 - o.656 correlation present in the observed 1.516 - 0.759 correlation could cause the 1.516 - 0.759 result to be incorrect. These interference effects would all tend to make the 1.516 - 0.759 correlation more negative than it actually is. It is conceivable that the interference could even shift the asymmetry from a small positive value to a negative value. From Figure 26 it can be determined that a value of A2 = 0.06 for the 1.516 - 0.759 correlation would be consistent with the lowest possible value for Q determined from the 1.516 - 0.656 data, namely Q = 0.11 ( >0). A value of A2 = 0.06 would correspond to an asymmetry of about 9% positive (if A4 is negligible). The smallest value for the observed asymmetry of the 1.516 - 0.759 correlation, considering the experimental error, is about 9% negative. Therefore, if it is conceded that the interference effects could shift the asymmetry from

022 0.05 A A4 \A^ (8 > 0) \^^^^ \ OI o 0 -o0ilC A4(EXP.) COVERS ENTIRE RANGE -0.2 A (8 O) -0.3 -0.4 (EYP) -~ 0 0.20 0.40 0.60 0.80 1.00 QF e f a Figure 25. A and A4 vs. Q for a 3(D,Q)2(Q)0 Secjuence.

H' 0.! A(8>o0) 3> 0 0^~0 ^ /^^^ ^ /r A H) A2 -0. CD Fjtj~~~~~~~~O IC -02~~~~~f I I 7/ 1I // —. -0 02 4.00.010 9Q 2 ~~~~~~~A4(EXP)) COVERS F: E~~~~~~~~~lflP~~~ENIE RANGE_ -0.3 ~~~~~~~~~~~OF Q 0 0.202 0.40 0.60 0.80. Q

9% positive to 9'% negative, the 5(Q)3(D,Q)2(Q)0 sequence will explain both the 1.516 MYev - 0.656 Mev and 1.516 Mev - 0.759 Mev correlations. Because the results of these correlations are so inaccurate and the interpretation so vague it is difficult to make a conclusion as to whether the 1.516 kev transition precedes or follows the 0.759 transition. However, the data is more nearly consistent with the sequence in which the 0.759 Mev transition precedes the 1.516 Mev transition, and on this basis it is felt that this is the correct order. This requires a new Cd110 level at 2.170 Mev and removes the level at 1.415 Mev. If this new level is actually present, it most certainly has a spin of 3 and probably positive parity as indicated by the correlation data. It was stated previously that several of the weak gamma transitions found in Cd10 would not fit into the accepted decay scheme shown in Figure 13. However, if one considers the new level order suggested by the correlation measurements, all of the gamma transitions reported by Antoneva, et al.7) can be arranged in a consistent level scheme. This scheme is shown in Figure 27. The transition energies and beta branching ratios are those reported by Antoneva(7l) and differ slightly from the values found by Siegbahn(70). The spin and parity values listed for the Cdll1 levels are those found in the present investigation. The new decay scheme retains the same positioning of the 0.655 Mev, 0.883 Mev, 0.932 Mev, and 1.386 Mev transitions as the former scheme, and therefore none of the correlation measurements are affected by the change. The fact that all of the transitions can be arranged in a consistent scheme gives strong support to the conclusion that the 0.759 Mev gamma ray precedes the 1.506 Mev gamma ray. Further discussion of this new level scheme will be presented in the next section.

6+ 0.088(65%) (2%) 0.1162.920 5+ (M5) 0.5 0 1'~~~ \ ~0.447 1.386 0.759 0.706 (MI+E2) (E2) 2.470 4(5,6) \4\ 4~ - ~~~~2.215 \\ \ - ~~~~ 1~j~2.160 3+ 0.932 ~~0.740 0.687 0.618 2,21.506 2.8(MI+E2) 0.815 1.480 0.883 (MIE2) (E2) 0.655 2+ ALL ENERGIES IN MEV 0.655 (E2) 0 02 Figure 27. Revised Level Scheme for Cdl

-90Summary and Discussion The directional correlation data for Cd110 presented in the previous sections is in good agreement with the assignment of 0+, 2+, 4 and 5+ for the ground state, 0.655 Mev level, 1.538 Mev level, and 2.920 Mev level respectively. The data indicate a preference for an assignment of 4- to the 2.470 Mev level, but spins of 5 and 6 are also possible. The assignments for these levels are supported by the beta decay data(70,71) and internal conversion coefficient measurements(70) The correlation results indicate that the 0.759 Mev gamma transition precedes the 1.506 Mev gamma transition, rather than being in the opposite order previously reported(70). Additional evidence for this positioning of the 1.506 Mev and 0.759 Mev transitions is provided by the fact that all of the gamma transitions reported by Antoneva, et al.(7), can be placed in a consistent level scheme. This scheme requires new levels at about 1.475 Mev and 2.160 Mev. If this new scheme is correct, the correlation data indicate a spin of 3 and probably positive parity for the 2.160 Mev level. Figure 27 shows the revised decay scheme. The spin and parity assignments made in the present investigation are listed beside the appropriate Cd110 levels. With these assignments, the 0.655 Mev, 0.759 Mev and 0.885 Mev transitions are pure E2 radiation, the 1.386 Mev transition is a mixture of (86.5 + 1.5)% M1 and (13.5 + 1.5)% E2 radiation, the 0.932 Mev transition is a mixture of (98.0 + 1.8)% El and (2.0 + 1.8)% M2 radiation, and the 1.506 Mev transition is a mixture of MI and E2 radiation (degree of mixture uncertain). According to the revised decay scheme, the second excited state has an energy of about 1.475 Mev, and a weak cross-over transition occurs from this state to the ground state. This would be consistent with a

-91spin value of 2+ for the 1.475 Mev level. Therefore one might expect a weak beta transition of about 1.40 Mev occurring between the 1+ Agl0 level and the 1.475 Mev Cdll0 level. There is actually some evidence for this beta transition, because Antoneva(71) had reported the possibility of a beta transition with end-point energy of just about 1.40 Mev (dotted line in Figure 27). Since the CdllO nucleus consists of 48 protons (closed shell minus 2) and 62 neutrons (closed shell plus 12), it might be expected that Cd10 would exhibit some vibrational level structure. The ratio of the energies of the second and first excited states is 2.25 according to the new level scheme, and the 1.480 Mev cross-over transition is much weaker than the 0.815 Mev transition. If the spin of the 1.475 Mev level is 2, then both of these results suggest that the first two excited states are probably the result of vibrational excitations. Additional evidence for vibrational level structure is provided by the Coulomb excitation results for Cd10, which show that the cross-section for Coulomb excitation of the first excited state is larger than that expected for a single particle excitation(65,78, 79) If the new level scheme is considered, the relative intensities of the gamma transitions can be explained quite satisfactorily by the spin, parity, and multipole assignments which were made on the basis of the correlation results. The fact that the transitions occurring from the second excited state are much weaker than those occurring from the third excited state is plausible if one considers the manner in which the 1.475 Mev level is fed. If the spin of this level is 2+ as indicated, a direct transition from the 2.920 Mev state (5+) would require M3 radiation, and this transition could not compete with the 0.759 Mev (E2) and

-921.386 Mev (Ml + E2) transitions. A direct transition from the 2.470 Mev level (4-) to the 1.475 Mev level would require M2 radiation, and this transition could not compete with the 0.932 Mev gamma which is almost pure El radiation. Moreover, a transition from the 1.538 Mev level (4+) to the 1.475 Mev level would require E2 radiation and could not compete with the 0.883 Mev (E2) transition because of the large transition energy difference. The observed gamma rays which feed the second excited state are the 0.740 Mev and 0.687 Mev transitions. These are weak due to the competition from the higher energy gamma rays of comparable multipole order. Therefore if one considers the spins shown in Figure 27, the small intensities for the 0.815 Mev and 1.480 Mev gamma transitions relative to the 0.883 Mev gamma intensity can be explained. If the spin assignments for the 2.470 Mev and 0.655 Mev levels are 4- and 2+ as indicated in Figure 27, one might expect an M2 gamma transition of 1.815 Mev occurring between these levels. Some evidence for a weak transition of this energy has been found by Dzelepov(83) However, he reported that the existence of this gamma ray was questionable. Because of the success in fitting all of the gamma transitions into this new level scheme and the apparent explanation of the intensities in terms of the spin, parity, and multipole assignments indicated by the correlation measurements, it is reasonable to conclude that this is the correct level scheme and that the assignments for the CdllO levels are correct. Moreover, it is apparent that the first and second excited states in Cd110 are mainly due to vibrational excitations and that the spin of the second excited state is probably 2+.

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