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The decay of 124 SB Johnson, John R. 1973

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15124> 124 THE DECAY OF Sb by JOHN R. JOHNSON B.Sc. The University of British Columbia 1967 M.Sc. The University of British Columbia 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April, 1973 In presenting this thesis i n p a r t i a l f ulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted, by the Head of my Department or by his representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department The University of B r i t i s h Columbia Vancouver 8, Canada Date y t a i-r, I ITS Abstract i i The gamma-rays, beta rays and conversion electrons emitted in the 124 124 beta decay of Sb -» Te have been observed using Ge(Li) and Si(Li) detectors both singly and in coincidence. The measured energies and intensities of the different transitions involved in this decay together with the coincidence results have allowed us to construct the decay scheme. The angular momentum of most of the states and the parity of a l l of the states of Te populated in this decay have been deduced, some of them for the fi r s t time, and others as confirmations of previous assignments. We have also been able to assign collective parameters to many of these states, in terms of the vibrational model of nuclei, from the reduced branching ratios calculated from the gamma ray intensities. I l l Table of Contents Abstract i i List of Tables v List of Figures v i i Acknowledgements ix Chapter I Introduction 1 Chapter II The Vibration Model of Even-Even Nuclei 1 The Collective Model - • 7 2 The Simple Vibrational Model '7 3 Anharmonic Corrections 11 4 Semi-Microscopic Description of Te 13 Chapter III Gamma-Ray Singles Spectroscopy 16 1 Peak Fitting 17 2 Efficiency Calibration 24 3 Energy Calibration 30 10/ 4 Sb Gamma Spectrim 34 Chapter IV Gamma-Gamma Coincidence 1 Experimental Arrangement 54 2 Random Coincidences 58 3 Corrections to Coincidence Spectra for 59 Background Events 10/ 4 Coincidence Gamma Spectra of Sb 64 Chapter V Electron Spectra Using Si(Li) Detectors 1 Beta Spectra a) General Considerations b) Beta Spectra Taken with a Si(Li) Detector 81 IV 10/ c) Beta Spectra of Sb - 94 2 Internal Conversion Electrons a) Internal Conversion Coefficients 100 b) K-Conversion Electrons in Coincidence with K-X-Rays 102 10/ c) K-Conversion Electrons of Te 105 Chapter VI Results of the ^^Sb investigation 1 Decay Scheme of 124Sb 1 2 4Te 115 2 Log ft Values 115 3 Spin and Parity Assignments 121 4 Summary of the Levels Populated in the 124sb 124Te D e c a y 130 5 Comparison to the Semi-Microscopic Model 139 6 Conclusion 141 Appendix A Phonon Number Representation for Vibrational States 143 Appendix B Electromagnetic Transitions 150 Appendix C Beta Spectra of 1 5 2Eu 159 List of Tables Chapter III 1 Efficiency Calibration Standards 2 Energy Standards 3 Secondary Energy Standards 4 Energies and Intensities of Gamma Transitions in 1^4'Sb Decay 25 31 31 43 Chapter IV 1 Description of Electronics for Coincidence Measurements 2 Coincidence Results 3 Transitions in Coincidence with 603 KeV Transition 4 Transitions in Coincidence with the 646 KeV Transition 56 73 78 79 Chapter V 1 Relative Intensities of Conversion Electrons from 152EU 2 Beta Transitions from 124Sb 124 3 Conversion Electrons of 4 Conversion Coefficients Sb 88 101 111 112 Chapter VI 1 Evidence.for the Levels of the Sb Decay 124 Te Populated in 2 Log ft Values and Most Likely j"^ Assignments for Levels in ^ ^Te 118 119 V I List of Tables (Cont.) 3 E2 Relative Reduced Branching Ratios 132 4 Relative Rates of Transitions from Negative Parity States Compared to Single Particle Estimates 136 5 Comparison of Reduced Transition Rates follows page 140 B-l Reduced Transition Rates 157 C-l (S~ Transitions in 1 5 2Eu -^152Gd 163 C-2 Relative Intensities 163 v i i List of Figures Chapter III 1 Components of the Peak Fitting Function 18 2 Ratio of Heights of the Gaussians 20 3 Ratio of Widths of the Gaussians 21 4 Difference in Position of the Gaussians 27 5 Efficiency of Ge(Li) Detector 29 6 Energy Calibration 33 121\ 7 Gamma Spectrum of Sb 35 8 Ratios of Escape Peaks 48 9 Sum Peak Identification 51 10 High Energy Spectrum taken with a Lead Absorber 52 Chapter IV 1 Electronic Arrangement used for Coincidence Measurement 55 2 Typical Output of the TAC 57 22 3 Na Spectra 60 4 Typical On-Peak and Off-Peak Gates 62 5 Gamma Spectrum in C omcidence with 603 KeV Transition 66 6 646 KeV On-Peak Coincidence Spectrum 69 7 700-730 KeV On-Peak Coincidence Spectrum 71 Chapter V 1 Isotopes Used to Measure the Backscatter Fraction 2 Si(Li) Detector Chamber 83 84 V l l l List of Figures (Cont.) 3 Backscatter Spectrum of i J /Cs 86 4 Relative Effici ency of the 3mm Si(Li) Detector 89 137 5 High Energy Electron Spectrum of Cs 91 6 Shape Factors for the High Energy P> " Group of 1 3 7Cs. 92 7 Kurie plots for the High Energy G>~ Group of 1 3 7Cs 93 8 Electron Spectra of 124Sb 95 9 Total (electron + gamma) and Gamma Spectra in Coincidence with the 1691 KeV Transition 97 10 Residue after Subtraction of the Two Spectra in Figure V-9 98 11 Kurie Plots 99 124 12 K-Conversion Electrons of Sb 106 124 13 Low Energy K-Conversion Electrons of Sb In Coincidence with K-X-Rays 109 Chapter VI 1 Decay Scheme of 124Sb ->124Te 116 2 E2 Relative Reduced Branching Ratios 134 3 Enhancement Factors for Transitions from Negative Parity States 137 4 Comparison to the Semi-Microscopic Theory of Lopac - 140 A-l Simple Vibrational States 148 152 C-l Partial Decay Scheme of Eu 160 C-2 Kurie Plots of 1 5 2Eu /£' Spectra - 161 i x Acknowledgements I wish to express my gratitude to Dr. K. C. Mann for guidance and encouragement throughout the course of this work. I also thank the University of British Columbia Van de Graaff group for making some of their equipment available to me. This project was supported, in part, by Grants-in-Aid of Research to Dr. K. C. Mann from the National Research Council of Canada. I also wish to acknowledge the assistance of the National Research Council through awards to me of N.R.C. Bursaries, and of the H.R. MacMillan Fellowship Foundation through a Fellowship Award. Chapter I Introduction 1 It has been known for a long time now that many low energy excita-tions of nuclei could be explained in terms of quantized motions of the nuclear matter.^ These excitations, called collective states, are dis-tinguished from other low energy excitations, called particle states, by their much larger transition rates. The mathematical description of these collective states, called the collective model of the nucleus, has 2 3 been developed by Bohr, and others. This collective model has been most successful in describing nuclei that have stable deformations from a spherical shape. The low energy collective excitations of these "deformed" nuclei can be adequately ex-plained in terms of rotations and/or vibrations of the nucleus. However, there are many nuclei that do not have stable deformations but s t i l l have 2 3 4 low energy collective excitations. There have been attempts ' ' to des-cribe these excitations in terms of vibrations about their spherical equilibrium shape. This "vibrational model" has not been nearly as successful as the so-called "rotational model" used to describe the de-formed nuclei, although i t does, in general, allow one to classify the different type of collective vibrations that can be assumed to take place in these spherical nuclei, as explained in Chapter II. There are a few spherical nuclei, however, (^2Ni, reference 5, and ^ "^Cd, reference 6) for which the vibrational model is almost as successful in describing the low energy excitations, as the rotational model is for deformed nuclei. The rather limited success of the vibrational model led to the in-clusion of features of the nuclear shell model into the description of collective motion. 7 8 9 Belyaev , Kiss linger and Sorensen and others, have shown that the collective features of nuclei can be accounted for by the coherent motion of many nucleons, where the individual nucleons are described by their shell model wave functions. This approach was successful in describing the mechanisms that caused stable deformed equilibrium shapes, "shell closure" effects, and many other features that could only by introduced in a phenomenological way into the collective model. However, detailed calculations using only the shell model become prohibitively difficult when the numbers of protons and neutrons are not "close to one of their 25 "magic numbers", the f i l l e d , or closed, major shells. In this case the collective model can be used to describe the motion of the inner nucleons, or the core, while the shell model approach is used to describe the outer-most nucleons. In general, there is no criterion that can be used to say which of the nucleons should be treated as the core, and which as shell model nucleons. This combined description is often called the unified mode1.2 The simplest nuclei to describe in this manner are the odd mass 2 8 26 nuclei ' ' . The collective model is used to describe a l l but the "un-paired" nucleon, and shell model wave function of the un-paired nucleon is coupled to the collective motion by the change in the shell model potential i t causes. Again, the most successful calculations 26 using this description of odd mass nuclei were for the deformed nuclei. Kisslinger and Sorensen^ used this model to describe the odd-mass spherical nuclei, although they used a microscopic description of the core rather than the collective vibrational model described in Chapter II. Their description of the core involved the "quasi-Boson" or "random 10 phase" approximation. In this approximation the even-even core is described in terms of the "correlated pairs."^ That i s , a nucleon close to the Fermi surface may spend part of the time in a shell model state ij m> , where j and m are.the shell model spin and spin projection. The rest of the time the nucleon is in a state \j'm'> which can be any of the nearby (in energy) shell model states. During the time that i t is not in the state |j m> , the "pairing force"7 that coupled i t to another nucleon in the state |j - m> to form a total spin of 0 is broken. The two nucleons, one in state |j - m> and the other in any of the states (j m> or |j'm'> therefore form a correlated pair. The collective motion is then described as coherent excitations of many pairs of |j'm'> and |j - m> shell model states. The extent to which these pairs can be treated as Bosons (integer spin particles) is the quasi-Boson approxi-mation. This approximation is the same as assuming that the interaction between one member of a pair (a half-integer particle, or Fermion) with another member of any other pair, is not coherent for a l l the pairs that make up the collective motion, and that these interactions tend to cancel each other;^ hence the term, random phase. The interaction that causes the pairs to move coherently is the "residual interaction"; that i s , the part of the potential between the nucleons that remains after the shell model potential is subtracted. This interaction is introduced phenomeno-logically by requiring that iL^account for the systematic variations in the observed collective properties of nuclei as the number of protons and/or neutrons is varied within a major shell. The quasi-Boson approximation was used by Kisslinger and Sorensen 8 in an earlier work to describe successfully the ground and first excited states of singly closed shell, even-even nuclei, in which the number of 1 protons or neutrons corresponds to a closed major shell. More recently, /this quasi-Boson representation has been used to describe higher energy excitation of even-even spherical nuclei with neither the protons nor the neutrons having closed major shells. Detailed calculations for this type of nucleus quickly become as difficult as the simple shell model calcu-lations, although the mathematical formalism of the quasi-Boson approxi-mation allows one to extend the region for which one can do detailed calcu-lations a l i t t l e further away from closed shells. 13 One method of circumventing this difficulty is to describe the motion of one type of nucleon, say the neutrons, by the vibrational model, and then describe the protons by the quasi-Boson formalism, where now the quasi-Bosons are acted upon by the residual potential that is perturbed by the collective motion. These types of calculations are often called semi-microscopic. In order to deduce the effects of the collective motion on the quasi-Boson states, and vice versa, accurate measurements of energy levels and transition probabilities are required over the entire range of proton and neutron numbers for which this semi-microscopic model may possibly be valid. For this reason, we have decided to re-investigate the excited states of 12^Te populated in the beta decay of *2^Sb. *2^Te, with 52 protons 1 0 / and 72 neutrons is an even-even spherical nucleus and the Sb beta decay populates states in this nucleus above 2 MeV excitation energy, the approxi-mate energy at which the first particle states (or non-coherent quasi-boson states of the two extra core (Z=50) protons) are expected to be found. After this investigation was begun, a theoretical semi-microscopic theory 124 14 of Te was published by Lopac. This theory will be briefly described in Section II-4 and will be compared to the experimental results of this investigation in Section VT-5. The ^24Sb beta decay has been investigated in the past using magnetic spectrometersJ-^and the gamma transitions depopulating the excited states 124 40 of Te, using Nal detectors. More recently, the gamma transitions 1 7 1 Pi *3 f\ have been measured using good resolution Ge(Li) detectors ' ' . The 124 76 77 80 excited states of Te populated by coulomb scattering ' ' and by the reactions (n, H )^"*, (3He,d) and (p,t) 7 4, have also been recently investigated. However, we felt that with the combined detection of gamma, beta and conversion electron transitions, and by using coincidence meas-urements, that we could make a useful contribution to our knowledge of 124 the excited states of Te. The measurements of the gamma transitions' intensities and energies are reported in Chapter III. The coincidence measurements between the gamma transitions are reported in Chapter IV. The results of the investi-gations involving beta transitions and conversion electron transitions are summarized in Chapter V. It was possible, using a l l these data, to construct the decay scheme of ^"^ S^b -+^24Te, and to assign spin and parity and to establish the nature (whether mainly collective or particle) of the 124 states of Te populated in this decay. This will be described in 124 Chapter VI. The Sb sample that was used in our investigations was ob-tained from New England Nuclear, Inc., where i t was prepared by the Sb(n,X ) Sb reactions. The impurities expected to be found in the 122 125 sample were the short lived Sb(2.8 days) and the long lived Sb 19 (2.7 years).. These impurities were less than 1%. Individual sources were prepared for our measurements from this sample in the usual 44,48 way. 7 Chapter II The V i b r a t i o n a l Model of Even-Even Nuclei I I - l The C o l l e c t i v e Model The s t a r t i n g point of the c o l l e c t i v e model i s to describe the nuclear . 2,20 surface by •R- Ro ( 1 + / 1. <*>^Aj^*» T>» M'--~> I I - l where R q i s the radius of a sphere whose volume i s equal to the nuclear volume, and the Y-^'s are the s p h e r i c a l harmonics. The o^ U^Vs are expansion c o e f f i c i e n t s whose form depend on the equilibrium shape of the nucleus and the type of motion that i s assumed to describe the excited s t a t e s . The Hamiltonian of the c o l l e c t i v e motion w i l l be a function of the 's and t h e i r time d e r i v a t i v e s , o ( - ^ . The form the Hamiltonian takes depends on the d e t a i l e d assumptions made about the motion of the nuclear surface; that i s , do we assume that the d i f f e r e n t motions are coupled or not, are the v i b r a t i o n s harmonic or anharmonic, are the ro-ta t i o n s r i g i d or i r r o t a t i o n a l , i s the f l u i d compressible, homogeneous, etc. II-2 The Simple V i b r a t i o n a l Model The assumptions used f o r the simple v i b r a t i o n a l model are: a) The nucleus has a s p h e r i c a l e q u i l i b r i u m shape. b) The only c o l l e c t i v e motions are uncoupled harmonic v i b r a t i o n s about t h i s shape. c) The f l u i d i s incompressible and homogeneous. d) No p a r t i c l e states are involved. The potential energy of the harmonic vibrations about the spherical equilibrium shape is v = % i l C-J*>MI 1 where is the restoring force parameter and is the sum of surface 2 tension and coulomb energy terms. The kinetic energy is T = % A. e ^ a ^ f where B i s the mass transport parameter.2 B^ and C-^  do not depend on the orientation (/{), because spherical symmetry is assumed. 21 The momenta of the generalized coordinates are and therefore the kinetic energy can be written as < 6-; The Hamiltonian can now be written as H = with This Hamiltonian describes a system of uncoupled harmonic oscillators 2,20 whose frequencies are given by and, in general 10^  <c 10^  for J_ . This system can be quantized in the normal fashion by demanding that TT and c* obey the commutation relations. + "t 1 1 - 5 The Hermitian conjugates, oc/tand TT1 > can be derived from the fact that the nuclear surface must be real, i.e., therefore and O s c i l l a t i o n s with >\ =0 would describe v a r i a t i o n s i n the volume of the f l u i d while i t retained i t s s p h e r i c a l shape. These v i b r a t i o n s , sometimes c a l l e d breathing modes, are not allowed in this model as the f l u i d i s assumed to be incompressible. O s c i l l a t i o n s with "X =1 correspond to a v i b r a t i o n i n the p o s i t i o n of the centre of mass of the nucleus, without any v a r i a t i o n s i n the nuclear shape. For high energy (10-20 MeV), c o l l e c t i v e dipole ( }\ =1) o s c i l l a t i o n s are observed but these can be interpreted as o s c i l l a t i o n s of the proton f l u i d against the neutron f l u i d . These o s c i l l a t i o n s require that the protons and neutrons be treated separately, i n co n t r a d i c t i o n to the assumption that the f l u i d i s homogeneous. Quadrupole ( 7S=2), octupole. ( ?\ =3) and higher modes of v i b r a t i o n s are allowed. These v i b r a t i o n s , i f the model i s a p p l i c a b l e , w i l l describe the excited states of the nucleus. 20 Each mode of v i b r a t i o n can be treated as a p a r t i c l e of spin /\ , 7s p a r i t y (-1) , and p r o j e c t i o n A , onto the quantization a x i s . These p a r t i c l e s are commonly c a l l e d phonons. In the v i b r a t i o n a l model, therefore, an excited state of the nucleus i s described by the number and type of the phonon that make up the s t a t e . That i s , states can be made up o f , say, one quadrupole phonon, two quadrupole phonons, one octupole phonon, one octupole and one quadrupole phonon, e t c . The state functions for the low energy states i n v o l v i n g only quadru-pole and octupole v i b r a t i o n s are derived i n Appendix A using the number 21 r e p r e s e n t a t i o n . The t r a n s i t i o n s that are allowed i n t h i s model, t o -gether with t h e i r reduced t r a n s i t i o n p r o b a b i l i t i e s , are derived i n Appendix B. The basic features of the simple v i b r a t i o n a l model are described below. i) States in this model are characterized by the symbol , J being the angular momentum, n the parity, and n^ the number of phonons of character "A . The first excited state is 2p a one quadrupole phonon state; that i s , a 2+ state with n2=l. The symbol is used for the energy of this state. A state with two or more phonons is degenerate. There are three states with two quadrupole phonons, each with energy 2E^+. These states have Jfl^ = -i^, 22 and O^ . Similarly, there are five degenerate three quadrupole phonon states with J = 0+> 2+> 3 ^ ^ +^ a n ( j e a ch w i t h energy 3E2+; five degenerate one quadrupole (n2=l) one octupole (n-^l) states with J = 1 , 2", 3", 4" and 5", each with energy E9+ + Eo- , zl Jl where E _ is the energy of the one octupole phonon state, etc. 31 i i ) Transitions can occur only between states that differ by one phonon, and, for the emission of a gamma ray of angular momentum L, a phonon with >i = L must be created or destroyed. Also, since the parity of the phonons is (-1)^, the parity change of the transition must be > L (-1) = (-1) , and therefore only electric transitions are allowed (see Appendix B). Neither of these two restrictions are completely obeyed in real nuclei. One does find, however, that many even-even nuclei have a 2"*" first excited state, with a group of positive parity states at energies of approximately 2E-+ and 3E +. Quite often, a single 3 state is found 1 1 in the energy region between 2E + and 4E + , with a group of negative 21 21 parity states at about E«+ above this state. Many of these states have the large reduced transition rates expected of collective states. These 5 6 2A states are interpreted to be vibrational states and attempts ' ' have been made to explain them with the simple harmonic states derived in Appendix A as basis states. Anharmonic terms are added to the harmonic Hamiltonian as perturbations to account for the deviations from the simple harmonic vibrational states. II-3 Anharmonic Corrections There will be no attempt to derive these corrections here. The method is outlined in what follows, and a few attempts to use this method to describe vibrational nuclei are discussed briefly. The Hamiltonian in this case is H = H + 0( o<)3 + 0( o() 4 + o where HQ is the simple vibrational Hamiltonian of equation II-3. 0(o( ) + 0( oO^ .... stands for terms in the expansion parameters, or TT-^ of order 3, 4 The allowed combinations of and r r ^  are restricted by the requirement that H must be Hermitian and scalar.-' 21 The matrix of H is calculated in the basis provided by .the simple harmonic state functions (the eigenstates of HQ) and the eigenstates and eigenvalues obtained by diagonalizing this matrix. The coupling constants 2 between the harmonic terms (0(o() terms) and the anharmonic terms can then be treated as free parameters whose values can be adjusted to f i t the observed energies of the excited states of the nucleus under consider-ation. The transition rates are then calculated for these states, and hopefully, they will be in reasonably good agreement with those found experimentally. Although the form of the perturbed eigenstates obtained with the above diagonalization will not be derived here, i t is a simple matter to show which unperturbed eigenstates are coupled by anharmonic terms to 12 • third, fourth, etc., order in the expansion parameters. The expansion parameters are linear functions of the phonon creation and destruction operators, and a-^ (see Appendix A). Anharmonic terms to third order will therefore contain the number operators in the form A = a > / M <XVya. ^'M" B = C l \ ^ 0^>. A-V'A" c = a?** ft.\v A and D will couple the simple phonon states that differ by three phonons and B and C will couple states that differ by one phonon. Consider, for instance, that we wish to calculate the splitting of the two quadrupole phonon triplet to third order in oLf,^ a nd TT>,^  > where we only consider the coupling of quadrupole phonons (this is the simplest anharmonic correction available). We must consider as our basis set of states a l l quadrupole phonon states up to n2=5. Karmen and Shakin^ have used this simplest coupling to derive the eigenvalues of the first 9 quadrupole vibrational states. Their results required that the energy of the 4+ member of the two quadrupole phonon triplet, E,+ , had to be less than twice the energy of the one quadrupole 2^ state E9+, and that the 0+ member had to be below the 4+ member. Since this ordering has only been observed in a very limited number of vibrational nuclei, these third order corrections do not, in general, describe spheri-cal nuclei adequately. 24 Sorensen extended the basis states for the quadrupole case up to n£=7 (72 states) and included anharmonic coupling to fourth order in the quadrupole expansion parameters. The result was that the restriction E,+ 2^ 4. 2E + was removed, but that the restriction E + E,+ , remained. 1 2 2 The number of free parameters that must be fitted to the experimental data in Sorensen's expressions are greater than the number of known quadrupole vibrational states in any one nucleus. 23 Lipas has derived expressions for the splitting of the one quadru-pole-one octupole quintet (J = 1", 2", 3 , 4~ and 5") using this method. The basis he used consisted of the quadrupole states up to n2=4 and the octupole states up to n^ = 3. He considered anharmonic terms in H up to fourth order in the quadrupole and octupole expansion parameters. Any ordering of the 5 states could be achieved by different variations of the coupling constants, and, in order to get estimates of their relative strengths, at least one complete set of the five states must be observed. There is no nucleus for which such a group of states has been identified. This type of phenomenological description cannot be considered to be too successful, and has indicated the need to include other types of coupling in the collective description of spherical nuclei. That i s , the observed energies of the collective states can not be achieved by varying the coupling constants, as indicated above, between realistic limits. It is therefore assumed that another coupling of the vibrational states, 27 presumably via particle states, is required to achieve these results. Particle coupling is taken into account automatically in the microscopic 8 description of these nuclei. The semi-microscopic description, while i t does not consider particle states of one type of nucleon at a l l , does handle the particle states of the other type automatically. 124 II-4 Semi-Microscopic Description of Te ^"24Te has 2 protons and 22 neutrons outside the closed major shell of 50 protons and 50 neutrons. The semi-microscopic description of this 14 nucleus, as outlined by Lopac,^4 is i) The coherent motion of the 22 neutrons, and the polarization of the core by this motion, is given by the vibrational Hamil-tonian H (with or without anharmonic terms). V i i ) The excitations of the two protons are described by a quasi-Boson Hamiltonian, H . 1 2 4 i i i ) The eigenvalues and eigenstates of the excited states of Te are obtained by diagonalizing the matrix of the Hamiltonian H = H + H + H V p int obtained in the basis formed by the eigenstates of the Hamiltonian «V + V The form of H. , the interaction Hamiltonian between HTT and H , is int' v p' taken to be «int - -Z «f° Z-V^*0^ where r^ (j> ^  are the coordinates of the protons in the coordinate system used to describe the collective motion. The Y s are spherical harmonics. The cK-^'s are the surface expansion parameters and can be written as as shown in A ppendix A. The k(r^)'s are the proton radial wave functions whose matrix elements are treated as a free parameter that can be adjusted to give the best agreement with the observed energy levels. This type of interaction couples vibrational states that differ by one phonon. Lopac^"4 has chosen the harmonic quadrupole vibrations, including up to the three quadrupole phonon states to represent the collective motion. He has not considered octupole states. The shell model states chosen to describe the proton excitations were the ^ Sy^' 2c*5/2' ^ 3/2' 3^l/2 a n c^ T--\l/2 states> ^ n o t n e r words, a l l the shell model states above the Fermi energy at Z=52 and below the next closed major shell at Z=82. All these 28 29 states were used as Lopac and others have shown they are required in a similar description of the odd mass Sb isotopes, which have one proton outside the major shell. He was able to obtain reasonable agreement (as shown in section VI-5) with the experimental energy levels up to the two quadrupole phonon states. To achieve this agreement, he used a value of 0.7 MeV for the free coupling parameter, given by a = <k> % where <k> is the radial matrix element. Using this value of the coupling constant, he was able to calculate reduced E2 transition rates. The form of the electric quadrupole operator used was He sets e^ = 2e (e = proton charge) to account for the polarization of ef f the core by the proton. He then calls the effective charge of the vibrator and varies i t so that fO will give the observed reduced transition rate of the first 2^ excited state. The best f i t was obtained using e^ = 2.63e. Using this value he calculates ef f the reduced E2 transition rates of the higher energy states. Some of these will be compared to the experimental values found in our investi-gation in Chapter VI. 16 Chapter III Gamma-Ray Singles Spectroscopy The energies and intensities of the gamma rays emitted in the decay 10/ of Sb were measured with two different germanium lithium-drifted (Ge(Li)) detectors. When this investigation was begun, the best Ge(Li) detector available to this laboratory was a 30 cc. trapezodal detector with an energy resolution of 4.5 KeV at 1332 KeV. The largest multi-channel analyser (MCA) available was a 512 channel Northern Scientific, Model 600. In order to obtain suitable peak definition, eight different spectra were required to cover the energy range, 0-*3000 KeV, involved in this decay. Shortly after these spectra had been analysed, a much larger (45cc.) Ge(Li) detector with a resolution of 3.0 KeV at 1332 KeV, together with a 4096 channel MCA were purchased by the U.B.C. Van de. Graaff. The gamma spectrum of ^ "24Sb was re-analysed using this detector and the larger MCA. Although the energies and intensities of a l l gamma trans-itions found with both detectors agreed within experimental error, twenty-seven weak transitions were found with the large detector that were not found with the smaller one. Since the results obtained with the large detector were far superior, only the method of peak fitting, and energy and efficiency calibration, used for i t will be discussed here. The method of analysis was essen-tially the same for spectra obtained with either detector. The preamplifier used was a Tennelec, Model 135M, and the amplifier used was a Tennelec 203BLR, an active f i l t e r amplifier with baseline restoration. 17 III-l Peak Fitting The energies and intensities of unknown gamma transitions are usually found by comparison of their spectra to those of known gamma transitions. An accurate comparison requires that the areas and positions of the peaks in a spectrum can be consistently estimated. Good estimates can be made without any function to describe the peak shape if the height of the peak is much greater than the height of the background and i f the peaks do not overlap. In general, this is not the case, and so a function that des-cribes the peak shape must be found and this function fitted to the experimental data. The peak shape obtained with a Ge(Li) detector is a distorted Gaussian, an example of which is the "total function" curve shown in figure III-l. 3 0 There have been many attempts in the past to describe these peak shapes in terms of combinations of different functions, usually energy dependent. A number of different functions were tried in this investigation, and finally a combination of three gaussians and a "step function" (see figure III-l) , superimposed on a linear background, was chosen. The function chosen had the form: y = \?1 + P2X + Ei + E 2 + E3 + S with EL = P4 exp[ - (X-P5)2/2P| ] E2 = P7 exp[ - (X-Pg)2/2p2 ] E3 = PiQ exp[ - (X-Pn)2/2p22 ] S = P3 (rr/2 - Arctan[(X-Pi4)Pi3] Ei is the main gaussian with height P4, position P5, and standard deviation Pg. E 2 and E3 are the satellite gaussians with heights P7 and P^, positions Figure III-l 18 19 Pg and P]^ > and standard deviations Pg and P-^, respectively. S is the step-function, with height P3, step position P-^ and "steepness" Pjj. P^ + P 2 X is the linear background. The individual components of this function are plotted (by computer) in figure I I I - l . The 14 parameters used to generate the plot data were those found by fitting the function 22 to the peak at 1274 KeV in a spectrum of Na. This function was least-square fitted to known peaks in the energy region 120 -> 2600 KeV. The relationship of the satellite gaussians' parameters to the main gaussian's parameter were found as a function of energy to be Height ( See figure III-2) P 7 / P 4 = .126 + 5.0 x 10"5 x E(KeV) p10/p4 = -0 2 2 + 2-2 x 1 0~5 x E(KeV) Resolution (See figure III-3) P9/P6 =1.5 P12/P6 =3.2 Position (See figure III-4) ? 8 = P5 - (3.3 + .0026xE(KeV))/P6 P n = P5 - (8.6 + .005xE(KeV))/P6 The best position for the step, P14, was found to be the centre of the main gaussian (P4). The steepness of the step, related to P13, was not cri t i c a l as long as S reached its maximum (P-j) and its minimum (0) under the region of the peak. The value chosen was P-^g = 2.0. There are therefore only 2 + 4 x m independent parameters needed to f i t a region of a gamma spectrum containing m peaks superimposed on a linear background; the step height for each peak, and the height, resolution, and position of the main gaussian of each peak. In special cases the back-.3 Energy (KeV) 2 L T O T T 1200 1600 2000 2400 Energy (KeV) ground could not be approximated by a straight line. Therefore, in the o final fitting program an X term in the background was allowed for, a l -though in most cases the coefficient of this term was set equal to zero. The actual least-square fitting was done using the U.B.C. Computer Centre Library Subroutine RLQF3-'- (Restricted-Least-Square f i t ) . The areas of the peaks were taken as the sum of the areas of the three gaussians. The position of the peak was taken as the centre of the main gaussian. The error in peak areas and positions were calculated from the errors returned from this subroutine. The consistency of this fitting program was checked by fitting the peaks due to six different gamma transitons in the energy range 100 •* 2600 KeV. Different spectra were obtained for each peak by allowing the MCA to accumulate for different lengths of time. The positions and the normalized intensities found for each energy agreed to within the calcu-lated error. A check on the ability of the program to unfold overlapping peaks was performed in the following way. Two spectra of a single gamma tran-sition were taken and the peak parameters for each spectrum found. One spectrum was shifted relative to the other by a few channels by a shift of the spectrum origin and the two spectra added. The composite spectrum was then fitted and the parameters for each peak compared to those found from the individual spectra. The relative intensities of the two peaks were also varied. It was found, as expected, that the ability of the program to unfold peaks depended on their relative inten-sities and their separation. If the peaks were of about the same inten-sity a peak separation of about P^ /IO was required for the program to unfold the peaks. If one peak was 10 times more intense than the other, a separation of about was required. These requirements are only approximate as the ability of the program to unfold peaks depends on the height and shape of the background, as well as on the total intensity of the peaks. I l l - 2 Efficiency Calibration The sources used to measure the gamma-ray efficiency of the Ge(Li) detector are listed in table II I - l . The total efficiency (the product of solid angle and intrinsic efficiency) was calculated from the ratio of the total gamma ray intensity, I „ , to the measured intensity, I , at each energy. The total intensity was calculated from the data given in table II I - l . The source-detector distance was 10 centimeters. The standard sources were obtained from the International Atomic Energy Agency (IAEA), Vienna. They are encapsulated in plastic disks which are, in turn, cold welded into aluminum disks. A dummy disk is supplied with the sources. The standard sources were used to determine the efficiency of the detector over the energy range 120 —> 1350 KeV. The intensities of the secondary standards were found using this calibration and published relative intensities of the secondary standards' gamma-rays. In this manner, the efficiency was extended up to 2750 KeV. Y and °Th were used as secondary standards as they both have transitions in the energy range of the calibration sources whose relative intensities to higher energy transitions is well known. The uncertainty in the efficiency of the Ge(Li) detector for each calibration energy is the combination of the following uncertainties. 25 Table,III-l Efficiency Calibration Standards Source 57Co Strength( curies) at Jan.l 1970 11.43+.7% Half-life 271.6+.5days Transition Energy(KeV) 122 Relative Int. (7.) 85.0+1.7 203Hg 20.25+1.% 46.8+.2days 279 81.55+.15 1 1 3Sn 22Na 4.22X105 gamma/sec 9.16+1.0% 115.0+.5days 2.602+.005years 393 511 1275 181.1+. 2 99.95+.02 157CS 10.35+1.8% 30.5+.3years 662 85.1+.4 Mn 10.96+.7% 312.6+.3days 835 100.0 60 Co 10.57+.6% Secondary 5.28+.01years Standards 1173 1332 99.87+. 05 99.999+.001 88 Y Reference 32 898* 1836 2734 91.4+.7 99.4+.1 .62+.04 228 , Th Reference 33 583* 2614 100.0 117.4+1.0 *Used to calibrate secondary standards 26 a. Error in I due to uncertainty in the data used to calculate i t ; i.e., the uncertainties in the standards decay schemes, half-lives, and in i t i a l source strengths at t=0. The uncer-tainties listed in table III-l are for a quoted 957, confi-dence interval.3 2 b Random counting error: The MCA was run until at least 10^ counts had accumulated in each calibration peak, except for the 279 KeV transition of 203Hg and the 2734 KeV transition of 88 Y, where fewer counts were taken because of low intensity. The error is therefore less than 0.17,,except for the 279 and 2734 KeV transitions which had an uncertainty of 1.07,. c_ Peak fitting error: The error in the peak area (found with the fitting routine) was typically 0.1-*- 0.57>. d_ Error in the source-detector distance: Each source disk was placed in a holder fixed at 10 cm. from the detector. A spectrum of each source was taken, the source disk reversed, and the spectrum re-taken. The measured intensities were averaged, thereby cancelling any error due to the source material not being at an equal distance from the faces of the source disk. The individual disks could be replaced with less than .01 cm. difference in the source-detector distance. The error in the measured intensity is therefore approximately 0.27». e_ Absorption in the disk: The gamma ray absorption in the source disk was found by inserting the dummy disk between the sources and the detector and finding the decrease in measured intensity. The absorption ranged from (2.4 + .1)7, for . 122 KeV to (.85+ .10)% for 1332 KeV. f_ Analyser dead time: Once a pulse is applied to the input of a MCA, the input is blocked to a l l subsequent pulses until the first pulse has been analyzed. In general, large pulses take longer to analyse than small pulses. Therefore the time that the input is blocked, or the dead time, is a function of the pulse height. The time that the input is blocked per unit time is N Z ^ i m i l where m^  is the measured counts per channel,"fc\ the dead time for each channel, and N the total number of channels. Since the pulses arrive at the input randomly in time, the number of pulses lost for each channel is N ni-mi=ni £ m ^ i where n. is the true counts per channel. The correction for any channel in a given spectrum is 1 f=ni/mi= f w i l l , in general, be different for different spectra. The correction can be found by analysing the pulses from a pulser at the same time the spectrum is analysed, f is then just the ratio of the true pulse rate (as measured with a scaler)to the measured pulser rate, which can be found by fitting the pulser peak. The pulser pulses will not be random in time with respect to each other, but they will be random with respect to the true pulses. This will not affect 28 the result i f the time between pulser pulses is long compared to the analyser dead time. The pulse rate used was 1000/sec. Typical dead times are about 10""' sec. This method of dead time correction has the advantage of correcting for pulse summing at the same time. Pulse summing occurs when two individual pulses are separated by a time which is less than the time required by the amplifying system to respond to each individually. The pulses are then analysed as a single pulse. Since the pulser is applied to the input of the preamplifier, its pulses have the same probability as true pulses of being lost from the corresponding peak in the spec-trum. The error in this method of dead time and pulse summing correction is the error in the measured intensity of the pulser peak, which is the combination of the random counting error and the error in fitting the peak. The random counting error can be calculated i f the probability distribution, for the number of 35 pulses lost is assumed to be Poisson. This assumption is reasonable as the total number of pulses is large and the proba-bil i t y that any one is lost is small. This error is then just the square-root of the number of pulser pulses lost. The error in fitting the pulser peak can be minimized by insuring that the pulser peak is situated on a low background region of the spectrum. The total error in the efficiency, Io/l, was calculated from the proper combinations of the above errors for each calibration energy. 29 T o t a l Intensity/Measured Intensity E f f i c i e n c y of the 45cc. Ge(Li) Detector This error was used to weight the least square fitting of thel„/l data to a function of the form = a + b E - c E2 E<550 = a' +b'(E - 500) - C'(E-500)2 E>500 The results of the fits were: a = 19.5 + 1.0 a1 = 290.7 + 3.5 b = .46 + .03 (KeV)"1 b' = .656 + .008 (KeV)"1 c = (2.2 + .4) x 10"4 (KeV)"2 c* = (2.19 + .04) x 10-5 (KeV)" The large uncertainty in the paramters of the low energy f i t is a result of the large uncertainties in the calculation of I „ , and of the relatively large curvature of the efficiency function in this region. These functions are plotted in figure III-5. III-3 Energy Calibration The energy calibration of the gamma spectrum of ^2^Sb was done in two steps. The first consisted of measuring the energies of the intense gamma transitions in the decay of •L24Sb found in four hours of analysing using the standard sources listed in table III-2. The second step used these transitions as secondary energy standards for a much longer anal-ysing period (sixty hours) required to identify weak gamma transitions. The standard sources were used to calibrate the analysing system before and after the four hour run. The position of the peaks of the standard sources were found using the peak fitting routine described in section I I I - l . These positions were least-square fitted to a function o Table III-2 Energy Standards Source 57Co Energy(KeV) 121.97(.03) Source 2 0 7B i Energy(KeV) 1063.58(.06) 57Co 136.33(.03) 60Co 1173.23(.04) 226Ra 241.92(.03) Na 1274.55(.04) 203 Hg 279.191(.008) 60Co 1332.49(.04) 226„ Ra 351.99(.06) 2 2 8Th 1592.46(.10) n3 S n 391.70(.05) 226Ra 1764.45(.22) 22Na 511.006(.002) 88y 1836.13(.04) 2 2 8Th 583.14(.02) 2 2 8Th 2103.47(.10) 1 3 7Cs 661.64(.08) 2 2 6Ra 2204.25(.48) Mn 834.81(.03) 228Th 2614.47(.10) 88Y 898.04(.04) Table 88y III-3 2734.14(.08) Secondary Energy Standards Energy(KeV) Energy(KeV) 602.80(.06) 1045.17(.09) 646.02(.07) 1325.56(.ll) 722.90(.07) 1691.05(.09) 790.78(.08) 2091.0(.2) 968.20(.09) 2614.47(.10) * 2 2 8Th peak in background the form E(KeV) = a + b x (Chan) The results of the fits were: Before a= 51.26 + .03 KeV b= .71506 + .00003 KeV/Chan After a= 51.30 + .04 KeV b= .71504 + .00003 KeV/Chan Figure III-6 shows the distribution of the energies of the standard sources over the calibration range. The width of the line drawn through the points is much larger than the error associated with any point. The energies of the transitions found in the four hour run were cal-culated from the average of "before" and "after" parameters. The width of the peaks in this run were the same as the width of peaks found in much shorter runs (10 min.), indicating that no appreciable fluctuations in the gain of the system had occurred during this period. 1 0 / The energies of Sb transitions used to calibrate the sixty hour run are given in table I I I - 3 . The positions of the peaks corresponding to these transitions for the sixty hour run were fitted to a straight line with the results a = 51.34 + .07 KeV b = .7150 + .0001 KeV/Chan. The f u l l widths-at-half-maximum (FWHM) of the peaks in the sixty hour run were larger than the peaks in the four hour run by approxi-mately 2 x 10"4 KeV/Chan. This peak broadening corresponds to a gain instability of the total analysing system of ,027o. The energy cali-Figure III-6 33 Energy Calibration 34 bration of the sixty hour run was not affected appreciably by this in-stability as i t was obtained from the secondary standards whose positions were, of course, subjected to the same fluctuations. 1 0 / III-4 Sb Gamma Spectrum The gamma spectrum of the decay of ^ ^Sb to ^"24Te obtained in sixty hours of analysing is shown in figures III-7 (a-h). The positions and areas of the peaks of this spectrum were found using the fitting program described in section III-2. The energies and intensities of the gamma transitions corresponding to these peaks were calculated using the appropriate calibration functions described in sections III-3 and III-4. Table III-4 gives the results of these calculations. Included for com-parison are the results of another recent investigation of this decay by M 3 6 Meyer. The gamma spectrum contains single and double escape peaks, sum peaks, along with the f u l l energy peaks resulting from the gamma transi-tions in the decay, and in addition, peaks resulting from radioactivity in the laboratory other than Sb. These "background" peaks were iden-tified by removing the source and taking a background run for the same length of time as for the total spectrum. Only one background peak (444 KeV) overlapped a true peak. The peaks resulting from single and double escape of the positron annihilation radiation were identified by taking spectra of Co, Y, Bi^O-7, 226^ a n ( j 228^h sources. The ratios of the areas of the escape peaks to the f u l l energy peaks were found. These ratios were plotted as a function of energy (see figure III-8) and this.graph used to identify escape peaks in the total spectrum. o Counts/Chan. U l o o> N5 4 * * 121.73 •159.45 254.4 336.02 344.4 •351.2 371.0 400.0 (^)Z-III Counts/Chan. U< 10 •444.18 •468.8 481.4 525.4 V -602.80 C 632.4 646.02 662.7 669.2 709.4 713.9 722.9 735.4 765.4 (qU-III'STi Counts/Chan. o Ul Ul o •790.78 816.9 856.9 867.6 f-900.0 911.5 968.2 976.0 1014.7 1045.19 1054.4 1069.1 1086.2 1112.2 1120.3 LZ (3)Z.-III '3x3 Counts/Chan. o T U l o 1179.1 1199.3 1248.3 1263.5 1301.4 1325.6 1355.2 1368.2 1376.0 1384.9 X .*' 5-. . . v 1408.1 1436.6 1445.0 1489.0 1505. 8C (PU-III Counts/Chan. i—« i—• i—' o o o (ji .p- ro m ui ro ui cr> to 1526.3 1579.9 1622.4 1691.05 1720.3 1732.1 1764.7 ( 9 ) Z - I I I o c r PJ 3 . ro CO a o CN Counts/Chan. h-» h-1 I-4 O O O Ul CO N3 Cn 4> K> Ul Ul NS vO -p-CO o Si a •1918.6 •1941.4 .1957.7 £ 1 1971.1 CN _ co •2016.2 •2039.3 -2091.0 • • . • • •2098.7 2107.5 2172. : t 2182.6 if - 2204.7 07 '%T& Counts/Chan. o LO to -1— o 4> to U l -2283.3 -2293.7 I" •2323.4 .1 • i I •2450.2 2454.4 .2614.5 (S)i-HI - S T I Counts/Chan. o o |sj U l K> N) U l LO to U l —i 1 1 i 1—: n 1 »"~ -X. ' •>> 2681.3 h 2693.1 i v .«• •• • * i • ;</ Table III-4 43 124r Energies and Intensities of Gamma Transitions in Sb Decay This Work Energy(KeV)  Meyer 36 121.73(.15) 159.4(.2) 185.4 239.4(.2) 244.6(.2) 254.4(.3) 254.4 336.0(.2) 335.8 344.4(.2) 351.2(.6) 371.0(.2) 370.4 380-390 385.9 400.0(.2) 400.0 444.2(.l) 444.0 468.8(.3) 468.6 473-479 476.5 481.4(.2) 481. 498.6(.3) 498.4 525.4(.2) 525.5 550-555 553.8 602.80(.06) 602.72 632.4(.7) 632.4 646.02(.07) 645.82 662.7(.5) 662.5 669.2(.l) This Work Intensity  Meyer 36 205(40) 140(40) 400 200(40) 230(60) 120(20) 100 560(100) 790 1000(130) 500(200) 290(100) 200 100 800 1300(150) 5300 1700(150) 3500 300(100) 300 100 350 200(100) 650 200(100) 500 1300(100) 3100 <100 <200 106 106 1200(300) 1100 74000(1600) 72300 150(30) 250 5770(100) Comment a b J e Table III-4(cont.) 44 This Work Meyer This Work Meyer Commen 709.4(.l) 709.3 13600(900) 14300 713.9(.l) 713.8 23900(1000) 24000 722.90(.07) 722.78 109700(2000) 113000 745.4(.2) 735.9 1400(300) 1300 765.4(.5) 765.3 90(30) 280 771-777 775. <50 90 779.1(.2) 660(80) - b 790.78(.08) 790.77 7500(150) 7200 816.9(.l) 816.8 640(60) 790 856.9(.4) 856.9 220(60) 230 867.6(.4) - 180(50) - b 900.0(.2) 899.8 110(40) 140 911.5(.4) - 140(50) - b 935-942 937.9 <50 65 j 968.20 968.25 20000(400) 18400 976.0(.3) 796.6 1000(200) 850 995-1000 997.0 <50 60 j 1012-1019 1014.5 <50 85 j 1045.19(.09) 1045.24 18900(400) 18500 1054.4(.5) 1054.8 100(50) 85 1069.l(.l) - 2300(120) - f 1086.2(.2) 1086.3 300(50) 340 1112.2(.2) - 730(100) a 1120.3(.6) - 120(70) - b 1160-1165 1163.2 <50 190 j 1179.9(.l) - 8800(250) - g 1199.3(1.0) 1198. 80(60) 60 1238.0(1.0) 1235? 60(30) 60 b Table III-4(cont.) 45 This Work Meyer This-Work Meyer Comment 1248.3(.3) - 50(100) - i 1250-1260 1253.4 ^50 80 j 1263.4(.4) 1263.1 440(100) 300 1267-1273 1269. <50 120 j 1325.6(.l) 1325.5 16400(400) 14200 i 1355.2(.l) 1355.2 11200(350) 9300 1368.2(.l) 1368.2 27100(600) 23600 1376.0(.2) 1376.1 5300(250) 4300 1384.9(.9) 1385.2 310(70) 530 1385-1390 1388.7 <100 ^100 j 1408.1(.3) - 1300(200) - a 1436.6(.l) 1436.7 13600(400) 10200 1445.0(.2) 1445.3 2900(250) 2100 1450-1457 1453.2 <100 180 j 1462.2(.5) - 3000(500) - b 1489.0(.2) 1489.0 6900(250) 5490 1505.(1.) 1505.6 50(40) 50 1526.3(.2) 1526.3 4400(200) 3900 1553-1560 1557. <50 230 j 1579.9(.8) 1579.7 1500(500) 2000 h 1622.4(.3) 1622.4 300(50) 240 1691.05(.09) 1691.02 504000(10000) 490000 1720.3(.2) 1720.4 940(70) 850 1732.1(.2) - 100(50) -1764.7(.4) - 240(50) - b 1845-1855 1851.5 <25 20 j Table III-4(cont.) 46 This Work Meyer This Work Meyer Comment 1918.6(.2) 1918.7 570(40) 530 1941.4(1.0) - 28(20) - g 1945-1952 1950.4 <2Q 30 j 1957.7(1.0) - 45(15) -1971.1(.4) - 20(20) - i 2016.2(.4) 2015. 70(20) 90 2039.3(.2) 2039.2 660(40) 610 2079.(2.) 2078.5 £800 110 2091.0(.2) 2091.0 57600(1400) 56100 2098.7(.3) 2099.0 500(200) 400 2107.5(.3) 2108.0 550(100) 420 2145-2155 2151.5 <5 8 j 2172.(1.) 2172. 12(4) 10 2182.6(.2) 2182.6 400(30) 410 2204.7(.4) 2203.? 80(20) 8 b 2283.3(.5) 2283.2 70(20) 80 2293.7(.3) 2293.7 250(50) 300 i 2323.4(.8) 2323.1 10(4) 24 2450.2(.7) - 24(4) - b 2454.6(1.0) 2454.4 9(4) 7 2614.6(.2) - 780(20) - b 2681.3(.5) 2681.4 20(5) 16 2693.1(.6) 2693.9 24(5) 26 i Comments 152 a) Background from Eu b) Natural radioactivity background Table III-4(cont.) 47 c) Backscatter peaks from 603,646,709,714, and 723 KeV transitions have energies from 179-189KeV. 152 d) Background from J Eu subtracted. e) Data normalized to this peak. f) DouWe excape peak from gammas with energy = E+2 mQc2. g) Single excape peak from gammas with energy = E+moc. h) Intensity of single excape peak from 209lKeV transition subtracted. i) Corrected for one-detector-coin.-sum events. 36 j)Maximum intensity for transitions found by Meyer Figure III-8 48 1400 1600 1800 2000 2200 2400 2600 Energy of Full Energy Peak (KeV) 49 Sum peaks can be divided into two groups, those which result from random coincidences of pulses, and those which result from true coinci-dences between cascading gamma transitions. The rate of random sums between two peaks with energy E^, E^ and count rates R^ , R^  that sum to a peak at energy E^ + E2 is ' Rl+2 = 2 ^ R1R2 where 7j" is the maximum time between pulses 1 and 2 for them s t i l l to be analysed as a single pulse of energy E^ + E^. Tj' can be found by measur-ing the random sum rate of a transition with itself. The 603 KeV transi-tion was used for this calculation with the rates found from the sixty hour run. R = 6.43 x 107/ 60 hrs. 603 R603 + 603 ^ 2 0 0 0 (N o p e a k w a s f o u n d a t 1 2 0 6 K e V) The result was t< 5 x 10"' sec. The maximum area of random sum peaks for any two transitions in the decay were calculated using this value. In every case the area was too small to be distinguishable above the background. Sum pulses that result from cascading gamma transitions will always have an energy equal to the sum of the transition energies i f the lifetime of the intermediate state is short compared to 'f . The summing rate will be 2 Rl+2 - Ki % % 2 where K^  is a constant depending on the details of the decay scheme. In general, a peak at energy E^ + E2 can be the result of a cross-over transition or coincidence sum pulses, or both. A plot of N2 Y or / Nx x * against source-detector distance N l + 2 / V Nl+2 i where N^, ^ and a r e Pea^ areas at energy E^, E2 and E^ + E^ res-pectively, will reveal the nature of the peak at E^ + E 2. A straight line with zero slope indicates that the peak is entirely due to a cross-over transition. A straight line with positive slope indicates that i t is a sum peak, and a curve indicates that i t is a combination of the two. Plots such as these are shown in figure III-9 for the cascades 603 - 1691 KeV and 603 - 2091 KeV. The true and sum nature of the peaks at 2293 and 2693 KeV is immediately apparent. The asymptotic values of these curves were found from much larger graphs and the intensities of the 2293 and 2693 KeV transitions calculated. 2 The constant K^  in the above equation can be estimated for these cascade transitions from the slope of these graphs in the region where the sum term dominates (small source-detector distance). This constant will be, in general, different for different cascade transitions. Once the decay scheme is known, however, the ratio of K^  to for any other two transitions j and k, can be calculated (see chapter IV), and therefore the contribution to any peak at energy Ej + E^ due to coincidence summing of transitions j and k can be estimated. The usual method of identifying sum peaks is to place an absorber 38 between the source and the detector. The absorber will reduce the measured intensity of the low energy transitions much more than high energy ones. The sum peak will therefore be greatly reduced, while any contribution to the peak from a cross-over transition will be only 124 slightly reduced. Figure 111-10 is a high energy spectrum of Sb with 7.5 cm. of lead between the source and detector. The peaks at 2293 and 2693 KeV have been reduced much more than the other peaks in this energy region. (See figures III-7(g) and (h) for comparison.) This spectrum 51 Figure III-9 Sum Peak Identifacation tl 16 2tj- 24 28" r (inches) Source-Detector Distance Fig.III-10 High energy spectrum taken with a lead absorber. 52 7*7573 +Z'0^Z 1'ZZZZ L'VOZZ S'£0TZ. 0*160Z i • J— 4 I'C693 e"T89Z I' 9*7l93_ < I e • z^zz -\ } • • • vo m CN o o o o o •UBqo/saunoo 53 was taken with the 30 cc. Ge(Li) detector and therefore the peaks are much wider than those in figure III-7. Gamma-Gamma Chapter IV Coincidence Measurements 54 IV-1 Experimental Arrangement The gamma-gamma coincidence spectra were taken using the coincidence arrangement shown in figure IV-1. This type of coincidence arrangement is called fast-slow coincidence. The fast coincidence is performed on the fast negative logic pulses obtained from each detector using the constant-fraction timing discrim-inators (C.F.T.D.). These logic pulses are used as start and stop pulses for a time-to-amplitude converter (TAC). The TAC output produces an output pulse whose voltage is proportional to the time difference between, the start and stop pulses. The time spectrum of the TAC will contain a peak situated on a flat background, as shown in figure IV-2. The peak represents coincidence events between the two detectors and the background represents random events. The slow coincidence is performed on the outputs of the three single channel analysers (SCA). SCA#1 was set on a single peak in the energy spectrum obtained from detector #1, commonly called the gate detector. SCA#2 was set on the coincidence peak in the time spectrum produced by the TAC. SCA#3 was set to accept a l l pulses from detector #2 above a given lower level. This lower level discrimination is required to reject 39 pulses that are too small to give a proper fast logic pulse from CFTD#2. The three coincidence output was used to gate the amplified output of detector #2, commonly called the analog detector. The gated spectrum from detector #2 will contain the peaks resulting from gamma transitions that are in coincidence with the gamma transition Figure IV-1 Electronic Arrangement used for Coincidence Measurements H.V. 1 Amp 1 S C A 1 Scaler 1 Preamp 1 Det D<|t -<- 1 X Preamp 2 Source T F A 1 f H.V. 2 C.F.T.D. 1 T F A 2 > CF T.D. > Variable Delay Fast Coincidence Stop Start Scaler T A C Scaler 5 Scaler 3 S C A 2 Scaler 4 S C A 3 Variable Delays and Coincidence Unit Delay and Gate Generator Scaler 6 Amp 2 To MCA Input To MCA Gate Table IV-1 56 Description of the Electronics used for the Coincidence Measuremenfes Detector#l: A 7cc. planer Ge(Li) detector frabricated by P.Taminga at the University of B.C. Detector#2: A 30 trapezodal. Ge(Li) detector obtained from Nuclear Diodes. Preamp#l&2: Tennelec 125 FET preamplifiers TFA#1&2 : Ortec 454 Timing Filter Amplifiers CFTD#1&2 : Ortec 453 Constant-Fraction Timing Discriminators Variable delay: Coaxial Cable TAC :0rtec 437A Time-to-Amplitude Converter SCA#1,2&3 :0rtec 420A Single Channel Analysers Amp#l : Tennelec Active Filter Amplifier Amp#2 : Tennelec 203BLR Active Filter Amplifier with Baseline Restoration Variable Delays : Nuclear Chicago 27351 Coincidence Unit &Coin. Unit Delay and Gate : Ortec 416 Generator Scalers :Tennelec 562; Only 2 scalers were available. The scalers 1-6 are points in the curcuit where the count rates were monitored. MCA :Either; Nuclear Diodes 110 (128Chan) Nuclear Diodes 160 (1024Chan) Northern Scientific 600 (512Chan) The best MCA available at any time was used. Fig IV-? Typical output of the TAC. Illustrating the coincidence and random gates 58 selected with the gate detector. It will also contain events that are in coincidence with the background under the gate peak and random coinci-dence events. IV-2 Random Coincidences The rate of random coincidences in the output of the TAC can be found 37 from the usual formula, Nf = 2 ^ N„N IV-1 R 2 3 where is the start rate, ^  the stop rate, N^ the fast random rate and 2 ?J the width of the gate set on SCA#2. Not a l l of these random coincidences will meet the energy requirements set by SCA#1 and SCA#3. The random rate in the actual gate pulses will therefore be reduced by the factors N^ /N2 and N^/^, where N^  and are the count rates measured by scalers 1 and 4 respectively. The random rate for the coincidence spectrum is therefore just = 2TN,N. IV-2" R J- 4 g where N^ is the slow random rate. The validity of these equations was checked using a ^ Co source. A gate corresponding to 2 t = 20 + .1 <\sec. was set on the level background of the output of the TAC. The gate detector SCA was set on the 1332 KeV peak of the ^ Co spectrum^ and the analog SCA was set to accept a l l pulses above 500 KeV. The measured results were 2 = 5.30 x 10 counts/sec. 3 N2 = 6.82 x 10 counts/sec. = 3.12 x 104 counts/sec. N. = 2.08 x 104 counts/sec. 4 = 4.2 + .1 counts/sec. R '^ NS = (2.3 + .5) x IO"2 counts/sec. R -The calculated results were, N^  = 4.25 + .01 counts/sec, and R Ns = (2.2 + .1) x 10" counts/sec, both in agreement with the measured R values. 22 60 A Na source was substituted for the Co source and the measured random rates again were found to agree with the calculated ones. In addition, a coincidence spectrum was taken with the gate set on the 1275 KeV peak. The resulting single and coincidence spectra are shown in figure IV-3. The singles spectrum has a peak corresponding to the 511 KeV positron annihilation radiation and a peak corresponding to the 1275 KeV gamma transition4^ that follows the positron decay of 22Na to the excited 22 state of Ne. The coincidence spectrum contains only the 511 KeV peak except for a small peak at 1275 KeV due to random coincidences. The expected number of counts in this random peak was calculated by replacing N^ in equation IV-2 by the count rate for this peak obtained from the singles spectrum. The calculated and measured random rates were again in good agreement. i.e. ^ = Gate Rate = 340/sec. N, = 1274 KeV peak rate = 1.1 x 105/hr. 4 2 t = 20 f\ sec. Expected random rate = 1.5/hr. Measured random rate = 1 3 + 4 / 1 0 hrs. Random rates were calculated in this way for every coincidence spec-trum taken, and the contribution to peak intensities, i f appreciable, sub-s tracted. IV-3 Corrections to Coincidence Spectra for Background Events The contribution to a coincidence spectrum from the background under CN c c c • c X, u 05 4J n 3 O u *° _ <u cl Total Spectrum NJ 5z ») CO •a . to o rt H OQ O 25 Spectrum in coincidence with the 1274KeV peak o 30 60 Chan. No. 90 120 61 the gate peak can be found by taking on-peak and off-peak coincidence spectra. Typical on-peak and off-peak gates are shown in figure IV-4 The peak areas in the off-peak coincidence spectra must be corrected for any difference in accumulation time from the on-peak spectrum, for the difference in height of the background, and for the difference in source intensity i f the half-life of the source is not large compared to the accumulation time. The difference in random coincidence rates, i f appre-ciable, must also be taken into account. Suppose that the gate peak shown in figure IV-4 was due to transition 1 in the general decay scheme Then the gate would contain pulses due to transition: 1 plus the background resulting from transitions 2, 3, 4 and 5. The rate of coincidences detected between the on-peak gate and transition 2 would be Nl ! 2( t ) = W A ^ A ^ + NB(t>K2 I V " 3 The fir s t term represents the coincidence rate for transitions 1 and 2, and the second the coincidence rate for the background and 2. "£-^'and £ 2 are the Fig.IV-4 62 8000 7000 6000 5000 40oq 300d 200Cf lood-220 230 240 Chan. No. Typical on-peak and off-peak gates. The peak in this figure is the 646KeV peak in the spectrum of 124Sb efficiencies (intrinsic and solid angle) for gamma 1 in the gate detector 2 and gamma 2 in the analog detector respectively, f = I 9/I A is called A -i A the feeding ratio, and is the relative probability that level A is popu-lated by transition 2. b^ = I^/I^ is called the branching ratio and is the relative probability that level A decays via transition 1. ^ (t) 1 S the rate at which level A is populated, which of course decreases with -t/r/ time by the factor e , where t is the lifetime of the source. Ng(t) -t/t the background rate under the peak which also decreases as e is a constant. The rate of coincidences between the off-peak gate and transition 2 will be Nl-2 - NB( t ) K2 I V'4 If the on-peak coincidence spectrum is allowed to accumulate from times t Q to t-^  and the off-peak from t 2 to t^, the number of counts in the peak due to transition 2 will be On-peak Con = ^ N^ 2(t)dt IV-5 to 2 1 -toft- - t i /r = t : [ 6 1VA bA IA ( o ) + V o ) K 2 ] ( e " e } Off-peak rt 3 - t 2 / t -t3/t Coff = \ N^(t)dt = tKjNj(o) (e Z -e ) IV-6 4 The number of true coincidences between transition 1 and 2 will be .true = Con - *2 N»<°> X T(t)C o f f IV-7 K2 N£(o) with T(t) - ' ( e - ^ - e ^ l ^ ) / (e"t 2 / t : - e " ^ ) 64 putting t t - t o - t 3 - t o.- At - t R and t j - t Q = tp, and if ^ t £.c t and t2-OC^, then R t , T(t) = e D r fcR IV-8 t R+At The ratio N /N' can be estimated from the shape of the gate detector B B spectrum in the region of the gate peak. The ratio K^/Ky, is unity i f the backgrounds for the on-peak and off-peaks have exactly the same origins. This will only be true i f no Compton scattering events from a higher energy transition contribute to one gate but not the other. 124 IV-4 Coincidence Gamma Spectra of Sb 124 Gamma coincidence measurements of the nucleus Sb were taken with three different gates. They were the 603 and 646 KeV transitions, and the energy region 700 - 730 KeV, which contains the 709, 714 and 723 KeV transitions. On-peak and off-peak spectra were taken for a l l three gates. After analysing these spectra it was felt that no more information could be obtained with the equipment used by selecting other gates. The coincidence spectra for the 603 KeV gate were taken in three parts. The energy regions 100 - 750 KeV and 700 -1700 KeV were analysed with the 512 channel MCA. The energy region 1600 - 2750 KeV was analysed with the 1024 channel analyser. The on-peak and off-peak spectra for the f i r s t two regions are shown in figure IV-5(a) and (b) respectively. A portion of the on-peak spectrum of the high energy region is shown in figure IV-5(c). The portion of the spectrum above 2120 KeV did not contain any peaks and is therefore not shown. 65 The on-peak coincidence spectra for the 646 and 700 - 730 KeV gates are shown in figure IV-6 and IV-7 respectively. The high energy regions of each spectrum that did not contain any peaks is again omitted. These spectra were analysed with the 1024 channel M C A . The area of the peaks in the on-peak and off-peak spectra for each gate were found and the number of true coincidences calculated using equation IV-7. The data used for these calculations and the results are tabulated in table IV 2(a-e). The true coincidence results can be categorized in the following way. Consider the decay scheme I If the gate is set on transition 1, the number of detected true coincidences for transitions 2, 3 and 4 will be Cl-2 - *1 V A V A Cl-3 - M B ^ A ? 1 4 2 c. , = £\ £,f b-f b I. 1-4 1 4 A A B B A Other coincidence rates can be written in a similar manner. Using the Fig.IV-5(a) Low energy region of ^2^Sb gamma spectrum in coincidence with the 603KeV transition. Fig.IV-5(b) 67 1 9 / Medium energy region of the Sb spectrum in coincidence with the 603Kev transition t T69T Z39T 08ST 6871 S77T 9C7I SZZl 08TT 9801 6901 S70I 9£6 896 i . • . V. 1 j •••• .** • M . « *' CD y . w :•: « T.6L i . . . • •«. % u 4-1 o CD p. rt tu a. i 14-4 CO . CN O UO CN * O m CN •umjo/snunoQ Fig.IV-5(c) 68 High energy region of iZ^Sb in coincidence with the 603KeV transition. 8013-1603 o o 6£03-8T6T-ozn-1691-«•. . • * • * * • • « i* * : -.v.. : • o oo o CO O c o CN o CN O O IT! O O CN O O •UBijo/sriunoo F i g . IV-6(a) Low energy portion of the 646KeV on-peak coincidence spectrum 69 16L 60 L 979-J o o <r « o o ro eo9 ITS-J4. .-•.1 i • t • o o • o c Csl (fl o • * o o o o m o o CN o o CM •uuqo/saunoo CM Fig. IV-6(b) High energy portion of the 646KeV on-peak coincidence spectrum. 68vT SvvT 0811 SvOI 9£6 o o in o o CN o o o m o CSI • UBU.3/s z\ unoQ Fig. IV-7(a) Low energy portion of the 700-730KeV on-peak coincidence spectrum 71 IT! CM •UBqo/S3unoo F i g . IV-7(b) High energy p o r t i o n of the 700-730KeV on-peak coincidence spectrum 72 89CI' o o O O vO O S3 896-c ctj o o in o H ° o o m o o CM o o o m o CM •UBqo/s^unoo CM Table IV-2(a) Energy region 100-750KeV in coincidence with 603KeV transition tR=2Xl05sec. tD=2.0lXl05sec. ot=0 NB/N^».76 Energy(KeV) Con Coff true 400 170 30 135+100 440 180 20 165+100 525 200 20 180+100 603 24700 27900 -400+1000 646 11000 2700 8400+300 668 1150 24 1130+50 709 2800 800 2200+500 714 2600 100 2500+500 723 12900 2400 11000+700 735 25 TableIV-2(b) 25+20 Energy region 700-1700KeV in coincidence with 603KeV t: t =2xl05sec. R t D-2. 0lXl05sec. At=0 NB/NB=.76 791 280 60 230+50 968 400 140 290+50 1045 350 40 320+30 1086 40 15 28+20 1325 80 90 10+20 1355 210 15 200+30 1368 350 200 200+100 1376 40 - 40+30 1436 190 25 170+40 Table IV-2(b) (cont.) Energy(KeV) Con Coff true 1445 22 15 10+20 1489 40 40+30 1526 46 46+30 1580 38 38+30 1622 30 30+25 1691 6730 230 Table IV-2(c) 6550+100 Energy region 1500-2700KeV in coincidence with:603KeV tR=117hrs t d =120hrs At=+5hrs N /N' = B B = .76 1720 5 5+4 1918 5 5+4 2039 16 16+10 2091 740 20 725+100 2108 5 5+4 Table IV-2(d) Energy region 100-2000KeV in coincidence with 646KeV transition tR=116hrs tD= 504hrs At= 46hrs NB/N^ =.9 603 3300 200 3100+200 646. 45 40 5+15 709 65 25 40+20 7.23 80 70 10+20 791 20 -: 20+10 976 4 - 4+3 1045 62 20 40+15 1180 3 2 1+2 1445 11 3 8+4 1489 3 2 1+2 1525 10 2 8+4 Table IV-2(e) Energy region 100-2000KeV in coincidence with 700-730KeV gate tR=167hrs tD=120hrs ^t=lhr N B / N B = * 9 Energy(KeV) Con C Q f f C t r u e 603 4600 400 4200+500 646 35 15 20+10 714+723 120 20 100+15 968 14 2 12+4 1368 15 5 10+4 definition of f and b one can write, Cl-2 62 h = X — Cl - 3 £3 S Cl-2 ~ ^2 h X-Cl - 4 €4 *4 fB bB where the I's are the total intensities found from the singles spectrum. Now, i f the true coincidence results are normalized such that where transitions 1 and 2 are known to be in coincidence, then, i f for a general transition k Cl - k = I. , transitions 1 and k are in total coincidence. If 0 <Z C < I, then transition 1 and k are in partial 1-k k H coincidence. Knowledge of whether two transitions are directly, or in-directly, in coincidence is often useful in deducing the decay scheme of the isotope being studied. It should be noted that i f the levels have an appreciable probability of decaying by the electron conversion process, then these transitions must be taken into account in the feeding and branching ratios. The true coincidence data for the 603 and 646 KeV gates were normalized and compared to the singles data. The 1691 KeV transition was used to 77 normalize the 603 KeV gate data. The comparison of the singles and coincidence intensities is given in table IV-3. The 603 KeV transition was used to normalize the 646 KeV gata data; the comparisons are given in table IV-4. In these tables, a cyross (x) under the coincidence column means that that transition is judged to be in either total or partial coincidence. A question mark is used when there is some doubt about the correct assignment. The coincidence data for the 700-730 KeV gate were not analysed in the above manner as the three transitions in this gate make exact analys impossible. The transitions found to be in coincidence with this gate are the 602, 646, 714, 723, 968 and 1368 KeV transitions. Table IV-3 Transitions in coincidence with 603KeV transition Energy(KeV) Normalized Coin. Data 400 900 440 1000 525 1200 646 69300 709 14000 714 16000 723 105000 735 750 791 7500 968 11700 1045 14800 1086 500 1355 11600 1368 17600 1376 4000 1436 14000 1445 500 1489 3300 1526 4000 1580 2800 1622 2000 1691 5.04X105 Error Singles % Intensity 60 1300 60 1690 60 1300 13 74000 20 13600 20 23900 5 109700 80 1400 40 7500 20 20000 10 18900 80 300 7 11200 25 27100 75 5300 10 13600 100 3800 75 6900 70 4400 75 3200 75 300 5.04X105 Coincidence Total Partial x x X X X X X ? X X X X X X X X ? X ? X X ? X ? X X Table IV-3(cont.) 1720 300 80 935 ? ? 1918 320 80 520 ? ? 2039 800 60 660 x ? 2091 59500 15 57600 x 2108 440 80 550 ? ? Table IV-4 Transitions in coincidence with 646KeV transition Energy(KeV) Normalized Error Singles Coincidence Coin. Data °L Intensity Total Partial 603 106 106 x 709 15000 25 13600 x 791 8500 50 7500 x 976 1500 50 1000 x 1045 24000 35 18900 x 1445 4500 50 3800 x ' 1525 4000 60 4400 x 80 Chapter V Electron Spectra Using Si(Li) Detectors V-l Beta Spectra a) General Considerations The j9 ~ (electrons (-), positrons (+)) particles emitted in 41 the decay of a nucleus have an energy distribution given by N(W)+dW = pw(W0-W)2 F ( T Z,W) Sth(p,q). V-l N(W)_j_ = the number of ^  ^ particles emitted in the energy inter-val dW P = electron's momentum 2 W = electron's total energy = E + M QC W = energy difference between i n i t i a l and final nuclear states, o called the end-point energy + F(+"Z,W) = Fermi function; which corrects the & spectrum for the distortion due to the Coulomb interaction with the nucleus. St^(p>q) = Shape factor. In general, S is a function of the electron's (p) and associated neutrino's (q) momenta. The form of the function depends on the .angular momentum (J) and parity (TT ) changes, or the degree of forbiddenness, involved in the decay under consideration. 42 Theoretical shape factors have been calculated by Kotani and Ross. For instance, allowed spectra, with AJ=0,1; ATT= No, have 5^=1, while first-forbidden transitions ( AJ = 0,1,2; ATT= Yes) and second-forbidden transitions (.AJ=2,3; £>TT = No) have a shape factor of the approximate form, Sth = "^p 2 + q 2 + C' the values of 7\ and C varying with the atomic number of the daughter nucleus, and with the order of forbiddenness and total energy of the decay. A comparison of the experimental shape factor, given by S = N(W)dW V-3 pW(W0-W)zF to different theoretical values will define the forbiddenness of the transition, i f the experimental shape of the spectrum, N(W)dW, is known accurately enough. Both SgXp and St^ depend on WQ, which is not usually known beforehand. However, since WQ appears in both formulae in the form (WQ - W)2, a small error in WQ will not affect the comparison i f the com-parison is not extended too close to WQ. Once the shape factor is known, the function / N(W)dW^ I pWFS J can be plotted as a function of total energy. This plot, called a Kurie 41 plot, will be a straight line with energy intercept WQ. This value of WQ, i f different from the one used in the original calculation of S, can be used to re-calculate S, and a new WQ found from the energy intercept of a Kurie plot. This iterative procedure can be continued until a consistent estimate of W is found, o b) Beta Spectra taken with a Si(Li) detector The Si(Li) detectors used in this investigation have been described in detail elsewhere44 They are a 3 mm. planar detector with a .2 micron Si02 window and a 5 mm. planar detector with a 2 micron Au window. Both Si(Li) detectors were calibrated for the backscatter fraction, resolution, 82 and efficiency, as described below.. A beta spectrum taken with a silicon lithium-drifted detector Si(Li) will not have the shape given by equation V-l. Electrons that are scattered into, or out of, the detector and lose only part of their energy in the detector, will distort the spectrum. The distortion can be corrected for i f the spectra of mono-energetic electrons at different energies are taken, and the distribution of scattered electrons found. This distribution varies with the source-detector geometry, source thickness, source backing, etc. It is therefore impossible to measure this distribution using an electron.gun, magnetic spectrometer, or any other a r t i f i c i a l source for the mono-energetic electrons. The mono-energetic electrons used in this investigation were the 1 109 207 K-conversion electrons emitted in the decays of Cs, Cd and Bi. ry These sources were deposited on thin (170y/g/cm ) aluminum backings using the sublimation technique described in reference 44. This method of source preparation results in very l i t t l e scattering from the source backing or the source i t s e l f . (All electron sources used in this investigation were prepared in this way.) These sources also emit gamma rays and L, M,..." conversion electrons 137 along with the K-conversion electrons. Cs also has two 3^ groups associated with its decay (see figure V-l). An attempt was made to reduce the background due to these other transitions by only analysing those events in one Si(Li) detector that were in coincidence with the K-X-rays detected in the other Si(Li) detector. (See figure V-2 for the arrangement of the Si(Li)'s detectors. The electronics used for these coincidence measurements are shown in figure IV-1.) Unfortunately, the K-electrons 137 are not the only particles in coincidence with the K-X-rays. In Cs, (ZZZ j T7] Vacuum Liquid Nitrogen Vacuum | Source and Absorber Control Source Si(Li) Detector Absorber Absorber Vacuum X Si(Li) Detector Source Steel Vacuum Chamber Source and Absorber Arrangement O ro rr >xl n> H* O OO rt • o n < I O ro I fD i-i Ge(Li) Detector Chamber Arrangement for Si-Ge Coin. co 85 the beta transitions populating the 662 KeV level are also in coincidence. 109 207 In the two electron capture isotopes, Cd and Bi, the K-X-rays re-sulting from the electron capture decays, cannot, of course, be distinguished from the K-X-rays following the electron conversion process, and therefore some contribution to the background from the gamma transitions and the 207 L, M,.. . conversion processes, is to be expected. The Bi decay has an added complexity in that the X-rays resulting from a K-conversion process for one transition will be in coincidence with the gammas, etc., of the other transitions. 107 Figure V-3 is the coincidence spectrum for Cs. The flat region of the spectrum between the K-conversion peak for the 662 KeV transition and the start of the 0~ group with endpoint energy equal to 514 KeV was used to estimate the number of scattered electrons detected. Coincidence 109 907 spectra of Cd and Bi were also taken and the number of scattered electrons estimated from the flat portions of those spectra also. The "backscatter" fraction, defined by f(E) = Nb/ Nfc, where N is the number of scattered electrons detected and N the total -b t number detected, was estimated by extrapolating these flat regions to zero energy. The results were Isotope E(KeV) f(E) (3mm. det.) f(E) 109Cd 620 .454 - .561 137 Cs 624 .521 .634 207 Bi 482 .528 .621 207 Bi 972 .589 .690 2000 V Contribution of ,3" group with ED=514KeV K552^ o n v e r s :'- o n Electron Peak 1500 c J3 O to c1000\ o o |<- Region used to estimate-*] backscatter • • • • _ • „ • * 500 Extrapolation to 0 energy X l / 1 0 20 30 40 50 60 Chan. No. 70 80 90 100 87 The best straight line through these points was f(E) = .0015 x E(KeV) + .45 (3mm det.) V-4 f(E) = .0016 x E(KeV) + .54 (5mm det.) As well as the correction for scattered electrons, the spectrum must be corrected for the change in the resolution of the system as a function of energy. The efficiency of the detector, i f i t varies with energy, must also be taken into account. The relative efficiency for electrons that lose a l l their energy in the detector was calculated by measuring the intensities of conversion 152 electron transitions in Eu. These intensities were compared to those measured with a magnetic spectrometer by Malmsten et al.4"* (See table V-l.) The ratios of the intensities using the 3mm detector are plotted as a func-tion of energy in figure V-4. No variation of efficiency with energy is evident. This result was also found for the 5mm detector. The resolution of the system as a function of energy was also found 152 from the conversion peaks of Eu. The result was for 5mm det. D(E) (FWHM) = (7.9 + .0087 E(KeV))% The correction to a beta spectrum taken with the Si(Li) detector can now be calculated. The correction to be subtracted from the first N-l channels due to electrons scattering out of the energy region asso-ciated with the last (the Nt'1) channel i s4^ for 3mm det. D(E) (FWHM) = (7.2 + .0082 E(KeV))% V-5 AN = f(E N) ADNCc(N) V-6(a) AD N = D(EN) AE D(0)EN Table V - l 152 R e l a t i v e I n t e n s i t i e s of Conversion Electron from Eu Identity This Workup Ma1msten45(I2) Ij^ /12 +7, K-122 34500. +37, 1570. +47, 22.0+77, L-122 17100. +3% 725. +107, 23.6+137, K-244 1140. +37, 53. +47, 21.6+77, L-244 360. +37, 13.2+127, 27.2+157, K-344 1370. +3% 72. +77, 19.0+10% L-344 416. +37, 17.3+127, 24.0+157, K-411 78. +57, 3.5+107, 22.2+157, K-586 17.3+57, 1.1+207, 15.7+257, K-615 17.3+57, .8+107, 21.6+157, K-656 17. 4+57, .6+177, 29.0+227, K-675 3. 5+207. .2+257, 17.7+457, K-689 62.9+57, 2.6+107, 24.2+157, K-779 . 42.0+57, 1.9+107, 22.1+157, K-867 21. 5+57, 1.0+107, 21.5+157, K-964 69.5+57= 2.9+87, 24.0+137, K-1086 37.0+57, 1.7+177, 21.8+227, K-1112 38.2+57, 2.0+107, 19.1+157, K-1408 19.0+37, .8+127, 23.2+157, F i g . V-4 R e l a t i v e E f f i c i e n c y of the 3mm. S i ( L i ) Detector 89 o o o o o o o o o oo > CU U cu o o <r o o CN o m o cn CN CM >-< ( 2 I / T l ) OT3Fa 90 with D(E) obtained from equation V-5. CC(N) = C(N) = counts in channel N. E^ j is the energy corresponding to channel N. AE is the energy per channel of the spectrum. The correction to the first N-2 channels due to the counts in the th second to last, or (N-l) channel, is V l = f(EN-l> ^DN-1 Cc^" 1) V-6<b> l-f(E N_!) where C (N-l) = C(N-l) -The correction to the first N-j channels is V j = f<EN-J> ADN-j Cc(N-j) where Cc(N-j) = C(N-j) - j r ' Ak V-6(c) k=N-j+l The corrected spectra, given by the Cc's, should have the shape given by equation V-l. To check that this was so, a spectrum of the high energy 137 group in the decay of Cs was taken, the correction applied, and the shape factor and end-point energy calculated. The total and the' 137 corrected high energy spectrum of Cs is shown in figure V-5. 47 The theoretical shape factor for this /3 transition is = /\p2 + q2 with /\ = .03. The endpoint energy has been measured 40 to be 1174 KeV. A plot of (S£Xp - Stj1)/SeXp using these values is shown in figure V-6. If values of )\ = .02 or }l = .04 were used, the function (SeXp - Stn)/Sexp did not fluctuate about zero. A least square f i t of the data in the form pWFSth 0.1 0.05 Xi u cn i X 0- (U X CO <u. •.05 •.4 Average of every 5 channels plotted 110 140 170 200 Chan. No. 230 260 290 320 3* o o O 3* (D PT 09 fD 3 CD H OQ 00 n o c o t-h Co n CO vO to yielded an end-point energy of 1172 + 4 KeV, as shown in figure V-7. Since these experimental values are in excellent agreement with the accepted ones the correction technique described above was assumed to be valid. Since Si(Li) detectors are also sensitive to gamma radiation, mainly by the Compton process, the background due to gamma transitions will often interfere with the electron spectrum analyses. Much of this background can be removed by taking coincidence spectra of the electrons in coinci-dence with the gamma transition depopulating the level fed by the j8 decay These coincidence measurements can also be used to establish the decay scheme and to measure the individual j& spectra when there are two or more competing J$ transitions involved in the decay. Of course, background due to other gamma transitions also in coincidence with the gamma transition used as a gate will remain. An estimate of this remaining background can be obtained by inserting a thin absorber between the source and detector, and the coincidence spectrum re-taken. The absorber should be chosen, i f possible, such that a l l the electrons in coincidence with the gate are absorbed, while the gamma intensity is not appreciably affected. 152 The 0 decay of Eu was investigated using these coincidence tech-niques. A short summary of the procedure used and the results obtained is reported in Appendix C. c) Beta Spectra of 124Sb An attempt was made to analyse the f%~ transitions in the decay of 124 Sb in the manner described above. The gamma transitions chosen as gates were the 603, 645, 709 +714, 723, 1691 and 2091 KeV transitions. These are the most intense transitions in the decay, and are essentially the only gate possibilities. Only the coincidence spectra taken with the 10 c efl X. if 21 M10 c 3 o o 10 Total electron spectrum Spectrum in coincidence with the 603KeV gamma transition - "v»v-Scale: E(KeV)=3.53KeV/chan+391.KeV 120 240 Chan. No. 360 480 Pi I-1 ro o rt o 3 CO ft) o rf i-i T) Cu H-09 o • l-h < I-1 1 ro oo -P-CO cr vO 96 603, 1691 and 2091 KeV gates were good enough that shape factors and end-point energies could be c a l c u l a t e d . The jQ~ t r a n s i t i o n s found i n c o i n c i -dence with the 645, 709 +714 and 723 KeV gates were weak, and only approxi-mate end-point energies could be estimated. The 30cc Ge(Li) detector was used as the gamma-ray gate detector. The 3mm S i ( L i ) detector was used as the analog detector for ^ " s p e c t r a with end-point energies less than 1500 KeV. The 5mm S i ( L i ) detector was used f o r JQ spectra with end-point energies above 1500 KeV as the 3mm detector i s not th i c k enough to stop completely a l l electrons with energies 50 above 1500 KeV. 10/ Figure V-8 i s the t o t a l singles electron spectrum of Sb, along with the spectrum found i n coincidence with the 603 KeV gate. The coincidence spectrum was corrected using equations V-6 and the shape fa c t o r and end-point energy c a l c u l a t e d from the corrected data for the energy region 1500-2000 KeV. The r e s u l t s are shown i n figur e V - l l ( a ) Because of the s i m i l a r i t y of the two spectra shown i n fi g u r e V-8, i t i s immediately apparent that the /3" group feeding the l e v e l depopulated by the 603 KeV gamma t r a n s i t i o n i s the highest energy /S> t r a n s i t i o n at meas-urable i n t e n s i t y i n the Sb decay. I t i s also apparent that a l l the e l e c t r o n s , at l e a s t down to approximately 500 KeV, are i n coincidence with the 603 KeV gamma t r a n s i t o n . This f a c t implies that a l l the excited nuclear 124 states populated by the beta t r a n s i t i o n s from Sb, with end-point energies above 500 KeV, decay mainly v i a the 603 KeV t r a n s i t i o n . This i m p l i c a t i o n i s confirmed by the large number of gamma t r a n s i t i o n s found i n coincidence with the 603 KeV gate i n the gamma-gamma coincidence measurements. Figure V-9 shows the t o t a l coincidence spectrum and the coincidence spec-Fig. V-9 97 Total (electron+gamma) and gamma spectra in coincidence with the 169lKeV gamma transition o o o O O r - 1 S •uHBqo/S3unoo Electrons in coincidence with the 169lKeV gamma transition 600 500 400 300 200 100 Region used for Kurie plot o o vO vO i i 50 100 150 Chan. No. 200 Fig.V-ll(a) 99 v. S=l Is CO cs z a. • S=.9p2+q2-o i n 4,2 4.4 4.6 4.8 5.0 5.2 W(m0c2) 5.4 Fig. V-ll(b) rs Ico p. \ \ "S=l co o -H r--s CM O CM CM -s=i 1.2 1.4 1.6 1.8 2.0 2.2 W ( m o C 2 ) 2.4 100 2 trum taken with a 50 mg/cm absorber between the source and detector for the 1691 KeV gate. The difference between these two spectra is plotted in figure V-10. The spectrum of figure 10 was corrected for scattering, and the shape factor and end-point energy calculated. Similar spectra were obtained and analysed using the 2091 KeV gate. The results of these calculations are plotted in figure V-U(b). The results of the coincidence measurements are tabulated in table V-2 along with the approximate end-point energies found using the other gates. Approximate log ft values, which are the logarithms of the comparative halflives of the transitions,4 1 are also given in table V-2. The log ft values were calculated from the estimated relative intensities of the transitions. The relative intensities were estimated to be 20 %, 50 %, and 10 % for the ft transitions found in coincidence with the 603, 1691 and 2091 KeV gamma transitions respectively. The intensities of the transitions found in coincidence with the 645, 709 + 714 and 723 KeV gates were each estimated to be approximately 5 "L. V-2 Internal Conversion Electrons a) Internal Conversion Coefficients An excited state of a nucleus may lose its energy by transferring i t to a bound atomic electron, a process called internal conversion. The electron will then be emitted with energy E^ - Eg , where is the binding energy of the electron before emission. The energy transfer is by a direct interaction between the bound electron and the same multipole field which otherwise would have resulted in the emission of a gamma ray. The transition probability for internal conversion therefore contains the same nuclear wave functions as the transition probability for gamma emission?2 Table V-2 Beta Transitions from ^2^Sb Gate 603 646 709+714 End Point Energy(KeV) 2320+5 ~1600 Shape Factor .9p2+q2 ~1000 Forbiddeness ,st 1st or 2n d ,st 0nd 1 or 2 723 ~1600 ,st „nd 1 or 2 1691 634+15 Allowed 2091 240+40 Allowed 102 The internal conversion coefficients (I.C.C), defined by o( = We/W^  , where Wg and are the transition probabilities for internal conversion and gamma emission respectively, are almost independent of the nuclear wave functions. The ICC s then depend only on the energy difference between the i n i t i a l and final states, on the spin and parity change of the transition, and on the angular momentum, parity and binding energy of the electron being converted. Theoretical conversion coefficients have been 53 calculated by Sliv and Band for the K( otk), LT( o ^ ) , L T I ^ L ) A N D I j n ^ ^ L J I X ^ a i - o m ^ - c states. Similar calculations have been done by Rose.54 Once the intensities of the conversion electrons and gamma rays for a given transition have been measured, the experimental conversion coeffi-cients can be calculated. They are where Ij,, I ; L T > ' * " ' A N D *8 a r e t*i e n o r m al iz ed intensities for the K, Lj., ... , conversion electrons, and gamma rays, respectively. A compari-son of experimental ICC's to the theoretical ones for different spin and parity changes can be used to deduce the spin and parity changes of nuclear transitions. b) K-Conversion Electrons in Coincidence with K-X-rays 1 0 / The spectrum of Sb taken with a Si(Li) detector has a very large background due to transitions, Compton scattered gamma rays, etc. The conversion electron peaks, which are superimposed on this background, could not be identified except for those due to the transitions of 603, 646, 709, 714 and 723 KeV. This large background can be reduced by analysing only those events that are in coincidence with the K-X-rays. Of course, some of the 0" particles and gamma rays will be in coincidence with the K-X-rays, but the K-conversion electron intensities will be enhanced over 103 a l l others. The relationship between the K-conversion electrons in coincidence with the K-X-rays and the total K-conversion electrons can be found by con-sidering the decay scheme in which the transitions can take place by either the internal conversion or gamma process. Then if the gate detector is set on the K-X-ray peak,the rate of coincidences for K-conversion electrons from transition 1 will be NK-X = " v ^ X € K l F v ^>K n^ is the total rate the K- shell vacancies are produced (equal to the ' sum of a l l K- conversion electrons emitted). £ ^ and £. ^  are the total efficiencies for the K-X-rays in the gate detector and the K^  conversion electrons in the analog detector respectively. (j) is the K- fluorescent K yield"*"* which is the probability that a K- shell vacancy will result in the emission of a K-X-ray, rather than Auger electrons. F^ is the fraction of the K- shell vacancies that could result in a K-X-ray in coincidence with the K,- conversion electrons. For this simple decay scheme 104 IK1 XK, F v Xl + *2 h + h • • I T ^ f B nv 1 1 + * 1 + C* nv In these equations, the Ij,'s a^e the intensities of the K-conversion electrons, the I's are the total transition rates, and the o('s and the 2 3 Ckv's are the total and K-conversion coefficients. f_ and f„ are the K a n feeding ratios defined in chapter IV (equation IV-5). Similarly, the coincidence rate for the ^-conversion electrons is NK-X = \ with i K : o< o( 9 2 K-i i KA A 2 n v and the b's are also defined in chapter IV (equation IV-5). If the efficiency of the analog detector is independent of electron energy, the ratio of the coincidence rates is just NK-X „ \ Dl NK-X V* 1 2 and, i f the products o(^b^, cx^f^, etc., are small compared to unity the ratio is equal to the ratio of the true intensities, K, / ^ The same type of equations can be written for a general decay scheme, The D factors w i l l , in general, contain many more terms, but they will always be of the form D = 1 + <f- cK„ g. with the g.'s a l l less than one. For i K. l I 124 Sb, i t can be shown that x K i for a l l transitions, and therefore the relative intensities of the K-conversion peaks found in coincidence with the K-X-rays and the relative intensities of the total K-conversion peaks are essentially equal. 124 c) K-Conversion Electrons of Te 124 A spectrum of Sb taken in coincidence with the K-X-rays is shown in figure V-12(a+b), along with the total spectrum. The enhancement of the K-conversion peaks is immediately apparent. The 3mm Si(Li) detector was used as the analog detector and the 5mm Si(Li) detector as the gate de-tector. The electronics used were those shown in figure IV-1. 125 The peak identified as K-427 is due to a Sb contamination in the source material. This contamination was not noticed when the gamma spectra 124 were taken because the amount of Sb radiation was much greater than the 125 125 Sb radiation at that time ( Sb has a 2.7 year lifetime, compared to 60 days for 1 2 4Sb).4° The peak at 1386 KeV has not been identified. It may be due to Counts/Chan. u> o I o to o o 4> K-371 K-400 K-427( 1 2 5Sb) K-440 CE-603 •K-498 K-525 •K-603 •L-603(Random) K-646 K-709 K-735 K-765 K-791 K-968 •K-1045 901 qS 30 suoa^oaxa uoTsa9AUO0->i (B)ZT-A *STI 10 2 • 10 Total m CN CO rH I w inoo vO coco co r-lr-l r-l I I I CO r-r-l CO cr»c> vo COvO CM r-l I I w in i Wo ^ c o 102r c 3 O C_> 10 i n vO t-i i vO In coincidence with K-X-rays O CM I » ,.V< \~ 600 720 Chan. No, 840 960 o 108 K-conversion electrons from a transition of 1418 KeV that was not found in the gamma spectra, either because the gamma intensity was too weak or the transition was between two J=0 states, in which case there would be no gamma radiation. 12 A-The low energy region (60 - 600 KeV) of the Sb electron spectrum was re-taken four months after the spectrum in figure V-12. The coincidence spectrum is shown in figure V-13. The expected increase in the relative 125 amount of Sb contamination was calculated from the lifetimes of the two isotopes and found to agree with the increase in the relative intensity 125 of the K-427 peak. Other K-conversion electron peaks from the Sb con-tamination were identified using its known decay scheme. The relevant transitions are shown below. Fig. V-13 Low Energy K - C o n v e r s i o n E l e c t r o n s o f ^ - 2 4Sb . In C o i n c i d e n c e w i t h the K-X-rays 109 eo9->i-60T-1-601-sa-601^1-86S-3-ezz-ao 007-3-7S3-3 ... V. 9££-3 V A •j J . 651 -3 X ••V; 867~3 :\ 979 -ao rT87"3 \. 897-3 .4 Z97-3 :-v 777-3 vo in <t m CN o o o o o 'UT2tp/s:junoo 110 125 The reason that the L-109 conversion electron peak of Sb appears in the coincidence spectrum is that a portion of the gammas from the 35 KeV transition would also lie in the region of the gate set on the K-X-rays (K-X-ray energies of Te range from 27.2 - 31.8 KeV). The Compton edges (CE) and Compton backscatter (BS) peaks were identified by inserting an absorber between the source and detector and re-taking the coincidence spectrum. It should be noted that the efficiency of the 3mm detector for electrons decreases rapidly above 1500 KeV electron energy. The high energy (1400 - 2100 KeV) portion of the electron spectrum was re-taken using the 5mm detector as the analog detector and the 3mm detector as the gate. The efficiency of the 5mm detector should be constant up to approximately 50 2300 KeV. 1 0 / The intensities of the K-conversion p eaks of ^HSb were calculated from the coincidence spectra and their relative intensities given in table V-3. The results of a recent study, using a magnetic spectrometer, by GrcLgor'ev et al5*' is included for comparison. Table V-4 lists the experimental K-conversion coefficients, calculated using the gamma intensities listed in table III-4 and the electron intensities of table V-3. The 603 and 646 KeV transitions were used to normalize the electron intensities to the gamma intensities by assuming these transi-57 tions were pure E2.. The theoretical conversion coefficients for the different multi-polarities were taken from tables compiled by Sliv and Band53 Multi-polarities were assigned to the different transitions by comparing these coefficients to the experimental ones. Many of the transitions could not be unambiguously assigned because of the large uncertainty in the experi-Table V-3 Conversion Electrons of 124Sb Peak Intensity . This Work Gregor'ev5 Peak Intensity This Work Gregor'ev56 K-159 2.3(.2) K-765 .035(.02) .06(.02) K-254 .10(.08) K-791 ,44(.08) .44(.03) K-336 ..12(.08) K-968 .24(.08) •33(.03) K-371 .10(.08) K-1045 .18('.08) *25(.03) K-400 .45(.08) K-1325 .35(.l) .30(.03) K-444 .35(.15) K-1355 .17(.l) .20(.02) K-468 <.14 K-1368 .14(.05) .22(.03) K-481 <.07 K-1376 .035(.03) -K-525 .14(.08) K-1418 •25(.l) -K-603 100. 100. K-1437 .28(.l) .17(.03) K-646 5.4(.5) 6.6(.3) K-1489 .1401) .13(.02) K-709 1.4(.5) 1.2(.l) K-1526 .035(.03) <.04 K-714 1.6(.5), 1.6(.2) K-1657 .2(.l) -K-723 5.7(.5) 6.5(.3) K-1691 2.7(.4) 2.5(.2) K-735 .04(.02) K-2091 .24(.06) .2(.04) Table V-4 Conversion Coefficients 112 Transition Exper. Energy (KeV) o(KXl03 159 500+250 254 39+30 336 10+6 371 16+12 400 16+4 444 8+2 468 < 20 481 <16 498 18+14 525 4.8+3.5 603 4.2 646 3.5 709 4.7+2.0 714 3.1+2.0 723 2.4+.5 736 .9+. 7 765 15+12 791 2.6+.6 968 .53+.2 1045 .43+.2 1325 .9+. 3 1355 .67+.4 1368 .23+.2 1376 .3+. 3 1437 .92+.4 Theoretical oi^ El E2 Ml 51 300 178 10.3 55 45 6.5 24 23 5.0 17 17 4.1 14 15 3.1 10 11 2.8 8.6 9.8 2.6 7.8 9.2 2.4 7.2 8.3 2.O., 5.9 7.0 1.6 4.2 5.2 1.3 3.5 4.4 1.1 2.7 3.5 1.0 2.7 3.5 1.0 2.6 3.4 1.0 2.6 3.3 .90 2.3 2.9 .86 2.0 2.5 .57 1.4 1.7 .49 1.2 1.5 .31 .70 .84 .30 .67 .80 .3 .67 .80 .3 .66 .79 .27 .60 .72 M2 1210 Assumed Po M1,E2 220 M1,E2 90 El 66 Not M2 52 M1.E2 37 M1,E2 33 Not M2 30 Not M2 28 22 M1,E2 15 E2 13 E2 9.4 M1,E2 9.4 M1,E2 9.3 E2 9.2 El 7.8 6.6 M1,E2 4.3 El 3.4 El 1.9 M1,E2 1.8 M1.E2 1.8 El 1.8 El 1.6 Ml,E2 113 Table V-4(cont.) 1489 .9+.7 .26 .55 .66 1.5 Ml,E2 1526 .35+.3 .25 .52 .62 1.4 (El) 1657 - - EO 1691 .24+.08 .21 .42 .49 1.1 El 2091 .19+.08 .15 .28 .32 .66 El mental coefficients. A further complication at low energies arises because the theoretical Ml and E2 coefficients are almost identical. The different types of transitions (Ml, E2, etc.), along with the allowed changes in spin and parity for each type, are discussed in Appendix B. 115 Chapter VI 124 Results of the Sb Investigation VI-1 Decay Scheme of 124Sb -*124Te 1 0 / 1 0 / The decay scheme of Sb Te was constructed using the gamma-ray energies and intensities from the singles spectra (table III-4), the gamma-gamma coincidence results (tables IV-2,3 and 4), and the beta-gamma coincidence results (table V-2). In addition, the results of other inves-tigations provided useful evidence or confirmation in the assignments of a few levels and transitions. In particular use was made of the results of recent studies of the decay ^2 4I —»^24Te by Ragaini et a l7 2 and by LaGrange;73 of the reactions 123Sb(3He,d)124Te and 1 2 6Te(p,t)1 2 4Te by Auble and B a l l ,7 4 1 2 3Te(n, 5 )1 2 4Te by Bushnell et a l ,7 5 1 2 4Te(p,p1)1 2 4Te by Rao et a l? 6 and 124Te(d,d')124Te by Christensen et a l .7 7 1 0 / 1 0 / Figure VI(a) and (b) shows the decay scheme of Sb —»• Te deduced in this investigation. The values of the spin J , and parity T V , quoted for the levels are derived in section VI-3. Table VI-1 summarizes the evidence that supports the placing of the levels. Only seven of the twenty-two levels could not be unambiguously placed using the coincidence results alone. These levels were positioned by energy and intensities fits of the gamma transitions found in the decay and the results of the 124 I decay and reaction studies. Only the placement of levels at 1657, 2335 and 2484 KeV remain in some doubt. VI-2 Log ft Values The relative intensites of the beta transitions from the 3" ground state of ^24Sb to a l l the levels of ^ "24Te populated in this decay were calculated, along with their log ft values, from the gamma-ray intensities Fig. VI-l(a) 116 E(KeV) 2886. Decay Scheme of 124Sb -*124Te 2,3" -2+ f 1,2^ .3,4+ 2+d); 2,3,4+^ 2+^ 2,3,4+—: 2,3,4+-^ 1,2+^ 2+ -3+(2,4) " 2+(3,4) " 0+ 2+ 4+ Fig. VI-l(b) 117 <J- ro . . OS r-l vD . f Csl v£> CN! I—I 00 CO CO oo Csl CS| Jti <!• <f in . . . CO 00 o r-~ <f r-l Csl 4 OS oo oo CO Ov O csi vOO o VO VvC _I CM 00 • vo in co co r-i r-CO o o oo vO O r-4 O r -<t- CO 00 CM JL vO CO • •00 os av ro <f o-CM CSS in m CM E(Ke 2886 2775 2710 2701 2693 2681 2641 2521 2483 2454 2335 2323 2293 2225 2182 2091 2039 1957 V) .1 .2 .5 .6 .9 .0 .1 .4 .4 .4 .0 .1 .9 .2 .7 .5 .4 .7 1657.2 1325.7 1248.8 602.8 124 Te Decay Scheme of 124Sb -*124Te Table VI-1 118 Evidence for the levels of ^24Te populated in the ^24Sb decay Level This Investigation Others 124, (KeV) Coin. Energy- and l-l Inten. Fit *"""TI Reactions 602.8 x x x x x 1248.8 x x x x x 1325.7 x x x x x 1657.2 x x x 1957.7 x (x) x x x 2039.4 x (x) x - x x 2091.5 x x x x 2182.7 x x x 2225.2 x x x x 2293.9 x x x x x 2323.1 (x) x x x 2335.0 x (x) x 2454.4 x x x 2483.7 x x 2521.4 (x) x x x 2641.1 x x x x 2681.0 x x x x 2693.9 x x x x x 2701.6 x x x 2710.5 x x x 2775.2 x x x (x) 2886.1 x x (x) 119 given in table III-4. They are listed in table VT-2. Included for comparison are beta intensities calculated from the beta-gamma coinci-72 dence measurements. The log ft values found by Ragaini et al for the 1 0 / decay from the 2 ground state of I are also listed. The allowed values of J and TT of the levels that are consistent with these log ft values are listed in column 6. The log ft values listed in table VT-2 are about 3 larger than the usual log ft values quoted for different degrees of forbiddenness. That is 41 Usual From log ft 124sb Allowed 0,1 No 3-6 6-9 1st forbidden 0,1,2 Yes 6-10 9 2nd forbidden 2,3 No 10 ? 12 A* The fact that the Sb beta transitions are hindered by about a 1 0 / factor of 1000 and the I beta transitions by about a factor of 100 can possibly be explained by considering the single particle configur-78 ations of the i n i t i a l and final nuclei. 10/ Sb has one proton and 23 neutrons outside the doubly closed shell of 50 protons and 50 neutrons. These "extra core" nucleons couple together to give a ground state value of 3 . The simplest shell model description of this configuration is the coupling of a 5^/2 Pr o t o n t o a n unpaired hn/2 neutron produces a 3" state, and the other 22 neutrons couple to form a 0+core. ^24T ^as 3 p r ot 0ns and 21 neutrons outside the doubly closed shell. These extra core nucleons couple to produce a 2 ground state. In this case a %-j j2 unpaired proton couples to a hn/2 unpaired neutron to give a 2 state and the other 2 protons and 20 neutrons form a 0+ core. The ground state Table VI-2 ; 120 Log ft values and most likely J assignments for levels in 1 2 4Te jevel Beta feed from 124Sb Log ft (KeV) 0 7o from X in ten. 0 from /£>' inten. 0 124Sb 124-r 8.1 0+ 602.8 22.6 20 10.1 7.6 1,2,3,4+ 1248.8 2.5 5 9.4 9.8 1,2,3,4+ 1325.7 3.6 5 9.5 7.8 1,2,3,4+ 1657.2 .01 - 12.3 9.4 0+ 1957.7 2039.4 1.7 4.2 5 9.7 9.2 9.7 9.6 1,2,3,4+ 1,2,3,4+ 2091.5 .7 9.8 8.9 1,2,3,4+ 2182.7 .2 10.3 - 1,2,3,4+ 2225.2 .1 10.5 8.8 1,2,3,4+ 2293.9 54.0 50 7.7 6.9 2,3" 2323.1 .06 10.5 8.6 1,2,3,4+ 2335.0 .04 10.6 10* 1,2,3,4+ 2454.4 .001 9-11 8.2 1,2,3,4+ 2483.7 .3 9.5 8.8 1,2,3,4+ 2521.4 .03 10,3 8.3 1,2,3,4+ 2641.1 .1 9.3 7.9 1,2,3,4+ 2681.0 1.0 8.2 7.8 1,2,3,4+ 2693.9 9.0 10 7.2 7.4 2,3" 2701.6 .6 8.4 7.1 * 2710.5 .08 9.3 - 4+ 2775.2 .5 7.8 - 4" 2886.1 .007 7.4 6.7 2,3" *See discussion in Section VI-3 12 A particle configuration of Te has no unpaired protons or neutrons and its 0+ ground state particle configuration consists of 2 g^ protons and 8 S7/2' ^  ^ 5/2' a n <^ 8 n i l / 2 n e u t r o n s • 1 9 / A beta transition from Sb to the ground state particle config-124 n uration of Te requires that an r.=5 ( n i i/2^ neutron decays to an =^4 ( g ? p r o t o n and and I =3 (d5/2^ Pr o t o n change to an ^.=4 (g7/2) proton. Both of these transitions are called ^.-hindered and can 79 produced hindrance factors as large as 1000. On the other hand, a 124 beta transition from I to the ground state particle configuration of 12 A-Te only requires that an / =4 (Sy^) proton decay to an /.=5 (h-j^ /2^ neutron and these transitions will not be hindered as much as the Sb beta transitions. VT-3 Spin and Parity Assignments The allowed spin and parity (J^) of the levels populated in the 124 Sb decay were deduced from the gamma transition intensities, conver-sion coefficients (table V-4), log ft values, and the results of refer-ences 72 to 77. The justification for each assignment is explained below. The identifying abbreviations T(E) for an EL or ML transition of energy E, and L ( E ) ^ for a level with spin J and parity TT at excitation energy E are used in this discussion. The levels are also discussed in terms of the simple vibrational model. The relative reduced branching ratios from the positive parity levels, and the relative transition probabilities from the negative parity levels, used in this section are derived in section VI-4 and are listed in tables VI-3 and VI-4 respectively. 122 602.8 KeV Level = 2+ This level is a well established 2+ collective state.74>76>77 j t ^ s interpreted to be the one quadrupole phonon state. 1248.8 KeV Level = 4 + The E2 transition [T(646)E2] to the 2+ 603 KeV level [L(603)2+] limits J~* to 0+, 1+, 2+, 3+ or 4 +. The log ft=9.4 forbids the 0+ assignment. Since there is no transition to ground the 1+ and 2+ 80 •+-assignments are ruled out. (of, erf') measurements give a 4 assign-ment and a large reduced transition rate. This level is therefore inter-preted to be the 4 + member of the 0+, 2 +, 4* two quadrupole phonon triplet. 1325.7 KeV Level Jn = 2 + The T(723)E2 and T(1325)E2 to L(603)2+ and L(0)0 + respectively restrict J^5 to 1+, 2+. ( o( , c< ' ) experiments^ require the 2+ assignment. This level is interpreted as the 2+ member of the two quadrupole phonon triplet as i t decays preferentially to the one quadru-pole phonon (603 KeV) state. That i s , from table VI-3 B(E2; 2+ 2+) = 138 B(E2; 2+ 0+) 2 0 where J refers to a j " ^ state with j phonons. The single particle j value for this ratio is close to one, while the simple vibrational model forbids transitions that change the phonon number by more than one. 1657.2 KeV Level = 0+ 2+ The evidence for this level is the weak T(1054) to L(603) , E0 0+ T(1657) to L(0) , and the results of the reaction measurements of 75 74 Bushnell and Auble and Ball. Assuming that these transitions are 123 not misplaced, then the only J assignment consistent with these transitions and the log ft value is 0"*". 124 The log ft =12.3 for the Sb decay to this state was calculated by assuming that there were no weak gamma transitions populating this level that were not observed. We interpret this level to be the 0+ member of the two quadrupole phonon triplet, although i t could be the 0**" member of the three quadru-pole phonon states. The two phonon assignment is more likely i f the splitting of these two phonon states is the result of the coupling of the two extra core protons to the coherent vibrations of the 22 extra core neutrons, as is assumed by Lopac (see section II-4). 1957.7 KeV Level j"" = 2+(3+, 4+) The T(1355)M1'E2 to L(603)2+, T(709)Ml'E2 to L(1248)4+, and T(735)E1 from L(2693)3 restrict j " ^ to 2+, 3+, or 4+. The weak + + T(1957) to L(0) would rule out a l l but the 2 assignment i f this transi-tion has not been misplaced. This level is assumed to be a three qudrupole phonon state as i t decays preferentially to the two phonon states (see table VI-3). The reduced branching ratio to the two phonon states is J 2 The simple vibration model reduced transition rates from the three to two quadrupole phonon states (see A ppendix B, table 1). B(E2;J* 2j) .16 B(E2;2+ l\ 4/7 K2 .55 B(E2;2j 4j) 36/35 K^  B(E2;3+ ^ 2+ 15/7 K2, B(E2;3+ 4+ 6/7 K2 B(E2;4+ 2+ 11/7 K2 2.5 1.1 B(E2;4+ -» 4+ 10/7 K2 The best description of the 1957 KeV level in terms of the simple vibra-tional model is that i t is the 2+ member of the 0+, 2+, 3+, 4+ and 6+ three quadrupole phonon states. 2039.4 KeV Level J-" = 3+ (2"1", 4+) The Ml or E2 transitions, T(1436), T(790) and T(714), to L(603) , L(1248)4+ and L(1325)2+ restrict J1 1 to 2+, 3+, or 4+. A weak transi-tion to ground cannot be ruled out as, although the 2039 KeV transi-tion was found in coincidence with the 603 KeV transition, the error in the intensity was large. 2+ The experimental relative reduced branching ratios to L(603) , L(1248)4+ and L(1325)2+ are 1:10.9:57.8. (See table VI-3.) The 2039 level is therefore assumed to be a three quadrupole phonon state. The best spin assignment from the viewpoint of simple vibrational model is 3+ as indicated by the reduced branching ratios to the two phonon states. That is Experimental Theory A - 2 + J t = 3 + J t -3 3 3 - 57.8 = 5.3 .55 2.5 1.1 10.9 2091.5 KeV Level J1 1 = 2+(l+) The T(1489)M1'E2 to L(603)2+ restricts J to 0+, 1+, 2+, 3+, or 4+. The log ft of 9.2 from the 3" 124Sb ground state rules out 0+. 125 The (n, & ) results of Bushnell75 gives = 0+, 1"**, 2*. A weak transition to ground from this level cannot be ruled out as i t would be masked by the intense T(2091) from L(2693). The radically different nature of this state compared to the three phonon states at 1957 and 2039 KeV is apparent from the relative re-duced branching ratios from these three states as shown in table VI-3. As this level does not preferentially decay to the two phonon states i t is assumed to be a two particle state. It could possibly be the 2 (Sy^^ proton state, where the two protons have total spin 2, rather than 0, as is the case for the ground state. 2182.7 KeV Level J1* = 1+, 2+ The T(2182) to L(0)0 + limits to 1* 2+ 3" (E3 transitions 124 cannot be excluded). The log ft = 10.5 for the decay from the Sb ground state indicates that the parity is positive. This limits + + the choice to 1 or 2 . A comparison of the reduced branching ratios from this level (see table VI-3) reveals its collective nature. Since the transitions to the two phonon states are enhanced over those to the one phonon and ground states, this level is probably mainly a three, or possibly a four quadrupole phonon state. 2225.1 KeV Level = 2 +, 3 +, 4+ The T(1622) to L(603)2+, and T(976) to L(1248)4+ implies that 2£ J£ 4. The log ft value of 10.5 requires a positive parity assign-ment to this level. The T(468), which is not M2 (from its conversion 3-coefficient), from the well established L(2693) is consistent with the J = 2 , 3 , or 4 assignment. This level is another multi quadrupole phonon state as i t decays preferentially to the two phonon states. That i s , the relative reduced 2 + /+ 2+ branching ratios to the L(603) , L(1248)^ and L(1325) are 1:42:7. It could be the 4"*" member of the three quadrupole phonon quintet. 2293.9 KeV Level = 3~ The T(1691)E1, T(1045)E1, and T(968)E1 to the L(603)2+, L(1248)4+ 2+ TT and L(1325) respectively uniquely determine J to be 3-. This assignment is consistent with the log ft values and reaction studies. This level is taken to be the one octupole phonon state. The E3 reason for this assumption is that the T(2293) is enhanced over the El T(1691) , compared to the single particle estimates, by a factor of 4 3.5 x 10 . [Table VI-4 lists the relative (not reduced) branching 124 ratios of a l l the negative parity states populated in the Sb decay in terms of single particle units normalized to the value one for transitions to the 603 KeV level.] 2323.1 KeV Level J1* = 2+ 0+ 124 T(2323) to L(0) and the log ft for the Sb decay of 10.5 set Tt + + practical limits to J of 1 and 2 . The T(371), which is not M2, 3-from the L(2693) requires that T(371) is E l , as Ml or E2 transitions require A"U = +1. Therefore J -4- 1 and the 2 assignment is the only remaining choice. It would seem likely, on the basis of the reduced branching ratios, that this level is a multi-quadrupole phonon state. 2335.0 KeV Level J = 2+, 3+, 4+ This level is placed by T(1086) and T(1732) to the L(1248)4+ and 2+ 72 L(603) , respectively. Ragaini, Walters and Meyer find T(1086) in 124 the I decay but place i t between a supposed level at 2412 KeV and 36 124 L(1325), as do Meyer, Walters and Ragaini in their study of the Sb 7 6 decay. A level at 2.335 MeV is found in (p,p') scattering by Rao, and - 74 a level at 2.34 MeV in the (JHe,d) reaction by Auble and Ball. There is no evidence for a level at 2412 KeV in either of these experiments, or in the (n, cf ) reaction studied by Bushnell.75 The possible J * ^ values are restricted to TV = + from the log ft values and J=2,3 or 4 from T(1086) to L(1248)4+ and T(1732) to L(603)2+. The relative reduced branching ratios (see table VI-3) indicate that L(2335) is a multi quadrupole phonon state because of its prefer-ential decay to two phonon states over the one phonon state. 2454.4 KeV Level = 2+ (1+) 0+ The T(2454) to L(0) and log ft = 10.6 are consistent with a •n + + 3 74 J assignment of 1 or 2 . The ( He,d) reaction populates a level + + + at 2.45 MeV with J = 2 or 6 . If these levels are the same the 1 assignment is ruled out. No comment can be made about the nature of this level as weak transitions to the one and two quadrupole phonon states might exist but they were not found in this investigation. An upper limit on the intensities of these transitions of 50 (on the normalized scale of table II-4) would make the reduced branching ratios to the one and two phonon states greater than the reduced branching ratio to ground. 2483.7 KeV Level j"*7 = 2+, 3+, 4+ M l F2 Ml E2 The T(525) ' and T(444) ' to the positive parity L(1957) and L(2039) respectively, together with the log ft of 9.5 and 8.8 for the ^24Sb and ^2 4I beta decays limit the JU possibilities to 1*", 2+, 3 , or 4 . This level decays only to the three qudrupole phonon states at 1957 128 and 2039 KeV. A possible explanation is that this level is an almost pure four quadrupole phonon state. Since there is no 1+ four phonon state the value is 2+, 3+, or 4+. 2521.4 KeV Level J1 1 = 1+, 2+ The log ft values of 10.3 and 8.3 for the 124Sb and 1 2 4I beta decay limit J1 1 to 1+, 2 +, 3 + or 4+. The (n,* ) reactions 7 5 populates a level at 2522.7 with = 0+, 1+ or 2+. Assuming that these are the same levels, the assignment 1+ or 2+ would be correct. 2+ The nature of this level will be discussed along with the L(2681) 2641.1 KeV Level 3~^ = 3+, 4 + (1 +, 2+) The position of this level is determined by the coincidence found between T(2039) and T(603). The log ft values limit j"" to 1+, 2+, 3+ + 0+ , + or 4 . As no transition to L(0) was observed the 1 or 2 assignments seem unlikely, although they cannot be ruled out i f this is a collective state that decays preferentially to the 2* one quadrupole phonon state. Transitions to the two quadrupole phonon states were not found but they could easily exist and be masked by large background in that energy region of the singles gamma spectrum (figure III-7). 2681.0 KeV Level J1 1 = 2+ The T(2681) to L(0)0 + and T(159)Ml'E2 to L(2521)J+, along with a log ft.value of 8.2 for the 124Sb beta decay require that is 1+ or 2+. The (n, t ) reaction 7 5 populates a level at 2681.1 KeV with J* = 0 + or 2 . The 2 assignment is therefore assumed. Transitions from this level to L(2182) and L(2521) were found, which suggests some coupling between these levels that does not exist for other levels in this energy region. The relative E2 reduced branching ratios to the L(0)0 +, L(2182)( 4 ) + and L(2521)2+ are l:4.5xl04 : 1.4xl07. 129 T(159) may have a large Ml component which would make the reduced branching ratio of that transition smaller than 1.4 x 107. However, this transition would s t i l l be enhanced over the T(2681) to L(0)0 +. It is possible that this level is a mixture of collective and particle excitations, with the collective motion similar to that of L(2182) and the particle configuration similar to that of 1,(2521). 2693.9 KeV Level = 3" 0+ Kl 2+ The T(2693) to L(0) , the T(2091) to L(603) , and the log ft = 7.2 require that this level is 3". In table VI-4, we see that the enhancement of the E3 transition 2+ to ground over the El transition to the one quadrupole state, L(603) , 4 A is 2.0 x 10 . This value is close to the enhancement of 3.6x10 found 3-for the E3 transition from L(2293) , the one octupole phonon state. E2 The T(400) that connects these two 3" states is enhanced over the El 6 T(2091) by a factor of 1.1 x 10 . The two enhanced transitions, E3 E2 T(2693) and T(400) , are the only ones allowed by the simple vibra-3-tional model i f L(2693) is the 3" member of the one quadrupole-one octupole phonon quintet (1", 2", 3", 4", 5 ). We therefore assume that 3-L(2693) has this character. 2701.6 KeV Level J71" = 2", 3" The T(1376)E1 to L(1325)2+ restricts J7 7 to l " , 2", or 3". The i o / log ft of 8.4 for the Sb decay to this level eliminates the 1" assignment. This level decays preferentially to the two quadrupole phonon states rather than the one quadrupole phonon state as is shown by the data in El 9+ v\ table VI-4. The enhancement of the T(1376) to L(1325)^ over T(2098)tJ-2+ to L(603) suggests that L(2071) is possibly a two quadrupole-one 130 octupole state. 2710.5 KeV Level J1T= 4+ The T(2107) and T(1384) to L(603)2+ and L(1325)2+, along with the log ft of 9.3 for the 124Sb decay restrict J1* to 1+, 2+, 3+, or 4+. A level at 2.71 MeV with J77" = 3+ or 4+is found in the (3He,d) reaction.7 4 The 4"*" assignment is assumed as this level is not populated by the - 124 beta decay from the 2 I ground state. The T(1384) to the two phonon L(1325)2+ is slightly favored over 2+ the T(2107) to the one phonon L(603) as shown in table VI-3. The 4+ possibility of a weak transition to L(1248) can not be excluded since a relatively large background peak occurs at this energy (1462 KeV). There is not enough information to attempt to interpret the character of this state. 2886.3 KeV Level j"71" = 2", 3" The log ft of 7.4 for the 124Sb decay and 6.7 for the 1 2 4I decay exclude a l l jn values except 2", 3 . The only transition found from 124 this level in the Sb beta decay is the T(2283). Transitions to 124 the two phonon levels from this level are found in the I decay where the relative number of beta transitions to L(2886) is greater than in 124 the Sb decay. 124 124 VI-4 Summary of the Levels Populated in the Sb -» Te Decay a) Positive Parity Levels The relative reduced branching ratios of a l l the positive 124 parity states populated in the Sb decay were calculated from the measured transition intensities by assuming that the transitions to other positive parity levels were pure E2. The only other transition multi-polarity that is expected to be of any importance is Ml (see Appendix B). 131 Ml transitions are not allowed by the vibrational model, but may result from vibrational states mixing with particle states for high energy * 81 levels. Because the reduced branching ratios have energy dependence 2L+1 E , any Ml component is expected to be small except for low energy . . 82 transitions. The relative reduced branching ratios were calculated using formula B-5, i.e. R' 1 = E2 II El 12 and the R's normalized to the transition to the 603 KeV level whenever i t existed. The energies and intensities of the transitions were taken from table III-4. Table VI-3 lists the results of these calculations, which are shown schematically in figure VI-2. The broad lines in figure VI-2 represent transitions whose reduced branching ratios are greater than 107, of the total for that level. These broad lines do not necessarily correspond to intense transitions. The dominant feature of this "reduced branching ratio decay scheme" is that most levels do not decay with approximately equal probability by a l l transitions that are allowed by spin and parity selection rules. These levels decay preferentially by lower energy transitions, supposedly to levels that differ by the fewest number of quadrupole phonons. The best examples of this feature are the enhanced transitions from the levels at 1325 KeV, 1957, 2039, and 2225 KeV and 2483 KeV, which are 132 Table VI-3 E2 Relative Reduced Branching Ratios From To Reduced Phonon Assignment Level Level Branching of (KeV) (KeV) Ratio Initial State 603(2+) 0(0)+ 1 one quadrupole phonon 1248(4+) 603(2+) 1 two quadrupole phonons 1325(2+) 0(0+) 1 two quadrupole phonons 603(2+) 138 1657(0+) 603(2+) 1 two quadrupole phonons 1957(2+) 0(0+) 6.3xl0"4 three quadrupole phonons 603(2+) 1 1248(4+) 30.0 1325(2+) 4.7 2039(3+) 0(0+) * three quadrupole phonons 603(2+) 1 1248(4+) 10.9 1325(2+) 57.8 2091(2+) 0(0+) * (no phonons) 603(2+) 1 1248(4+) <- 2 1325(2+) .4 2182(1+,2+) 0(0+) .053 three quadrupole phonons and particle 603(2+) 1 1325(2+) 3.1 2225(2,3,4+) 603(2+) 1 three quadrupole phonons 1248(4+) 42.3 -133 Table VI-3 (Cont.) 1325(2+) 6.3 2323(2+) 0(0+) 603(2+) 1248(4+) 1325(2+) 2.3xl0-4 1 <.5 <.5 four quadrupole phonons and particles 2335(2+,3+,4+) 603(2+) 1248(4+) 1325(2+) 1 31 <5 multi-quadrupole phonons 2454(2+) 0(0+) 1 particle state 2483(2+,3+,4+) 1957(2+) 2039(3+) 1 3.0 four quadrupole phonons 2521(l+,2+) 603(2+) 1 1 2641(3+,4+) 603 (2+) 1 1 2681(2+) 0(0+) 603(2+) 2 82(1+,2+) 2521(l+,2+,3+, 4+) 1 * 4.5x104 ' 1.4xl07 multi-quadrupole phonons and particles 2710(4+) 603(2+) 1248(4+) 1325(2+) 1 <2 4.6 multi-quadrupole phonons < * See discussion rTT 2+ ? 3,4+ 2+ ? 4 0 2,3,4 2+ >3 2,3,4+->3 2+ -3 4+ -4 2+ -0 2+ ~ 3 3+ _ 3 2+ -2 0+ _ 2 2 2+ 0+ - T T " T Energy(KeV) 2710 2681 2641 2521 2483 2454 2335 2323 2225 2182 2091 2039 1957 1657 1325 1248 603 w N> Fd fD h-1 P rt . < f» 00 • fD &. < c H n 1 fD ro Q. w f-i p 0 o a 30 * l P rt H» o CO 135 identified as 2, 3, and 4 quadrupole phonon states respectively. These transitions a l l have An2=l a n d a r e therefore allowed by the simple vibrational model described in Appendix A. They are labelled with an A (for allowed) in figure VI-2. Other levels that are assumed to be mainly multi-quadrupole v i -brational states of the ground state particle configeration are the 2182, 2323, 2335, and 2710 KeV levels. The selection rule, / A I I ^ I , is not expected to be obeyed as well for transitions from these levels as i t is for the lower phonon number levels because anharmonic terms are 5,6 expected to be important. One should also expect mixing of the ground state particle configuration with excited particle state configurations at these energies, and this would induce transitions between levels that differ by more than one quadrupole phonon.14 Levels that are not assumed to be quadrupole vibrations of the ground state particle configuration are the 2091, 2454, 2641, and 2681 KeV levels. These levels are assumed to be excited particle or "particle-hole" configurations. The 2681 KeV level is interesting in that i t decays preferentially to the 2521 KeV level. It may be that i t is a quadrupole phonon state of the 2521 KeV particle configuration, although there is no theoretical justification for this statement. b) Negative Parity Levels The intensities of transitions from the negative parity levels found in this investigation have been compared to the single particle estimates given in reference 83 by assuming that the transi-tions have the lowest allowed electric multipolarities. The transition intensities from each level were normalized so that the ratio of the experimental value to the single particle estimate for the transition 136 Table VI-4 Relative Rates of Transitions from Negative Parity States Compared Particle Estimates Level Transition To Multipolarity Level Ratio 2293(3") E3 0(0+) 3.5xl04 El 603(2+) 1 El 1248(4+) .16 El 1325(2+) .21 El 1957(2+) .14 El 2039(3+) .07 2693(3") E3 0(0+) 2.0xl04 El 603(2+) 1 El 1248(4+) .15 El 1325(2 ) 1.7 El 1957(2+) .56 El 2225(2+,3+,4+) .46 E2 2293(3") l.lxlO6 El 2323(2+) .90 2701(2",3") El 603(2+) 1 El 1325(2+) 37 El 2039(3+) 9-5 2775(4") E3 603(2+) 1 El 1248(4+) 4.8x10" E3 1957(2+) 5.6xl06 2886(2',3") El 603(2+) 1 Fig. VT-3 Enhancement Factors for Transitions from Negative Parity States > 00 u co c w vO m r - l CO CO CO m Ov r- i n oo oo r-. O CTv CM CTv CM CO i n CM <J- co oo r - r - vO CO CM CM O CTv CO CM o CM CM CM CM CM CM CM CM 1-1 r H vO iV cn CM CO CM w co w w co + •+_+ + N m s t co CM CM <t + CM CO O r-l O O O o o CM n CM CM co A O CO CO CO CM CM 138 to the 603 KeV level was unity. The enhancement factor for the other transitions from a given level over the transition to the 603 KeV level is then compared to the single particle estimate E H = WBW x N603 I(ELB;EB) sp The T(E]j) e Xp a r e the transition intensities listed in table III-4, I(EL ;EB) are the single particle estimates for EL transitions of B f B energy E„, and N is the normalizing factor. These enhancement a bUJ factors are listed in table VI-4 and are displayed schematically in figure VI-3. The broad lines connecting levels in figure VI-3 represent transi-tions that are enhanced over the single particle estimates by at least a factor of 100. The semi-broad lines represent transitions that are enhanced by factors of 10 to 100. Transitions allowed by the simple vibrational model with the phonon numbers given in the figure,, are labelled A; i.e., / \ ^ 2 = ^ - £21 An-^1. Transitions that are allowed when coupling between the quadrupole and octupole vibrations are taken into account, as described in Chapter II, are labelled A1. The selection rules in this case as 6.^ = 1 and/or Atig=l. The 3" level at 2293 is assumed to be the one-octupole vibrational state. The next 3" level, at 2693, is assumed to be the 3" member of the one quadrupole-one octupole states. The E3 transition to ground from this level is not allowed in the simple vibrational model without coupling but is allowed in the coupling model. It also has an enhanced E2 transition to the one-octupole state, which is allowed by the simple model. The level at 2701 is assumed to be a two quadrupole-one octupole 139 state. The only evidence to support this assignment is its negative parity and slightly enhanced transition rates to the 2+ quadrupole phonon state at 1325 KeV and the 3" quadrupole phonon state at 2039 KeV. The 4" level at 2775 is also assumed to be a two quadrupole-one octupole state as the supposed E3 transitions to the 1 quadrupole level at 603 KeV and the three quadrupole level at 1957 are greatly enhanced. The level at 2886 KeV may be a one quadrupole-one octupole state. It may also be a negative parity particle configuration. VT-5 Comparison to the Semi-Microscopic Model Figure VI-4 gives the comparison of the energies of the low energy positive parity states found in this investigation to those derived by Lopac using the semi-microscopic theory, as explained in section II-4. + 124 The 6 experimental level was not found in the Sb decay but has been identified in (o( , o\') scattering8^ and (o(,2n) reactions.**4 -It is also possible to compare some reducing branching ratios to those calculated by Lopac. These are given in table VI-5. The experi-mental ratios were calculated from the ratios given in table VI-3. The theoretical ratios were calculated from the reduced transition proba-bil i t i e s given in table 4 of reference 14. These ratios are a l l infinite in the simple vibrational model theory. It appears, from the energy levels of figure VI-4, and also from the reduced branching ratios in table VI-5, that this semi-microscopic theory gets progressively less accurate as the number of quadrupole phonons is increased. This trend is to be expected as Lopac has assumed that the excitations of the 22 extra-core neutrons can be ade-140 Fig. VI-4 Comparison of experimental results to the semi-microscopic theory Theory Experimental n 2 J7 7 E(KeV) E(KeV) n 3 2+ 2600 3 4+ 2172 3 3+ 2020 0 4+ 1990 0 2+ 1828 0 6+ 1798' 2 0+ 1719 2 2225 4+ 3 0 2091 2+ 2039 3+ 3 1957 2+ 3 X1747 6+ 0 """• : 1657 0+ 2 2+ 1360 1234 1325 1248 2+ 2 2 1 2+ 547 0 0 ^ 0 603 2+ 1 0 0+ 0 Table VI-5 Initial State(Kev) 1325(n2=2) 2039(n2=3) 2225(n2=3> 2091(n2=0) Final Ratios States(Kev) Experiment Theory 603(n2 = l) 22~*21 0(n2=Q) 3 3 - ^ 2 i 138 290 1325 (n2=2) 33 ^22 603(n2=l) 59.8 800 1325 (n2=2) 43~-*22 603(n2=l) 3^ 1 + - 2 t 6.3 00 603(n2=l) 2Q 1325 (n2=2) 1_ 2-5 —2+ 0 2 141 quately described by simple harmonic quadrupole vibrations involving only the quadrupole states up to n2=3. The interaction Hamiltonian he used coupled states that differ by one quadrupole phonon. Since he was only trying to reproduce the splitting of the n2=2 (two quadrupole phonon) states, this assumption is valid. However, to reproduce the splitting of the three quadrupole phonon states, and to calculate their transition rates, one must include, at the very least, the four quadrupole phonon states. VI-6 Conclusions 124 124 The levels populated in the beta decay of Sb to Te have a l l been assigned parity values on the basis of log ft values, conversion coefficients, and decay scheme considerations. In addition, many of the levels have been assigned definite spin values, and, for those that could not be assigned unambiguously,the choice has been narrowed to, at most, three different values. 124 The excited states of Te populated in this decay have been discussed in terms of the vibrational model, which, as shown in sections VI-3 and VI-4, is adequate in describing the general features of this nucleus in a semiquantitative way. Quadrupole and octupole phonon 124 numbers have been assigned to many of the excited states of Te. Some of the assignments are fairly speculative. However, in spite of the fact that current theory for spherical "vibrational" nuclei such as 19/ Sb is not by any means in such satisfactory shape as that for deformed "rotational" nuclei, i t is possible to use i t , as has been done in this thesis, to recognize and categorize, with some reasonable assurance, the types of excitations that exist. It is to be hoped that in the near future, improvements in theory will lead to our further understanding of these interesting nuclei. 143 A-l Appendix A Phonon Number Representation for Vibrational States A-l Creation and Destruction Operators Introduce the operators aW = A ^ + i B T T^ and require that ^ - 5 A"2 In these equations, and I T ^ ^ are the generalized coordinates 5 8 and conjugate momenta, respectively, that describe the motion of the nuclear surface R,where ( H £ £ ^Xj-O'tV A-3 R = Ro „ n-^^ is the number of 2^-pole phonons with orientation M that are des-cribed by the state function 3r . The number of 2' -pole phonons is = £ _ A-4 that i s , < £ . « > ~ a"X~3E = A-5 With the proper choice of A and B in e^qation A-l, a will destroy and a"^ will create a r\ yU. type phonon when operating on A-2 Energy Levels By substituting equations A-l into equation A-5 one gets 58 £ _ [ A 2 U , J 2 + B 2lTT^| 2.+ iAB( c ^ - T ^ - T W o t ^ -A-6 Now, using the relationships (given in chapter II) <-tf*^ \ ^ t - O ^ T T ^ A-7 and the ccmimutation relationship equation A-6 becomes [ A2 } ol-hM \ 2 + B 2 J TT^^ 2 ] _ "KAB ( 2 >> + 1 ) = Nv, Multiplying by "tn ^ .A = VJy % C N> A 6Ca> + 0) A _ 9 If equation A-7 is compared to the Hamiltonian of equation II-3 H one can make the identifications _ 1 _ = irx LO^ 6 1 " Co, _ ^ - A- 1 0 2B,, a and using >«J-)^  = C» , one gets £ > = L A ) ^ K (N-V, + 2 ^ + 1 ) A-ll which is the excitation energy of a state containing N - ^ ^ 2 -pole phonons. A-3 Commutation Relations for a^^ and . From equation A - l , the commutation relationship is E a >^' ^ - A 2 i ^ d \ w ~ ^ ) 145 The first two terms are zero as [ O ( > m , p/y^] = [ T T ^ T*T>'] = 0. The third term can be written, with the aid of equations A-7 and A-8 as [ a><+ > *">>' ] = iAB( [ T T ^ ^'.^.1 + L ^ 7 l ^ , ^ ^ = iAB( -12 fc^ &*M.) which, using equations A-10, reduces to C a > ^ » al'^ - - S>» ^ A-12(a) It can be shown, in a similar manner, that £ a ^ , a \ < ^ - = [ a ^ , a v < t t. ] = 0 A-12(b) A-4 The Hamiltonian The Hamiltonian of equation II-3 can be written as a function of the creation and destruction operators by solving euqations A-l for c<^ and T T T , ^ and using A and B from equations A-10. That i s , substituting Kb. . . . . . A-13 into gives A-5 State Functions The state functions, represented by 5 in equation A-2, can be ex-pressed in terms of the creation and destruction operators, a"*^  and A>^A. > operating on the vacuum state, \0> . The vacuum state i s , of course, the ground state. A state containing one /X. type phonon can be written as 146 The spin of this state"^ will be J = 7\ and the parity, T"> = (-1)^ • A state containing two phonons can be written as where Q, ^  represents the sum over the appropriate vector addition co-efficients. The allowed values of angular momentum ( J ) and parity (TT) of these states are | \ - \ \ < ^ < \ + V IT •= (-V'r^V^ States with three phonons will be ^123 ^.x*. aKM^ a \ s ^ il 6 > with the restrictions on J given by Ij' - >3| < J <c J'+ ^3 where J1 is the intermediate angular momentum^ of the coupling of ^ X^  and "^ 2 with restrictions I \ < 1* £ X ^ V The parity of the three phonon state is given by TT = (-1)^' (-1)V (-1)^ The allowed values of J for states with two or more phonons will be reduced by symmetry considerations i f any two phonons are indistinguishable. That i s , since the phonons have integer spin and therefore must obey Bose-61 Einstein statistics, the state functions must remain the same i f the two indistinguishable phonons are exchanged. The state functions describing the lower energy states, which involve only quadrupole and octupole phonons, are written explicitly below. The notation used is 132n2j^-^^J-^y , which is a state containing n2 quadrupole phonons coupled to give a spin j 2 , n-j octupole phonons coupled to give a spin j , and j 2 and coupled to give a total spin of J, with projection 147 onto the quantization axis, M. no - 1 D3 :: D_ 121 002M> = a2M l 0 > _n2 =2 n3^_0_ 1J200JM> = ~= ^  C(22J; m M-m) x al at.. \ 0 > 2m 2n-m The convention used to write the Clebsch-Gordon coefficients C(22J; m M-m) = C( >>l >2 J; M\ M-/^ ) M = +*2 60 is that of Rose. The restrictions on J from the symmetry requirements can be deduced from the following considerations. The interchange of phonons does not affect a 2 m a^ , as they commute for a l l m and M-m (see equation A-12(b)). The Clebsch-Gordon coefficients 60 have the symmetry property 'C(J1J2J; m1 M-m1) = C (JiJ 2J; m^M) = ( - l )jl+ J2 "J C ( j 2 j x J; m2 ml M) The interchange of phonons will therefore have the effect of multiplying |J200JM> by ( - l )j l + i 2~J, and J must be even for the function to be symmetric. The allowed values of J are 0, 2,and 4. The parities of these 3 degenerate states will be positive. n2=3 "3=0 C22J } y ( J 3 0 0 J M > = [ 2+4 (2J1 + 1) \ J < 2 J 3 1 x £_ [ C (2J'J; T M - a- ) C (22J; v <r . \> ) xa2M-(T a2tf-\> 4>> ^ 0 > 62 The < 1 b l } < is a six-j symbol (Racah coefficient). Fig. A-l Energy J 1 4.5 1,2,3,4,5J 4.0 3.5 0,2,2,4, 3.0 0,2,3, 4,6 2.0 0,2,4 -±-1.0 State Function IJ 2n2J3n3J M > \2131JM> |J400JM> 100313M> IJ300JM> U200JM> 121002M> I000000> 149 63 It has been shown that the values of J not allowed by symmetry considerations are.1 and 5. The allowed values of J for this state are 0, 2, 3, 4 and 6. The parity i s , of course, positive. ?2 = 0 n3 = 1 |00313M> = a^M \ 0> The spin is 3 and parity is negative. ?2 ~ 1 n o = 1 12131 J M> = 4=<^L C (23J; m. M-m) 12- m 2m 3M-m The allowed values of J in this case are 1, 2, 3, 4 and 5, and the parity is negative. 64 The allowed values of J for this case are 0, 2,2, 4,4,5, 6, 8 and the parity is positive. A spectrum of these states is shown in figure A-l. The ratio L C ^ / U ^ 3.5 was chosen as this is approximately the ratio of the energies of the-124-first 3- state to the first 2+ state found in Te. The transitions between these states that are allowed by the simple vibrational model, which will be determined in Appendix B, are also shown. 150 Appendix B  Electromagnetic Transitions B-l General Considerations The probability for a transition from a state \ M^ TT^  "> to a state \jf M^ TT^ "^  with the emission of a photon with angular momentum L i s , for 65 the long wavelength approximation B-l \J.M^ Tl r>and fJ^ M^ TTprefer to the spin, spin projection, and parity of the in i t i a l and final states respectively, k is the wave number, related to the energy difference (E) between the i n i t i a l and final states by E="nck. The long wavelength approximation requires that kR <^< 1, where R is the radius of the radiating body; for example, the radius of the nucleus for nuclear transitions. The approximation is valid whenever the spherical Bessel functions, j ^ (k,r), which are contained in the multipole operators, T IM' n^^, can be adequately represented by^ j_(kr) = (kr)L  L (2L+1).! for a l l r such that the reduced transition probabilities B(tTL; J.M. JfMf) = KJfMf-Hfl n^^i^^l 2 B"2 are non-vanishing. This expression described the reduced transition probability for a transition from a given substate M. of J. to a given substate M,, of J... A i i f f more useful quantity, for most cases, is the reduced transition probability for transitions from a l l the substates of J to a l l the substates of J... i t 151 This probability is the sum over the final states and the average over 6 7 the i n i t i a l states. That is J. J f B( OX; J. J ) = 1 Z £ B(<TL; J.M.J.M,) 2J.+1 M . = M f = _ J f B-3 The values of L and M of the multipole operator for which the B( "sTL; J.—^J..) will be non-zero can be deduced from angular momentum x r conservation to be |J - J I ^ L ^ J £ + J f 1 f 1 B-4 M + M = M _ i f Parity must also be conserved, and therefore terms in VYP that do not ' • I M have parity = T\. *TT- will not contribute in the calculation of x f xT 6 7 BC^ vTL; —T? J^)- ^\ L M ° a n b e d^- v^ d e d i n t o two parts for each value of L L+1 allowed L , one with parity (-1) and the other with parity (-1) . If T\ i"^ Vf = (_i)^> then only the part of ftf^ w^- t n this parity will contri-bute. In this case, r f fm is called an electric 2^-pole operator and written as l^l^T The transition is called an electric 2^-pole transition and is given the identification, E L . For instance, i f L=2, TT =1, the f \ E 2M is an electric quadrupole operator and the transition is E2. Similarly, i f TT^TTj; = (-l) 1^*, only the part of fl\ with this parity will contri-bute. These terms are called magnetic; that i s , for L=2, "sT = -1, \ 2M p/^ Is a magnetic quadrupole operator and the transition is M2 The total transition probability from a state with spin to one with spin J , with the emission of a photon with any of the allowed values of L is T ( J. -=> J ) = <z— T i f ' r IM - £ - - , r 152 = 4 8 ( L + 1 ) k 2 L + 1 ^ < K J f M f T Y f | ra^ J-M.-XY £ L [ ( 2L + 1 ) ! ' ] 2 (2J.+1) ^  M ^ 1 1 1 The individual T T W will alternate between electric and magnetic terms as IM E M n\ and /Ifl have opposite parity. The relative sizes of the T 's can LM ^ LM r J M 6 7 be shown, quite generally, to depend on k and R as 4 - < K R > 2 L for electric transitions and M 2L+2 of (kR) LM for magnetic transitions. Therefore, since k R « l in this approximation, only the firs t term in the sum need be considered i f i t is electric and only the firs t two need be considered i f the first is magnetic. The multipolarities of transitions between states )J.M.T\.> and |J^M^TT£> with the emission of a photon with angular momentum L are tabu-lated below for spin changes up to \ - = 3. 1-J - J J T\i"Uf Multipolarity ( ^  L ) 0 1 (EO) M 1 + E 2 -1 (MO) E 1 1 1 M 1 + E 2 -1 E l . 2 1 E 2 -1 M 2 + E 3 3 1 M 3 + E 4 -1 E 3 EO and MO electromagnetic transitions cannot take place with the 6 8 emission of a photon as the minimum allowed photon angular momentum is Also, as the maximum allowed L is J^ + J^, no photons can be emitted in J^ =0 ->J^=0 transitions. These transitions may take place only with the emission of conversion electrons, or if the energy difference is large 2 enough (^ 2M Q C ) , electron-positron pairs. 153 Experimental transition rates are usually compared to theoretical transition probabilities by comparing ratios of reduced branching ratios to ratios of reduced transitions probabilities. That i s , for transitions 1 and 2 in the decay scheme the ratio 1 ( k 2 ) ^r i B-5 bA f k ^ 2 L 2 + 1 is compared to the ratio B( vTLi; J t ) B-6 B( ^ I ^ ; JL —* j | ) The b 's are the branching ratios defined in Chapter IV and the B's and the reduced transition probabilities given in equation B-3. These comparisons are often a critical test of the model used to calculate the 69 reduced transition probabilities. B-2 Simple Vibration Model Transitions The multipole operators for transitions between collective states • 70 can be written as "WlM = {f^ ^ YLM (e'^> B " 7 154 ^ B-8 yt?(r) is the charge density, j(r) is the current density, and L is the photon angular momentum operator ( = - i r_ x V ). With the assumptions of the simple vibrational model given in Chapter II, = 3 Ze 41TR-and j(r) = />(r) V(r) c where V(r) is the velocity density given by7''" v(r) - % / £ . c ^ ^ C e ^ ) The electric multipole operators can easily be evaluated. where R is the nuclear radius defined in equation A-3. Therefore which, to first order in becomes nO E = 3 Ze R J ^ using the transformation of equation A-13 this becomes = *L ( aLM+ C-DM *L-M> B-9 with KL " 3 Z e ^ (__A_ 41T \ 2 ^  BL B-10 155 The magnetic operators are much more difficult to evaluate. The results of reference 71 quoted by Davidson7^ for ~)\-type surfaces is rT| M = -3 Ze i k R1*1 [L(L+2^+l)(2 V l ) ] ^ C(L >\-l"X; 000) L L M 8 ^ ° L+1 The (and the ) can again be expressed in terms of the creation and destruction operators given in Appendix A. o n iy connect states that differ by one phonon. That i s , transitions will only occur between \-}2n2i3n3J^'5> states (see Appendix A) for which /^n^ = 1 or ^n^ = 1, but not both. These allowed transitions are shown in figure A-l. Furthermore, since depends on C (L>i-lX;000) LM which i s non-zero only i f L + ) \ - l + )\ is even, and since 2, the lowest order magnetic multipole transitions are octupole. The reduced transition probabilities between the states given in Appendix A using the electric multipole operators of equation B-9 were calculated. The results are tabulated in table B-l. Two sample calcu-lations are given below. a) Transitions from one-phonon states to the ground state E2 E3 121002M>—•> 0 or l003l3M>-5»0 2 B(EL;J->0) = _ J £ _ ICOl^f at, I 0>l 2J+1 m u l L J w j + ....2 |<0\a a \0>\ 2J+1 m mL J V L from equation A-12 + = C r a+  aLMLajMJ OjM°M LMj + JMj *LML therefore B(EL;J-*0) = K2 ' B-ll XJ 156 Transitions from two phonon states to one phonon states 12200J.M> |21002M> i i Only E2 transitions are allowed. B(E2;J.-^ 2) = 1 4r 4 r l<0\ao. W\E 2JT+1- Mi Mf 2 ^ X-i-Z.C(22J ;/(M. -A) a + a + 10>\2 f l / ^ 1 1 2 2M. -X B _ 1 2 The matrix element can be reduced with the aid of the Wigner-Eckhart theorem,^ which states that <^ JfMf \ T m j J.M> = CC^Uf; M MLMf) x ^ J f \ T L \ J £ ? Therefore equation B-12 becomes B(E2;J.->2) = K? / 9 1 lc(J.22;M.MM fK 2(2J.+1) M-M. L x |<0 a2a2a+a+10>l2 B-13 60 The Clebsch-Gordon coefficients have.the symmetry property C(J1J2J3;m1m2m3) = (-1) jl "ml / 2J3+l\ ^ A 2 j 2 + i J x C(J3JiJ2;m3,-m1m2) and orthogonality ^ I C(J1J2J3;m1m2m3)^ 2 = 1 mi Therefore the sum over in B-13 is one. [The symmetry condition is used because the number of final substates is always the same for these transitions, whereas the number of i n i t i a l states varies with J^'] The commutation relations (equations A-12) for the creation and destruction operators can be used to achieve the result 157 Table B-l Reduced Initial State Final State Multipolarity Transit: n2 n3 n2 n3 Rate 1 0 2+ 0 0 o + E2 4 2 0 0+,2+4+ 1 0 2+ E2 2K2 3 0 0+ 2 0 2+ E2 2 3 0 2+ 2 0 0+ E2 7/5K2 3 0 2+ 2 0 2+ . E2 4/7K2 3 0 2+ 2 0 4+ E2 36/35K2 3 0 3+ 2 0 2+ E2 15/7 K| 3 0 3+ 2 0 4 + E2 6/7 K2 3 0 4 + 2 0 2+ E2 11/7 K2 3 0 4 + 2 0 4 + E2 10/7 K2 0 1 3" 0 0 0+ E3 K 2 K3 1 1 l-,2-,3-,4",5- 0 1 3" E2 1 1 l-,2-,3-,4-,5- 1 0 2+ E3 that + + + . + + a 2a 2a 2a 2 - a 2a 2 + a 2a 2a 2a 2 + + + = 2 + 3a2a2 + a 2 a 2a 2a 2 Therefore equation B-13 reduces to B(E2;J. 2) = 2(2J.+1) M. = 2K2 B-14 2 This simple result could have deduced from the fact that there are two phonons in the n2=2 state, and either one of them could cause the transitions to the n2=l state; whereas there is only one phonon to cause transitions between the n =1 and n =0 J 2 2 states. Therefore a transition from a two phonon state to a one phonon state is twice as probable as a transition from the one phonon state to the ground state. 159 Appendix C 152 Beta Spectra of Eu 152 1 5 2 Eu decays by electron emission (jS ) to Gd and by positron emission (y3 +) and electron capture to 152Sm with a lifetime of 12 years.40 The gamma transitions following these decays have been studied in this 48 + laboratory to T.G. Walton. The spectra have been measured by 49 C.R. Brown, also in this laboratory, using a magnetic spectrometer. It was felt that an analysis of the p ~ spectra using a Si(Li) detector would be useful for completeness, and also as a check on the usefulness and accuracy of this type of y3~ analysis. A short summary of the pro-cedure used and the results obtained follows. The 0~ transitions that populate the different excited states of 152 Gd were identified by obtaining coincidence spectra of electrons (using the 3mm Si(Li) detector as the gate detector) in coincidence with gamma transitions selected with the 30cc Ge(Li) detector (used as the gate detector). The gamma transitions used as gates are shown in figure C-l. The electronics used were those shown in figure IV-1. Coincidence spectra were taken for each gate with and without an absorber between the Si(Li) detector and source so that the Compton background could be subtracted. The difference spectrum between the two spectra for each gate was corrected for scattering and the shape factors and end-point energies found as described in Chapter V. The Kurie plots of the five p transitions found are shown in figure C-2(a) and (b). The results are listed in table C-l. The relative intensities of the five j3 transitions was difficult to calculate from the coincidence spectra as different intensity sources and source-detector geometry was used to minimize the random rates for each gate. Average of every 5 points plotted rS=.77p2+q2 S=.79p2+ q2 9 \ s0 \ > CD O * l CN LO O > LO n n> •3 t-> H-O OQ rt • CO o O 1 l-h ro r-1 Ul fD o rt H 250 300 350 400 450 Chan. No. \ V Average of every 5 points plotted v 1 s < 1-50 100 150 200 Chan. No. as N5 163 Table C-l A " Transitions in ^ 52Eu -==)^ 52Gd Gate Transition Shape Factor End-Point Energy (KeV) (KeV) 344 .79p2 + q2 1456 - 2 411 .77p2 + q2 1052 + 10 779 1 679 t 5 678 .79p2 + q2 377 + 20 1299 1 - . 177 + 50 Table C-2 End-Point Relative Energy (KeV) Intensity(7o) Forbiddenness' 1456 30+2 1st 1052 5+2 1st 679 45+5 allowed 377 10+3 1st 177 10+5 allowed * The degree of forbiddenness was assumed from the form of the shape factor. 164 Therefore the coincidence spectrum gated with the 344 KeV gamma transi-tion was used, since most of the transitions from higher excited states 152 48 in Gd decay via the 344 KeV level. This coincidence spectrum was analysed by subtracting the group that feeds the 344 KeV level using the calculated shape for this group. The remainder was then used to find the contribution of the next highest energy group, and this sub-tracted. This procedure was repeated until only the lowest energy group remained. 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