Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Beta and gamma ray spectroscopic analysis of the radiations emitted in the decay of selenium 75 Schneider, Harvey Roy 1961

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1961_A1 S2 B3.pdf [ 8.08MB ]
Metadata
JSON: 831-1.0085881.json
JSON-LD: 831-1.0085881-ld.json
RDF/XML (Pretty): 831-1.0085881-rdf.xml
RDF/JSON: 831-1.0085881-rdf.json
Turtle: 831-1.0085881-turtle.txt
N-Triples: 831-1.0085881-rdf-ntriples.txt
Original Record: 831-1.0085881-source.json
Full Text
831-1.0085881-fulltext.txt
Citation
831-1.0085881.ris

Full Text

BETA AND GAMBIA RAY SPECTROSCOPIC ANALYSIS OF THE RADIATIONS EMITTED IN THE DECAY OF SELENIUM 7 5 HARVEY ROY SCHNEIDER B.Sc.(Hons.) The University of Alberta, 1954 M.A. The University of B r i t i s h Columbia, 1957 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1961 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e . r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s ' f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Physics  T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a . D a t e January 23rd, 1961.  Wat ^ntersttg of ^§rtttsh (Eolmttbra FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of HARVEY SCHNEIDER B.Sc, (Hons.) University of Alberta 1954 M.A., University of British Columbia 1957 MONDAY, JANUARY 23, 1961 AT 2:30 P.M. IN ROOM 302, PHYSICS BUILDING COMMITTEE IN CHARGE Chairman: G. M. SHRUM K. C. MANN W. E. McLEOD J. B. WARREN E. V. BOHN J. R. PRESCOTT T. E. HULL G. M. GRIFFITHS J. GRINDLAY External Examiner: DR. F. SCHMIDT University of Washington, Seattle, Wash. SPECTROSCOPIC ANALYSIS OF THE RADIATIONS EMITTED IN THE DECAY OF Se75. ABSTRACT The nuclear energy levels of As 7 5 • have been investigated through the study of the Se 7 5 decay scheme. The internal conversion spectrum as well as the photoelectron spectra using bismuth and lead radiators were measured with a modified thin lens magnetic spectrometer. A technique was developed for accurate determination of the transmission of the spectrometer in order to obtain the absolute conversion electron transition intensities. The gamma ray intensities were determined from the spectrum measured with a Nal. (Tl) scintillation spectrometer in conjunction with the results from the photoelectron spectra. From these measurements the absolute conversion coefficients for eight transitions were obtained. In addition coincidence techniques employing a slow-fast co-incidence system (resolving time 10 7 sec) were used to measure gamma-gamma coincidences, conversion electron-gamma coincidences and gamma-gamma directional correlations. A one hundred channel kicksorter was used to facilitate accumulation of the data at the relatively low coincidence counting rates. Multipolarities of the following transitions were determined (energies in kev), 98(E2); 121(E1); 136(E1); 198(M1 + E2); 265 (Ml -0.12<4(E2) < +0.07); 279(M1 + E2, 6 — -0.46+0.16); 304 (E3) and 401 (El). Also detected but for which multipolarities could not be determined was a 66 kw transition and a very weak 572 kev gamma transition. In addition the existence of a 24 kev and a 77 kev transition was inferred from the intensity measurements. An energy level diagram for As 7 5 has been constructed with the following energy levels and spin assignments (energies in kev), 572 (1 +), 477(?), 401 (f +), 304 (| +), 279 (! -), 265 (1 -), 198 (| -), 0 ( f- -). It was concluded that the ground state of Se7S has even parity. GRADUATE STUDIES Field of Study. Nuclear Spectroscopy Theoretical Nuclear Physics F. A. kaempffer Cosmic Rays and High Energy Physics J. R. Prescott Physics of Nuclear Reactions G. M. Griffiths Quantum Theory of Radiation F. A. Kaempffer Advanced Quantum Mechanics F. A. Kaempffer Noise in Physical Systems R. E. Burgess Introduction to Low Temperature Physics J. M. Daniels Related Studies: Analogue Computers E. V. Bohn . Digital Computers tt E. V. Bohn Servomechanisms E. V. Bohn Numerical Analysis F. M. C. Goodspeed i i ABSTRACT 75 The nuclear energy leve l s of As have been investigated 75 through the study of the Se decay scheme. The int e r n a l conversion spectrum as well as the photoelectron spectra (using bismuth and lead radiators) were measured with a modi-f i e d thin lens magnetic spectrometer. A technique was de-veloped for accurate determination of the transmission of the spectrometer in order to obtain the absolute conversion electron t r a n s i t i o n i n t e n s i t i e s . The gamma ray i n t e n s i t i e s were determined from the spectrum measured with a Nal(Tl) s c i n t i l l a t i o n spectrometer i n conjunction with the r e s u l t s from the photoelectron spectra. From these measurements the absolute conversion c o e f f i c i e n t s for eight t r a n s i t i o n s were obtained. In addition coincidence techniques employing a slow-ly f a s t coincidence system (resolving time 10 sec) were used to measure gamma-gamma coincidences, conversion electron-gamma coincidences and gamma-gamma d i r e c t i o n a l c o r r e l a t i o n s . A one hundred channel kicksorter was used to f a c i l i t a t e accumulation of the data at the r e l a t i v e l y low coincidence counting rates. M u l t i p o l a r i t i e s of the following t r a n s i t i o n s were determined, (energies i n kev), 97(E2); 121(El)j 136(El); 199(H1+E2)j 265(Ml,-Q.12<S(E2)<+0.07)j 279(M1+E2, S =-0.46 +0.16)| 304(E3) and 401(El). Also detected but for which i i i m u l t i p o l a r i t i e s could not be determined was a 66 kev tran-s i t i o n and a very weak 572 kev gamma t r a n s i t i o n . In addition the existence of a 24 kev and a 77 kev t r a n s i t i o n was inferred from the i n t e n s i t y measurements. 75 An energy l e v e l diagram for As has been constructed with the following energy l e v e l s and spin assignments, (energies in kev), 572 (7/2 +), 477 (?), 401 (5/2 +), 304 (9/2 +), 279 (5/2 - ) , 265 (3/2 - ) , 199 (1/2 - ) , 0 (3/2 - ) . 75 It was concluded that the ground state of Se has even p a r i t y . i v TABLE OF CONTENTS CHAPTER I THEORY 4 I. Beta Decay 4 (i) Fermi Theory of Beta Decay 5 ( i i ) Selection Rules 6 ( i i i ) Kurie Plot 7 (iv) Comparative H a l f - L i f e 8 (v) K-Capture 9 II. Radiative and Internal Conversion Transitions in Nuclei 10 (i) Multipole Radiation 10 ( i i ) Internal Conversion and Conversion C o e f f i c i e n t s 12 ( i i i ) Gamma-Gamma Di r e c t i o n a l Correlation 14 CHAPTER II APPARATUS 19 - I. The Gamma Ray S c i n t i l l a t i o n Spectrometer 19 (i) General Description 19 ( i i ) The S c i n t i l l a t i o n Detector 20 ( i i i ) E l e c t r o n i c s 23 II. The Magnetic Spectrometer 24 (i) Some Remarks on Thin Lens Spectrometers 24 ( i i ) The Modified Thin Lens Spectrometer 27 III. The Coincidence System 30 (i) Introduction 30 ( i i ) The Gamma-Gamma Coincidence System 33 S t a b i l i t y Monitoring 38 Location of the Pulse Analyzer Window Position 39 ( i i i ) The Beta-Gamma Coincidence System 40 IV. Kicksorter Remote Control 45 V CHAPTER III MEASUREMENTS 46 I. The Source 46 75 II. The Gamma Ray Spectrum of Se 47 (i) The Photoelectron Spectrum 47 ( i i ) The S c i n t i l l a t i o n Spectrum 50 ( i i i ) Gamma Ray Transition I n t e n s i t i e s 52 (a) Relative I n t e n s i t i e s from the Photoelectron Spectra 52 (b) Analysis of the Composite Peaks i n the S c i n t i l l a t i o n Spectrum 54 (c) Determination of the Gamma Ray Transition I n t e n s i t i e s 56 III. The Internal Conversion Spectrum 61 (i) Source Preparation 61 ( i i ) Measurement of the Internal Conversion Spectrum 62 IV. Coincidence Measurements 65 (i) Gamma-Gamma Coincidences 65 ( i i ) Internal Conversion Electron-Gamma Coincidences 69 ( i i i ) Gamma-Gamma Dir e c t i o n a l Correlations 71 CHAPTER IV ANALYSIS. OF THE RESULTS 77 I. Previous Investigations of the Decay of S e 7 5 77 II. Interpretation of the Experimental Results 82 (i) The As ^  Energy Levels 82 ( i i ) T r a n s i t i o n M u l t i p o l a r i t i e s and Energy Level Spins 88 ( i i i ) T r a n s i t i o n Lifetimes 99 (iv) The S e 7 5 Decay Scheme 104 (v) Discussion 107 v i APPENDIX I DETERMINATION OF ELECTRON INTENSITIES FROM MAGNETIC SPECTROMETER DATA 114 1) Spectrometer Adjustment 114 2) Spectrometer Transmission 115 3) Intensity Determination 117 APPENDIX II Nal(Tl) GAMMA RAY DETECTION EFFICIENCY 118 APPENDIX III ANALYSIS OF GAMMA-GAMMA DIRECTIONAL CORRELATION DATA 120 1) Least Squares F i t to the Data 120 2) Correction for F i n i t e Angular Resolution 121 3) D i r e c t i o n a l Correlation Measurements With Unresolved Photopeaks 124 BIBLIOGRAPHY 130 v i i LIST OF ILLUSTRATIONS CHAPTER I Figure 1 CHAPTER II Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 A Simple y-y Cascade to follow Page 15 Block Diagram of the Basic Gamma Ray S c i n t i l l a t i o n Spectrometer 19 The Nal(Tl) S c i n t i l l a t i o n Detector 21 The Source-Detector Assembly 21 S c i n t i l l a t i o n Detector E l e c t r o n i c s 23 Radial Displacement of Electron T r a j e c t o r i e s from the Magnetic Axis 25 The Modified Thin Lens Spectrometer 28 Block Diagram of a Gamma-Gamma Coincidence Spectrometer 30 Block Diagram of a Fast-Slow Coincidence System 30 Block Diagram of the Fast-Slow Gamma-Gamma Coincidence Spectrometer 33 C i r c u i t Diagram of the Fast Coincidence Driver 34 Pulse Timing i n the Gamma-Gamma Coincidence System 37 Block Diagram of the Channel 2 Gain S t a b i l i t y Monitor 39 Channel 2 Amplifier Output Delay and Attenuator C i r c u i t 40 Block Diagram of the System Used to Determine the Portion of the Gamma Ray Spectrum Accepted by the Pulse Height Analyzer 40 v i i i Figure 16 Figure 17 Figure 18 Figure 19 CHAPTER III Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Gamma Ray Detector Used i n the Beta-Gamma Coincidence Measurements 41 Gamma Ray Detector Assembly i n the Magnetic Spectrometer 41 Block Diagram of the Beta-Gamma Coincidence System 42 Beta-Gamma Coincidence Response as a Function of the Delay on the Gamma Side 44 Source and Radiator Holder for the Photoelectron Spectrum 48 S e 7 5 Photoelectron Spectrum Using a 1.9 mg/cm2 Bismuth Radiator 49 S e 7 5 Photoelectron Spectrum Using a 7.2 mg/cm2 Lead Radiator 49 S e 7 5 S c i n t i l l a t i o n Gamma Ray Spectrum Above 150 kev 50 S e 7 5 S c i n t i l l a t i o n Gamma Ray Spectrum Below 150 kev 50 S e 7 5 S c i n t i l l a t i o n Gamma Ray Spectrum Above 350 kev 51 S c i n t i l l a t i o n Spectrum of the Arsenic X Rays Produced i n the Se? 5 Decay 51 S e 7 5 Internal Conversion Electron Spectrum 62 S e 7 5 Gamma Spectrum i n Coincidence with the 66 kev Gamma Tran s i t i o n 66 S e 7 5 Gamma Spectrum i n Coincidence with the 199 kev Gamma Transition 66 An Example of the Conversion Electron-Gamma Coincidence Spectra 70 Kicksorter Measurements Showing the Portion of the 265-280 kev Composite Peak Accepted for each D i r e c t i o n a l Correlation Measurement 72 ix Figure 32 Figure 33 Figure 34A Gamma-Gamma Dir e c t i o n a l Correlation Results 73 82 75 75 75 The Decay Scheme of Ge—> As « — S e Theoretical Values of A 9 as a Function of g for the 5/2(1)5/2(1,2)3/2 Cascade Figure 34B Theoretical Conversion C o e f f i c i e n t as a Function of S (E2,M1 Mixing) for the 280 kev Transition Figure 35 Figure 36 Figure 37 Figure 38 APPENDICES Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Theoretical Values of A 2 as a Function of S for the Cascade I a ( l ) I b ( l , 2 ) 3 / 2 for Several Values of I a and I D Theoretical Values of A 2 for the 5/2(1)3/2(1,2)3/2 Cascade as a Function of s (small values of s ) 75 The Decay Scheme of Selenium Comparison of the Energy Level Diagrams of B r 7 9 , As 75 and A s 7 7 94 94 94 94 104 113 Anthracene Crystal with Internal C s l 3 7 Source Mounted on the Photomultiplier 116 Method Used f o r Cooling the Photomultiplier-Anthracene Crystal Assembly 116 C s 1 3 7 Beta Spectrum Measured with the Anthracene Crystal 116 I n t r i n s i c Photopeak E f f i c i e n c y of a l | r , x l " Nal(Tl) Crystal 116 Geometry of the Detection System for the Measurement of y-y D i r e c t i o n a l Dis-t r i b u t i o n s 121 Angular Detection E f f i c i e n c y of the l£"xl" Nal(Tl) Crystal Used i n the y-y D i r e c t i o n a l Correlation Measurements 121 X ACKNOWLEDGMENTS To Dr. K.G. Mann who suggested the research described i n t h i s thesis and whose discussions and encouragement throughout the work were of invaluable assistance I wish to express my deepest gratitude. The help of the other members of the nuclear spectroscopy laboratory i s also g r a t e f u l l y acknowledged. In p a r t i c u l a r , the assistance of F.A. Payne, who set up the magnetic spectrometer and spent many hours operating the instrument, was sincerely appreciated. Thanks are also due to Dr. J.B. Warren who made the kicksorter f a c i l i t i e s of the Van de Graaff group available to me and to Dr. B.L. White whose discussions concerning the operation of the kicksorter were most useful. F i n a l l y , I wish to express my gratitude to the National Research Council for f i n a n c i a l support in the form of two Studentships during the course of t h i s work. INTRODUCTION The analysis of the radiations emitted by radioactive nuclei (nuclear spectroscopy), with a view to determining nuclear decay schemes and hence the systematics of nuclear structure, has been a continuing study for the past f i f t y years. The early measurements in t h i s f i e l d were hampered by a lack of adequate experimental techniques, as well as by the f a c t that the a v a i l a b i l i t y of radioactive isotopes was limited. This s i t u a t i o n changed during the 1940's when construction of nuclear reactors made r e a d i l y available a great number of a r t i f i c i a l l y produced radioactive isotopes. At t h i s time also, the demand for more precise measurements resulted i n the design of magnetic spectrometers with greatly improved resolution and transmission c h a r a c t e r i s t i c s , and i n advances i n e l e c t r o n i c techniques such as the devel-opment of coincidence counting as a useful tool i n the determination of decay schemes. In 1950 two more s i g n i f i c a n t advances were made. On the experimental side there was the development of the s c i n t i l l a t i o n counter, which among other things greatly i n -creased the usefulness of the coincidence counting technique, and on the t h e o r e t i c a l side there was the introduction of the s h e l l model theory of the nucleus. The l a t t e r develop-ment provided for the f i r s t time a t h e o r e t i c a l basis f o r the discussion of the experimental r e s u l t s . Later the s h e l l -2-model was complemented with the concept of c o l l e c t i v e motions of the nuclear core (the u n i f i e d model) which successfully accounted for a number of energy l e v e l s of higher mass nuclei not predicted by the single p a r t i c l e s h e l l model. During the past decade the investigation of nuclear decay schemes and energy leve l s has been the major concern of a large number of research groups, so that today consider-able information regarding nuclear decay schemes i s available. Because many of the decay schemes are complex i t i s not sur p r i s i n g to f i n d , i n some cases, that measurements re-ported by d i f f e r e n t authors on a p a r t i c u l a r decay scheme are not in complete agreement, or perhaps that the data available does not allow an unambiguous determination of the energy le v e l s or spin assignments. In such cases further study of 75 the decay i s warranted. This applies to the decay of Se , the subject of t h i s thesis. 75 The Se decay was studied i n some d e t a i l by Schardt and Welker in 1955 and on the basis of the i r measurements a decay scheme complete except for the fact that unambiguous spin and pa r i t y assignments could not be made to a l l of the energy l e v e l s , was proposed. This scheme was la t e r changed 75 somewhat with the discovery of an isomeric As state. More recently gamma ray multipole assignments made by Schardt and Welker on the basis of th e i r conversion c o e f f i c i e n t s were c a l l e d into question by the re s u l t s of gamma-gamma angular co r r e l a t i o n measurements, and energy l e v e l l i f e t i m e measure-ments. -3-To s e t t l e the questions regarding t h i s decay therefore, the present reinvestigation was undertaken. -4-CHAPTER I THEORY I. Beta Decay The i n s t a b i l i t y against decay of ce r t a i n nuclei by the emission of a negatron or positron (beta decay) or capture of an o r b i t a l electron (K capture) i s well known. Unlike other nuclear spectra, beta ray spectra have the unique property of being continuous. That i s , the energy of the emitted beta p a r t i c l e s may have any value from zero up to some maximum which i s c h a r a c t e r i s t i c of the decay and i s equal to the energy difference between the i n i t i a l and f i n a l nuclear states. The conservation of energy, momentum, and angular momentum i n the beta process, can be understood only i f a second p a r t i c l e , the neutrino, i s emitted simultaneously in the decay. This hypothesis was o r i g i n a l l y put forward by Pauli and used by Fermi ( 1 ) i n developing his theory of beta decay. It i s only recently that d i r e c t evidence for the existence of the neutrino has been obtained ( 2 ) . In beta decay processes the number of nucleons A, i s the same i n the i n i t i a l and f i n a l nuclear states. The t r a n s i t i o n involves the transformation of a neutron i n the o r i g i n a l nucleus into a proton in the f i n a l nucleus (or vice versa). The beta t r a n s i t i o n s can therefore be i n -dicated by: (Z,A) (Z±l,A)+e ++y (positive or negative electron emission). -5-(Z,A) + e~—>(Z-1,A) + ( o r b i t a l electron capture), + where Z a atomic number, e~- s positron or negatron and 9 s neutrino. (i) Fermi Theory of Beta Decay A t h e o r e t i c a l account of beta decay f i r s t formulated by Fermi (1) i n 1934 remains v a l i d today without great modi-f i c a t i o n despite the fact that the understanding of the decay process has i n recent years undergone a thorough r e v i s i o n with the demonstration of the non-parity conserving proper-t i e s of weak interactions. According to t h i s theory the p r o b a b i l i t y per unit time that a beta p a r t i c l e w i l l be emitted with momentum between p and p + dp i s , Bl| 2 F ( Z , p ) p 2 ( E 0 - E p ) 2 d p 1. In t h i s equation g i s Fermi*s fundamental coupling constant responsible f o r the magnitude of the int e r a c t i o n leading to beta decay. |M| i s the t r a n s i t i o n matrix element dependent upon the i n i t i a l and f i n a l state nuclear wave functions, the electron and neutrino wave functions, and s p e c i f i c assumptions regarding the form of the inte r a c t i o n causing the t r a n s i t i o n of a neutron to a proton or vice versa. The Coulomb f i e l d factor F (Z,p) describes a perturbation on the electron wave function by the nuclear Coulomb f i e l d . C l a s s i c a l l y the e f f e c t of the nuclear Coulomb f i e l d described P(p)dp g 2 7 T 3h 7C 3 - 6 -by F (Z,p) i s an acceleration of positrons and a deceleration of negatrons emitted i n beta decay, r e s u l t i n g i n a r e l a t i v e increase i n the number of low energy negatrons and a decrease in the number of low energy positrons observed i n beta spectra. The term p 2 ( E Q - E p ) 2 , where p i s the beta p a r t i c l e momentum, E Q the dis i n t e g r a t i o n energy and Ep the beta p a r t i c l e energy, i s known as the s t a t i s t i c a l factor. It i s t h i s term that takes into account the s t a t i s t i c a l d i v i s i o n of the d i s i n t e -gration energy between the beta p a r t i c l e and the neutrino. ( i i ) Selection Rules The beta decay int e r a c t i o n can r e s u l t i n the electron and neutrino being emitted i n the s i n g l e t state, i . e . spins a n t i - p a r a l l e l so that the t o t a l spin S = 0, or i n the t r i p l e t state with spins p a r a l l e l (S =• 1). The s i n g l e t state i s pro-duced through what are c a l l e d Fermi interactions and the t r i p l e t state through Gamow-Teller interactions. The t o t a l spin S i s a l l the angular momentum radiated i n the so-called "allowed" t r a n s i t i o n s . Since the expectation value of the electron and neutrino wave functions s t i l l have a f i n i t e value at a distance from the centre of the nucleus, i t i s possible that o r b i t a l angular momentum (L) as well, may be radiated, although i t s p r o b a b i l i t y i s r e l a t i v e l y much smaller. Transitions in which one or both p a r t i c l e s are emitted with o r b i t a l angular momentum di f f e r e n t from zero are c a l l e d "forbidden" t r a n s i t i o n s . The degree of forbiddeness i s given by the t o t a l o r b i t a l angular -7-momentum radiated. For allowed transitions,the difference between the angu-l a r momentum of the parent and daughter nucleus, -AJ, i s given by the following s e l e c t i o n r u l e s : A J - 0 no p a r i t y change (Fermi s e l e c t i o n rule) A J » 0,±1 no p a r i t y change (Gamow-Teller s e l e c t i o n rule) (0-*0 not possible). In cases where £ J = 0 and the i n i t i a l and f i n a l nuclear states do not both have zero spin, both s i n g l e t and t r i p l e t emissions are expected. ( i i i ) Kurie Plot For allowed t r a n s i t i o n s 5 the t r a n s i t i o n matrix element i i 2 |M| i s independent of the beta p a r t i c l e energy. Equation 1 can therefore be put i n the form, h - Const. (E 0-E p) 2. Within a constant m u l t i p l i c a t i v e factor P(p) i s obtained from the measured momentum d i s t r i b u t i o n of the beta spectrum, and the values of F(Z,p) for various Z and p have been tabulated (3). For a p a r t i c u l a r decay therefore, i f the value of the square root on the l e f t hand side of (2) i s plotted versus E p, a straight l i n e which intersects the absisca at E a = E r e s u l t s . p o Such a graph, c a l l e d a Kurie p l o t , i s very useful i n P(P) p 2F(Z,p) -8-determining the disi n t e g r a t i o n energy for a beta t r a n s i t i o n . A departure from l i n e a r i t y of the Kurie plot i s a strong i n d i c a t i o n that the t r a n s i t i o n i s forbidden, but a l i n e a r p l o t on the other hand does not necessarily guarantee an allowed t r a n s i t i o n . (iv) Comparative H a l f - L i f e The t o t a l p r o b a b i l i t y per unit time that a beta-active nucleus w i l l decay i s obtained by integrating (1). This integration y i e l d s , ^max X - \ P(p)dp - C |M( 2f(Z,p m a x) 3. o where P rmax f ( Z , P a a x ) " \ p 2(E 0-E^)P(Z,p)dp . Numerical values f o r f ( Z , p m a x ) have been extensively tabulated (4). Since ?v i s inversely proportional to the h a l f - l i f e t, of the decay, (3) can be rewritten as, Const. f t = 0 4. | M | The f t product r e f l e c t s the magnitude of the t r a n s i t i o n matrix which decreases with increasing forbiddeness of a t r a n s i t i o n . Consequently the f t value can provide a useful -9-c r i t e r i o n for the c l a s s i f i c a t i o n of beta t r a n s i t i o n s . The O 1 O f t values range from about 10 sec. to about 10 sec. and for convenience therefore log f t values are usually used. Empirically i t i s found that t r a n s i t i o n s with log f t values between 3 and 6 are generally allowed. F i r s t forbidden tr a n s i t i o n s usually have log f t values between 6 and 9 while for second forbidden t r a n s i t i o n the range i s 10 to 13. There are of course exceptions which do not f i t these c l a s s i f i -cations. The determination of the log f t value for a p a r t i c u l a r beta t r a n s i t i o n i s f a c i l i t a t e d by the nomographs prepared by Hoszkowski (5). (v) K-Capture The c a l c u l a t i o n of the decay constant for K-capture decay d i f f e r s i n two respects from that f o r electron emission. F i r s t , since the neutrino i s i n t h i s case emitted with a discrete energy, the s t a t i s t i c a l factor has the form 2 2 ( E Q + mc - E^) , where E^ i s the binding energy of the electron i n the K s h e l l . Secondly, for the electron wave function^the K electron eigenfunctions are used. The decay constant can s t i l l however be written i n a form s i m i l a r to (3), v i z . X k = C k |M|2 f k ( Z , E Q ) 5. The function f k ( Z , E Q ) i s of course d i f f e r e n t from f ( z > P m a x ) > -10-but has also been calculated and tabulated for various Z and E 0 . Hence i t i s also possible to determine log f t values for K-capture t r a n s i t i o n s . II. Radiative and Internal Conversion Transitions i n Nuclei ( i ) Multipole Radiation In general, the nucleus remaining aft e r a beta decay process,is found i n an excited state. The passage from t h i s state to the ground state i s usually accompanied by the emission of gamma radiat i o n . Several gamma quanta may be emit-ted i f the de-excitation goes by steps through several i n t e r -mediate states. (A competing de-excitation process by inte r n a l conversion i s discussed l a t e r . ) Electromagnetic r a d i a t i o n i s c l a s s i f i e d by multipole orders L, according to the amount of angular momentum L (in units of h) ca r r i e d off by each quantum. A further d i s t i n c t i o n between two classes of radi a t i o n , e l e c t r i c 2^ pole and magnetic 2 L pole i s made because of p a r i t y differences. C l a s s i c a l l y these r e f e r to the ra d i a t i o n that would be emitted by o s c i l l a t i n g e l e c t r i c or magnetic 2 L poles. If the spins and p a r i t i e s of the i n i t i a l and f i n a l nuclear states between which a gamma t r a n s i t i o n occurs are ( J i , i r i ) and (JffVf), (where a value +1 for TT i s referred to as even p a r i t y and -1 referred to as odd p a r i t y ) , then the conservation of angular momentum and par i t y imposes cert a i n -11-s e l e c t i o n rules on the gamma ray m u l t i p o l a r i t i e s possible i n the t r a n s i t i o n , v i z . " J f j ^ L — J i + J f 7T L and _A « (-1) for e l e c t r i c multipole r a d i a t i o n , TT f - ( - 1 ) L for magnetic multipole r a d i a t i o n . The gamma t r a n s i t i o n p r o b a b i l i t y between two nuclear states i and f, i s d i r e c t l y proportional to the square of the matrix element of the multipole moment between i and f, i. e . i f the wave functions for the states are ^  and and the multipole operator i s Ji , the matrix element re-quiring evaluation i s , \ ^ | ^ 7 M | ^  >^ • ~^ i s u s e d to denote either an e l e c t r i c or a magnetic multipole operator and M i s the magnetic substate quantum number. The calculated value of t h i s matrix element i s dependent upon the type of nuclear model assumed. Moszkowski (6) has made estimates of the t r a n s i t i o n p r o b a b i l i t i e s f o r various multiple radiations, by using an extreme singl e p a r t i c l e model, namely a proton i n a central v e l o c i t y independent p o t e n t i a l . These estimates, although very crude, do i n cert a i n cases provide a basis for the discussion of the ex-perimentally measured values. Two general statements regarding the t r a n s i t i o n p r o b a b i l i t i e s can be made: 1) Magnetic multipole t r a n s i t i o n p r o b a b i l i t i e s are smaller than those f o r the corresponding e l e c t r i c multipole; 2 ) the t r a n s i t i o n p r o b a b i l i t y decreases very r a p i d l y with increasing multipole order L. -12-The second statement means that although a l l multipole t r a n s i t i o n s s a t i s f y i n g the sel e c t i o n rules could occur, i n practice only the lowest permitted multipole order i s ob-served. In many cases therefore, L • - . An exception occurs i n certai n cases where a magnetic multipole t r a n s i t i o n i s the lowest permitted order. In t h i s case the reduced magnetic multipole t r a n s i t i o n p r o b a b i l i t y may make competition by e l e c t r i c multipole radiat i o n of the next higher order possible. Only magnetic dipole plus e l e c t r i c quadrupole (M1+E2) mixtures have so far been i d e n t i f i e d . ( i i ) Internal Conversion and Conversion C o e f f i c i e n t s A nucleus i n an excited state can make a t r a n s i t i o n to a lower state, not only by emission of a gamma quantum, but also by the competing process of in t e r n a l conversion. That i s , the int e r a c t i o n between the o r b i t a l electrons and the nucleus makes possible a d i r e c t transfer of the nuclear e x c i t a t i o n energy to one of the electrons. The electron i s then emitted with energy equal to the nuclear e x c i t a t i o n energy minus i t s binding energy i n the atom. The K s h e l l electrons being nearest the nucleus experience the largest i n t e r a c t i o n with i t , and therefore are most frequently involved i n the conversion process. Both de-excitation processes, i n t e r n a l conversion and gamma ray emission, have t r a n s i t i o n p r o b a b i l i t i e s that depend upon the matrix element, </\^ \Ji^ *n t n e s a m e -13-way. By defining the conversion c o e f f i c i e n t as a r a t i o of the i n t e r n a l conversion to gamma ray t r a n s i t i o n p r o b a b i l i t i e s , a quantity, which i s independent of s p e c i f i c assumptions re-garding the interactions within the nucleus, i s obtained. The conversion c o e f f i c i e n t i s however strongly dependent upon the following factors: 1. The t r a n s i t i o n energy. 2. The atomic number Z, of the emitting nucleus. 3. The atomic s h e l l or sub-shell, from which the conversion electron i s ejected. 4. The mu l t i p o l a r i t y L of the competing gamma tr a n s i t i o n . 5. The character of the nuclear t r a n s i t i o n ( i . e . e l e c t r i c or magnetic). Rose (7) has calculated the values for the conversion c o e f f i c i e n t s f o r a range of t r a n s i t i o n energies, a l l atomic numbers up to 95, e l e c t r i c and magnetic multipoles up to L = 5^and fo r electrons ejected from the K , L j L J J L J J J a r*d M s h e l l s . Experimentally the conversion c o e f f i c i e n t s are obtained by d i v i d i n g the measured conversion electron i n t e n s i t y by the corresponding gamma ray i n t e n s i t y , i . e . the K conversion c o e f f i c i e n t would be given by, -14-where i s the number of K s h e l l electrons (due to a pa r t i c u l a r t r a n s i t i o n ) ejected per second; N ' i s the number of corresponding gamma photons emitted per second. From a comparison of the measured c o e f f i c i e n t s with Rose's calcu-l a t i o n s i t i s possible to est a b l i s h the m u l t i p o l a r i t y and character of the gamma ra d i a t i o n involved i n the t r a n s i t i o n . In cases where the gamma tr a n s i t i o n s consist of mixed m u l t i p o l a r i t i e s , e.g. M1+E2, the th e o r e t i c a l conversion c o e f f i c i e n t i s equal to the weighted average of the con-version c o e f f i c i e n t s , for the two components. The weights are proportional to the r e l a t i v e i n t e n s i t i e s of the two components. ( i i i ) Gamma-Gamma Di r e c t i o n a l Correlation Although the p r o b a b i l i t y for emission of a photon by a radioactive nucleus i s , i n general, a function of the angle between the d i r e c t i o n of emission and the nuclear spin axis, i s o t r o p i c d i s t r i b u t i o n s of gamma rays are measured i n a l l but very exceptional cases*. This i s o t r o p i c d i s t r i b u t i o n i s of course accounted for by the fac t that the emitting nuclei are randomly oriented i n the source. If i n the decay,two successive gamma tr a n s i t i o n s occur, then while the photons of each t r a n s i t i o n separately have i s o t r o p i c d i s t r i b u t i o n s i n space, there w i l l be i n general a corre-* The exceptional cases being when the source i s included i n certain c r y s t a l s , and cooled i n a magnetic f i e l d to very low temperatures to produce nuclear alignment. -15-l a t i o n between the directions of emission of the two photons emitted i n the cascade. This c o r r e l a t i o n arises because the direc t i o n s of emission of both photons are re l a t e d to the orientation of the angular momentum of the intermediate nuclear state. More s p e c i f i c a l l y , the co r r e l a t i o n can be explained i n the following way. Consider three energy l e v e l s with spins l a , lb and Ic between which two gamma rays, y^ and y^ occur i n cascade (see F i g . 1). Each l e v e l has 21+1 (where I i s the l e v e l spin) de-generate magnetic substates. The gamma tr a n s i t i o n s can therefore be broken down into components involving t r a n s i t i o n s between the magnetic substates (m-states) of the l e v e l s . Each component m^-^m^ say, between s p e c i f i c m-states possesses a character-i s t i c d i r e c t i o n a l d i s t r i b u t i o n which i s dependent only upon the m u l t i p o l a r i t y of the gamma ray and change i n the magnetic quantum number (^ ra). If a l l of the ma and m^  states are equally populated for any ar b i t r a r y quantization axis, (this i s true for randomly oriented n u c l e i ) , then the sum of the d i r e c t i o n a l d i s t r i b u t i o n s of a l l of the components for either the o r T 2 t r a n s i t i o n s i s a constant, i . e . the y^ and y^ d i s t r i b u t i o n s are separately i s o t r o p i c . An anisotropic y^ Ic 2U+ » K\„ states 2I, + I states Zl, •>•> F i g . 1 -16-d i s t r i b u t i o n , for example, may be obtained by a l t e r i n g the r e l a t i v e populations of the mb states. The d i r e c t way for doing t h i s i s by cooling the source to a very low temper-ature i n the presence of a strong magnetic f i e l d (nuclear alignment). There i s however another way, which involves choosing the quantization axis i n such a way that t r a n s i t i o n s between certai n m^  states are not observed. This i s accomplished by allowing the propagation d i r e c t i o n of y^ to e s t a b l i s h the quantization axis. Since a photon c a r r i e s i n i t s d i r e c t i o n of motion only angular momentum +h or -ft, m^  states which would involve Am = o t r a n s i t i o n s w i l l not be observed with t h i s choice of the quantization axis. If i t i s assumed that the ma states are equally populated then t h i s leads to an unequal population of the mfe states and a consequent d i r e c t i o n a l dependence of emission p r o b a b i l i t y of <y2 r e l a t i v e to the quantization axis. That i s , the direc t i o n s of emission of -y^ and y 2 are correlated. A convenient form f o r expressing the d i r e c t i o n a l c o r r e l a t i o n W(0) between y and y 2 i s : W(©) = 1 + A 2P 2(cos e) + A 4P 4(cos 0) + ... + A vP y(cos ©) 6. The c o e f f i c i e n t s A v depend upon f i v e parameters; the multipole orders and L 2 of the gamma rays and the spins *a> *b> a n d *c °* t h e n u c l e a r states. The maximum value for ) i s established by the condition, -17-^max = M i n < 2 L i * 2 I b ' 2 L2> 7* Calculation of the c o e f f i c i e n t s A v i n (6) f o r various com-binations of the spin and multipole order parameters have been made by Biedenharn and Rose (8) and are tabulated. Experimentally the gamma-gamma correlations are ob-tained by measuring the coincidence counting rate between two detectors, each set to accept only one of the gamma rays s as a function of the angle between the detectors. A least squares f i t to the data of a function of the form i n (6) then yie l d s values for A v which can be compared with the the o r e t i c a l calculations. Since the values for A v depend upon L^, L 2 , I a , and I c , the d i r e c t i o n a l c o r r e l a t i o n measurement alone never allows a complete determination of a l l of these parameters. The measurement can, however, be extremely useful i n determining the spins of the lev e l s involved, when the gamma ray m u l t i p o l a r i t i e s are known from say, the in t e r n a l conversion c o e f f i c i e n t s . A more complex s i t u a t i o n arises when one or both of the gamma rays i n the cascade are mixed multipole t r a n s i t i o n s . For the case where only one of the gamma tr a n s i t i o n s i s mixed, (L^ and multipoles, say) and S i s the r a t i o of the reduced matrix elements for the two components i n the mixed tran-o s i t i o n , i . e . S gives the r a t i o of the in t e n s i t y of the L-^  pole to the pole, the d i r e c t i o n a l c o r r e l a t i o n function i s , W(0) = WT + S2WTT + 2SW T T T 8. 18-where Wj and W J J are the co r r e l a t i o n functions for the cascades I a (L^ I b (L 2) I c and I a (I^) lb (L 2) I c respectively and W J J J i n the contribution due to the i n t e r -ference between and L-^  and i s given by, W I I I = ZAvIXI M c o s 0> 9» even T T T » The values f o r A v* x f o r the case where 1^  = 1^  + 1 can be calculated using tables prepared by Biedenharn and Rose (8). These authors have also treated the case where both gamma tr a n s i t i o n s are mixed. -19-CHAPTER II APPARATUS I. The Gamma Ray S c i n t i l l a t i o n Spectrometer (i) General Description The e s s e n t i a l components of a s c i n t i l l a t i o n spectrome-ter are shown i n bloek diagram form i n f i g . 2. The operation of th i s type of spectrometer depends upon the fact that for certain phosphors, the in t e n s i t y of the s c i n t i l l a t i o n produced when a gamma photon interacts with the phosphor material^ i s proportional to the energy absorbed. The most commonly used phosphor for gamma ray detection i s sodium iodide i n the form of a single c r y s t a l and activated with approximately 0.1% thallium iodide. This phosphor has the highest known s c i n t i l l a t i o n e f f i c i e n c y , i . e . s c i n t i l -l a t i o n i n t e n s i t y per Mev of energy absorbed. In addit i o n , the r e l a t i v e l y high atomic number ( 5 3 ) of iodine means that an appreciable f r a c t i o n of the gamma rays incident on such a c r y s t a l w i l l be absorbed through a photoelectric process, (provided of course <, that the gamma ray energy i s not too great, i . e . less than ^ 1 Mev). For such an inter a c t i o n with subsequent absorption of the iodine x-ray }the s c i n t i l -l a t i o n i n t e n s i t y then bears a di r e c t r e l a t i o n to the energy of the absorbed gamma photon. >. If thi s s c i n t i l l a t i o n i s converted into an e l e c t r i c a l pulse with a photomultiplier, then the r e s u l t i n g pulse S c i n t i l -l a t i o n Detector Linear Amplifier — i Pulse Height Analyzer - — < — i .> V High Voltage Power Supply Scaler Figure 2 Block Diagram of the Basic Gamma Ray S c i n t i l l a t i o n Spectrometer. -20-height also i s proportional to the gamma ray energy. In general then, when gamma rays from a radioactive source are detected with a s c i n t i l l a t i o n counter, the analysis of the counting rate as a function of pulse height w i l l show peaks at pulse heights corresponding to the energies of the gamma rays t o t a l l y absorbed i n the c r y s t a l . That i s , a plot of the counting rate versus pulse height yields the gamma ray spectrum. The amplifier shown i n f i g . 2 between the photomulti-p l i e r and the pulse height analyzer i s necessary because the pulse amplitudes at the photomultiplier c o l l e c t o r are usually too small to be analyzed d i r e c t l y . It w i l l also be noted that i n the same figure the pulse height analyzer and scaler have been enclosed i n a dashed block. The sig n i f i c a n c e of t h i s i s that when a multi-channel pulse height analyzer (or "kicksorter") i s used, both the pulse height analysis and storin g of the data i s accomplished by thi s one instrument. ( i i ) The S c i n t i l l a t i o n Detector A 1^" x 1" Nal(Tl) c r y s t a l assembly, commercially available from the Harshaw Chemical Co 0 ) was used for most of the gamma ray measurements. This was o p t i c a l l y coupled to the photocathode of a selected RCA 6342 photomultiplier tube. In the course of the investigation two o p t i c a l coupling f l u i d s were t r i e d , one being DC200 s i l i c o n e o i l 21 and the other a mixture of petroleum j e l l y and mineral o i l . Both worked equally well. The latter coupling f l u i d had the advantage that i t did not tend to flow as readily from between the crystal and photomultiplier as did the silicone o i l when the assembly was mounted horizontally. The photomultiplier used was selected on the basis of a high gain and good resolution. The selection was made from a group consisting of three RCA6342, two RCA6342A and two DuMont 6292 tubes. Comparison of these tubes was accomplished by coupling the Nal(Tl) crystal to each one in 137 turn and using i t to measure the well known Cs gamma ray spectrum. The photomultiplier selected had the highest gain and gave a resolution of 8% for the 661 kev photo-peak of C s 1 3 7 . Construction of the s c i n t i l l a t i o n detector, i.e. the crystal photomultiplier assembly, is illustrated in f i g . 3. Black ele c t r i c a l tape plays the dual role of holding the crystal onto the photomultiplier while also acting as a light tight seal preventing extraneous light from getting onto the photocathode. For the measurement of the 12 kev As X-rays a l j " diameter by 5 millimeter thick Nal(Tl) Harshaw crystal assembly with a 0.001" aluminum window was used. The method of mounting this on the photomultiplier was identical to that used for the i f " x 1" crystal. To prevent distortion in the measured gamma ray to follow page 21 H C H - S W N V No. I (TO C r i s t a . ! Av=>e.m\,\^ R C A 6 3 ' ! r i P^otorr ,v j l t \phe .> r Tape. \ fJfapp'^H Figure 3 The Nal(Tl) Sci n t i l l a t i o n Detector, Source -W . J L e a d $ K \ e l d ^ Cov-^poi->ev-it^ n 11 11 at i o n D ttectov-Figure 4 The Source-rDetector Assembly for the Measurement of Both the y ray spectrum and y-y Coincidences. to follow page 21 lav sV\avj l"*lV' NcJ(TO Crystal K^^mU, RCA&34-2- Pv»otor^olt\!3\ie.> Tape, v /*a .pp>*t \ Figure 3 The Nal(Tl) Sci n t i l l a t i o n Detector, As L e a d S V n e l d C o m p o n e n t i n t i 11 at i o n De.tec.tov Figure 4 The Source-Detector Assembly for the Measurement of Both the y ray spectrum and y-y Coincidences. -22-spectrum caused by the detection of scattered r a d i a t i o n from surrounding materials (e.g. walls, bench top, etc.) the detector was mounted on a l i g h t aluminum stand, twelve inches from the bench top and at least two feet from any wall or other p o t e n t i a l scattering surface. This mounting i s i l l u s t r a t e d i n f i g . 4. The lead s h i e l d shown around the detector, i n t h i s figure, was necessary to reduce the counting rate due to background radia t i o n . The placing of lead so near the crystal,can however, give r i s e to another problem. That i s , the fluorescent lead X-rays caused by the photoelectric absorption in the lead of gamma rays from the source,may be detected by the c r y s t a l , r e s u l t i n g i n the appearance of an 80 kev peak i n the gamma ray spectrum. To reduce the p r o b a b i l i t y of t h i s happening 1the collimator hole of the s h i e l d was machined so that i t s inside surfaces were p a r a l l e l to the cone defined by the point source and the periphery of the c r y s t a l . With t h i s design,no lead X-rays were then de-tected, and the use of a graded s h i e l d , such as that d i s -cussed by B e l l (9), on the inner surfaces of the collimator hole was unnecessary. In a n t i c i p a t i o n of gamma-gamma coincidence and d i r e c t i o n a l c o r r e l a t i o n measurements to be discussed l a t e r , two detectors are shown i n f i g . 4. One of these detectors i s f i x e d i n pos i t i o n while the other can rotate i n a horizontal plane, about a point defined by the interse c t i o n -23= of the two counter axes. Rotation was possible from 90° to 270° with provision fo r locking the detector i n pos i t i o n at 15° i n t e r v a l s . The source was placed at the centre of rotation and held equi-distant from the two detectors by rods marked 1 and 2 in the diagram. This insured that the source was at a l l times accurately centred with respect to the detectors and no change i n counting rate was therefore evident as the movable detector was rotated to i t s various positions. ( i i i ) E l e c t r o n i c s Included i n the detector assembly shown i n f i g . 4 was a preamplifier for the purpose of providing a low output impedance to the cable to the main amplifier. F i g . 5 i s a schematic diagram of the detector e l e c t r o n i c s . It w i l l be seen from t h i s that actually two preamplifiers are used with each detector, one being a 6J6 cathode follower and designated as the slow preamplifier while the other, designated as the fa s t preamplifier i s a plate loaded 6AK5 with a pulse transformer output. The slow preamplifier has a gain of 0.3 and derives i t s input from the eighth dynode. The dynode load r e s i s t o r i s 1 megohm, so that the output pulse has a decay time of approximately 30 microseconds. A r e l a t i v e l y long decay time i s necessary to prevent double d i f f e r e n t i a t i o n of the pulse when i t i s fed into the main amplifier. This would produce a p o s i t i v e overshoot along with the amplified pulse. to follow page 23 RCA 6342 Figure 5 S c i n t i l l a t i o n Detector El e c t r o n i c s . - 2 4 The main amplifier was a commercially available unit, (Atomic Instrument Co., Model 215 Non-Overloading Amplifier, maximum gain 6400$ r i s e time 0.2 u,see). The low l e v e l output of thi s amplifier was modified to provide a 100si. output impedance. From t h i s low l e v e l output the pulses were fed v i a 250 feet of RG 7/U coaxial cable to a kicksorter located i n the Van de Graaff Laboratory. Since the pulses were sent down the cable at a low l e v e l (< 1 v o l t ) , ampli-f i c a t i o n was necessary at the other end before pulse height analysis could be performed. For t h i s purpose a Dynatron Type 1430A amplifier was employed. The output of t h i s amplifier was then fed into a 100 channel kicksorter (Computing Devices of Canada Ltd.) which performed the pulse height analysis and stored the data. II. The Magnetic Spectrometer ( i ) Some Remarks on Thin Lens Spectrometers The th i n lens beta ray spectrometer, f i r s t used by Deutsch, E l l i o t and Evans (10), belongs to the class known as h e l i c a l spectrometers. The c h a r a c t e r i s t i c feature of any spectrometer i n thisu class i s the use of an a x i a l l y symmetric magnetic f i e l ^ w i t h the source and detector placed along the f i e l d &|pis. In the case of the thi n lens spectrometer t h i s r i e l t f f s produced b y a r e l a t i v e ^ short (compared with the source to detector distance) current carrying c o i l , with the a x i a l source and detector located -25-on opposite sides of the c o i l and equidistant from i t . With t h i s arrangement, electrons leaving the source w i l l again return to the axis at some other point. The location of the int e r s e c t i o n of the electron t r a j e c t o r y with the f i e l d axis depends, of course, on the electron momentum and the magnetic f i e l d strength. Or, for the p a r t i c u l a r case with f i x e d source and detector positions, the magnetic f i e l d strength (determined by the current flowing i n the c o i l ) determines the momentum of the electrons focussed on the deteetor. In f i g . 6 the r a d i a l displacement from the axis of electron t r a j e c t o r i e s (for monoenergetic electrons) as a function of the distance along the axis i s i l l u s t r a t e d . Ring Focus Source Magnetic Axis F i g . 6 Radial Displacement of Electron Trajectories from the Magnetic Axis for Different Emission Angles. It w i l l be noted from t h i s figure that the point of - 2 6 -i n t e r s e c t i o n of the t r a j e c t o r i e s with the axis also depends upon the emission angle. Since i n practice a range of emission angles must be accepted, t h i s r e s u l t s i n an imprecisely defined focus (spherical aberration) with a consequent l i m i t a t i o n on the instrument resolving power. As a matter of f a c t , i n order to keep the spherical aberration within tolerable l i m i t s , i t i s necessary to r e s t r i c t the electrons to low emission angles. Because of i t s r e l a t i v e l y low cost and easy con-s t r u c t ionjthe thin lens spectrometer occupied a prominent position among the instruments used for the study of nuclear decays for many years. More recently however, spectrometers such as the Siegbahn-Slatis intermediate image spectrometer, which have a x i a l f i e l d gradients chosen so as to minimize the spherical aberrations, and hence givi n g greatly improved transmission and resolution have come into greater use, with a r e s u l t i n g decline i n the use of the t h i n lens spectrometer. Because of the low magnetic f i e l d i n the v i c i n i t y of the source and the easy a c c e s s i b i l i t y to the source, the th i n lens spectrome-ter i s r e a d i l y adapted f o r beta-gamma coincidence measure-ment, using a s c i n t i l l a t i o n detector for the gamma rays. In view of t h i s and the f a c t that the modifications d i s -cussed below provide a s i g n i f i c a n t improvement i n i t s performance, the th i n lens spectrometer must s t i l l be - 2 7 -considered a very valuable tool for the analysis of nuclear decay schemes. ( i i ) The Modified Thin Lens Spectrometer The modifications to achieve improved performance of the thin lens spectrometer used for some of the measure-ments i n the present investigation,have been described by Mann and Payne (11). These modifications consisted of ri n g focus detection and asymmetric placement of the source and detector along the spectrometer axis with respect to the magnet. It i s well known that the electron t r a j e c t o r i e s in an a x i a l f i e l d spectrometer exhibit a r i n g focus property. That i s , the t r a j e c t o r i e s reach maximum convergence o f f the magnetic axis, i n a plane nearer to the source than the a x i a l focus (see fo r example f i g . 6). Since there i s c y l i n d r i c a l symmetry,this maximum convergence occurs i n a rin g . By placing a detector at t h i s r i n g focus the spherical aberrations of the thin lens f i e l d are not as important. It i s therefore possible to use the higher electron emission angles, (and thereby increasing the transmission), which were prohibited by excessive aber-rations i n the conventional th i n lens spectrometer. Because the s i z e of the vacuum chamber of the spectrometer i s a fi x e d parameter i n t h i s modification, the higher emission angles could only be achieved by moving the source nearer the magnet. The modified -28-spectrometer i s i l l u s t r a t e d schematically i n f i g . 7, Detection of the electrons at the r i n g focus was achieved with an anthracene c r y s t a l r i n g (5.15 cm radius), o p t i c a l l y coupled to the photocathode of a f i v e inch photo-m u l t i p l i e r (DuMont 6364) through a short l u c i t e l i g h t pipe. Magnetic s h i e l d i n g i n the form of a mu-metal s h i e l d inside a Fernetic-Conetic s h i e l d kept the gain of the photo-m u l t i p l i e r independent of the magnetic f i e l d strength for magnet currents up to 4.5 amps, which was higher than the maximum required to focus the highest energy conversion 75 electrons (400 kev) i n Se The e n t i r e detector assembly including a voltage divider to supply the proper potentials to the photo-m u l t i p l i e r dynodes was mounted i n the vacuum chamber with only two external connections brought through Kovar seals. These were the connections to c o l l e c t o r and the photo-m u l t i p l i e r focussing electrode. Through the l a t t e r connection the pote n t i a l of the focussing electrode was adjusted with a potentiometer to some value between zero and that of the f i r s t dynode so that the photomultiplier gain was maximized. The high voltage to energize the photomultiplier was supplied through a 10 K-n c o l l e c t o r load r e s i s t o r which was outside the vacuum. The photomultiplier output pulses occurring across t h i s load were coupled v i a a 50 pf condenser to a 6J6 cathode follower and thence by cable to an amplifier and scaler. -29-Two sets of b a f f l e s plus the central lead b a f f l e to s h i e l d the detector from d i r e c t gamma ra d i a t i o n were used. The e x i t b a f f l e s consisted of two aluminum discs 1/8 inch thick mounted d i r e c t l y i n front of the s c i n t i l l a t o r such that they defined an annular s l i t , 3 millimeters wide. The entrance b a f f l e s , also of aluminum were mounted on the source holder i n front of the source so that they defined an annular s l i t through which electrons with emission angles between 17.4° and 21.3° would pass. Two controls outside the vacuum could move the source and entrance b a f f l e s , through a rack and pinion arrange-ment, i n a plane perpendicular to the spectrometer axis. This feature was necessary to centre the source so that the r i n g focus was concentric with the e x i t b a f f l e s . To centre the source the in t e n s i t y of a prominent conversion peak was measured as a function of the source po s i t i o n in the source plane. The pos i t i o n giving maximum int e n s i t y determined the proper source position. To eliminate defocussing e f f e c t s due to the h o r i -zontal component of the earth's magnetic f i e l d , the spectrometer was positioned so that i t s axis was i n the magnetic meridian. The e f f e c t of the v e r t i c a l component was eliminated by two current carrying compensating c o i l s located above and below the spectrometer. Since no iron i s used i n the construction of t h i s instrument,the magnet current i s d i r e c t l y proportional to -30-the momentum of the focussed electrons. This current was supplied to the magnet through a regulator capable of 4 regulation to 1 part i n 10 . A voltage derived from a Rubicon potentiometer and coupled into the regulator, determined the magnitude of the magnet current. With the spectrometer set up as described here the 137 Cs 661 kev K conversion peak had a resolution of 1.30% at a measured transmission of 0.56%*. III . The Coincidence System (i) Introduction A coincidence counting system for the study of time-correlated t r a n s i t i o n s i n nuclear decays, consists e s s e n t i a l l y of two (or more) ra d i a t i o n detectors and a coincidence c i r c u i t which produces an output pulse i f and only i f i t receives input pulses simultaneously from the two detectors. (More p r e c i s e l y , the input pulses must occur within the resolving time of the coincidence c i r c u i t . ) Because of i t s energy proportionality, high detection e f f i c i e n c y and short decay times, the s c i n t i l l a t i o n de-tector i s i d e a l l y suited as the detector f o r coincidence spectrometry. In f i g . 8 a simple system for measuring gamma-gamma coincidences, using two sodium iodide s c i n t i l l a t i o n * See Appendix I. to follow page 30 Scintillation Detector Scintillci t/on Dei t c t o r > PoUe Htitjht ->-Comci i ence t\ r-co i t Sea I C V Figure 8 Block Diagram of a yy Coincidence Spectrometer \ P u l s e H e i c ^ t A •> ti Ui^ f«r \ ScmtiU at i on Detector Fast Coin c i A e wee C i»-1 u i t V Slow Coincide nee CI i'C o 11 V bc i nti llcitioh Dettctov -3>— N / Pulse \ / 'sea Figure 9 A Fast-Slow Coincidence System. -31 spectrometers i s i l l u s t r a t e d i n block diagram form. With t h i s system one pulse height analyzer i s set to accept the photopeak pulses of a p a r t i c u l a r gamma ray. The second pulse height analyzer i s then scanned i n steps over the entire pulse height spectrum and the coincidence spectrum i s determined from the coincidence counting rate recorded at each step. If conventional pulse amplifiers are used, the r i s e -time of the pulses into the pulse height analyzers w i l l be approximately 0.2 microseconds. This means that the output from the pulse height analyzer w i l l be delayed by an amount dependent, i n part, upon the discriminator voltage l e v e l . Since i n the course of a coincidence measurement the discriminator l e v e l i s changed and hence the r e l a t i v e delay of the pulses into the coincidence c i r c u i t i s also changed, i t i s necessary to have a c o i n c i -dence resolving time larger than the magnitude of t h i s discriminator dependent delay, i . e . the resolving time must c e r t a i n l y be larger than the amplifier risetime. An even more serious l i m i t a t i o n on the minimum value for T i s imposed when the pulse height analyzer c i r c u i t s used are of the type i n which the output pulse appears when the t r a i l i n g edge of the input pulse crosses the d i s c r i m i -nator l e v e l . Hence instead of the r e l a t i v e delay of the pulses into the coincidence c i r c u i t being governed by the pulse r i s e t i m e , i t i s , i n t h i s case, dependent on the pulse decay time which i s generally much longer. -33 t h i s coincidence counting method with a fast coincidence c i r c u i t of the i r own design,achieved resolving times o f ^ 10~ 9 sec. ( i i ) The Gamma-Gamma Coincidence System Fi g . 10 i s a block diagram of the fast-slow system used to measure gamma-gamma coincidences. The components within the dashed rectangle represent a fast-slow c o i n c i -dence chassis commercially available from Borg-Warner Co. Other commercially manufactured ele c t r o n i c s used i n t h i s system included an Atomic Instrument Co. Model 215 non-overloading amplifier, a Tracerlab Model RLA1 amplifier and two Type 1430A Dynatron Radio Ltd. amplifiers, as well as an Atomic Instrument Co. Model 510 sin g l e channel pulse height analyzer and a Computing Devices of Canada 100 channel kicksorter. Two outputs are taken from each of the photomulti-p l i e r s of the s c i n t i l l a t i o n detectors, one being the voltage pulses developed across a 10 K J i c o l l e c t o r load and the other, pulses developed across a 1 megohm load i n the eighth dynode c i r c u i t . Pulses from the l a t t e r output i n Channel 1 are treated in the same manner as they were for the measurement of the gamma ray spectrum. That i s , from the preamplifier, the Channel 1 slow pulses are fed through an amplifier and thence at a low l e v e l v i a 250 feet of cable to a second amplifier and ending f i n a l l y at the 100 channel kicksorter. The slow output pulses to follow page 33 Channel 1 Channel 2 F a s t Di->ve.r Ampti $-ie , ( i e , i - D e t e c t o r 1 Oetectov 2 Pve -r 0 . 0 5 /ts.ec. De \ c i ^ line 1 _Z_ v F a a Driv t f •4 S V i a p e r _Z_ AnciU\?.e.>-s \ " s A ~ 2 ~ 0 ut p u t Sat C v . C j & 250 f t Rfa7/j JT J I K Amplif ier D\o<>e l<ick s o r t t v 1 Giate Figure 10 Block Diagram of Fast=Slow Gamma-Gamma Coincidence Spectrometer. -34-from Channel 2 on the other hand are amplified and then fed into a single channel pulse height analyzer, the output of which goes to the slow coincidence c i r c u i t . At the same time the f a s t pulses from the c o l l e c t o r s , which may have a non-linear amplitude dependence on gamma ray energy due to space charge e f f e c t s i n the l a s t a m p l i f i -cation stages of the photomultiplier, are used to operate the f a s t coincidence c i r c u i t . From the c o l l e c t o r the pulses are fed onto the grids of the 6AK5 preamplifiers. These tubes are operated at a gain of f i v e . Pulse trans-formers i n the output reverse the phase and give an output impedance of 100 ohms to match to the coaxial cable. (The c i r c u i t diagram for the f a s t preamplifier i s shown in f i g . 5.) Because the f a s t coincidence c i r c u i t requires an input of 20 milliamps into 1 K i l ^ t h e pulses from the f a s t preampli-f i e r s cannot be fed d i r e c t l y to t h i s c i r c u i t but must go instead to a f a s t coincidence driver c i r c u i t . The driver c i r c u i t was designed to produce the re-quired 20 milliamps pulse to the f a s t coincidence input when i t received an input pulse of 5 m i l l i v o l t s or greater. The schematic c i r c u i t diagram of t h i s driver i s shown in f i g . 11. B a s i c a l l y i t consists of a two stage amplifier with a gain of 100, a Kandiah type discriminator (13) with a trigger s e n s i t i v i t y of^O.5 v o l t s , and an output stage capable of d e l i v e r i n g the required 20 milliamps into 1 Ksi . When the photomultipliers were operated with near Amp 1 i f i e r AA/V Kandiah Discriminator Output 15 k 2w - • v150v 0,01 39k 6AkS > - I -0.1 V\AA-• 6OK + 3oov 3 0 0 -AAAA-6 A H 6 ,60 k IWIOO 5 k o-l loo*< 4- 300v -15K • &0K 0-1 so^S I K O.OI >loK • lOOK lOK 4 - 2 o o v Figure 11 C i r c u i t Diagram of the Fast Coincidence Driver. O Hj O 1 •a p CK3 C O -35-th e maximum rated anode - cathode voltage (1,500 v o l t s ) , as 75 they were throughout the Se measurements, the t o t a l ab-sorption i n the Nal(Tl) c r y s t a l of a 265 kev gamma ray produced a 1.5 vo l t pulse at the output of the f a s t pre-amplifier. In view of the 5 m i l l i v o l t s e n s i t i v i t y of the driver c i r c u i t t h i s means that the i n i t i a l development of the pulse produces the driver output to the f a s t c o i n c i -dence c i r c u i t . That i s , the timing at the f a s t c o i n c i -dence input i s determined by the front edge of the fa s t preamplifier pulses and i s independent of pulse height, (due to the f i n i t e risetime of the pulses), f o r pulses with amplitudes above ^50 m i l l i v o l t s (corresponding to ^  9 kev gamma rays). A s i m p l i f i e d version of the f a s t coincidence c i r c u i t i s i l l u s t r a t e d i n f i g . 10. It i s e s s e n t i a l l y a Rossi c i r c u i t with the addition of a shorted delay l i n e i n the output to shape the pulses. The length of t h i s delay l i n e determines the resolving time of the c i r c u i t . The diode at the open end of t h i s l i n e i s back biased so that pulses due to only one tube being cut off w i l l not be passed but overlapping (coincident) pulses from the two tubes w i l l be passed. The coincidence pulses are ampli-f i e d and shaped to a f l a t top 0.5 microsecond pulse before being fed v i a a delay l i n e to the slow coincidence c i r c u i t . The delay l i n e which i s RG65/U cable giving approximately two microseconds delay, i s necessary to -36-allow the Channel 2 slow pulses to be amplified and analyzed i n the pulse height analyzer. Imposing the slow coincidence condition then selects from a l l the f a s t coincidence pulses only those that s a t i s f y the additional requirement that the Channel 2 pulse corresponds to a gamma ray i n the energy range selected by the pulse height analyzer. The slow colncidenee output i s shaped by a univibrator to a f l a t top po s i t i v e pulse 2 microseconds long and twenty vol t s i n amplitude, and appears as the output from the fast-slow unit. This 2 microsecond pulse i s attenuated by a factor of 100 with a frequency compensated attenuator, and then sent v i a a second 250 foot cable to the kicksorter. At the input of the kicksorter there i s a l i n e a r diode gate. When the kicksorter i s switched to i t s coincidence mode of operation,this gate i s biased closed and a p o s i t i v e pulse with an amplitude greater than 15 vo l t s i s required at the kicksorter coincidence input to open the gate, and allow analysis of a pulse that may occur at the main (pulse height analysis) input. In the present case the 2 micro-second output pulse from the fast-slow unit was amplified to approximately a 25 v o l t amplitude and then applied to the coincidence input of the kicksorter. The Channel 1 pulses after amplification by a second amplifier were fed into the main kicksorter input. Because considerable delay e x i s t s between recording -37-a coincident event by the detectors and the appearance of the pulse at the output of the fast-slow u n i t , the Channel 1 pulse must also be delayed i f i t i s to appear at the kick-sorter input i n the proper time r e l a t i o n with t h i s gate pulse. The delay required was 2.7 microseconds, and was provided by four feet of H.H. 2500 delay l i n e * , incorporated into the Channel 1 preamplifier. In f i g . 12 the r e l a t i v e timing of some of the pulses occuring i n the system just described, are i l l u s t r a t e d . The f a s t outputs from both photomultipliers and the slow output from the Channel 2 photomultiplier a l l occur at time t = o. The pulse l a b e l l e d "Channel 2 Slow Coincidence Input", i s the pulse height analyzer output after pulse shaping. This pulse i s delayed by the amplifier, pulse height analyzer, and shaper el e c t r o n i c s . It w i l l also be noted that the delay of t h i s pulse depends to some extent on the baseline discriminator s e t t i n g of the pulse height analyzer. Pulses with minimum and maximum delay due to t h i s e f f e c t are shown. The fourth pulse i l l u s t r a t e d i s the fa s t coincidence output delayed by the RG65/U cable. The pulses i n 3 and 4 constitute the inputs to the slow c o i n c i -dence c i r c u i t . I t w i l l be seen that both input pulses are delayed by an equal amount and cannot be delayed out of coincidence by a l t e r i n g the pulse height analyzer baseline discriminator voltage l e v e l . The 2 microsecond fast-slow Available from Columbia Technical Corp., New York 22, N.Y. to follow page 37 Microseconds Q - 1 2 3 4 S 6 7 1. Fast Preamplifier Output 2. Channel 2 Slow Output 3. Channel 2 Slow Coin c i -dence Input 4. Fast Coinci-dence Output, Delayed 5. Fast-Slow Coincidence Output 6. Channel 1 Slow Output, Delayed * The two pulses shown here represent the maximum and minimum delay of the pulse height analyzer output pulse. The delay i s dependent on the pulse amplitude and the baseline discriminator s e t t i n g . Figure 12 Pulse Timing i n Gamma-Gamma Coincidence System. -38-output pulse shown i n 5 appears simultaneously with the a r r i v a l of the fa s t coincidence pulse at the slow c o i n c i -dence input. This pulse serves as the kicksorter gate pulse and as i s shown i n 6, the 2.7 microsecond delay of the delay-l i n e plus the delay introduced by the ele c t r o n i c s r e s u l t s i n the Channel 1 pulse (signal) and the gate pulse appearing at the kicksorter delayed by equal amounts, i . e . i f a c o i n c i -dent event i s detected i t w i l l be recorded by the kicksorter. S t a b i l i t y Monitoring By varying the angle between the detectors and measuring the gamma-gamma coincidences with the system just described, i t would be possible to determine the d i r e c t i o n a l c o r r e l a t i o n of a gamma-gamma cascade. Since, however, these measurements usually involve counting over a period of sever-a l days, severe requirements are placed on the s t a b i l i t y of the e l e c t r o n i c s . In the present case, while every attempt was made to achieve a highly stable system, and to a large measure t h i s was r e a l i z e d , there were occasions when s l i g h t changes i n the amplification were noted. Therefore when the gamma-gamma d i r e c t i o n a l c o r r e l a t i o n measurements were made a gain s t a b i l i t y monitor was added to Channel 2. Only the s t a b i l i t y of Channel 2 was monitored because i t i s the most c r i t i c a l , s i n c e the s h i f t s can af f e c t the r e l a t i v e per-centages of gamma rays accepted i n the pulse height analyzer window. This monitor arrangement i s i l l u s t r a t e d i n the -39-block diagram i n f i g . 13. It consisted of a second singl e channel pulse height analyzer connected to the output of the Channel 2 amplifier, a count rate meter at the output of the pulse height analyzer and a pen recorder to record the count rate. By s e t t i n g a narrow window of the pulse height analyzer half way up the side of an intense peak i n the gamma spectrum i t was found that gain s h i f t s of 0.5% produced very noticeable changes i n the pulse height analyzer counting rate. Very small s h i f t s were corrected f o r by a l t e r i n g the baseline settings of the pulse height analyzers. I f , however, a large s h i f t (>0.5%) was apparent during the course of a run the measurement was discarded. Location of the Pulse Height Analyzer Window Position In a coincidence measurement i t i s important to know what portion of the spectrum f a l l s within the acceptance window of the pulse height analyzer. This could be done by measuring the spectrum one point at a time with the pulse height analyzer and then from the c a l i b r a t i o n of the instrument determine the portion accepted for p a r t i c u l a r baseline and window width settings. There i s , however, an easier way for accomplishing t h i s by using the kicksorter. E s s e n t i a l l y the method consists of using the pulse height analyzer output as the kicksorter coincidence gate and the input to the pulse height analyzer as the s i g n a l . In p r a c t i c e , using the same arrangement as i l l u s t r a t e d to follow page 39 CKcih\--e.l 2 D e t e c t o r 1 De.tec.tov 2 pva ->1 Fat Cow. C i i i t h c e ,4 11$ t e r £ I ow C o i n c i d e Pol iC A w a I y* e v 5 e T o k \ t k 4 o r t e r Pew Figure 13 Block Diagram of Channel 2 Gain S t a b i l i t y Monitor. -40-i n f i g . 10, the pulse height analyzer gate pulse was obtained from the fast-slow coincidence output with the fa s t c o i n c i -dence switch ( S f a g t ) open, i . e . the fast-slow unit merely acts as a pulse shaper i n t h i s arrangement. The input to the pulse height analyzer - or the Channel 2 amplifier output -obviously must be delayed to arri v e at the kieksorter i n coincidence with the gate pulse. Therefore, the amplifier output i s delayed by 2.6 microseconds and attenuated by a facto r of 1000 with the c i r c u i t shown i n f i g . 14 before being sent to the kicksorter v i a the cable connected to the Channel 1 amplifier i n f i g . 10. A block diagram showing the connections f o r t h i s case i s given i n f i g . 15. Operating the kicksorter i n i t s anticoincident mode re s u l t s i n the complete pulse height spectrum of the gamma rays detected by the Channel 2 detector being recorded. By switching to the coincident mode of operation only the pulses f a l l i n g within the pulse height analyzer acceptance window w i l l be recorded. A comparison of the two kicksorter r e s u l t s f o r these two measurements then determines the portion of the spectrum accepted i n the pulse height analyzer window. An example of the r e s u l t s of the foregoing type of measurements can be seen i n f i g . 31. ( i i i ) The Beta-Gamma Coincidence System It i s sometimes d i f f i c u l t to analyze the gamma-gamma coincidence r e s u l t s because the r e l a t i v e l y poor resolution to follow page 40 O O l 50< -II v A A A A -H.H. 2500 Delay XW<n_ ~ L i n e 2 , 6 M-sec. 3K 2.9 K HE • loon. To Kicksort-er v i a 250' of Cable Figure 14 Channel 2 Amplifier Output Delay and Attenuator C i r c u i t . Channel 2 D e . t e c . t o v 1 D e t e c t o r 2. >1 Y Amp \> ? i t r S l o w 1 H e u ^ f Atte*\ Jat'>r A IT\ p \ i £ \ e v Cm t e. Figure 15 Block Diagram of the System Used to Determine the Portion of the Gamma Ray Spectrum Accepted by the Pulse Height Analyzer. to follow page 41 Harshaw l " x l | " Nal(Tl) Crystal Assembly RCA 6342 Photomultiplier i f " diameter x 5§" long Lucite Light Pipe ///////////////////////////77^ 3E Figure 16 Gamma Ray Detector Used i n the Beta-Gamma Coincidence Measurements. Spectrometer Vacuum Chamber Aluminum Fernetic-Conetic ™ Magnetic Shield y Detector Assembly ft ft Preamplifier Electronics Figure 17 Gamma Ray Detector Assembly i n the Magnetic Spectrometer. -42-focussing was very small f o r the range of magnetic currents 75 necessary f o r focussing the Se conversion electrons. It should be noted that a small photomultiplier gain s h i f t with increasing magnetic f i e l d was tolerable since each coincidence measurement was made with a p a r t i c u l a r con-version electron energy focussed in the magnetic spectrome-ter, i . e . the magnetic f i e l d , and hence the photomultiplier gain, was constant during each coincidence measurement. The gamma ray detection assembly as i n s t a l l e d i n the magnetic spectrometer i s shown i n f i g . 17. A lead s h i e l d around the Nal(Tl) c r y s t a l was necessary to prevent Compton scattered gamma rays from the surrounding brass, from being detected. The electronics used i n the conversion electron-gamma coincidence measurements were e s s e n t i a l l y the same as those used f o r the gamma-gamma coincidence measurements. Fi g . 18 i s a block diagram i l l u s t r a t i n g the arrangement used. Since l i n e a r i t y between pulse height and s c i n t i l -l a t i o n i n t e n s i t y i s not required at the beta detector, only one preamplifier, a 6J6 cathode follower that re-ceives i t s input s i g n a l from the c o l l e c t o r of the 5" photomultiplier was used for t h i s detector. The pre-amplifiers on the gamma side were i d e n t i c a l with those described previously. Fast coincidence s e l e c t i o n of the pulses from the fa s t gamma preamplifier and beta preamplifier was made to follow page 42 |9 C o."C V> o £ 4 Pa \ \ o w e r Af" p\i^>er x 2 Fast D r i v e n -Discri mm a. toy Sea lev Detect or Fast-Co iv\c\ device. 0.0.7 ^t** f a s £ 0.6 .^s Co\nt\ device A t-v,p\\ W v n-A rv\ c> \ \ ^»e. r R\c\<Sovtev date Figure 18 Block Diagram of the Beta-Gamma Coincidence System. -43 i n a fashion s i m i l a r to that described for gamma-gamma coincidence measurements. In t h i s case, however, the beta cathode follower out-put pulses required a further amplification by a factor 2 before being fed to the f a s t coincidence driver. The beta output pulses were also amplified and then fed into a voltage discriminator i n the same way as was done when simply measuring the beta spectrum. For the coincidence measurements, however, the discriminator out-put went not only to the sca l e r but also to the slow coincidence c i r c u i t . The other input to the slow c o i n c i -dence c i r c u i t came from the f a s t coincidence output after a delay of 0.6 microseconds. (This delay was necessary to compensate f o r the delay i n the amplifier and d i s -criminator.) As i n the gamma-gamma coincidence measure-ments, the shaped 2 microsecond pulse at the output of the fast-slow.unit was used as the coincidence gate pulse at the kicksorter f o r the pulses from the gamma detector. So that'; the gamma pulses would arr i v e at the kick-sorter i n tjhfe proper time r e l a t i o n with the gate pulses, a 1 microsecond H.H. 2500 delay l i n e was placed i n series with the kicksorter input cable. It w i l l be noted from f i g . 18 that a variable delay l i n e was incorporated between the f a s t driver output and the f a s t coincidence input on the gamma detector side. This was necessary to compensate f o r the difference -44-between the t r a n s i t time of the electrons i n the 5 inch photomultiplier used as the beta detector, and the 2 inch photomultiplier used i n the gamma detector. To determine the magnitude of th i s t r a n s i t time difference the spectrome-ter magnet current was set to focus electrons of one of the 75 intense Se conversion t r a n s i t i o n s known to be i n c o i n c i -dence with a gamma t r a n s i t i o n . Conversion electron-gamma coincidences were then measured as a function of the delay introduced by the variable delay l i n e . The r e s u l t s of t h i s measurement fo r two values of the e l e c t r i c f i e l d strength between the photocathode and f i r s t dynode of the 5 inch photomultiplier are shown graphically i n f i g . 19. © +-> a « focussing electrode + 2 v o l t s focussing electrode + 350 v o l t s Y Delay Microseconds Fi g . 19 Beta-Gamma Coincidence Response as a Function of the Delay on the Gamma Side, As can be seen^the increased f i e l d strength reduced the t r a n s i t time by ~ 0.1 microseconds. For the con-version electron-gamma coincidence,measurements the -45-photomultiplier voltages giving the higher f i e l d strength between the photocathode and f i r s t dynode were used and the variable delay l i n e was set at 0.07 p,sec. It i s of interest to note that with a double pulser providing the input s i g n a l to both beta and gamma pre-amplifiers no r e l a t i v e delay between the input pulses to the f a s t coincidence c i r c u i t was detectable. This i n -dicates that the delays measured above can arise only i n the photomultipliers. IV. Kicksorter Remote Control In order to reduce the handicap imposed by the separation of the kicksorter from the res t of the appa-ratus used i n these measurements, a remote control unit for the kicksorter was b u i l t . With t h i s unit i t was possible to control the COUNT,PRINT, and ERASE modes of kicksorter operation from the spectrometer location. -46-CHAPTER III MEASUREMENTS I. The Source 75 The Se source used in these measurements was prepared by the i r r a d i a t i o n of natural selenium with slow neutrons i n 74 the NRX reactor at Chalk River. The 0.87% Se i n natural 75 selenium was converted to Se through a (n,<y) reaction. Other radioactive isotopes are produced i n t h i s i r r a d i a t i o n . 79 Except f o r Se , however, the l i f e t i m e s of these are no more than a few minutes so that by the time the source was used 79 none of these were present. Se has a h a l f l i f e greater than 6.5 x 10 4 years. This, together with the f a c t that the 78 neutron absorption cross section of Se i s very small, means that radiations from t h i s isotope are n e g l i g i b l e . During the course of these measurements two sources were required. Each one consisted of 7 milligrams of selenium i n the form of a p e l l e t which had been i r r a d i a t e d with slow neutrons for two weeks. The a c t i v i t y of each source was approximately one m i l l i c u r i e . Except for the photoelectron spectrum measurement, described below, only a f r a c t i o n of t h i s source was necessary for any of the other measurements made. Therefore upon completion of the photoelectron spectrum measurement the me t a l l i c source was dissolved i n concentrated n i t r i c acid. Evaporation of the r e s u l t i n g s o l u t i o n l e f t a white powder residue of selenium dioxide -47-(SeG2) which i s water soluble. Hence aqueous solutions formed from t h i s residue were used i n a l l subsequent source preparations. I I . The Gamma Ray Spectrum of Se (i) The Photoeleetron Spectrum To study the gamma ray spectrum with the magnetic spectrometer, use i s made of the photoelectric e f f e c t . That i s , the gamma rays are allowed to undergo photoelectric absorption i n a thin radiator, with the magnetic spectrome-ter then being used to analyze the energies of the ejected photoelectrons. For each gamma t r a n s i t i o n one or more peaks may be observed i n the photoelectron spectrum. These occur because the photoelectric absorption can take place i n any of the atomic s h e l l s . The photoelectron then has an energy equal to the absorbed photon energy less the binding energy of the ejected electron i n the atom. In practice peaks corresponding to absorption i n the innermost s h e l l s only (K,L,M) are observed. Provided i t i s energeti-c a l l y possible absorption i n the K s h e l l i s most probable and therefore accounts f o r the most intense peaks i n the photoelectron spectrum. Since the photoelectric cross-section per unit mass 5 increases approximately as Z , elements of high atomic number are preferred as radiators. In the present measure-ments, both lead and bismuth were used as radiator material. -48-The bismuth radiator material was prepared by evapo-o r a t i n g s 1.9 mg/cm of bismuth, in a vacuum upon aluminum 2 f o i l of thickness 1.25 mg/cm , while the lead was prepared o by r o l l i n g lead f o i l to a 7.2 mg/cm thickness. A four millimeter diameter c i r c l e was cut out of each of these f o i l s and used as a radiator f o r a photoelectron spectrum. The source holder and manner of mounting the radiator are shown i n f i g . 20. Aluminum Cotton Packing Bismuth or Lead Radiator Fi g . 20 Source and Radiator Holder for the Photoelectron Spectrum. In t h i s source holder design the amount of aluminum around the source i s kept to a minimum i n order to reduce the production of Compton electrons, which appear with a broad energy d i s t r i b u t i o n i n the measured spectrum and can cause some d i f f i c u l t y i n analyzing the photoelectron spectrum. Approximately 1/8" of aluminum was l e f t between the source and radiator to absorb the in t e r n a l conversion electrons emitted by the source, (there are no primary 75 beta p a r t i c l e s emitted i n the Se decay). Beeause the -49-r a d i a t o r s were thin, the p r o b a b i l i t y of photoelectric absorption of the gamma photons was small. Hence, i t was necessary to use the entire one m i l l i c u r i e source to produce a reasonable photoelectron counting rate. F i g . 21 i s the measured photoelectron spectrum from the bismuth radiator and f i g . 22 the corresponding spectrum using the lead radiator. Beneath the peaks i n both spectra a continuous d i s t r i b u t i o n (Gompton electrons produced i n the source holder) i s shown. Assuming no Gompton electrons are produced i n the radiator, because of i t s small thickness, the shape and in t e n s i t y of the Compton d i s t r i b u t i o n shown i n f i g s . 21 and 22 was obtained by removing the radiator from the source holder and re-measuring the spectrum. The photoelectric absorption i n the thin bismuth radiator was very small for the higher energy gamma rays, r e s u l t i n g i n low in t e n s i t y photoelectron peaks. The thicker lead radiator was therefore used to increase the i n t e n s i t i e s of these peaks. As a r e s u l t , p o s i t i v e i d e n t i f i c a t i o n of a peak corresponding to an electron energy of 215 kev (304 K peak) could be made in the lead spectrum while i t i s barely perceptible i n the bismuth spectrum. Unfortunately, the increased radiator thickness has an adverse a f f e c t on the peak shapes. This i s because the photoelectrons suffer some energy loss i n getting out of the thick radiator, with the r e s u l t that each peak has a long low energy t a i l . so I _J 200 1 zso _ L _ 300 _J 10.8-9.b-72-6.0-1.6-2.*-0- • 136 K 136 L 265 K Electron Energy Kev Figure 21 Se75 Photoelectron Spectrum 1.86 mg/cm2 Bismuth Radiator. .08 JO .12 .20 .36 C r o o a (TO © to Spectrometer Potentiometer Setting 50 _L_ 200 _J 2to _J 30o _l T Y> Electron Energy Kev 265 K MH 22-8 H 4 i 2H OH CO B • H a \ (0 4-> a o o 136 K 136 L 121 L 280 K + Gompton /' Background Figure 22 Se' 5 Photoelectron Spectrum 7.2 mg/cm2 Pb Radiator. INSET 265 L 1 J I 280 L / 1 ' 304 K 401 K Spectrometer Potentiometer Setting 401 L I .08 1G I .20 .24-— T " rr o Hj o M 3 •3 P © CO -50-Electron energies corresponding to the peaks were de-137 termined from the spectrometer c a l i b r a t i o n on the Gs 661 kev K conversion l i n e (Hp -.3381.28 + 0.5 gauss-cm) (14). From these energy determinations i t was possible to i d e n t i f y each peak according to the energy of the gamma ray tran-s i t i o n causing i t , and the atomic s h e l l from which the electron was ejected. The energy determinations were used only for i d e n t i f i c a t i o n of the tr a n s i t i o n s responsible for the peaks. More accurate t r a n s i t i o n energy measurements have been made by Edwards et a l . (15) and w i l l be used l a t e r i n the energy assignments to the excited states. ( i i ) The S c i n t i l l a t i o n Spectrum In f i g s . 23 and 24 the gamma ray spectrum measured with the previously described s c i n t i l l a t i o n spectrometer, i s shown. The source for t h i s measurement was i n the form of a small spot of selenium on a thin aluminum backing and placed 6 cm from the front face of the Nal(Tl) detector. (The l j " x 1" c r y s t a l was used i n t h i s case.) The two most prominent peaks i n the s c i n t i l l a t i o n spectrum are composite peaks, the lower energy one con-s i s t i n g of the unresolved photopeaks of the 121 kev and 136 kev gamma t r a n s i t i o n s and the higher energy one con-s i s t i n g of the unresolved photopeaks corresponding to the 265 kev, 280 kev and 304 kev gamma tr a n s i t i o n s . To enable analysis of t h i s spectrum, the photopeak p r o f i l e s of single gamma tr a n s i t i o n s i n the energy ranges of both of these to follow page 50 Kicksorter Channel Number 4-0 SO Go 70 80 90 loo Kicksorter Channel Number -1 1 1 1 X 20 30 4 0 SO > 60 70 -51-composite peaks must be known. This information was obtained by measuring the gamma ray spectra of H g 2 0 3 (one gamma tran-57 s i t i o n at 279 kev) and Co (two gamma tra n s i t i o n s at 123 kev - 90% and at 137 kev - 10%), with the same source-detector 75 geometry as was used for the Se spectrum. A discussion of 75 the use of these two spectra in the analysis of the Se spectrum i s deferred to the "Gamma Ray Tra n s i t i o n I n t e n s i t i e s " subsection. A photopeak corresponding to a very weak 570 kev gamma 75 t r a n s i t i o n , f i r s t found i n the Se decay by Langevin and Langevin (16) i s shown i n f i g . 25. This spectrum which contains the 401 kev peak as well, was obtained with the same arrangement used previously, but with a stronger source and 3/16" of lead between the source and the Nal(Tl) c r y s t a l . Also, the kicksorter input was biased so that only pulses corresponding to detection of gamma rays with energies higher than approximately 350 kev were recorded. The lead absorber was necessary, i n th i s case, to reduce the very high counting rate of the lower energy gamma rays, which were of no interest i n th i s measurement and which could cause count rate dependent i n s t a b i l i t i e s i n the photomultiplier gain. Using a l£" x 5 mm thick Nal(Tl) c r y s t a l with a 0.001" aluminum window, as the detector, the arsenic 75 X-rays r e s u l t i n g from K capture i n Se and Internal con-version i n As were measured. The X-ray photopeak i s i l l u s t r a t e d in f i g . 26. The use of the d i f f e r e n t c r y s t a l to follow page 51 0 4H 2H OH 401 kev Figure 25 S e 7 5 -y Ray Spectrum above 350 kev (3/16" Pb absorber between source and detector). 570 kev -r— 10 20 I 4-0 50 &0 70 I 30 Figure 26 n « S c i n t i l l a t i o n Spectrum Kev Q f t h e j^aenle x ra^ -^-L produced i n the Se?* / \ decay. bs/Channel / \ ( I f " x 5 mm Nal(Tl) / V Detector) 3 \ / ° V •/ 3o-25-20-4 15-10 H 5H 10 10 30 4-0 50 Kicksorter Channel Number so 70 -52-was dictated by two considerations; 1) the aluminum con-tainer of the 1" x I f " c r y s t a l being 0.025" thick w i l l absorb a very large f r a c t i o n of the low energy (11.8 kev) X-rays, and 2) the low energy X-rays are absorbed very near the surface of the Nal(Tl) c r y s t a l , meaning that the photons from the s c i n t i l l a t i o n s produced by detection of the X-rays must tr a v e l through e s s e n t i a l l y the f u l l thickness of the c r y s t a l before reaching the photo-cathode j there being less l i k e l i h o o d of the photons being absorbed or otherwise prevented from reaching the photocathode i n the thin c r y s t a l , better X-ray resolution i s attainable with i t . ( i i i ) Gamma Ray Transition Intensities (a) Relative In t e n s i t i e s from the Photoelectron Spectra In p r i n c i p l e the gamma ray t r a n s i t i o n i n t e n s i t i e s could be determined from the photoelectron spectrum. To do t h i s , however, i t i s necessary to take into account the va r i a t i o n of the photoelectric cross-section of the radiator with gamma ray energy and angle of emission of the photoelectron. The l a t t e r v a r i a t i o n i s d i f f i c u l t to calculate for the type of source-baffle geometry used i n the thin lens spectrometer and p a r t i c u l a r l y so when the source (radiator) i s too large to be treated as a point. For th i s reason, the photoelectron spectrum was used only to determine the r e l a t i v e i n t e n s i t i e s of tr a n s i t i o n s within small energy i n t e r v a l s , where i t could be assumed that the angular -53-dependence of the photoelectric cross-section was the same for a l l t r a n s i t i o n s in the i n t e r v a l . In p a r t i c u l a r , the two L s h e l l photoelectron peaks of the 121 kev and 136 kev tran s i t i o n s were used to determine the r e l a t i v e i n t e n s i t y of these two t r a n s i t i o n s , while the group of K s h e l l photo-electron peaks of the 265 kev, 280 kev and 304 kev tran-s i t i o n s were used to determine the r e l a t i v e i n t e n s i t i e s of these peaks. The manner in which the r e l a t i v e i n t e n s i t i e s were de-termined i s as follows: For the 121 kev and 136 kev tran-s i t i o n s , the areas of the L s h e l l photoelectron peaks (above the Compton background) in f i g . 21 were measured and then divided by the respective magnet current settings at the peak. This i s the usual method used to take into account the fact that the peak width increases with energy in such a way as to keep the spectrometer resolution constant. The r e s u l t i n g photopeak i n t e n s i t i e s were then corrected for the va r i a t i o n of the radiator photoelectric e f f i c i e n c y over t h i s energy range by using the L s h e l l photoelectric cross-section calculations of H a l l (17). The figures so obtained were then taken as a measure of the r e l a t i v e i n t e n s i t i e s of the 121 kev and 136 kev gamma tra n s i t i o n s . The,relative i n t e n s i t i e s of the 265 kev and 280 kev gamma tr a n s i t i o n s were obtained i n a si m i l a r way using the corresponding K s h e l l photoelectron peaks i n f i g . 21. -54-Because the 304 kev peak i s barely perceptible i n f i g . 21 the re s u l t s of the lead radiator measurements were used for t h i s t r a n s i t i o n . Since the 265 kev and 280 kev peaks are not completely resolved i n f i g . 22, the int e n s i t y of the 304 kev tr a n s i t i o n was determined r e l a t i v e to the sum of the 265 kev and 280 kev i n t e n s i t i e s . (b) Analysis of the Composite Peaks i n the  S c i n t i l l a t i o n Spectrum With the determination of the r e l a t i v e gamma ray tran-s i t i o n i n t e n s i t i e s , i t becomes possible to construct the pulse height d i s t r i b u t i o n s of the ind i v i d u a l components i n the composite peaks of the s c i n t i l l a t i o n spectrum in f i g s . 23 and 24. For the higher energy composite peak t h i s i s 203 accomplished by adjusting the 279 kev peak of the Hg s c i n t i l l a t i o n spectrum so that i t s maximum counting rate occurs at points corresponding to 265 kev and 304 kev as well as 279 kev. The peak counting rates of the three d i s -t r i b u t i o n s so obtained were then scaled according to the r e l a t i v e i n t e n s i t i e s of the respective gamma tr a n s i t i o n s . Summing the resultant d i s t r i b u t i o n s then gives a synthesized peak, the shape of which i s i n excellent agreement with the measured peak. Thevlower energy composite peak consisting of the 121 kev and 136 kev photopeaks was analyzed i n a si m i l a r 57 fashion using the Co gamma ray spectrum to es t a b l i s h the shape of the ind i v i d u a l d i s t r i b u t i o n s . In t h i s case, how--So-ever , two preliminary steps were necessary. In the f i r s t place, since the photopeak i n the C o 5 7 spectrum consists of the pulse height d i s t r i b u t i o n s due to two gamma rays, (90% 123 kev and 10% 136 kev) the pulse height d i s t r i -bution for a single t r a n s i t i o n i n t h i s energy range had to be deduced from t h i s measured d i s t r i b u t i o n . A good approximation to the single gamma t r a n s i t i o n pulse height d i s t r i b u t i o n was obtained by adjusting the peak position 57 of the Co peak to 137 kev and sca l i n g i t s peak height to 10% of i t s o r i g i n a l value. Subtracting the resultant 57 d i s t r i b u t i o n from the measured Co spectrum then gave the approximation to the pulse height d i s t r i b u t i o n of the 123 kev t r a n s i t i o n . The second requirement before analysis of the composite peak could be completed, involved subtraction of a continuous pulse height d i s -t r i b u t i o n under the composite peak. This d i s t r i b u t i o n i s the r e s u l t of Compton interactions of the higher energy gamma rays (primarily the 265 kev and 280 kev gamma rays) i n the Nal(Tl) c r y s t a l with the subsequent escape of the degraded photon. The shape of t h i s d i s -t r i b u t i o n could i n p r i n c i p l e be determined from the 203 Hg spectrum; however, Compton scattering within the source i t s e l f made the low energy portion of the spectrum unreliable for t h i s purpose. Instead therefore, -56-use was made of a coincidence spectrum obtained from the conversion electron-gamma coincidence measurements (to be discussed l a t e r ) , which consists of only the 280 kev photopeak plus i t s Compton d i s t r i b u t i o n (see f i g . 30). The r e l a t i v e l y small number of counts recorded i n the co-incidence measurement does not allow a very accurate de-termination of the shape of the Compton d i s t r i b u t i o n , but since i t i s small anyway, deviations i n shape from what i s shown i n f i g . 30 do not aff e c t the present analysis. Knowing the Compton d i s t r i b u t i o n under the low energy composite peak then makes i t possible to analyze t h i s peak in terms of i t s component peaks as before. The component d i s t r i b u t i o n s determined from the analysis for both composite peaks are also shown i n f i g s . 23 and 24. In f i g . 24 photopeaks corresponding to the 66 kev and 97 kev tr a n s i t i o n s as well, are shown. These were obtained by subtracting the 121 kev - 136 kev synthesized composite peak from the measured spectrum. (c) Determination of the Gamma Ray Transition  Inte n s i t i e s The r e l a t i v e gamma ray t r a n s i t i o n i n t e n s i t i e s determined from the photoelectron spectra, together with the measured number of counts/sec. i n the peaks of the s c i n t i l l a t i o n spectrum, for each gamma ray t r a n s i t i o n are summarized i n Table 1. By di v i d i n g the peak in t e n s i t y by the detection -56A-Gamma Transition Energy Measured Gamma Ray Transition Intensity Nal(Tl) Detection E f f i c i e n c y (c) F i n a l Gamma Ray Intensity Photo-electron Spectra (a) S c i n t i l -l a t i o n Spectrum (b) 66 kev CPS 64.3+6.4 x 10" 2 2.30+0.09 x 10 4 CPS 0.28+0.04 98 71.0+6.4 2.23+0.09 0.32+0.04 121 0.362+0.014 56.2+30 2.19+0.09 2.57+0.23 136 1.00+0.02 1503.+49 2.12+0.09 7.09+0.52 199 35.3+6.4 1,72+0.12 0.21+0.05 265 1.00+0.02 821.+19 1.15+0.07 7.14+0.60 280 0.44+0.013 355.+12 1.13+0.07 3.14+0.29 304 0.019+0.006 13.6+4.7 1.00+0.04 0.136+0.047 401 84.8+2.0 0.67+0.027 1.27+0.08 572 0.0054+ 0.00"1 (a) The 121 kev gamma ray in t e n s i t y i s quoted r e l a t i v e to the 136 kev gamma ray i n t e n s i t y while the i n t e n s i t i e s of the 279 kev and 304 kev gamma rays are given r e l a t i v e to the 265 kev gamma t r a n s i t i o n . (b) In t e n s i t i e s are defined as the number of counts in the s c i n t i l l a t i o n spectrum photopeaks. In the case of unresolved peaks the r e l a t i v e i n t e n s i t i e s from the photo-electron measurements are used to determine the ind i v i d u a l photopeak i n t e n s i t i e s . (c) Includes the geometric e f f i c i e n c y . TABLE 1 Measured Se Gamma Ray Int e n s i t i e s . -57-e f f i c i e n c y which appears i n column 4 of Table 1 the actual gamma ray t r a n s i t i o n i n t e n s i t i e s are determined and given i n column 5. The Nal(Tl) detection e f f i c i e n c i e s for the tr a n s i t i o n s above 136 kev are given by the product of the i n t r i n s i c photopeak e f f i c i e n c y (Appendix II) and the geometric e f f i c i e n c y ; the l a t t e r factor depending upon the c r y s t a l s i z e and the source to c r y s t a l distance, — both e a s i l y measured quantities. Since the pulse height d i s t r i b u t i o n s for the 66 kev, 97 kev, 121 kev and 136 kev gamma tran-s i t i o n s i n f i g . 24 are the entire pulse height d i s t r i b u t i o n s r e s u l t i n g from detection of these gamma rays, (as opposed to only photopeak measurement of the higher energy gamma rays), the i n t e n s i t i e s given i n column 3 of Table 1 represent the t o t a l number of photons detected per second for each t r a n s i t i o n . Consequently, the e f f i c i e n c y used to convert t h i s measure to the actual t r a n s i t i o n i n t e n s i t y was the calculated t o t a l c r y s t a l e f f i c i e n c y (18), together of course with the geometric e f f i c i e n c y . In the case of the 97 kev and 66 kev d i s t r i b u t i o n s a correction had to be made for the escape of the iodine X-ray. That i s , f o r these low energies the photoelectric absorption takes place near the c r y s t a l surface, with the re s u l t that the iodine X-ray produced has a f i n i t e proba-b i l i t y of escape. In such an event then, the pulse height produced corresponds to the detection of a gamma photon -58-30 kev lower i n energy. The f r a c t i o n of the photons detected with subsequent escape of the X-ray has been calculated by Axel (19), as a function of gamma ray energy. For the 66 kev and 97 kev tr a n s i t i o n s t h i s f r a c t i o n i s 0.1 and 0.044 re-spectively. A correction of a d i f f e r e n t nature had to be applied to the observed photopeak count rate of the 401 kev t r a n s i t i o n before i t s i n t e n s i t y could be determined. This correction arises from the fac t that, as w i l l be seen l a t e r , there are two intense gamma ray cascades, (121 kev - 280 kev, and 75 136 kev - 265 kev) i n the Se decay. If both gamma photons of a cascade are absorbed i n the Nal(Tl) c r y s t a l , the re s u l t i n g pulse height w i l l correspond to the detection of a 401 kev gamma photon. The counting rate i n the 401 kev peak due to such cascade detection can be calculated from the i n t e n s i t i e s of the cascade gamma rays and the corre-sponding c r y s t a l detection e f f i c i e n c i e s . Such a correction has been calculated and subtracted from the 401 kev photo-peak count to obtain the value 84.8 counts/sec. which appears in Table 1. The i n t e n s i t y quoted in Table 1 for the 572 kev gamma t r a n s i t i o n was deduced from the r e l a t i v e i n t e n s i t i e s of the 572 kev and 401 kev photopeaks in f i g . 25. Corrections were made for absorption i n the 3/16" of lead between the source and c r y s t a l , and for the photoelectric detection e f f i c i e n c y of the c r y s t a l for these two energies. -59-The number of counts in the X-ray peak i n f i g . 26 was used to determine the X-ray intensity. In t h i s case the detection e f f i c i e n c y i s simply the geometric e f f i c i e n c y since the i n t r i n s i c photopeak e f f i c i e n c y i s unity for t h i s energy. A correction, however, had to be made for the absorption i n the 0.001" aluminum window on the c r y s t a l . The source used for the int e r n a l conversion spectrum measurement, discussed below, was 3.95 times stronger than the one used for the gamma ray i n t e n s i t y measurements. So that the conversion c o e f f i c i e n t s may be e a s i l y calculated l a t e r , the gamma ray i n t e n s i t i e s were normalized, by multi-plying by 3.95 for comparison with the conversion electron i n t e n s i t i e s . The r e s u l t i n g i n t e n s i t y values appear i n column 2 of Table 2. Also included i n t h i s table are the r e l a t i v e gamma ray t r a n s i t i o n i n t e n s i t i e s , referred to the 265 kev t r a n s i t i o n , together with the r e s u l t s of the recent measurements of several other authors. It w i l l be noted that generally good agreement exists between the various i n t e n s i t y measurements. The present measurement gives a higher value for the i n t e n s i t i e s of the 121 kev and 97 kev gamma tr a n s i t i o n s than obtained by the other investigators. The disagreement i s however s l i g h t . For the 66 kev t r a n s i t i o n , on the other hand, the J e s u i t s of the present measurement d i f f e r s from the others by approximately a factor 2. The p o s s i b i l i t y that the Compton contribution of the higher energy gamma rays, Transition Absolute Relative Schardt & Grigoriev & Van den Bold -y Intensity y Intensity Welker Zolotavin et a l . (a) Relative yIntensity Relative y Intensity Relative y Intensity X ray „~ „ , „xl04 27.0+1.9„ „ — CPS 0.96+0.07 0.81+0.12 66 1.10+0.15 0.039+0.005 0.018+0.01 0.0153+0.0015 0.021+0.008 98 1.26+0.16 0.045+0.006 0.0661+0.015 0.055+0.003 0.058+0.006 121 10.2+0.9 0.36+0.03 0.28+0'Of -0.03 0.279+0.013 0.245+0.03 136 28.0+2 0.99+0.07 0.94+0.12 0.46+0.05 0.76+0.05 199 0.81+0.2 0.029+0.007 *0.03 0.026+0.002 0.036+0.004 265 28.2+2.2 1.00+0.08 1.00 1.00 1.00 280 12.4+1.1 0.44+0.04 0.457+0.04 0.41+0.025 0.52+0.05 304 0.54+0.2 0.019+0.007 0.02 0.025+0.003 401 5.0+0.3 0.18+0.014 0.248+0.025 0.223+0.023 0.28+0.02 572 0.021+0.004 0.0007+0.0002 0.0018+0.0006 (a) These i n t e n s i t i e s r e f e r to the source used for the i n t e r n a l conversion electron spectrum measurement. TABLE 2 Se Gamma Transition I n t e n s i t i e s -61-under the 66 kev photopeak, i s greater than was used i n the analysis of the s c i n t i l l a t i o n spectrum cannot be e n t i r e l y ruled out, though there i s no evidence from the present measurements for increasing t h i s background. Another possible explanation of t h i s difference, discussed l a t e r , involves the existence of a 77 kev t r a n s i t i o n which would not be resolved from the 66 kev t r a n s i t i o n i n the s c i n t i l l a t i o n spectrum and would therefore give a 66 kev in t e n s i t y that i s too high i f t h i s additional gamma t r a n s i t i o n i s not taken into account. III . The Internal Conversion-Electron Spectrum (i) Source Preparation To a t t a i n good electron momentum resolution with the thin lens spectrometer a source small i n si z e i s a pre-r e q u i s i t e . Also, the source material must not be too thick and must have s u f f i c i e n t a c t i v i t y to enable measurement of the spectrum without excessively long counting times. These conditions di c t a t e the use of a source with a high s p e c i f i c a c t i v i t y . To t h i s end, therefore, the source used i n the measurement of the i n t e r n a l conversion spectrum was prepared from a f r e s h l y i r r a d i a t e d selenium sample. The method for obtaining an aqueous solut i o n con-75 taining the Se has already been discussed. For the inte r n a l conversion-electron source a small drop of t h i s o solution was deposited on a very thin (240 p,gm/cm ) aluminum backing which was supported on an aluminum r i n g . This drop * Available from Geo. M. Whiley L t d o , V i c t o r i a Road, R u i s l i p , Middlesex, England. was reduced to red selenium i n a weak atmosphere of hydrazine (NHgNHg) and then sprayed with a collodion containing ether sol u t i o n , to bind the source to the backing and prevent s u b l i -mation in the spectrometer vacuum. Several such sources were prepared. The one f i n a l l y chosen for the measurement of the intern a l conversion spectrum had a diameter of 2.5 mm and an a c t i v i t y of approximately 20 u.c. (From t h i s i t was estimated 2 that the source thickness was approximately 2 mg/cm .) While a smaller source than t h i s would have been preferable the above choice represents a compromise between source s i z e , a c t i v i t y and thickness. ( i i ) Measurement of the Internal Conversion Spectrum After centring the source i n the spectrometer as described previously, the spectrum was measured by recording the counting rate as a function of the magnet current, which was increased i n steps. Regions of the spectrum that con-tained low i n t e n s i t y peaks were repeatedly scanned i n order to accumulate enough counts to give reasonable s t a t i s t i c a l accuracy. The spectrum, aft e r subtraction of the back-ground, (primarily photomultiplier noise) which was p e r i -o d i c a l l y measured during the course of the experiment, i s shown i n f i g . 27. Thirteen peaks, i d e n t i f i e d as K and L conversion l i n e s associated with eight t r a n s i t i o n s i n 75 As are evident in t h i s spectrum. It w i l l be noted that the peaks, p a r t i c u l a r l y the lower energy ones, have low energy t a i l s , due to absorption i n the source. Since the 98 K Figure 27 S e 7 5 Internal Conversion electron Spectrum. 2 mm diameter source 2 mg/cm2 . 8 H 6H 20 136 K 136 L v. 38 199 K M5 .205 .215 280^ 3 04 K 304 L Spectrometer Potentiometer Setting -63-i n t e n s i t y determination of the conversion t r a n s i t i o n s i s based on an area measurement of the peaks, s l i g h t d i s -tortions i n peak shape are inconsequential. In the present spectrum the only peak that may r e s u l t i n a somewhat doubtful i n t e n s i t y measure i s the one l a b e l l e d 98 K, which has a f a i r l y s i g n i f i c a n t d i s t o r t i o n . In Table 3 the conversion i n t e n s i t i e s determined according to the method outlined i n Appendix I are given for each peak that i s resolved in the conversion spectrum. The 136 K and 280 K peaks contain the two L conversion peaks of the 121 kev and 265 kev t r a n s i t i o n s respectively. The magnitudes of these L peaks were estimated i n the following way. From a knowledge of the 121 kev and 265 kev i n t e n s i -t i e s and a knowledge of the corresponding gamma t r a n s i t i o n i n t e n s i t i e s the K conversion c o e f f i c i e n t s for these two t r a n s i t i o n s were determined. (A complete discussion of the determination of the conversion c o e f f i c i e n t s i s given l a t e r . ) Using the conversion c o e f f i c i e n t s to e s t a b l i s h the m u l t i p o l a r i t y of the t r a n s i t i o n s , the t h e o r e t i c a l r a t i o of the K to L conversion i n t e n s i t i e s could be de-termined. The measured i n t e n s i t i e s of the 121 kev and 265 kev conversion peaks and the t h e o r e t i c a l K/L r a t i o s then gave the i n t e n s i t i e s of the corresponding L con-version peaks. The i n t e r n a l conversion i n t e n s i t i e s given in Table 3 have had the contributions of these L con-version peaks subtracted. Transition Absolute Relative Conversion Electron Intensity Conversion e Intensity Present Investigation Grigoriev & Zolotavin Schardt & Welker Metzger & Todd 24 kev 12.50+0.15 K 3.14+0.3 L 0.61+0.06 M 66 0.737+0.044 K 0.124+0.024 L+M 0.677+0.081 K 97 x l O 3 CPS 14.0+0.6 K 2.6+0.17 L 7.60+0.33 K 1.41+0.09 L 6.45+0.25 K 0.85^+0.043 L 0.159+0.02 M 7.15 K 1.165+0.135 L 121 4.07+0.21 K 2.21+0.11 K 1.54+0.02 K 0.212+0.013 L+M 1.73 K 136 7.84+0.23 K 0.80+0.10 L 4.26+0.12 K 0.43+0.05 L 3.84+0.05 K 0.38+0.01 L 0.061+0.006 M 4.20 K 0.515+0.054 L 3.77+0.2 K 199 0.115+0.025 K 0.062+0.013 K 0.073+0.3 K 0.008^+0.0003 L 0.064+0.007 K 265 1.84+0.03 K 1.00+0.016 K 1.00+0.03 K 0.135+0.01 L+M 1.00+0.081 K 1.00 K 280 0.906+0.03 K 0.085+0.015 L 0.492+0.016 K 0.046+0.008 L 0.492+0.03 K 0.064+0.003 L+M 0.534+0.054 K 0.536+0.016 K 304 0.244+0.024 K 0.132+0.013 K 0.161+0.008 K 0.0231+0.0016 ~ L+M 0.156+0.013 K 0.154+0.009 K 401 0.069+0.004 K 0.025+0.01 L 0.037+0.002 K 0.013+0.005 L 0.0376+0.0026 K 0.0044+0.0004 L+M 0.036+0.004 K 0.036+0.004 K 572 0.00055+0.00022 K TABLE 3: Se Internal Conversion Transition I n t e n s i t i e s -65 In Table 3 the inter n a l conversion i n t e n s i t i e s are also computed r e l a t i v e to the 265 kev t r a n s i t i o n , so that comparison with other recent measurements, also summarized in the table, can be made. IV. Coincidence Measurements (i) Gamma-Gamma Coincidences 75 Coincidences between gamma rays emitted i n the Se decay were investigated using the coincidence system described i n Chapter II and the detector assembly shown i n f i g . 4. The source, which was placed at the inte r s e c t i o n of the axis of the two detectors, consisted of a small amount of red selenium contained i n a l u c i t e holder, also i l l u s t r a t e d i n f i g . 4. This was prepared by placing a 75 drop of the aqueous Se - containing sol u t i o n i n the holder, and then reducing i t to red selenium. Coincidence spectra were recorded with the kicksorter for the pulse height analyzer set at the following positions i n the spectrumss 66 kev photopeak, 97 kev photopeak, low and high energy sides (separately) of the 121 kev - 136 kev composite peak, 199 kev photopeak, low and high energy sides of the 265 kev - 280 kev composite peak, and f i n a l l y the 401 kev photopeak. Prior to the actual measurement of each coincidence spectrum the gamma ray spectrum as measured in each detector was recorded with the kicksorter ("singles" -66 spectra). The Channel 1 spectrum was used together with the pulse height analyzer output counting rate during the c o i n c i -dence measurement, to determine the chance coincidence rate, (which was very low i n a l l cases), while the Channel 2 spectrum was used together with the arrangement i l l u s t r a t e d i n the block diagram i n f i g . 15 to determine the portion of the spectrum accepted i n the pulse height analyzer window. Measurements involving the two intense cascades, 121 kev - 280 kev and 136 kev - 265 kev, were completed with one or two hours of counting. For the other coincidence spectra however, longer times were required. In p a r t i c u l a r the measurement with the pulse height analyzer set to accept the 401 kev photopeak pulses and for which no s i g n i f i c a n t coincidences were recorded, extended over a period of t h i r t y hours. In f i g s . 28 and 29 sample coincidence spectra obtained when se t t i n g the pulse height analyzer window on the 66 kev and 199 kev photopeaks are shown. That the 66 kev and 199 kev t r a n s i t i o n s are i n coincidence i s c l e a r l y estab-lis h e d by these spectra. A peak at ^ 136 kev would be expected when the pulse height analyzer i s set on the 199 kev photopeak, since an appreciable number of 265 kev and 280 kev pulses ( r e s u l t -ing from Compton interactions i n the c r y s t a l ) f a l l within the acceptance window. Knowing the approximate shape of the Compton d i s t r i b u t i o n associated with the 265 kev and to follow page 66 121 -I- 136 kev Figure 28 S e 7 5 Y Spectrum i n Coincidence with the Counts/Channel 66 kev 7 Transition. Counts/Channel 1 199 kev \ / \ 265 + 280 kev Kicksorter Channel Number i 20-15-16-5 -17 60 1 -7-5-5 o -2.S-121 + 136 kev Figure 29 S e 7 5 rv Spectrum i n Coincidence with the 199 kev Y Transition. Kicksorter'»Channel Number —i— 2o 3 0 *0 -1— 50 —1— 6 0 ~1— lo -67. 280 kev gamma tr a n s i t i o n s , the number of 136 kev and 121 kev coincident counts expected during the measurement can be calculated. Such a ca l c u l a t i o n shows that not a l l of the , observed counts i n the 121 kev - 136 kev coincident peak can be accounted f o r i n t h i s way. Hence i t i s concluded that the 199 kev gamma t r a n s i t i o n i s i n coincidence with either the 121 kev or 136 kev t r a n s i t i o n , as well. S i m i l a r l y for the case with the pulse height analyzer window set on the 66 kev photopeak, a 265 kev - 280 kev coincident peak would be expected because of the 136 kev - 121 kev pulses that also f a l l within the acceptance window. In t h i s case, how-ever, the observed coincidence peak i s e n t i r e l y accounted for i n t h i s way. A peak due to either 136 kev or 121 kev gamma tr a n s i t i o n s also appears i n the coincidence spectrum when gating on the 66 kev photopeak pulses. This estab-l i s h e s that the 66 kev gamma t r a n s i t i o n i s also in cascade with either the 121 kev or 136 kev t r a n s i t i o n . A complete summary of the conclusions, based on these measurements, regarding what gamma tr a n s i t i o n s are in cascade, appears in Table 4. With the thin Nal(Tl) c r y s t a l (1§" x 5 mm) as the X-ray detector, coincidences between the^arsenic X-rays and the gamma rays were also measured. Because detection of the very low energy X-rays (11.8 kev) does not r e s u l t i n a pulse at the detector output with s u f f i c i e n t ampli-tude to trigger the fa s t coincidence driver r e l i a b l y , the Selected y Transition Coincident y Transitions ** Selected Coriversion-e Transition Coincident y Transitions Remarks X rays 400,280,265, 199,137,121 98,66 121 kev 280 121(K)* 280 No other y t r a n s i t i o n s observed i n coincidence 136 66, 199 265, (280) 136(E) 265 The presence of 66+200 kev y's i n the conversion electron-gamma coincidence spectrum cannot be rule d out 199 66 136, (121) 265 136, (121) 265(K) 136 No other y i n coincidence 280 121, (136) 280(K) + 265(L) 121 No other y i n coincidence 401 none 97 (K) none Within the s t a t i s t i c a l l i m i t s a l l counts could be accounted for by chance coincidences * (K) denotes the s h e l l i n which the conversion takes place. ** The p o s s i b i l i t y that the transitions indicated in brackets are i n coincidence with the selected t r a n s i t i o n could not be e n t i r e l y ruled out by these measurements. TABLE 4 Results from y-y and Conversion=electron -y Coincidence Measurements -69-coincidence system was modified s l i g h t l y , with the addition of an amplifier at the X-ray detector " f a s t " output and a delay l i n e between the gamma ray detector and the fast coincidence driver to compensate for the additional delay of the amplifier. The coincident gamma ray spectrum recorded as before with the kicksorter, when the pulse height analyzer was set to accept the X-ray pulses, was indistinguishable from the "sin g l e s " gamma ray spectrum. The X-rays r e s u l t primarily from the K capture decay 75 of Se . (The other process producing X-rays, to a lesser 75 extent, i s inter n a l conversion i n As .) Hence, i f there 75 was appreciable K capture decay to more than one As excited state, i t would be expected that the gamma tran-s i t i o n s p a r t i c i p a t i n g i n the decay of such states would have enhanced i n t e n s i t i e s i n the coincidence spectrum. Since t h i s i s not the case t h i s r e s u l t suggests that the Se^5 K capture goes predominantly to only one l e v e l 75 (besides possibly, the ground state) i n As ( i i ) Internal Conversion Electron-Gamma Coincidences The combination of the magnetic spectrometer and the s c i n t i l l a t i o n spectrometer for measuring beta-gamma co-75 incidences has been discussed previously. In the Se investigation t h i s was used to determine the gamma tran-s i t i o n s i n coincidence with the more intense i n t e r n a l conversion t r a n s i t i o n s . S p e c i f i c a l l y the spectra of the -70-gamma rays i n coincidence with the 97 K, 121 K, 136 K, 265 K and 280 K conversion t r a n s i t i o n s were measured. These measurements were carr i e d out by se t t i n g the current i n the spectrometer magnet so that electrons from the desired i n t e r n a l conversion t r a n s i t i o n were focussed on the anthracene detector and then recording the spectrum of the gamma rays i n coincidence, with the kicksorter. The coincidence counting rates were very low ( t y p i c a l l y 2 to 4 counts/minute), because of the comparatively low trans-mission of the magnetic spectrometer. Consequently measurements extending over many hours were necessary to determine each coincidence spectrum. The "sin g l e s " gamma ray spectrum was measured at the beginning and again at the end of each coincidence run. The r e s u l t s of these two measurements were averaged and used together with the conversion electron counting rate, which was determined p e r i o d i c a l l y during the run, with the beta spectrometer scaler, to calculate the chance c o i n c i -dence count. For most of the measurements the chance co-incidences amounted to less than ten percent of the t o t a l number of coincidence counts recorded. The exception to thi s statement i s the coincidence measurement with the 97 K conversion electrons. In t h i s case a l l of the c o i n c i -dence counts recorded could be accounted for by the chance coincidence c a l c u l a t i o n . In f i g . 30 the spectrum of the gamma rays i n c o i n c i -dence with the 121 kev conversion electrons i s shown to follow page 70 121+136 kev 2 - < 10*' / \ Se 3 S c i n t i l l a t i o n / \ y Spectrum (singles) 1.5-Counts/Channel Counts/Channel / \ 265+280 kev 1-Counts/Channel 0.5-1 ,1 1 1 ••• 1 1 1 2 0 30 • '4-0 SO 60 10 80 Kicksorter Channel Number 250-rH V r * \ / * 1 2 00- a a si T ray spectrum i n / ' i o \ coincidence with 121 kev / 1 10 -u conversion electrons / \ 150 _ Coun J00 -Coincidence */ \ 5 0 -• * * / \ " • / \ • • • . • • » * \ • • • \ * * K o— 1 i i i i I i 20 30 *0, 50 60 70 80 Kicksorter Channel Number Figure 30 An Example of the Conversion Electron-Gamma Coincidence Spectra. -71-together with the "sing l e s " spectrum for comparison. This spectrum, which contains only the 280 kev photopeak plus i t s associated Compton d i s t r i b u t i o n , was used to determine the approximate shape of the Compton d i s t r i b u t i o n of the 265 kev and 280 kev gamma rays under the lower energy photo-peaks i n the s c i n t i l l a t i o n spectrum. Also, the peak to t o t a l r a t i o for 280 kev gamma rays detected i n the 1§" x 1" Nal(Tl) c r y s t a l was determined from t h i s spectrum. The r e s u l t s of the conversion electron-gamma c o i n c i -dence measurements, summarized in Table 4, confirm the existence of the 121 kev - 280 kev and 136 kev - 265 kev cascades. ( i i i ) Gamma-Gamma Dir e c t i o n a l Correlations The d i r e c t i o n a l correlations of the 121 kev - 280 kev and the 136 kev - 265 kev cascades were studied i n some d e t a i l i n t h i s investigation. Because the component gamma ray pulse height d i s t r i b u t i o n s of these two cascades appear i n two unresolved peaks i n the s c i n t i l l a t i o n spectrum (121 kev + 136 kev composite peak and 265 kev + 280 kev composite peak), the co r r e l a t i o n measurements were concerned with measuring the coincidence counting rate as a function of the angle between the detectors, for d i f f e r e n t proportions of the 121 kev - 280 kev and 136 kev - 265 kev cascades accepted i n the coincidence channel. That i s , measurements were made with the pulse height analyzer window set to accept pulses from: -72-1) the high energy side of the 265 kev + 280 kev composite peak, (121 kev - 280 kev cascade favoured), 2) the low energy side of the same composite peak (136 kev-265 kev cascade favoured), and 3) the entire composite peak. In f i g . 31 the 265 kev + 280 kev composite peak i n the Channel 2 s c i n t i l l a t i o n spedtrum i s shown together with the kicksorter measurements of the portions of t h i s peak that were accepted in the pulse height analyzer window f o r each of the c o r r e l a t i o n measurements. S t a b i l i t y of the elec t r o n i c s was es s e n t i a l for these measurements since a s l i g h t amplification change, i n Channel 2 p a r t i c u l a r l y , would r e s u l t i n a very large change i n the r e l a t i v e f r a c t i o n s of the two gamma rays accepted i n the pulse height analyzer window. For t h i s reason therefore, the gain s t a b i l i t y monitor described e a r l i e r was added to the Channel 2 side of the coincidence system. For each of the three pulse height analyzer window positions, the coincidence spectrum was recorded with the kicksorter, for movable detector angles spaced at 15° inte r v a l s between 90° and 270°. Generally, af t e r a c o i n c i -dence count of an hour's duration the data stored i n the kicksorter would be printed out, the detector angle changed, and the coincidence measurement repeated. In t h i s way the coincidence spectrum was measured with the movable detector to follow page Pulse Height Analyzer Window Position A 265 kev y t r a n s i t i o n favored PulSe Height Analyzer Window Positio n B 280 kev y Transition favored 265+280 kev Composite Peak i n the Se 7^ y ray s c i n t i l l a t i o n spectrum Pulse Height Analyzer Window Positi o n C Entire Peak accepted 6'o •' -To Kicksorter Channel Number Figure 31 Kicksorter Measurements showing the portion of the 265-280 kev composite peak accepted for each d i r e c t i o n a l c o r r e l a t i o n measurements. -73-at each of the thirteen angles noted above. The order of angle coverage was random, and i n the course of each d i r e c t i o n a l c o r r e l a t i o n measurement several coincidence measurements were made at each angle. With the pulse height analyzer set on any portion of the 265 kev - 280 kev composite peak ?only one peak, com-posed of the 121 kev and 136 kev photopeaks, occurs i n the coincidence spectrum. (The r e l a t i v e i n t e n s i t i e s of the two photopeaks i n the coincidence spectrum depend of course upon the position of the pulse height analyzer window.) By taking the sum of the counts i n the photopeak only, as a measure of the coincident gamma ray i n t e n s i t y , the possible perturbing e f f e c t s on the c o r r e l a t i o n function by coincident scattered radiat i o n i s v i r t u a l l y eliminated. During the course of each coincidence measurement the t o t a l number of counts at the pulse height analyzer out-put was also recorded with a scaler. Dividing the c o i n c i -dence count by t h i s t o t a l pulse height analyzer count then compensated f o r very small count rate s h i f t s i n Channel 2 during the coincidence measurement. In f i g . 32 the 'measured d i r e c t i o n a l correlations f o r each of the three pulse height analyzer window positions are shown. The points f o r these graphs were obtained by adding the data for detector angles symmetric with respect to 180°, and the curves f i t t e d to these points were obtained by the method of least squares outlined in to follow page 73 •°f— 1 ! , 90° 220° 150 180° Detector Angle Figure 32 y y D i r e c t i o n a l Correlation Results f o r the 121 kev - 280 kev and 136 kev - 265 kev 7 y cascades| f o r three pulse height analyzer window positions on the 265-280 kev composite peak: The curve desig-nations A, B, and C r e f e r to the window positions shown i n figure 31. -74-Appendix III. Two least squares functions were determined for each set of points. In one case i t was assumed that A^ f1 0 i n the c o r r e l a t i o n function, W(©) - A q + A 2 P 2 (cos ©) + A 4 P 4 (cos © ) , while i n the other case A^ was taken equal to zero. The least squares determination of the c o e f f i c i e n t s for both of the above cases and a l l three c o r r e l a t i o n measurements are given i n Table 5. As can be seen the error associated with the A^ c o e f f i c i e n t s i s comparable with the value of the c o e f f i c i e n t i t s e l f i n each case. Hence the evidence would indicate that terms up to A 2 are s u f f i c i e n t to describe the correlations. Applying the method outlined i n Appendix III f o r de-termining the d i r e c t i o n a l c o r r e l a t i o n function of each cascade from the measured co r r e l a t i o n functions, we obtain, for the 136 kev - 265 kev cascade, W(©) - 1 - (0.036 + 0.015) P 2 (cos ©) , 11. and for the 121 kev - 280 kev cascade, W(0) - 1 - (0.43 + 0.06) P 2 (cos ©) . 12. Since only two measured c o r r e l a t i o n functions are necessary to determine the d i r e c t i o n a l c o r r e l a t i o n functions of the in d i v i d u a l cascades, the f a c t that three measurements were made, allowed three separate calculations Pulse Height Intensity Ratio Least Squares Determination of C o e f f i c i e n t s Analyzer of 265 kev y to W(©)-A n+A 2 P2(cos©)+A4P4(cose) W(9)=Ar +A2P2(cos©) Window 280 kev <y i n A A 2 Position PHA Window A o A2 A 4 High Energy 0.60 1.061 -.250 +0.008 1.062 -0.247 Side of +0.007 +0.012 +0.014 +0.007 +0.012 265,280 Peak Low Energy 8.63 1.254 -0.085 +0.017 1.256 -0.077 Side of +0.005 +0.009 +0.011 +0.005 +0.009 265,280 Peak Entire 2.23 1.250 -0.144 -0.0002 1.250 -0.144 265,280 Peak +0.003 +0.005 +0.006 +0.003 +0.006 TABLE 5 Summary of the Experimental Results from -y y D i r e c t i o n a l Correlation Measurements on the 121 kev - 280 kev and 136 kev - 265 kev yy Cascades. 76. of the d i r e c t i o n a l c o r r e l a t i o n functions of the two cascades. The r e s u l t s in equations 11 and 12 are the averages of these calcu l a t i o n s . In addition to the measurement of the above d i r e c t i o n a l c o r r e l a t i o n s , the same measurement was attempted for the 66 kev - 199 kev cascade. The r e s u l t s i n t h i s case indicate that there i s no c o r r e l a t i o n . S p e c i f i c a l l y , according to the present measurements, an upper l i m i t of 0.1 can be placed, on the anisotropy of the gamma rays emitted i n t h i s cascade. -77-CHAPTER IV ANALYSIS OF THE RESULTS 75 I. Previous Investigations of the Decay of Se The S e 7 5 isotope was f i r s t produced i n 1942 by Kent 75 et a l . (20), by bombarding As with deuterons. Later, Friedlander, Seren and Turkel (21) produced the same isotope through a (n,y) reaction by i r r a d i a t i n g natural selenium i n the thermal neutron -flux of a nuclear reactor. The half l i f e of t h i s a c t i v i t y , one of i t s f i r s t c h a r a c t e r i s t i c s to be determined, i s 127 days. Cork et a l . (22) established that the decay was by electron capture to As , with no competing positron emission. 75 Analysis of the radiations emitted by Se have been made by a number of groups i n an attempt to e s t a b l i s h i t s decay scheme. Among the early measurements were the con-version spectra obtained by Cork et a l . (22), and Jensen et a l . (23). The l a t t e r as well as Ter Pogossian and co-workers (24), also measured the photoelectron spectrum due to the gamma rays i n the decay. Agreement on the existence of tr a n s i t i o n s with the energies, (66, 97, 121, 136, 199, 265, 280, 305 and 402 kev) was very good. In addition, Cork and his group (22) observed conversion l i n e s corresponding to gamma ray energies of 24.7 and 80.8 kev though no evidence of these t r a n s i t i o n s was found by the other investigators at the time. -78-On the other hand, Cork's group did not observe a 76.6 kev t r a n s i t i o n reported by Jensen et a l . Consequently the proposed decay schemes d i f f e r e d through the inclus i o n of the 24.7 and 80.8 kev tr a n s i t i o n s in one case and the 76.6 kev t r a n s i t i o n i n the other. To resolve the c o n f l i c t between these decay schemes, Schardt & Welker (25) remeasured the in t e r n a l conversion 75 and photoelectron spectra of Se as well as the primary i 75 75 beta spectrum of <Se which also decays to As . Using s c i n t i l l a t i o n counters,they also measured gamma-gamma coincidences and d i r e c t i o n a l correlations. Evidence of the 24.7 and 80.8 kev tr a n s i t i o n s was found but not of the 75 76.6 kev t r a n s i t i o n . The As l e v e l scheme proposed on the basis of these measurements with l e v e l s at 200, 265, 280, 305, 401, 477 and 628 kev was i d e n t i c a l to that of Cork et a l . with the addition of the two lev e l s at 477 kev and 628 kev which are apparently excited only through the 75 beta decay of Ge . This l e v e l scheme appeared also to be consistent with the Coulomb ex c i t a t i o n r e s u l t s of Temmer & Heydenburg (26) who observed t r a n s i t i o n s with energies of 200, 283, 574 and 814 kev. The l a t t e r two tra n s i t i o n s were accounted f o r by assuming they came from 75 l e v e l s not excited i n the K capture decay of Se . On the basis of th e i r measured conversion c o e f f i c i e n t s Schardt and Welker also i d e n t i f i e d the m u l t i p o l a r i t i e s of the gamma ray tr a n s i t i o n s and then made plausible assign--79-ments to the le v e l s . This decay scheme did not account for the lack of co-incidences expected between the 97 kev y ray and some other t r a n s i t i o n s or for the pronounced 97 kev peak i n the gamma spectrum obtained by Lu, K e l l y & Wiedenbeck (27) using a c r y s t a l summing technique. These observations were l a t e r explained by Schardt (28), Axel & Vegors (29), and Campbell & Stetson (30) a l l of whom found that the 305 l e v e l which i s fed by the 97 kev t r a n s i t i o n i s an isomeric state with a half l i f e of approximately 17 milliseconds. In the o r i g i n a l Schardt and Welker decay scheme the mul t i p o l a r i t y of the 305 kev gamma ray had been quoted as E2, but i n view of the isomeric nature of the 305 l e v e l Schardt changed t h i s to E3. (This assignment also was consistent with the conversion c o e f f i c i e n t s within ex-perimental error.) This change required the most l i k e l y spin assignment of the 305 l e v e l to be changed to 9/2+ and of the 401 l e v e l to 5/2+. The l a t t e r change then meant that the conversion c o e f f i c i e n t s for the 401, 136 and 121 kev tr a n s i t i o n s would have to be explained on the basis of El+12 mixtures. •Results of gamma-gamma d i r e c t i o n a l c o r r e l a t i o n measurements have been reported on three occasions and while the co r r e l a t i o n functions do not agree within the errors quoted, they do appear to be i n agreement with the spin assignments made by Schardt. The p o l a r i z a t i o n -80-eorrelation r e s u l t s of Van den Bold et a l . (31) in p a r t i c u l a r confirm the even p a r i t y assignment to the 401 kev l e v e l . The l a t t e r measurement also indicated that the E1+M2 mixing of the 121 and 136 kev gamma tr a n s i t i o n s i s very small with these tr a n s i t i o n s being e s s e n t i a l l y pure dipole. The mean l i f e of the 265 kev l e v e l has been determined by Metzger (32) and by Langevin-Joliot and Langevin (16), through resonant sca t t e r i n g experiments with the 265 kev -y ray. The average of these two r e s u l t s i s 2 x 10" 1 1 sec. In view of t h i s short mean l i f e the large E2 component, pre-dicted by the conversion c o e f f i c i e n t s for the 265 kev tran-s i t i o n would not be expected. A d i r e c t i o n a l d i s t r i b u t i o n measurement of the resonantly scattered 265 kev y rays, by Metzger indicates that the 265 kev t r a n s i t i o n i s Ml with ]S|< 0.03,0. Such a small mixing r a t i o i s also at variance with the gamma-gamma d i r e c t i o n a l c o r r e l a t i o n measurements mentioned above. The discrepancy between the multipole assignments on the basis of the Schardt and Welker conversion c o e f f i c i e n t s and the other measurements just mentioned has led to the very recent remeasurement of the conversion c o e f f i c i e n t s , by Metzger and Todd (33) and by Grigoriev and Zolotavin (34). The l a t t e r group measured the conversion c o e f f i c i e n t s for a l l of the tra n s i t i o n s whereas the former measured only the intense t r a n s i t i o n s above 136 kev. The two sets of r e s u l t s are i n agreement and are about a factor 2.5 -81-less than the Schardt & Welker values. These new co-e f f i c i e n t s predict multipole mixing r a t i o s i n agreement with the d i r e c t i o n a l c o r r e l a t i o n and l i f e t i m e measurements. 75 The percentage of K capture decays to each of the As leve l s must be deduced from the t r a n s i t i o n i n t e n s i t i e s i n 75 the As . On the basis of th e i r i n t e n s i t y measurements, Schardt and Welker concluded that 80% or more of the decays go to the 401 kev l e v e l . Van den Bold et a l . , a f t e r care-f u l analysis of the gamma ray spectrum obtained with a s c i n t i l l a t i o n spectrometer gave the following K capture branching r a t i o s , 74% to the 401 l e v e l , 12% to the 280 kev l e v e l , 14% to the 265 kev l e v e l and 10% to the ground state of A s 7 5 *. These values are not i n agreement with Grigoriev and Zolotavin who quote 89% of the K capture decays $ 0 to the 401 kev l e v e l , 2.5% to the 280 kev l e v e l , 2.5% to the 265 kev l e v e l and 5% to the ground state. A 572 kev gamma ray which had previously been observed only i n the Coulomb ex c i t a t i o n experiments has been de-75 tected i n the Se decay by Langevin-Joliot and Langevin, and by Grigoriev and Zolotavin. * These K capture branching r a t i o s are calculated from the r e l a t i v e gamma ray t r a n s i t i o n i n t e n s i t i e s quoted by Van den Bold et a l . , and are not the same as the values, (which appear to be i n error) given on the decay scheme diagram i n t h e i r paper). -82-The l a t t e r group quotes the int e n s i t y of t h i s weak gamma ray as 0.1% of the t o t a l K capture decay rate and the former group gives i t s i n t e n s i t y as 0.04% of the K capture decay rate. 75 The gamma ray energies i n the Se decay have been measured with high precision by Edwards et a l . (15), using a bent quartz c r y s t a l spectrograph. Their values for the t r a n s i t i o n energies are 66.054, 96.741, 121.12, 135.99, 198.60, 264.62, 279.57, 304.0, 400.7 kev. 75 75 The basic Se and Ge decay schemes which have evolved from the foregoing investigations and which are consistent with the r e s u l t s of the present investigation are shown in f i g . 33. II. Interpretation of the Experimental Results (i) The A s 7 5 Energy Levels On the basis of the gamma-gamma and conversion electron-gamma coincidence r e s u l t s , summarized i n Table 4, the existence of the 121 kev - 280 kev and 136 kev - 265 kev cascades i s c l e a r l y established. Since no other gamma ray appears i n coincidence with the 265 kev t r a n s i t i o n , or with either of the 121 or 280 kev t r a n s i t i o n s , one of the tra n s i t i o n s i n each cascade must go to the ground state. Furthermore, the energy difference represented by these two cascades i s e s s e n t i a l l y the same, (400.7 kev and to follow page 82 -83-400.6 kev)*, indicating that both cascades are de-excitation modes of a l e v e l at t h i s energy. Additional evidence for a l e v e l at 400.7 kev comes from the observation that there are no t r a n s i t i o n s i n coincidence with the 401 kev gamma tran-s i t i o n . The sequence of emission of the gamma rays i n a cascade i s not determined by the coincidence experiment. However, examination of the t r a n s i t i o n i n t e n s i t i e s shows that the 280 kev t r a n s i t i o n i s more intense than the 121 kev tran-s i t i o n . This means then that the 280 kev t r a n s i t i o n must go to the ground state, i . e . there i s a l e v e l at 279.6 kev and the additional i n t e n s i t y must be accounted for by another t r a n s i t i o n to t h i s l e v e l . A t h i r d l e v e l at 264.6 kev cannot be established on the basis of t r a n s i t i o n i n t e n s i t i e s alone. However, i t w i l l be seen that a l e v e l at t h i s energy rather than at 136 kev re s u l t s i n more plausible spin assignments to the 75 l e v e l s . Measurement of the beta spectrum of Ge also indicate that there i s a l e v e l at 265 kev (25). A l e v e l at 198.6 kev ; P indicated by the beta 75 spectrum of Ge (25) and by the Coulomb e x c i t a t i o n r e s u l t s (26) accounts for the observed 136, 199, 66 kev gamma-gamma coincidences. * The t r a n s i t i o n energy determinations of Edwards et a l . w i l l be used through t h i s discussion for purposes of energy l e v e l evaluation. -84-The weak 572 kev gamma ray can be accounted for by a l e v e l at t h i s energy. The existence of such a l e v e l has previously been demonstrated by Coulomb e x c i t a t i o n ex-periments (26) and by H. & M. Langevin (16). The sum of the energies of the two remaining gamma tra n s i t i o n s 97 (96.7) and 304 (304.0) detected i n the present investigation i s 400.7 kev, strongly suggesting that these are i n cascade and represent another de-exc i t a t i o n mode from the 400.7 kev l e v e l . Placing a l e v e l at 304.0 kev then accounts for these two tran-s i t i o n s . This l e v e l has been found to be isomeric (28, 29, 30) with a half l i f e of 17 milliseconds, and for t h i s reason no coincidences between 97 and 304 kev tr a n s i t i o n s were observed i n the present investigation. The 24 kev t r a n s i t i o n observed by some investigators (25, 22, 34) represents a second mode of de-excitation of the 304.0 kev l e v e l to the 279.6 kev l e v e l . This was demonstrated by Schardt (28) who measured delayed coincidences between the 97 kev and 280 kev gamma tran-s i t i o n s . On the basis of the decay scheme outlined above the t r a n s i t i o n i n t e n s i t i e s (conversion electron plus gamma ray) to and from each l e v e l are given i n Table 6. The t o t a l K capture rate was obtained from the X-ray in t e n s i t y after correcting for the 55% fluorescence y i e l d i n arsenic and for the X-ray contribution due to Level (kev) Observed Intensity of Transitions to the Level (xlO 4 CPS) Observed Intensity of Transitions from the Level (xlO 4 CPS) Difference (xl04 CPS) Remarks 400.7 46.1+3.9 * 47.4+3.5 1.3+7.4 More than 88% of the K capture decays go to the 400.7 kev l e v e l 304.0 2.91+0.24 0.56+0.2 2.35+0.44 This difference gives the i n -ten s i t y of the 24 kev t r a n s i t i o n 279.6 12.6+1.3 12.5+1.1 0.1+2.4 264.6 28.9+2 29.5+2.4 0.6+4.4 198.6 ** 1.16+0.15 0.82+0.2 see text page 87 572 0.042+0.008 K capture decay rate to t h i s l e v e l i s equal to the y ray in t e n s i t y This value represents the t o t a l K capture rate, obtained from the inte n s i t y of the X rays (corrected for internal conversion and fluorescence y i e l d ) ** This represents the 66 kev t r a n s i t i o n f o r which a conversion c o e f f i c i e n t of 0.25 (Ml) was assumed i n calculating the intensity. TABLE 6: Transition Intensity Balance Based on the Decay Scheme in Fig. 37 and Transition Intensities i n Tables 2 and 3. -86-i n t e r n a l conversion. This yielded the value (46.1+3.9)xl0 for the number of K capture decays per second i n the source used f o r the i n t e r n a l conversion measurements. From the gamma ray and i n t e r n a l conversion electron t r a n s i t i o n i n t e n s i t i e s given i n Tables 2 and 3, for t h i s same source, the sum of the 97 kev, 121 kev, 136 kev and 401 kev t r a n s i t i o n i n t e n s i t i e s i s (47.4+3.5)xl0 4 tran-sitions/second. Since a l l of these t r a n s i t i o n s de-excite the 400.7 kev l e v e l , t h i s value must also represent the K capture rate to t h i s l e v e l . Comparison with the K capture rate deduced from the X-ray i n t e n s i t i e s then 75 leads to the conclusion that at least 88% of a l l Se 75 K capture decays go to the 400.7 kev l e v e l i n As . This i s i n agreement with the findings of Grigoriev and Zolotavin (34), but outside the value of 78% quoted by Van den Bold et a l . (31). The 304 kev t r a n s i t i o n was the only mode of decay from the 304.0 kev l e v e l observed i n the present i n -vestigation. Since, however, the i n t e n s i t y of the 97 kev t r a n s i t i o n which feeds the 304.0 kev l e v e l i s much greater than the 304 kev t r a n s i t i o n i n t e n s i t y , a second de-excitation mode i s indicated. Presumably t h i s i s the 24 kev t r a n s i t i o n between the 304.0 kev and 279.6 kev l e v e l s observed by others (20, 25, 34) but which could not be detected i n the present investigation because of instrumental l i m i t a t i o n s . The difference between the -87-97 kev and 304 kev t r a n s i t i o n i n t e n s i t i e s i s therefore taken as the 24 kev t r a n s i t i o n i n t e n s i t y . The i n t e n s i t i e s of the incoming and the outgoing tran-s i t i o n s are equal for both the 264.6 kev and 279.6 kev lev e l s i n d i c a t i n g n e g l i g i b l e K capture decays to these l e v e l s . The uncertainties associated with the i n t e n s i t i e s would allow a maximum of 6% of the K capture decays to the 279.6 kev l e v e l and 11% to the 264.6 kev l e v e l . This again i s i n agreement with Grigoriev and Zolotavin who quote 2.5% K capture decay to each of the 264.6 kev and 279.6 kev l e v e l s , but i n disagreement with Van de Bold et a l . who quote 12% decay to the 279.6 kev l e v e l and 14% decay to the 264.6 kev l e v e l . According to the present measurements }the 66 kev t r a n s i t i o n i s s i g n i f i c a n t l y more intense than the 198.6 kev t r a n s i t i o n . Such an observation cannot be accounted for by the decay scheme considered above. Using a double focussing spectrometer Grigoriev and Zolotavin (34) found a peak i n the photoelectron spectrum which they i d e n t i f i e d as being due to a 77 kev gamma ray. According to t h e i r decay scheme t h i s t r a n s i t i o n occurs between a l e v e l at 478 kev which i s weakly excited by the S e 7 5 K capture, and the 400.7 kev l e v e l . (The existence of the 477 kev l e v e l was f i r s t shown i n the beta decay of Ge 7 5) (25). Since a bismuth radiator was used to obtain the -88-photoelectron spectrum i n the present work, only L peak detection of t h i s gamma ray would be possible, and since the t r a n s i t i o n i s weak no such t r a n s i t i o n could be i d e n t i -f i e d . In the s c i n t i l l a t i o n spectrum the 77 kev gamma peak would not be resolved and i t s i n t e n s i t y would i n fact be added to what i s i d e n t i f i e d as the 66 kev photopeak. If therefore the r e s u l t s of Grigoriev and Zolotavin are accepted,, the 66 kev gamma int e n s i t y as determined from the photopeak area must be reduced by 19% to take into account the 77 kev gamma contribution. (This has been done i n Table 6 to obtain the value 1.16 x lO'* counts/sec. for the tr a n s i t i o n rate to the 198.6 kev lev e l . ) With t h i s correction the difference between the 66 kev and 198.6 kev t r a n s i t i o n i n t e n s i t i e s , while s t i l l f a i r l y large, can be accounted for by the uncertainties introduced i n subtracting the Compton contribution, due to the higher energy gamma rays, from under the 66 kev photopeak in the s c i n t i l l a t i o n spectrum. The 572 kev gamma ray was the only mode of decay from the 572 kev l e v e l , hence the K capture rate to t h i s l e v e l must be equal to the gamma ray in t e n s i t y , i . e . (0.05+0.01)% of the K capture decays go to the 572 kev l e v e l . ( i i ) T r a n sition M u l t i p o l a r i t i e s and Energy Level Spins Since the absolute i n t e n s i t i e s of both i n t e r n a l con-version t r a n s i t i o n s and the gamma tr a n s i t i o n s were determined, the conversion c o e f f i c i e n t f or a p a r t i c u l a r t r a n s i t i o n energy -89-i s simply given by d i v i d i n g the appropriate i n t e r n a l con-version i n t e n s i t y by the corresponding gamma i n t e n s i t y (see Tables 1 and 2). The conversion c o e f f i c i e n t s for the t r a n s i t i o n s detected i n the present investigation are summarized i n Table 7. Also included i n the table are the conversion c o e f f i c i e n t s determined by three other groups (25, 33, 34). As can be seen, apart from the values quoted by Schardt & Welker (25) the agreement between the various measurements i s excellent. Only one conversion c o e f f i c i e n t , that of the 96.7 kev t r a n s i t i o n i n the present investigation disagrees with the r e s u l t s of Grigoriev & Zolotavin (34). It should be noted, however, that the determination of the conversion c o e f f i c i e n t for t h i s t r a n s i t i o n i s in the present case one of the least accurate, because of a possible error (noted in Chapter III) in the 97 K conversion i n t e n s i t y de-termination, due to the e f f e c t s of absorption i n the source. To determine the m u l t i p o l a r i t i e s of the t r a n s i t i o n s , the experimental K s h e l l conversion c o e f f i c i e n t s are compared with Rose's t h e o r e t i c a l calculations (7). In Table 8 the measured c o e f f i c i e n t for each t r a n s i t i o n appears along with the t h e o r e t i c a l K s h e l l conversion c o e f f i c i e n t f o r m u l t i p o l a r i t i e s up to octopole for both e l e c t r i c and magnetic t r a n s i t i o n s . In column 9 of Table 8, the possible multipole assignments along with the maximum possible multipole mixing i s given on the basis of the measured Conversion C o e f f i c i e n t OK Transition Present Investigation Schardt & Welker Grigoriev & Zolotavin Bletzger & Todd 66 0.6+0.3 0.3+0.03 97 1.11+0.19 1.8+0.8 0.75+0.05 121 0.041+0.005 0.10+0.03 0.037 136 0.028+0.003 0.07+0.02 0.026 0.026+0.003 199 0.014+0.006 0.03 0.018+0.002 265 0.0067+0.0006 0.016+0.005 0.0025+0.0004 0.0062+0.0003 280 0.0073+0.0009 0.019+0.005 0.0076+0.0005 0.007+0.0004 304 0.04+0.016 0.03+0.01 0.043+0.006 0.045+0.007 401 0.0011+0.0002 0.0024+0.0005 0.0011 0.0012+0.0002 572 0.0020+0.0013 TABLE 7 Se K Conversion Coe f f i c i e n t s f Pheoretical Conversion C o e f f i c i e n t s Possible Transition Experimental E l E2 E3 Ml M2 M3 Multipole Assignment 66 * 2.2(-l) 3.0(0) 3.4(1) 2.5(-l) 3.65(0) 4.3 (1) 97 1.11+0.19 7.2(-2) 7.8(-l) 6.6(0) 8.8(-2) 9 . K - 1 ) 8.9 (0) E2+* 6%M3 M2+s7%E3 121 0.041+0.005 3.8(-2) 3.4(-l) 2.5(0) 4.7(-2) 4.0(-l) 3.4 (0) E1+<2%M2 Ml 136 0.028+0.003 2.65(-2) 2.2(-l) 1.45(0) 3.45(-2) 2.75 (-1) 2.1 (0) E1+*1.6%M2 199 0.014+0.006 8.6(-3) 5.5(-2) 2.8(-l) 1.3(-2) 7.7(-2) 4.4(-l) M1+ ^17%E2 E1+«17%M2 265 0.0067+0.0006 3.7(-3) 1.95 (-2) 8.0(-2) 6.2(-3) 3.1 (-2) 1.4-C-l) M1+«=8%E2 E1+*13%M2 280 0.0073+0.0009 3.2(-3) 1.6(-2) 6.4(-2) 5.4(-3) 2.6(-2) l . l ( - i ) M1+*26%E2 E1+^22%M2 304 0.04+0.016 2.5 (-3) 1.2 (-2) 4.6(-2) 4.5(-3) 1.95 (-2) 8.0(-2) E3 401 0.0011+0.0002 1.2(-3) 4.2(-3) 1.55 (-2) 2. 25 (-3) 8.3(-3) 2.85(-2) E1+^1.4%M2 * 2.2(-l) - 2.2 x 10~ TABLE 8 Comparison of Experimental and Theoretical Conversion C o e f f i c i e n t s f o r the Se 7^ Transitions. -91-conversion c o e f f i c i e n t s . Only one p o s s i b i l i t y for the m u l t i p o l a r i t y of the 401 kev t r a n s i t i o n e x i s t s on the basis of i t s conversion c o e f f i c i e n t . It i s E l with less than 1.4% M2. Now the 75 ground state of As i s known to have a spin of 3/2 with negative p a r i t y (35, 36), hence the above assignment means that the p a r i t y of the 400.7 kev l e v e l i s even with possible spins of 5/2, 3/2 or 1/2. The 136 kev t r a n s i t i o n also has only one possible assignment, v i z . E l + 4 l . 6 % M2. This means that the 264.6 kev l e v e l must have odd par i t y . In view of t h i s and i t s conversion c o e f f i c i e n t , the 265 kev t r a n s i t i o n must be Ml with less than 8% E2. The possible spins of the 264.6 kev l e v e l are therefore 5/2, 3/2 or 1/2. According to the conversion c o e f f i c i e n t the 280 kev t r a n s i t i o n could be either M1+E2 or E1+M2, the l a t t e r mixing i s , however, very u n l i k e l y . With the M1+E2 assignment then, t h i s means the 279.6 kev l e v e l has odd pa r i t y and possible spins of 5/2, 3/2 or 1/2. The odd pa r i t y of the 279.6 kev l e v e l and the conversion co-e f f i c i e n t f o r the 121 kev t r a n s i t i o n , then determines i t s m u l t i p o l a r i t y as E l with less than 2% M20 From the gamma-gamma d i r e c t i o n a l c o r r e l a t i o n measure-ments described previously, the co r r e l a t i o n functions f o r the 136 kev - 265 kev and 121 kev - 280 kev cascades have been determined. The co r r e l a t i o n function i n both cases can be adequately represented by a function of the form -92 1 + AgP 2 (cos © ) . The s t a t i s t i c a l uncertainty in the co e f f i c i e n t being larger than the c o e f f i c i e n t i t s e l f makes i t s existence dubious. In addition the conversion co-e f f i c i e n t s indicate that at least one gamma t r a n s i t i o n i n each cascade i s pure dipole and hence the A^ c o e f f i c i e n t would be expected to be zero on th e o r e t i c a l grounds. The Ag c o e f f i c i e n t s f o r both cascades are shown i n Table 9 along with some previously reported measurements. As can be seen there i s good agreement concerning the 121 kev -280 kev cascade but considerable v a r i a t i o n i n r e s u l t s for the 136 kev - 265 kev cascade. A comparison of the measured value of A^ (-0.43+0.06) obtained f o r the 121 kev - 280 kev cascade, with the the o r e t i c a l r e s u l t s of Biedenharn & Rose (8) shows immediately that none of the tabulated values based on pure multipole t r a n s i t i o n s agree with the experimental value. C l e a r l y therefore at least one of gamma rays i n the cascade must be a mixed multipole t r a n s i t i o n . From the conversion c o e f f i c i e n t s , t h e 121 kev t r a n s i t i o n i s expected to be pure E l , while the conversion c o e f f i c i e n t for the 280 kev t r a n s i t i o n indicates a dipole-quadrupole mixing (presumably M1+E2). As has been noted e a r l i e r , the d i r e c t i o n a l corre-l a t i o n function f o r gamma-gamma cascades involving one mixed multipole t r a n s i t i o n may be written as, W(O) - WT + § 2 W T T + 2 6w T X T Cascade Present Investigation A2 Schardt & Welker A * A2 Van den Bold et a l . V Lu et a l . A2 121-280 136-265 -0.43+0.06 -0.036+0.015 -0.40+0.03 -0.019 + 0- 0 1 -0.02 -0.464+0.016 -0.011+0.009 -0.41+0.03 +0.016+0.03 * Schardt & Welker used a correlation function with terms to P 4(cos 9). For t h e i r measurement, A 4 = -0.014+0.017 (121-280 cascade) A 4 = -0.012+0.012 (136-265 cascade) TABLE 9: Comparison of the yy Directional Correlation C o e f f i c i e n t s With Previous Measurements. -94-where, i n the present case, i s the co r r e l a t i o n function for the dipole-dipole cascade, W J J i s the co r r e l a t i o n function for the dipole-quadrupole cascade, W J J J i s the 2 dipole-quadrupole interference contribution and & i s the E2 _ i n t e n s i t y r a t i o . Ml On the basis of the conversion c o e f f i c i e n t s 5 t h e possible spins f o r both the 400.7 kev and 279.6 kev le v e l s are 5/2, 3/2 or 1/2. The spin 1/2 p o s s i b i l i t y f o r the 279.6 kev l e v e l can immediately be eliminated, since such a spin would imply an i s o t r o p i c d i r e c t i o n a l c o r r e l a t i o n between the 121 and 280 kev gamma rays. For each of the remaining combinations of energy l e v e l spins with the 3/2 ground state spin, the t h e o r e t i c a l values f o r A^ as a function of & were calculated using the tables compiled by Biedenharn & Rose (8). In f i g s . 35 and 34, A 2 i s plotted versus S for various energy l e v e l spin sequences. The experimental value for A (-0.43+0.06) i s also plotted, showing that only two possible spin sequences can account for t h i s value. The two sequences are, 1/2 (1) 3/2 (1,2) 3/2* with -1.8<S<-0.26 and 5/2 (1) 5/2 (1,2) 3/2 with -1.5<: S<-0.31. (The p o s s i b i l i t y of a 3/2 spin f o r the * Reading from l e f t to r i g h t t h i s notation gives the spin of the i n i t i a l state, the m u l t i p o l a r i t y of the f i r s t gamma ray (dipole), the spin of the intermediate state, the m u l t i p o l a r i t y of the second gamma ray (dipole + quadrupole) and f i n a l l y the ground state spin. to follow page 94 - . 5 W(©)=l+A 2P 2(cos©) .2 E l e c t r i c Quadrapple Ag experimental f o r 121-280 kev Cascade i i i i i i r~ .4 . 5 .6 . 7 . 8 . 9 I. . —1 1 1 1 — P — r - i — 4 5 6 7 8 9 1 0 B 4 a R experimental f o r 280 kev t r a n s i t i o n 4 5 6 7 8 9 I — i — ,3 TT —1 1 1—1 1 1 4 5 - 6 - 7 B 9 1 0 . Figure 34 A) Theoretical valves of A 2 as a function of f o r the Cascade •f(0|U iO'^ together with the experimental A 2 f o r the 121 kev - 280 kev Cascade. B) Theoretical Conversion C o e f f i c i e n t a K as a function of for the 280 kev t r a n s i t i o n together with the measured a K . To follow page 94 Figure 35 Theoretical values of An i n the y-y d i r e c t i o n a l c o r r e l a t i o n function, Vf\Q)=1+^2^2(cos9), as a function of the dipole-quadrapole mixing r a t i o (S) i n the second t r a n s i t i o n , for various energy l e v e l spin sequences.  2 3 «• S ; 6 7 b 9 lo Figure 36 Theoretical values of Ag, for the cascade, as function of the mixing r a t i o (small values of £ ) together with the measured A2 for the 136-265 kev y y cascade.  -95-406.7 l e v e l i s ruled out by t h i s r e s u l t ) . A spin of 1/2 for the 400.7 kev l e v e l i s u n l i k e l y for the following reasonss Because the K capture decay i s pre-75 dominantly to the 400.7 kev As l e v e l j i t i s expected to be 75 an allowed t r a n s i t i o n , i . e . A I = 0 or +1. The Se ground state has been measured and found to be 5/2 with unknown pa r i t y (37), hence with a spin assignment of 1/2 to the 400.7 kev l e v e l the K capture t r a n s i t i o n would have to be at least f i r s t forbidden. A 5/2 or 3/2 spin assignment on the other hand would be compatible with the expected allowed K capture decay, and of the two p o s s i b i l i t i e s only the 5/2 spin agrees with the co r r e l a t i o n data. This then sets the spin of the 279.6 kev l e v e l at 5/2 as well. Extending the above argument further, i t can be said, i n view of the 75 even p a r i t y of the 400.7 kev l e v e l , that the Se ground state probably also has even pa r i t y . In f i g . 34B the th e o r e t i c a l K conversion c o e f f i c i e n t for the 280 kev t r a n s i t i o n i s plotted as a function of | 81 • It can be seen from t h i s graph that the value for | S| predicted by the measured conversion c o e f f i c i e n t i s in excellent agreement with one of the two values given by the gamma-gamma d i r e c t i o n a l c o r r e l a t i o n measurement. S p e c i f i c a l l y the value of 8 according to these measure-ments i s (-0.46+0.16). According to Table 9 5A 2 for the 136-265 kev cascade i s (-0.036 + 0.0015). The only cascade involving pure -96-multipoles, occurring between i n i t i a l and f i n a l states with spins 5/2 and 3/2 respectively, and having a t h e o r e t i c a l value for A 2 agreeing with t h i s i s 5/2 (1) 3/2 (1) 3/2, for which A 2 - -0.04. The conversion c o e f f i c i e n t would allow up to 8% E2 mixing i n the 265 kev t r a n s i t i o n . From the curves of A versus S i n f i g . 35, i t i s seen then that i f such mixing occurs the cascade 5/2 (1) 5/2 (1,2) 3/2 with 0.13<S<0.17 would also have a th e o r e t i c a l value for A^ i n agreement with the measurement. Metzger"s (32) measurement of the angular d i s t r i b u t i o n of the resonantly scattered 265 kev gamma ray predicts an absolute value of & less than 0.03. This r e s u l t would therefore d e f i n i t e l y favour the 3/2 spin assignment to the 265 kev l e v e l . Evidence favouring the 3/2 spin assignment also comes from the beta decay of 75 Ge (25). The log f t value for the beta t r a n s i t i o n to the 264.6 kev A s 7 5 l e v e l i s 5.9 in d i c a t i n g that i t i s allowed. The ground state spin of G e 7 5 i s probably 1/2 (25) and hence the 3/2 spin assignment to the 264.6 kev l e v e l i s to be preferred over a 5/2 assignment. In f i g . 36,Ag i s plotted versus S (for small S ) for the 5/2 (1) 3/2 (1,2) 3/2 cascade. The graph shows that the range of values f o r I which give A i n agree-ment with the measured value i s from -0.12 to +0.075 which i s i n agreement with the conversion c o e f f i c i e n t l i m i t s . This r e s u l t together with Metzger's (32) measure--97-ment strongly suggests therefore that the 265 kev t r a n s i t i o n i s pure dipole (Ml). The e x i s t i n g data does not dictate a s p e c i f i c spin assignment to the 198.6 kev l e v e l . From the K conversion c o e f f i c i e n t i t i s known that the 199 kev t r a n s i t i o n i s mixed M1+E2. The present K conversion c o e f f i c i e n t measurement, as well as that of Grigoriev and Zolotavin (34), would allow up to 17% E2 mixing. The fac t that there i s an E2 component in the 199 kev t r a n s i t i o n has also been demonstrated by Coulomb e x c i t a t i o n measurements (26). The above assignment means that the spin of the 198.6 kev l e v e l must be 5/2, 3/2 or 1/2. With either a 5/2 or 3/2 spin assignment t h i s l e v e l would have the same assignment as either the 279.6 or 264.6 kev l e v e l s , and consequently a 202.1 kev t r a n s i t i o n from the 400.7 kev l e v e l to the 198.6 kev l e v e l would be expected with an i n t e n s i t y comparable to that of the 121 kev or 136 kev t r a n s i t i o n s . The absence of such a t r a n s i t i o n therefore rules out the possible spin assignments 5/2 and 3/2 leaving spin 1/2 as the only al t e r n a t i v e . In the present investigation, as well as that of Van den Bold et a l . (31), i t was found that the anisotropy * The gamma-gamma d i r e c t i o n a l c o r r e l a t i o n anisotropy i s defined as W(180°) - W(90°) W(90°) -98 of the 66 kev - 199 kev gamma-gamma cascade i s very small. From the present experiment an upper l i m i t of 0.1 i s placed on i t s value, i . e . i f the co r r e l a t i o n i s written as 1 + A 2P 2 (cos 0) then |A2|< 0.05. While i t might be tempting to view t h i s e s s e n t i a l l y i s o t r o p i c gamma-gamma co r r e l a t i o n as confirmation of the 1/2 spin assignment to the 198.6 kev l e v e l , t h i s can i n fact not be done since the M1+E2 mixing i n the 199 kev t r a n s i t i o n can also produce i s o t r o p i c correlations f o r the other two possible i n t e r -mediate state spins with appropriate values of S • That t h i s i s the case can be seen by r e f e r r i n g to f i g s . 34A and 35, and noting that a l l curves cross the A 2 = 0 axis for some value of 6 . The 304 kev K conversion c o e f f i c i e n t i s i n best agreement with an E3 assignment. Moreover, such a multi-p o l a r i t y i s consistent with the observed 17 msec, half l i f e of the 304 kev l e v e l . This assignment implies an even p a r i t y for the 304 kev l e v e l , which together with K conversion c o e f f i c i e n t of the 97 kev t r a n s i t i o n means that the l a t t e r t r a n s i t i o n must be E2. The absence of any in d i c a t i o n of lower multipole mixing i n either of the 97 kev or 304 kev tr a n s i t i o n s makes a 9/2 spin assignment to the 304 kev l e v e l the most l i k e l y one. This spin along with the 5/2 spin of the 279.6 kev l e v e l then means that the 24 kev t r a n s i t i o n i s most l i k e l y M2, -99-( i i i ) T ransition Lifetimes By means of fluorescence scattering experiments Metzger (32) and H. & M. Langevin (16) have determined the mean l i f e of the 265 kev gamma t r a n s i t i o n . The values quoted are 1.6 + 0.2 x lO"" 1 1 seconds and 2.4 + 0.3 x 1 0 - 1 1 seconds respectively. In the following discussion the average (2.0 x 10" 1 1 seconds) of these two measurements w i l l be used. In addition H. & M. Langevin were able to —9 deduce the mean l i f e of the 400.7 kev l e v e l (1.5+0.4x10 sec.) from t h e i r measurements. As was noted e a r l i e r the half l i f e of a second l e v e l , the 304.0 kev l e v e l , has also been measured and found to be 17 + 0.7 msec. (28, 29, 30). From these l i f e t i m e measurements and a knowledge of the r e l a t i v e t r a n s i t i o n i n t e n s i t i e s from the present investigation, the mean l i f e t i m e s of a number of the gamma tra n s i t i o n s can be calculated. To be more s p e c i f i c consider the case of the 400.7 kev l e v e l which has, as noted above, a mean l i f e of Q 1.5 x 10"° sec. This means that the t r a n s i t i o n p r o b a b i l i t y T, for decay from t h i s l e v e l per unit time i s 0.67 x 10 9 sec""'". From the conversion i n t e n s i t i e s given i n Table 3 and the gamma i n t e n s i t i e s i n Table 2 one finds that the 401 kev t r a n s i t i o n represents 13.2% of a l l t r a n s i t i o n s from the 400.7 kev l e v e l , and hence the p r o b a b i l i t y for decay per unit time v i a t h i s mode i s (0.132)(0.67 x 10^ s e c " 1 ) . From t h i s the mean l i f e t i m e for the 401 kev tran--100-s i t i o n i s found to be 1.1 x 10 sec. In a s i m i l a r fashion the mean l i f e t i m e s of the other t r a n s i t i o n s (97 kev, 121 kev, and 136 kev) that de-excite the 400.7 kev l e v e l can also be calculated. The r e s u l t s of these cal c u l a t i o n s , together with the r e s u l t s f or the 24 kev and 304 kev t r a n s i t i o n s , that de-excite the 304.0 kev l e v e l are summarized i n Table 10. Rather than the mean t r a n s i t i o n l i f e t i m e s (gamma plus i n t e r n a l conversion), the mean gamma t r a n s i t i o n l i f e t i m e s are tabulated. These two li f e t i m e s d i f f e r by a factor (1 + a) where a i s the in t e r n a l conversion c o e f f i c i e n t , i . e . " ^ t r a n s i t i o n = — — 13. 1+a Since for the 265 kev t r a n s i t i o n was obtained from the fluorescence scattering measurements, no c a l c u l a t i o n f or i t was necessary. From the mean l i f e t i m e for the 265 kev gamma t r a n s i t i o n and the r e l a t i v e i n t e n s i t i e s of the 265 kev and 66 kev t r a n s i t i o n s , however, Jj" f o r the 66 kev tr a n s i t i o n could also be calculated. The motivation for the determination of the mean gamma ray t r a n s i t i o n l i f e t i m e s was to enable a comparison of the empirically determined values with the predictions of the single p a r t i c l e model. In column 6 of Table 10 th i s comparison i s made through the r a t i o £~ / ^ S p / where ^ S p i s the mean gamma ray t r a n s i t i o n l i f e t i m e calculated, f o r the single p a r t i c l e model, from a formula given by Moszkowski (38). The calculations are based on the Parent Measured Total Transition M u l t i p o l a r i t y Y T r a n s i t i o n T V . * * Level Mean L i f e Mean Lifetime ^sp (y+Convers ion) 400.7 kev (1.5+0.4)xl0- 9 401 kev £1 l . l x l 0 " 8 s e c 2.2xl0 6 sec 136 E l 2.3xl0" 9 1.8xl0 4 121 E l 7 . l x l O " 9 4 x l 0 4 97 E2 5xl0"" 8 5.5xl0 - 2 304.0 (1.2+0. 5 ) x l 0 ~ 2 304 E3 5.8xl0~ 2 11 24 M2 2.5 * 42 264.6 (2+0.2)xlO""i:L 265 Ml 2 X 1 0 " 1 1 12 66 Ml l . l x l O " 9 9 * The conversion c o e f f i c i e n t f or the 24 kev t r a n s i t i o n i s assumed to be 165 (M2). * Tgp i s the Y t r a n s i t i o n meanlife, calculated on the basis of the single p a r t i c l e model. TABLE 10: Transition Lifetimes Based on Fluorescent Scattering Experiments -102-t r a n s i t i o n multipole.assignments given i n column 4. The r e s u l t s i n column 6 are i n accord with the measure-ments on other nuclear isomers (39). That i s , the measured li f e t i m e s are approximately equal to or longer than those predicted by the single p a r t i c l e model, with the exception of a large number of E2 t r a n s i t i o n s , p a r t i c u l a r l y in deformed nuc l e i , which exhibit t r a n s i t i o n p r o b a b i l i t i e s from 10 to 100 times larger than expected by t h i s model. In the present case the 265 kev and 66 kev Ml t r a n s i t i o n s , as well as the 304 kev E3 t r a n s i t i o n and the 24 kev M2 t r a n s i t i o n a l l have measured and calculated l i f e t i m e s that do not d i f f e r by unexpectedly large factors (i.e.<50) -tending to confirm the multipole assignments to these t r a n s i t i o n s . The 97 kev E2 t r a n s i t i o n has a l i f e t i m e 550 times shorter than expected t h e o r e t i c a l l y and appears therefore to f a l l into the class of f a s t E2 t r a n s i t i o n s . The group of 401 kev, 136 kev, and 121 kev, E l tran-s i t i o n s have l i f e t i m e s longer than the th e o r e t i c a l s i n g l e 6 4 4 p a r t i c l e values by factors of 2.2x10 , 1.8x10 and 4x10 respectively. Such large deviations from the the o r e t i c a l predictions have been noted f o r a l l known low energy E l tr a n s i t i o n s (39). This i s not an e n t i r e l y unexpected observation, since on the basis of the s h e l l model the low energy E l t r a n s i t i o n s are l i k e l y to be t r a n s i t i o n s involving at least one rather complex state. The mean l i f e t i m e of 280 kev gamma t r a n s i t i o n was -103-determined from the reduced nuclear t r a n s i t i o n p r o b a b i l i t y B(E2) obtained from Coulomb exci t a t i o n experiments (26), together with a knowledge of the M1+E2 mixing r a t i o obtained from the present measurements. B(E2) i s r e l a t e d to the inverse E2 t r a n s i t i o n p r o b a b i l i t y T (E2) by, V T (E2) = 1.23 x 10"*2 ( A E ) 5 B ( E 2 ) 2 I q + 1 s e c " 1 14. 7 2IX+1 where A E i s the energy difference between ground state and the Coulomb excited state i n kev (40). I Q i s the ground state spin and 1^ the excited state spin. B(E2) i s expressed i n units of e 2 x 10~ 4 8 cm4. For the 280 kev t r a n s i t i o n B(E2) i s 0.06 (26). Using t h i s value in the above r e l a t i o n and taking into account the fact that the 280 kev t r a n s i t i o n has 23% E2 mixing, the mean l i f e t i m e f o r t h i s gamma t r a n s i t i o n i s found to be 2.7 x 10" 1 0 sec. This value f a l l s within the l i m i t s set by the delay coincidence measurements of Schardt (28) and the fluorescence scattering measurements of Metzger (32) and of H. & M. Langevin (16). 75 Two other l e v e l s that are excited in the Se decay and that can also be Coulomb excited are at 198.6 kev and 572 kev. In the case of the 199 kev t r a n s i t i o n the intern a l conversion c o e f f i c i e n t allows up to 17% E2 mixing. -9 This, plus the value fo r B(E2) sets an upper l i m i t of 10 sec. on the l i f e t i m e of t h i s l e v e l . Nothing i s known about the multipole mixing, i f any, i n the 572 kev t r a n s i t i o n , -104-hence an upper l i m i t on the l e v e l l i f e t i m e i s f i x e d at 3.7 x IO" 1* sec. by the E2 t r a n s i t i o n p r o b a b i l i t y determined from the measured B(E2). The t r a n s i t i o n l i f e t i m e s based on the Coulomb e x c i t a t i o n measurements and comparisons with the single p a r t i c l e values are given i n Table 11. Again i n t h i s comparison i t i s noted that the E2 t r a n s i t i o n s are faster than predicted on the basis of the single p a r t i c l e model and the Ml component i n the 280 kev t r a n s i t i o n i s «— 200 times slower. 75 (iv) The Se Decay Scheme The r e s u l t s of the foregoing discussion are summarized i n the decay scheme shown i n f i g . 37. Electron capture t r a n s i t i o n s are shown to the 572 kev, 478 kev, 400.7 kev, 75 279.6 kev, 264.6 kev l e v e l s as well as to the As ground state. Log f t values, obtained by using the nomographs prepared by Moszkowski (41), for these t r a n s i t i o n s are 8.6, 8.2, 5.9, > 7.4, > 7.1 and>7.5 respectively*. The values for the t r a n s i t i o n s to the 279.6 kev, 264.6 kev 75 le v e l s and the As ground state were calculated for the maximum in t e n s i t y allowed by the r e s u l t s of the present investigation. No K capture decays are shown to the 304.0 kev or 198.6 kev l e v e l s since no evidence for such * 75 75 The Se ground state i s 864 kev above the As ground state according to the (p,n) threshold measurements on A s 7 5 by T r a i l and Johnson (42). This value was used in determining the log f t values. to follow page 104 Transition B(E2)* in units of e 2xl0~" 4 8cm 4 Calculated E2 Transition Probability T (E2) 7 E2 - mxxing r a t i o (S z) yTransition Mean1ife Ty Tsp 199 kev 0.022 l ^ x l O ^ e c " 1 0.17 10" 9sec 1.9xl0" 2** 280 0.06 8.5xl0 8 0.23 2.7x l 0 ~ 1 0 10" 1 (E2) 2.2xl0 2(Ml) 572 0.072 2.7xl0 1 0 3.7x10" 1 1 10' 1 ** * Obtain from Coulomb ex c i t a t i o n experiments (26). This i s the r a t i o of the measured E2 t r a n s i t i o n p r o b a b i l i t y to the single p a r t i c l e E2 t r a n s i t i o n probability. TABLE 11: Transition Lifetimes from Coulomb Ex c i t a t i o n Experiments. -106-decays was obtained in the present measurements. The log f t value of 5.9 for the decay to the 400.7 kev l e v e l supports the view that t h i s i s an allowed tran-75 s i t i o n and therefore that the Se ground state has even 75 p a r i t y . A l l remaining As l e v e l s except the 304.0 kev l e v e l which has a 9/2+ assignment, have odd p a r i t y . (The odd p a r i t y assignment to the 478 kev l e v e l i s preferred on the basis of the r e s u l t s of Schardt & Welker (25).) The weak electron capture i n t e n s i t i e s to a l l but the 400.7 kev l e v e l are explained then by the f a c t that these t r a n s i t i o n s are at least "1" forbidden. The log f t values being larger than 7.1 for any of these decays supports t h i s i d e n t i f i c a t i o n . In f i g . 37 also, the 80 kev t r a n s i t i o n detected by some authors, has been included between the 279.6 kev l e v e l and the 198.6 kev l e v e l * . * Very recently a paper by deCroes & Backstrom (43) has appeared i n p r i n t reporting on t h e i r measurements on the S e 7 5 decay. The reported conversion c o e f f i c i e n t s are i n good agreement with the present r e s u l t s and the r e s u l t s of Grigoriev & Zolotavin and Metzger & Todd. In the i r conversion spectrum however, deCroes & Backstrom found two additional peaks, one of which they i d e n t i f i e d as a 188 K peak and the other as a 203 K peak. The 188 kev peak which was observed with an i n t e n s i t y equal to the 199 K peak should have been observed i n the con-version spectrum of the present investigation as well as in the conversion spectra of Schardt & Welker (25) and Grigoriev & Zolotavin (34). The measurements of Grigoriev & Zolotavin should also have shown the 203 K peak. None of these investigations gave any i n d i c a t i o n of such conversion peaks, hence the weight of evidence i s against the existence of the 188 kev and 203 kev t r a n s i t i o n s . Because of the incl u s i o n of the 188 kev and 203 kev t r a n s i t i o n s , the decay scheme of deCroes & Backstrom d i f f e r s from that presented i n f i g . 37 -107-(v) Discussion There appears to be l i t t l e doubt that the decay scheme of 34Se7^4-^ to i t s daughter nucleus 33 A g 7^42 i s n o w uniquely and unambiguously assigned. The sequence of energy leve l s and t h e i r decay, together with t h e i r respective spins, p a r i t i e s and m u l t i p o l a r i t i e s form a sel f - c o n s i s t e n t scheme in agreement with the experimental r e s u l t s obtained i n t h i s laboratory and i n others. The mass of experimental evidence includes the r e s u l t s of magnetic spectrometer analysis of gamma rays and conversion electrons, s c i n t i l l a t i o n spectrome-ter analysis of gamma spectra, gamma-gamma and conversion electron-gamma coincidences, angular c o r r e l a t i o n measurements on successive gamma rays and elsewhere from the r e s u l t s of resonance fluorescence and Coulomb ex c i t a t i o n experiments. The r e s u l t i s a rather complex scheme involving perhaps s i x K capture t r a n s i t i o n s of varying i n t e n s i t i e s , and possibly 75 13 t r a n s i t i o n s between the states of As In the present state of knowledge of possible nucleonic configurations i n nuclei we are unable to predict the f i n e r d e t a i l s of the scheme arrived at on the basis of experiment. However, the limi t e d success of a number of nuclear models makes possible cer t a i n general comments on some of the features of the decay. These comments must be rather general i n nature and when offered as a possible explanation of a certai n mode of decay must not be considered as anything but a plausible -108-statement i n accordance with our li m i t e d knowledge of nuclear behavior. 75 75 Since Se and As are odd A n u c l e i , one might expect cer t a i n features of the sing l e p a r t i c l e s h e l l model to be apparent. According to t h i s model the fourth neutron and proton s h e l l s are being f i l l e d i n t h i s region of the periodic table (36). S p e c i f i c a l l y 5 i n the case of 75 As , there are 14 neutrons and 5 protons outside of the closed t h i r d s h e l l . The simple s h e l l model predi c t i o n for the ground state configuration of these nucleons i s , ( p ^ 4 ( f s ; j ) 6 ( p ^ ) 2 ( g v / ) 2 J = 0 for the neutrons and (Py4>4<Vj-5fe f o r the protons, leading to a predicted ground state spin of 5/2-. In f a c t , the measured spin i s 3/2-. This ob-servation can be understood i f p a i r i n g energy, which favors the premature occupation by nucleon p a i r s of l e v e l s of higher t o t a l angular momentum, i s taken into account. In t h i s case, i t must be assumed that two protons are in say, the f 5 / i l e v e l leaving the odd proton i n a p % / i state, which accounts for the measured spin. S i m i l a r l y 75 for the Se ground state nucleon configuration, the s h e l l model predicts, (p 5 /) 2(f^) 6(p^) 2(gsy, ) J = % f o r the 4 9 neutrons and (p, ) (f,-.) _ n for the protons, with a VV 7 i J = U ground state spin therefore of 9/2+. Pairing energy, however, might put two neutrons i n the g»/? state leaving the odd neutron i n the p^ state and giving 1/2- as the 75 ground state spin. Actually the measured spin of Se i s -109-5/2 with undetermined pa r i t y . Furthermore, the quadrupole —28 o moment of t h i s nucleus, +1.1 x 10 cnr4 i s also anomalously high. These observations indicate that the s t r i c t s i n g l e p a r t i c l e model i n which the observed nuclear properties are attributed to the l a s t odd nucleon i s probably a gross o v e r - s i m p l i f i c a t i o n i n t h i s case, and that at least the ef f e c t of the other nucleons outside of the closed s h e l l 75 should be considered. Thus, i n the case of Se 9 Aamodt & Fletcher (37), who measured the spin and quadrupole moment of t h i s nucleus using microwave spectroscopy techniques, suggest that the most l i k e l y ground state neutron con-figurations consistent with t h e i r r e s u l t s are (P|)(g>,) 2 ( g % ) 3 j=»>'/^  '»' a n d < f ? z ) 5 J-*/* . Other configurations that have t o t a l angular momentum 5/2 predict the wrong magnitude and/or sign for the quadrupole moment. In view of the even p a r i t y assignment to t h i s l e v e l on the basis of the present investigation, the second configuration appears to be most l i k e l y choice of the three alternatives. 3 9 The proton configuration (p ,^) (f ^  )* ^ has already been mentioned as a possible ground state con-75 f i g u r a t i o n for As . Mayer & Jensen (44) have calculated the magnetic dipole moment for t h i s configuration and f i n d i t to be 2.21 n.m. Closer agreement with the measured value of 1.44 n.m. was achieved by Arima & Horie -110-(45) who assumed that the proton pair i s i n the g?^ state rather than the f if state. The calculated magnetic moment in t h i s case i s 1.6 n.m. The assumption concerning occupation of the g9/^ state i s not an unreasonable one since the four l e v e l s i n the fourth s h e l l are r e l a t i v e l y close together (36), and the larger p a i r i n g energy i n the 9/2 spin state may therefore favor i t s early occupation by a proton pa i r . 75 Now l e t us consider the excited states of the As nucleus. A l l states except two, those at 304.0 kev and 400.7 kev have negative p a r i t i e s . If we l i m i t the con-figurations involved only to the f i v e protons outside of the closed s h e l l and note that the s h e l l model predicts a cluster of f,^ , p 3 / , p^ and g 9 / i states immediately avail a b l e , then presumably the odd p a r i t y configurations must be characterized by a pair of protons or none at a l l i n the g ^ state and an odd number of protons i n either the p^ , p^ or f ^ states. Hence i t would not 75 be s u r p r i s i n g i f a l l negative p a r i t y states i n As had preferred spins of 1/2, 3/2 or 5/2. This i s the case. Even p a r i t y states presumably have the odd p a r t i c l e i n the g*, state. The assignment of 9/2+ to the 304.0 kev l e v e l i s consistent with t h i s reasoning. The other p o s i t i v e p a r l j ^ state i s the 400.7 kev l e v e l with a 5/2+ spin. Many purely a r b i t r a r y assignments could be written f o r t h i s state but beyond noting that the con-- I l l -f i g u r a t i o n probably has one or three protons i n the gq / 2 state 5other speculations seem f r u i t l e s s . The departure from the sing l e p a r t i c l e concept i s very c l e a r l y shown i n Tables 10 and 11, where the measured tran-s i t i o n p r o b a b i l i t i e s are compared with those predicted by the sing l e p a r t i c l e theory. It i s pointed out by De-Shalit & Goldhaber (46) that i f the nucleon configuration of a p a r t i c u l a r state i s mixed, i . e . more than one configuration with the same J and e s s e n t i a l l y the same energy i s associated with the state, then the t r a n s i t i o n p r o b a b i l i -t i e s f o r t r a n s i t i o n s involving such a state, are expected to be considerably d i f f e r e n t from the sing l e p a r t i c l e predictions. That such configuration mixing occurs i n the 75 As l e v e l s cannot be stated with any certainty here, since the t r a n s i t i o n p r o b a b i l i t i e s for the case of mixed configurations have not been calculated, though q u a l i -t a t i v e l y such a description could presumably account f o r the observed t r a n s i t i o n p r o b a b i l i t i e s . A second model worthy of some consideration when 75 t r y i n g to account f o r the As l e v e l s , takes into account the f a c t that nuclear core excitations might be expected i n t h i s mass range. S p e c i f i c a l l y , there i s reason to believe that for mass 75 nuclei the coupling between the l a s t odd nucleon and the nuclear core i s strong enough to cause appreciable p o l a r i z a t i o n of the nuclear shape (40), with a r e s u l t i n g coupling scheme c h a r a c t e r i s t i c of -112-the deformed nu c l e i . If t h i s i s so ; then i t i s conceivable that c e r t a i n of the A s 7 5 l e v e l s could be i d e n t i f i e d as r o t a t i o n a l states. For odd A n u c l e i , the states within a r o t a t i o n a l band have the spin sequence, I Q , I Q+1, I Q+2, +—, where I Q i s the spin of the lowest energy l e v e l i n the band. The energies of the other r o t a t i o n a l l e v e l s r e f e r r e d to t h i s one are given by, where $ i s the "moment of i n e r t i a " of the nucleus. The strong Coulomb ex c i t a t i o n of the 279.6 kev l e v e l and the 572 kev l e v e l (26) together with the spin sequence, 3/2-, 5/2- and possibly 7/2-, suggests that these two l e v e l s along with the ground state, may approximately be considered states within a r o t a t i o n a l band. The f a c t that the r a t i o of the energies of l e v e l s i s 2.0 : 1 while the value predicted by equation 15 f o r the above spin sequence i s 2.4 : 1, supports t h i s view. According to t h i s model the other l e v e l s are con-sidered to be i n t r i n s i c excitations involving the odd proton coupled to the core. That i s , the odd p a r i t y states could be explained by a P 3 / 2 or f$/2 proton coupled to the core and the even p a r i t y states by a s i m i l a r coupling of a gg/2 proton. The number of l e v e l s that can be Coulomb excited i n As , the enhanced E2 t r a n s i t i o n p r o b a b i l i t i e s r e l a t i v e to the single p a r t i c l e expectations and the i n h i b i t e d -113-E l t r a n s i t i o n p r o b a b i l i t i e s (47) a l l can i n p r i n c i p l e be explained by t h i s model. 75 In conclusion i t might be noted that the As energy l e v e l scheme has many features i n common with the energy 77 l e v e l diagrams of As (which has two additional neutrons) 79 (48) and Br (which has two additional neutrons and two 75 additional protons) (49). The s i m i l a r i t y between the As 77 and As schemes has been pointed out by Schardt (28). In f i g . 38 the three l e v e l diagrams are reproduced. The 3/2-ground state spin, the occurrence of an isomeric state with a 9/2+ assignment and the large number of low energy states are features common to these energy l e v e l diagrams. Presumably therefore any th e o r e t i c a l description of the 75 As l e v e l scheme should also be applicable to the other two nuclei as well. E Mev 1 - 0 7 0 . 6 H Q S 0 . 4 h0.3 •0.2 hQl Br 79 3 As 75 2 ' \ 3 2 2 As 7 7 5 _ _ 2 1 A 2 2 Figure 38 Comparison of the Energy Level Diagrams of B r 7 9 , A s 7 5 , and A s 7 7 , 0 o H M o •d p TO M CO -114-APPENDIX I DETERMINATION OF ELECTRON INTENSITIES FROM THE MAGNETIC SPECTROMETER DATA (1) Spectrometer Adjustment The preliminary adjustments of the magnetic spectrometer V were made using the 661 kev ( t r a n s i t i o n energy) conversion 137 l i n e of Cs . That i s , the source position (distance of the source to the magnet and i t s p o s i t i o n i n the source plane) the b a f f l e s at the source end of the spectrometer (entrance b a f f l e s ) and the b a f f l e s at the detector (exit b a f f l e s ) , were adjusted to give optimum transmission and resolution of t h i s l i n e . Having selected the entrance b a f f l e s and source po s i t i o n , the s i z e of the e x i t b a f f l e was decreased in steps from maximum aperture. At each step the peak shape was measured. Up to a point, as the exit b a f f l e s were closed down, the resolution improved while the peak height remained constant, i n d i c a t i n g that the ex i t b a f f l e s l o t width was greater than the width of the focussed beam. A further decrease i n the e x i t b a f f l e s i z e resulted i n a decided reduction i n the peak height. Therefore the exit b a f f l e used was the smallest one that did not cause a decrease i n the peak height. At t h i s point the e x i t and entrance b a f f l e s are sa i d to be matched. The maximum 661 conversion electron counting rate -115-(peak counting rate) was then proportional to the t o t a l number of conversion electrons emitted per second. The constant of pro p o r t i o n a l i t y i s defined as the transmission of the spectrometer. (2) Spectrometer Transmission The problem of determining the transmission of the 137 spectrometer l i e s i n the c a l i b r a t i o n of the Cs source. S p e c i f i c a l l y , i t i s necessary to know the number of 661 kev conversion electrons emitted per second. The following method was adopted to achieve t h i s c a l i b r a t i o n . From a large piece of anthracene c r y s t a l a cylinder was cut 8 mm in diameter by 6 mm high. The cleavage plane of the c r y s t a l was perpendicular to the axis of the cylinder, enabling i t to be cleaved into two cylinders 8 mm x 3 mm. A small indentation was made i n the centre of the cleaved face of one of the cylinders, and into t h i s a drop of soluti o n containing a very small quantity of 137 Cs was deposited. After drying, the two cleaved faces were f i t t e d together. In e f f e c t then t h i s formed a c y l i n d r i c a l c r y s t a l with a source at the centre. The dimensions of the cylinder were chosen so that a l l of the conversion electrons from the source would be absorbed. One face of t h i s c r y s t a l assembly was coupled with DC 200 s i l i c o n e o i l , to the centre of the photocathode of a RCA 6342 photomultiplier. A bright aluminum f o i l -116-r e f l e c t o r held the c r y s t a l i n place as shown in f i g . 39. A pulse height analysis of the output of the photo-m u l t i p l i e r showed the 661 kev conversion peak with a resolution of 18%. Since cooling the photomultiplier r e s u l t s i n an i n -creased gain, and consequently better r e s o l u t i o n , the photo-m u l t i p l i e r assembly was placed i n a dewar as i l l u s t r a t e d i n f i g . 40. With t h i s arrangement the photomultiplier and c r y s t a l were cooled to about 100°K by pre-cooling the dewar with l i q u i d nitrogen and allowing a small amount to remain in the bottom of the dewar when i t was placed around the photomultiplier. A pulse height analysis of the photomultiplier output in t h i s case resulted i n the spectrum shown in f i g . 41. The resolution of the 661 kev conversion peak i s 15%. To determine the number of conversion electron counts in the peak i t was necessary to subtract the contribution from the primary beta spectrum, from which the conversion peak i s not e n t i r e l y resolved. This was done by making a Kurie plo t of the high energy portion of the beta spectrum. From the l i n e a r extrapolation of t h i s plot the shape of the beta spectrum under the peak was determined. After subtracting the small contribution from the weak high energy beta group i t was determined that 31.5 +_ 0.6 conversion electrons were emitted per second, by the source i n the anthracene c r y s t a l . A c a r e f u l comparison to follow page 116 Light Tight Cover • RCA 6342 Photomultiplier Anthracene Crystal with C s 1 3 7 source in the centre Aluminum F o i l S i l i c o n e O i l 137 Figure 39 Anthracene Crystal with Internal Cs Source Mounted on the Photocathode of a Photomultiplier. 10 Conductors cast i n Ara l d i t e  Liquid Nitrogen Voltage Divider Dewar Photomultiplier Anthracene C r y s t a l with C s 1 3 7 Source Figure 40 Method used for Cooling the Photo-multiplier-Anthracene Crystal Assembly shown i n figure 40. to follow page 116 to 0) •p a •H s o CO \ iH CD a a a xi o \ CO •p a o Figure 41 C s 1 3 7 Beta Spectrum measured with the Anthracene Crys t a l Total Absorption Spectrometer. Primary Beta Spectrum Internal Conversion Electron Peak (661 kev Transition) Kicksorter Channel Number — i — 6 0 — I 6 5 l — 7 0 3 5 I 4 0 4 5 5 0 5 5 7 5 8 0 8 5 9 0 Figure 42 I n t r i n s i c Photo-peak E f f i c i e n c y of a l " x l $ " Nai(Tl) C r y s t a l for a source distance of 7 cm. Gamma Ray Energy i n Mev. . 2 .4 - r . 5 — r . 6 i 1 \—i— . 7 . 8 . 9 1 0 -117-137 of the gamma ray i n t e n s i t i e s of t h i s source and the Cs source used i n the magnetic spectrometer then indicated that, 22,750 + 750 conversion electrons were emitted per second by the magnetic spectrometer source. Comparing th i s with 127.4 +0.8 counts/sec, the peak counting rates of the K + L conversion electrons i n the magnetic spectrometer spectrum, then gives the transmission of the spectrometer as 0.56 + 0.02%. (3) Intensity Determination The value f o r the spectrometer transmission determined above, applies s t r i c t l y only when the resolution i s the 137 same as for the Cs spectrum. The i n t e n s i t y of a peak with poorer resolution can be determined by f i r s t adjusting i t s resolution to that of 137 the Cs spectrum while keeping the area under the peak constant, and then taking the maximum counting rate of the adjusted peak and multiplying i t by the transmission de-termined above. This of course i s an approximation, which gives good r e s u l t s so long as the resolutions do not d i f f e r greatly. Because of self-absorption i n the source the 75 resolution of the conversion peaks in the Se spectrum i s 137 somewhat poorer than f o r the Cs peak. Consequently the approximation outlined above must be used to determine the i n t e n s i t i e s . -118-APPENDIX II Nal(Tl) GAMMA RAY DETECTION EFFICIENCY The t o t a l gamma ray detection e f f i c i e n c y of Nal(Tl) c r y s t a l s , i . e . the p r o b a b i l i t y that a gamma photon w i l l interact i n some way with the c r y s t a l has been calculated, using measured absorption c o e f f i c i e n t s , for various c r y s t a l s i z e s , source to c r y s t a l distances and gamma ray energies up to 10 mev (18). In general, however, i t i s easier to determine the counts i n the photopeaks of gamma ray spectra rather than the counts i n the t o t a l pulse height d i s t r i b u t i o n of each gamma t r a n s i t i o n . For t h i s reason Lazar et a l . (50) combined the above mentioned c a l c u l a t i o n with the r e s u l t s of measurements on certa i n gamma spectra to obtain the i n t r i n s i c photopeak e f f i c i e n c i e s for three c r y s t a l s i z e s and a limi t e d range of gamma ray energies. The method employed to obtain the i n t r i n s i c photopeak e f f i c i e n c i e s consisted of measuring the gamma ray spectra i n which only one gamma ray appears and then determine the r a t i o of the number of counts in the photopeak to the number of counts i n the t o t a l pulse height d i s t r i b u t i o n of the gamma t r a n s i t i o n . Multiplying t h i s r a t i o by the t o t a l detection e f f i c i e n c y then yie l d s the photopeak e f f i c i e n c y . For the i f " x 1" c r y s t a l the photopeak e f f i c i e n c y has been determined for gamma rays i n the energy -119-range 0.3 to 2 Mev. In f i g . 42 the r e s u l t s of Lazar et a l . are reproduced i n graphical form together with the addition of one more point at 279 kev. This point was obtained by determining 75 the peak to t o t a l r a t i o at t h i s energy from a Se gamma ray coincidence spectrum containing only the 279 kev gamma ray d i s t r i b u t i o n ( i . e . the r e s u l t s of the coincidence measurement with the 121 kev conversion electrons were used). -120-APPENDIX III ANALYSIS OF GAMMA-GAMMA DIRECTIONAL CORRELATION DATA (1) Least Squares F i t to the Data As has been stated previously the d i r e c t i o n a l corre-l a t i o n function i s most conveniently written as a series of Legendre polynomials. If w(©^) i s the measured value of the c o r r e l a t i o n function at angle Q^, (©^ = 0°, 15°, 30°, 45°, 60°, 75° and 90° for the S e 7 5 measurements), the equations of condition are then of the form, w(© i) = a Q + a 2 P 2 (cos © i ) + a 4 p 4 ( c o s © 4 ) 1 5 -(It i s assumed here that a l l the measured data has equal weight.) Let, d i = ao + a 2 p 2 ( c o s Q\) + a 4 P 4 ( c o s 9^) - w(© i) 16. Then for a least squares f i t , a Q , a 2 , and a^ must be chosen so that "ZJ d i s a minimum. That i s , i 17. For the angles © i given above, these p a r t i a l derivatives y i e l d the normal equations, 18. -121-^ P 4 ( c o s Q±) Vi(9±) = 1.531 a Q + 1.320 a 4 + 1.879 a 4 20. i The sums on the l e f t can be calculated from the data. Equations 18, 19, and 20 can then be solved for a Q, a 2 and a^ to y i e l d the experimental d i r e c t i o n a l c o r r e l a t i o n function. (2) Correction f o r F i n i t e Angular Resolution The t h e o r e t i c a l gamma-gamma d i r e c t i o n a l c o r r e l a t i o n functions are calculated f o r point sources and point de-tectors. In practice i t i s usually possible to achieve a f a i r approximation to a point source and no correction for t h i s w i l l be considered. The detectors on the other hand, usually Nal(Tl) c r y s t a l s , deviate considerably from the idea l by subtending an appreciable angle at the source. Therefore i n order to compare the measured c o r r e l a t i o n functions with the t h e o r e t i c a l calculations i t i s necessary to apply a correction to the measured function for t h i s e f f e c t . This s o l i d angle correction has been treated i n various approximations by several authors (51, 52, 53, 54). The following considerations are based primarily on the discussions i n a paper by Lawson and Freunfelder (51). It i s assumed that the d i r e c t i o n a l c o r r e l a t i o n function W(Q) of successive gamma rays, y and y i s being measured (W(©) = 1 + A 2P 2(eos ©) + A 4P 4(cos ©)), and that the ex-perimental arrangement consists of two i d e n t i c a l c y l i n d r i c a l detectors (Nal(Tl) c r y s t a l s ) equidistant from the source as shown i n f i g . 43. The d i r e c t i o n a l c o r r e l a t i o n function to follow page 121 i -OS et O f •H •P <D 03, .2-Gamma Ray Energy 121-136 kev Detector Collimator Edge 10-0.8-0.6-0.4-0.2 Gamma Ray Energy Detector Collimator Edge IT 10 15 -10° -5° 15" -15' -10° -5° Angular Position of the Detector Relative to the Collimated Beam Di r e c t i o n Figure 44 Angular Detection E f f i c i e n c y of l " x l $ " Nal(Tl) C r y s t a l used i n the Gamma-Gamma D i r e c t i o n a l Correlation Measurements. -122 measured with the system illustrated in f i g . 43 can be expressed as follows, / r t N jW(9')c X t 0Qg uL<U-^d-n-i W(9) = 7 ; ; 21. where, ^ -y^(a^) is the detection efficiency of the detector for y emitted at an angle with respect to the detector axis. £y (a ) is similarly defined for y . d i l 1 and dO-g are the solid angle elements for y^ and y respectively at the angles a-^ and a„, In equation 21 integrals of the following form are involved, ^ ( c o s 0 ' ) S Y 1 ( a 1 ) £ Y 2 ( a 2 ) d H 1 d n 2 22. Skipping the intermediate steps, this can be written as, I = k P v ( c o s 9) J ^ C Y J ) J v ( Y 2 > 2 3 -where k is a constant and, ,-amax J vW]_) = \ P, (cos a^) ^y^ctj) sin a^a 24. o a „ v is the half angle subtended by the crystal at the max source. A similar expression can be written for J ( Y 2 ) . The measured correlation function therefore can be written in the form, w(9) = 1 + Q 2A 2P 2(cos 9) + Q 4A 4P 4(cos 9) 25. -123-where Q v i s c a l l e d the attenuation c o e f f i c i e n t and i s given by, Q y = J * ^ ^ 2 6 „ Jo <Yl> Jo ^ 2> Comparing the c o e f f i c i e n t s of the co r r e l a t i o n function de-termined by a least squares f i t to the data with the co-e f f i c i e n t s i n equation 25, the c o e f f i c i e n t s of the actual c o r r e l a t i o n function can be determined, i . e . , A v - ±L 27. Q v To determine the values of the attenuation c o e f f i c i e n t s Q y , the angular detection e f f i c i e n c i e s ^<y(a) must be measured and the integr a l s (y) evaluated numerically. For the gamma rays i n the Se'^ decay, i t i s assumed that the angular detection e f f i c i e n c i e s for the 121 kev and 136 kev gamma rays are equal, as are the e f f i c i e n c i e s for the 265 kev and 280 kev gamma rays. These e f f i c i e n c i e s were determined by measuring the in t e n s i t y of the (121, 136) kev composite photopeak, as well as the in t e n s i t y of the (265, 280) kev composite photopeak i n a highly collimated beam, as a function of the angle between the beam and the detector axis. F i g . 44 shows the v a r i a t i o n of in t e n s i t y with angle for both energies. Because r a t i o s of the integr a l s (equation 24) are involved i n equation 26, only the r e l a t i v e angular -124-e f f i c i e n c i e s , which can be obtained d i r e c t l y from f i g . 44 are necessary. Using these e f f i c i e n c i e s the integrand of equation 24 was plotted as a function of the angle a for each of the two gamma ray energies and f o r V = 0, 2, 4. The areas under these curves then gave the value of the corresponding inte g r a l . The appropriate r a t i o of these areas were then calculated to give, Q = 0.890 Q 4 - 0.682 as the attenuation c o e f f i c i e n t s for the d i r e c t i o n a l corre-l a t i o n s of the (121-280) kev and (136-265) kev cascades i n S e 7 5 . (3) D i r e c t i o n a l Correlation Measurements  with Unresolved Photopeaks Consider the simple case of measuring the coincidence counting rate for a cascade y-.y0, using two pulse height analyzers operating i n coincidencej one accepting only photopeak pulses due to y , while the other accepts only y 1 2 photopeak pulses. The coincidence counting rate in th i s case would be, C(Q) = N ^ f - ^ f g ^ W ^ C © ) 28. where, i s the number of y^ photons emitted per second. £g a r e photopeak e f f i c i e n c i e s of the detectors for the respective gamma rays. -125-f , f are the fr a c t i o n s of the t o t a l photopeak pulses that f a l l within the acceptance windows of the respective pulse height analyzers, W^g(Q) i s the d i r e c t i o n a l c o r r e l a t i o n function for and y0 (uncorrected f o r the f i n i t e r e s o l u t i o n of the detectors), and ^ g i s the c o r r e l a t i o n function normalizing factor so that, Unfortunately, s c i n t i l l a t i o n spectra are usually more complex than the one considered above, r e s u l t i n g , for example, in pulses due to more than one gamma t r a n s i t i o n f a l l i n g within the pulse height analyzer window. A case 75 i n point i s the spectrum of Se where both of the two most prominent peaks consist of a pair of unresolved photopeaks, one being composed of the 121 kev and 136 kev photopeaks and the other of the 265 kev and 280 kev photo-peaks. In addition^the 121 kev t r a n s i t i o n s and the 280 kev t r a n s i t i o n s are i n cascade, as are the 136 kev and 265 kev t r a n s i t i o n s . This means that coincidence counts from one cascade cannot be determined without interference from the other. With the pulse height analyzers set to accept photopeak pulses as before, the coincidence counting rate when the above composite peaks are involved w i l l now be, o -126-C(0) - N 1 C 1 f 1 f 3 1 2 £ 2 f 2 7 ? 1 2 W 1 2 ( O ) + N 3 e 3 f 3 P 3 4 f 4 f 4 7 3 4 W 3 4 ( 0 ) 29. where, we consider the cascades to be Y]/y2 and y^y^ (see f i g . 45). Also, account has been taken, through the introduction of the factors £-|_2 and P34, of the possi-b i l i t y that not a l l of the gamma rays detected belong to yy cascades, i . e . ft12 i s the p r o b a b i l i t y that y^ I S i n cascade with Y 2« (^I 2 ^  1 when either y^ i s not the only mode of decay from the intermediate s t a t e ? o r y 2 i s not the only mode of decay to the intermediate l e v e l ) . (^ 34 i s defined s i m i l a r l y f o r y^y^.' To make these considerations d i r e c t l y applicable to 75 the Se measurements,we make the following i d e n t i f i c a t i o n s : F i g . 45 r l ^2 ^3 ^4 75 -^> 265 kev y -r> 136 kev y -> 280 kev y 121 kev y For the Se measurements also, the coincidence system was d i f f e r e n t from that considered above. A kicksorter was used to record the entire spectrum i n coincidence with the -127-output of the pulse height analyzer, which was set to accept a f r a c t i o n of the 265 - 280 kev photopeak pulses, i . e . fg = f ^ = 1 in equation 29, f o r t h i s arrangement. A further s i m p l i f i c a t i o n of equation 29 can be made by noting that the pulse height analyzer counting rate due to photopeak pulses of y^ f a l l i n g within i t s acceptance window i s given by, Sh i f t s i n the discriminator voltage l e v e l s i n the pulse height analyzer can a l t e r the analyzer counting rate as well as the coincidence counting rate. To minimize the e f f e c t of such s h i f t s the coincidence counting rate i s divided by the pulse height analyzer counting rate. This normalized co-incidence count, as a function of detector angle, then de-termines the measured d i r e c t i o n a l c o r r e l a t i o n function w(9). Thus we have, n i - N i £ i f i 30. Hence equation 29 becomes, C<9) - Vl?127l2W12 (9) + n 4 V 3 4 ? 3 4 W 3 4 ( 9 ) 31. w(9) = C(9) b12 W 1 9(9) + r j b 3 4 1+r^ W 3 4(9) 32. n 2+n 4 where, b12 = ^12 ^ 1 1 12 b34 = ^34 £ 3 ^ 3 4 and ( i r e f e r s to a s p e c i f i c d i r e c t i o n a l -128-c o r r e l a t i o n measurement) Now, W 1 2(0) a n a w 3 4 ( ® ) c a n D e expressed as follows. W 1 2(0) = 1 + A 2P 2(cos 0) + A 4P 4(cos 0) 33, W 3 4(0) = 1 + B 2P 2(cos 0) + B 4P 4(cos 0) 34. Also, for a s p e c i f i c r a t i o ( r ^ of <y4 counts to <y2 counts i n the pulse height analyzer window, the measured corre-l a t i o n function, obtained from a least squares f i t to the data i s , wjL(0) = a Q i + a 2 i p 2 (cos 0) + a 4 i p 4 ( c o s © ) 3 5 • Substituting equations 33 and 34 into 32 and equating the r e s u l t i n g c o e f f i c i e n t s of the Legendre polynomials to those in equation 35 gives, a o i ( l + r i ) = b 1 2 + r ± b 3 4 36. a 2 i ( l + r i ) = b 1 2A^ + *±*34P2 37'• a 4.(l+r.) = b 1 2 A 4 + r i b 3 4 B 4 38. If w^(0) i s determined f o r two values of r ^ , then the set of s i x equations represented by 36, 37 and 38, can be solved for b 1 2 , bg 4, A 2, A 4 , B 2 and B 4 . Correcting f o r the f i n i t e angular resolution of the detectors then leads to the yy d i r e c t i o n a l c o r r e l a t i o n functions for the (121 - 280) kev and (136 - 265) kev cascades. -129-v i z . W(©) B2 1 + — P 0(cos 0) + B 4 Q 4 P., (cos 0) 39. W(9) 1 + A 2 P 0(cos 0) + — P.(cos 0) 40. where and Q 4 are the attenuation c o e f f i c i e n t s determined i n the previous section. In p r i n c i p l e the gamma t r a n s i t i o n branching r a t i o s can also be determined from the values of b ^ and b^^, however, i n practice more accurate determinations are possible from the t r a n s i t i o n i n t e n s i t y measurements. 130-BIBLIOGRAPHY 1. E. Fermi. Z e i t s . f. Physik 88, 161 (1934). 2. C.L. Cowan, E. Reines, F.B. Harrison, H.W. Kruse, A.D. McGuire. Science, 124, 103 (1956). 3. Appendix II. "Beta and Gamma Ray Spectroscopy." Edited by K. Siegbahn. 4. E. Feenberg and G. Trigg. Rev. Mod. Phys. 22, 399 (1950), 5. S.A. Moszkowski. Phys. Rev. 82, 35 (1951). 6. S.A. Moszkowski. Chap. XIII. "Beta and Gamma Ray Spectroscopy". 7. M.E. Rose. "Internal Conversion C o e f f i c i e n t s " . North-Holland Publishing Co. 8. L.E. Biedenharn and M.E. Rose. Rev. Mod. Phys. 25, 746 (1953). ~ 9. P.R. B e l l . "Beta and Gamma Ray Spectroscopy", p. 161. 10. M. Deutsch, L.G. E l l i o t and R.D. Evans. Rev. S c i . Inst. 15, 178 (1944). 11. K.C. Mann and F.A. Payne. Rev. S c i . Inst. 30, 408 (1959). 12. R.E. B e l l , R.L. Graham and H.E. Petch. Can. J. Phys. 30, 35 (1952). 13. K. Kandiah. Proc. Inst. Elec. Eng. (London) II 101, 239 (1954). ~* 14. G. Lindstrom, K. Siegbahn and A.H. Wapstra. Proc. Phys. Soc. B 66, 54 (1953). 15. W.F. Edwards, C.J. Gallagher and J.W.M. DuMond. B u l l . Am. Phys. Soc. 4, 279 (1959). 16. H. Langevin-Joloit and M. Langevin. Jour, de Phys. et l a Rad. 19, 765 (1958). 17. H. H a l l . Rev. Mod. Phys. 8, 358 (1936). 18. O.R.N.L. Mathematics Panel. Handbuch der Physik Vol. XLV, p. 110. -131-19. P. Axel. Rev. S c i . Inst. 25, 391 (1954). 20. C.V. Kent, J . H . Cork and W.C Wadey\ Phys. Rev. 61, 389 (1942). 21. H.N. Friedlander, L. Seren and S.H. Turkel. Phys. Rev. 72, 23 (1947). 22. J.M. Cork, W.C. Rutlege, C.E. Branyan, A.E. Stoddard and J.M. LeBlanc. Phys. Rev. J79 , 889 (1950). 23. E.N. Jensen, L.J. L a s l e t t , D.S. Martin, F.S. Hughes and W.W. Pratt. Phys. Rev. 90, 557 (1950). 24. M. TerPogossian, J.E. Robinson and C S . Cook. Phys. Rev. 75, 995 (1949). 25. A. Schardt and J. Welker. Phys. Rev. 99, 810 (1955). 26. G.M. Temmer and N.P. Heydenburg. Phys. Rev. 104, 967 (1956). 27. D.C. Lu, W.H. K e l l y and M.L. Wiedenbeck. Phys. Rev. 97, 139 (1955). 28. A. Schardt. Phys. Rev. 108, 398 (1957). 29. S.H. Vegors and P. Axel. Phys. Rev. 101, 1067 (1956). 30. E.C. Campbell and P.H. Stetson. Nucl. S c i . Abstr. 10, N24B, 58 (1956). 31. H.J. Van den Bold, J. Van de Geijn and P.M. Endt. Physica 24, 23 (1958). 32. F.R. Metzger. Phys. Rev. 110, 123 (1958). 33. F.R. Metzger and W.B. Todd. Nuc.Phys. 10, 220 (1959). 34. E.P. Grigoriev and A.V. Zolotavin. Nuc. Phys. 14, 443 (1960). 35. M.F. Crawford and A.M. Crooker. Nature 131, 655 (1933). 36. P.F.A. Klinkenberg. Rev. Mod. Phys. 24, 63 (1952). 37. L.C. Aamodt and P.C. Fletcher. Phys. Rev. 98, 1224 (1955). 38. S.A. Moszkowski. "Beta and Gamma Ray Spectroscopy". Chapter XIII. -132-39. M. Goldhaber and A.W. Sunyar. "Beta and Gamma Ray Spectroscopy". Chapter XVI. 40. K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther. Rev. Mod. Phys. 28, 432 (1956). 41. S.A. Moszkowski. Phys. Rev. 82, 35 (1951). 42. C.C. T r a i l and CH. Johnson. Phys. Rev. 91, 474 (1953). 43. M. deCroes and G. Backstrom. Ark. f. Fys. 16, 567 (1960). 44. M.G. Mayer and J.H. Jensen. "Elementary Theory of Nuclear S h e l l Structure". 45. A. Arima and H. Horie. Prog. Theoret. Phys. 12, 623 (1954). 46. A. De Sh a l i t and M. Goldhaber. Phys. Rev. 92, 1211 (1953). 47. A. Bohr and B. MOttelson. "Beta and Gamma Ray Spectroscopy". p. 481. 48. S.B. Burson, Jordan and J.M. LeBlanc. Phys. Rev. 96, 1555 (1954). 49. S. Thulin. Ark. f. Fys. 9, 137 (1955). 50. N.H. Lazar, R.C. Davis and P.R. B e l l . Handbuch der Physik. Vol. XLV, p. 128. Nucleonics 14, No. 4, 52 (1956). 51. J.S. Lawson and H. Freunfelder. Phys. Rev. 91, 649 (1953). ~ 52. M.E. Rose. Phys. Rev. 91, 612 (1953). 53. S. Frankel. Phys. Rev. 83, 673 (1951). 54. E.L. Church and J.J. Kraushaar. Phys. Rev. 88, 419 (1952). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085881/manifest

Comment

Related Items