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UBC Theses and Dissertations

Re-investigation of the excited states of Gd 154 1967

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The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of LEUNG-KAI NG B.Sc ( S p e c i a l ) , U n i v e r s i t y of" Hong Kong, 1961 M.Sc, U n i v e r s i t y of Hong Kong, 1964 FRIDAY, SEPTEMBER 22, 1967 AT 3:30 IN ROOM 301, HENNINGS BUILDING COMMITTEE IN CHARGE Research Supervisor: K.C. Mann E x t e r n a l Examiner: G.T. Ewan Chalk River Nuclear L a b o r a t o r i e s Atomic Energy of Canada Ltd.. Chairman: B„ N. Moyls M.P. Beddoes G .Mo G r i f f i t h s K.C. Mann J.W. Bichard D.L. L i v e s e y B.L. White Chalk R i v e r , Ontario RE-INVESTIGATION OF THE EXCITED STATES OF Gd 154 ABSTRACT The e x c i t e d s t a t e s of Gd 154 obtained from the decay of Eu 154 have been investigated,, P r e c i s e measurements of the energies and i n t e n s i t i e s of the gamma t r a n s i t i o n s have been made, using L i t h i u m - d r i f t e d Ger- manium d e t e c t o r s , A r e v i s e d decay scheme i s presented i n which a l l the gamma t r a n s i t i o n a l energies agree w i t h the corresponding energy d i f f e r e n c e s between l e v e l s to w i t h i n 1 Kev. A 1263.3 Kev l e v e l i s e s t a b l i s h e d by the . presence of a gamma t r a n s i t i o n of 892,7 Kev, Two other gamma t r a n s i t i o n s of energ i e s , 903.6 Kev and 582.1 Kev from the n e g a t i v e - p a r i t y l e v e l s to the 2 +beta e x c i t e d l e v e l have a l s o been discovered. The proper l o c a t i o n s of the 995.9 Kev and 1004,5 Kev i n the decay scheme are confirmed by a gamma-gamma coincidence method using a Germanium detector and a Na l ( T l ) s c i n t i l l a t o r . The energies and i n t e n s i t i e s of the i n t e r n a l conversion e l e c t r o n s and the beta t r a n s i t i o n s have been measured by an intermediate image spectrometer. Their values are q u i t e - c o n s i s t e n t w i t h the e s t a b l i s h e d decay scheme. T h e o r e t i c a l values of the energy l e v e l s and the branching r a t i o s f o r gamma t r a n s i t i o n s have been c a l c u l a t e d , using the Asymmetric Rotator Model (J.P, ' Davidson's treatment). The ' s t i f f n e s s ' parameter of the nucleus )A. and i t s asymmetry parameter TT obtained are 0.402 and 11.52 degrees r e s p e c t i v e l y . Comparison of the experimental and t h e o r e t i c a l energies of seven p o s i t i v e - p a r i t y l e v e l s gives a root-mean-square devia- t i o n of 1.5 %. Three out of the four experimental branching r a t i o s are i n good agreement w i t h the theo- r e t i c a l v a l u e s . The monopole t r a n s i t i o n p r o b a b i l i t y f o r the t r a n s i t i o n from the 0 + beta e x c i t e d s t a t e to the 0 + ground st a t e measured a l s o agrees w i t h the present t h e o r e t i c a l c a l c u l a t i o n , GRADUATE STUDIES F i e l d of study: Nuclear spectroscopy Nuclear Physics T h e o r e t i c a l Nuclear Physics S p e c i a l R e l a t i v i t y Electromagnetic Theory Elementary Quantum Mechanics Advanced Quantum Mechanics E l e c t r o n i c Instrumentation J.B. Warren Mo McMillan H 0 Schmidt P. R a s t a l l G.M. V o l k o f f F.A. Kaempffer M.P. Beddoes AWARDS 1957-60 Hong Kong Government Sc h o l a r s h i p 1964-67 Canadian Government Sc h o l a r s h i p under the Canadian I n t e r n a t i o n a l Development As s i s t a n c e Programs, RE-INVESTIGATION OP THE EXCITED STATES OF Gd 154 . LEUNG-KAI NG • B.Sc. ( S p e c i a l ) The U n i v e r s i t y o f Hong Kong, 1 961 M.Sc. The U n i v e r s i t y o f Hong Kong, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e Department of PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY'OF BRITISH COLUMBIA August, 1 967 In 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 the r e q u i r e m e n t s f o r an advanced deg ree a t the 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 make 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 and S t udy . I f u r t h e r a g r ee 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 may be g r a n t e d by t he Head o f my Department o r by hils r e p r e s e n t a t i v e s . It 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 no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment The U n i v e r s i t y o f B r i t i s h Co l umb i a Vancouve r 8, Canada ABSTRACT The . e x c i t e d s t a t e s o f Gd 154 o b t a i n e d f r om the decay o f Eu 154 have been i n v e s t i g a t e d . P r e c i s e measurements o f the e n e r g i e s and i n t e n s i t i e s o f t h e gamma t r a n s i t i o n s have "been made, u s i n g L i t h i u m - d r i f t e d Germanium d e t e c t o r s . A r e v i s e d decay scheme i s p r e s e n t e d i n w h i c h a l l the gamma t r a n s i t i o n a l e n e r g i e s agree v/ith t he c o r r e s p o n d i n g energy d i f f e r e n c e s between l e v e l s t o w i t h i n 1 Kev. A 1263-3 Kev l e v e l i s e s t a b l i s h e d by the pr e s e n c e o f a gamma t r a n s i t i o n o f 892.7 Kev. Two o t h e r gamma t r a n s i t i o n s o f e n e r g i e s , 903-6 Kev and 582.1 Kev f r o m the n e g a t i v e - p a r i t y l e v e l s t o the 2 + b e t a e x c i t e d l e v e l have a l s o been d i s c o v e r e d . The p r o p e r l o c a t i o n s o f the 995-9 Kev and 1004-5 Kev i n the decay scheme are c o n f i r m e d by a gamma-gamma c o i n c i d e n c e method u s i n g a Germanium d e t e c t o r and a N a l ( T l ) s c i n t i l l a t o r . The e n e r g i e s and i n t e n s i t i e s o f the i n t e r n a l c o n v e r s i o n e l e c t r o n s and the b e t a t r a n s i t i o n s have been measured by an i n t e r m e d i a t e image s p e c t r o m e t e r . T h e i r v a l u e s a re q u i t e c o n s i s t e n t w i t h the e s t a b l i s h e d decay scheme. T h e o r e t i c a l v a l u e s o f the energy l e v e l s and the b r a n c h i n g r a t i o s f o r gamma t r a n s i t i o n s have been c a l c u l a t e d , u s i n g the Asymmetric R o t a t o r Model ( J . P . D a v i d s o n ' s t r e a t m e n t ) . The ' s t i f f n e s s ' p a r a m e t e r o f the n u c l e u s ii and i t - 1 1 1 - asymrnetry parameter y o b t a i n e d are 0.402 and 11.52 degrees r e s p e c t i v e l y . Comparison of the e x p e r i m e n t a l and t h e o r e t i c a l e n e r g i e s of seven p o s i t i v e - p a r i t y l e v e l s g i v e s a root-mean- square d e v i a t i o n of 1.5 i°• Three out of the f o u r e x p e r i m e n t a l b r a n c h i n g r a t i o s are i n good agreement with t h e . t h e o r e t i c a l v a l u e s . The monopole t r a n s i t i o n , p r o b a b i l i t y f o r the t r a n s i t - i o n from the 0 + b e t a e x c i t e d s t a t e to the 0 + ground s t a t e measured a l s o agrees with the p r e s e n t t h e o r e t i c a l c a l c u l a t i o n . - i v - TABLE OF CONTENTS Page CHAPTER I INTRODUCTION . .. 1 CHAPTER I I THEORY . . .. 6 1. The C o l l e c t i v e Models . 6 \ \ 2 . The Asymmetric R o t a t o r Model 11 3 . The O c t u p o l e Case i n t h e Asymmetric R o t a t o r Model 1 7 4 . C a l c u l a t i o n s o f Reduced E 2 . T r a n s i t i o n P r o b a b i l i t i e s . 19. 5 . Other Forms o f E l e c t r o m a g n e t i c T r a n s i t i o n s 23 CHAPTER I I I THE DESIGN OF EXPERIMENTS 26 CHAPTER IV THE GAMMA SPECTROSCOPY '.' 2 9 . 1 . G e n e r a l C o n s i d e r a t i o n s 29 2 . I n t e r a c t i o n between Gamma Rays and t h e th e D e t e c t o r s 32 3 . Gamma-ray D e t e c t i o n A s s e m b l i e s 34 4 . Source P r e p a r a t i o n and Mounting ....... 42 5 . E x p e r i m e n t a l P r o c e d u r e s " 45 6 . R e s u l t s and A n a l y s i s 50 CHAPTER V GAMMA-GAMMA COINCIDENCE SPECTROSCOPY 62 1. G e n e r a l C o n s i d e r a t i o n s '. 62 . Page 2 . The C o i n c i d e n c e System 64 3 . E x p e r i m e n t a l P r o c e d u r e s . . . 70 4 . R e s u l t s . .... 72 CHAPTER V I THE BETA SPECTROSCOPY 74 1 . G e n e r a l C o n s i d e r a t i o n s 74 2 . The I n t e r n a l C o n v e r s i o n and P a i r P r o d u c t i o n 77 • 3 . The Beta S p e c t r o m e t e r • ••• 82 4 . P r e p a r a t i o n o f Beta Sources 8 6 5 . E x p e r i m e n t a l P r o c e d u r e s 88 6. R e s u l t s and A n a l y s i s ................... 90 CHAPTER V I I THE DECAY SCHEME AND MODEL FITTING 103 1 . The Decay Scheme 103 2 . Model F i t t i n g . 108 CHAPTER V I I I CONCLUSIONS 114 REFERENCES . . . . 1 17 - v i - LIST OF FIGURES AND TABLES " Page CHAPTER IV Fi g u r e 1 . The gamma spectrometer 35 F i g u r e 2 . E l e c t r o n i c c i r c u i t f o r the gamma spectrometer 3 6 F i g u r e 3 . Cs 134 spectrum taken from the gamma- spectrometer assembly . . . . . . . . . . . 38 F i g u r e 4 . Germanium d e t e c t o r assembly . . . . . . . . 40 F i g u r e 5 . Input stage of the low-noise p r e a m p l i f i e r . 4 l F i g u r e 6 . Co 60 gamma spectrum from 1 . 5 c.c, Ge d e t e c t o r 43 F i g u r e 7 . Co 60 gamma spectrum from 5 c.c. Ge d e t e c t o r . . 44 F i g u r e 8. Eu 154 gamma spectrum 48 F i g u r e 9 . Low-energy gamma peaks of Eu 154 49 T a b l e I . Gamma peaks used f o r energy c a l i b r a t i o n . 52 F i g u r e 1 0 . Gamma energy c a l i b r a t i o n curve . 53 Table I I . Gamma peaks used f o r i n t e n s i t y c a l i b r a t i o n 56 F i g u r e 1 1 . Gamma i n t e n s i t y c a l i b r a t i o n curve. To f o l l o w 56 Table I I I . E n e r g i e s and I n t e n s i t i e s of Eu 154 spectrum (gamma ) . . . . . . 58 F i g u r e 1 2 . Weak gamma peaks i n the Eu 154 spectrum . 60 T a b l e IV. Gamma peaks b e l o n g i n g to Eu 152 i m p u r i t y . 61 CHAPTER V F i g u r e 1 3 - I l l u s t r a t i o n of gamma-gamma c o i n c i d e n c e . . 63 F i g u r e 14- The gamma-gamma c o i n c i d e n c e system . . . . 65 F i g u r e 15- P h o t o m u l t i p l i e r output stages 67 F i g u r e 16. The t u n n e l diode d i s c r i m i n a t o r . . . . . . 69 F i g u r e 17a,b,c,d. The gamma-gamma c o i n c i d e n c e s p e c t r a 73 CHAPTER.VI F i g u r e 18. Beta spectrometer assembly 83 F i g u r e 19- Magnet c u r r e n t c o n t r o l c i r c u i t 84 F i g u r e 20a. Beta spectrum of Eu 154, low-energy p a r t . 91 F i g u r e 20b. Beta spectrum of Eu 154, high-energy p a r t 92 F i g u r e 20c. Beta continuum of Eu 154 • • - - 93 Table V. ' Data of b e t a c o n v e r s i o n peaks . . . . . . 95 Fi g u r e 20d- Expanded p o r t i o n of Eu 154 bet a spectrum. 98 Table V I . Comparison of K - i n t e r n a l c o n v e r s i o n c o e f f i c i e n t s 100 Table V I I . E n e r g i e s and r e l a t i v e i n t e n s i t i e s of be t a t r a n s i t i o n s 10.1 F i g u r e 21. The K u r i e p l o t s .102 CHAPTER VII Fi g u r e 22. The e x c i t e d s t a t e s of Gd 154 from the decay of Eu 154 . .'104 Table V I I I . T r a n s i t i o n a l i n t e n s i t i e s f o r gammas, c o n v e r s i o n e l e c t r o n s and b e t a s . . ... . . 105 - v i i i - Page T a b l e I X . Comparison o f t h e e x p e r i m e n t a l and t h e o r e t i c a l e n e r g i e s i n t h e q u a d r u p o l e c a s e . 110 T a b l e X. The b r a n c h i n g r a t i o s o f gamma t r a n s i t i o n s between p o s i t i v e - p a r i t y l e v e l s I l l - i x - ACKNOWLEDGMENTS I w i s h t o e x p r e s s my g r a t i t u d e t o Dr. K.C. Mann f o r h i s g u i d a n c e , encouragement and h e l p t h r o u g h o u t t h e work. I am a l s o i n d e b t e d t o Dr. J.P. D a v i d s o n o f t h e P h y s i c e Department, Kansas U n i v e r s i t y , Dr. T. Katoh o f th e N u c l e a r E n g i n e e r i n g Department, Nagoya U n i v e r s i t y , and Dr. D. Ki a n g o f t h e P h y s i c s Department, D a l h o u s i e U n i v e r s i t y f o r v a l u a b l e i n f o r m a t i o n g i v e n t o me; t o t h e members o f t h e Van de G r a a f f Group, i n p a r t i c u l a r Dr. G. Jon e s , Dr. G.M. G r i f f i t h and Mr. D.A. D a l b y f o r a l l o w i n g me t h e use o f some of t h e i r equipment; and t o t h e Computing C e n t r e S t a f f f o r t h e i r h e l p i n data p r o c e s s i n g . T e c h n i c a l a s s i s t a n c e by Mr. T. W a l t o n , Mr. E. P r i c e , Mr. A. F r a s e r and Mr. J . Lees a r e h i g h l y a p p r e c i a t e d . The p r e s e n t p r o j e c t i s sup p o r t e d by t h e E x t e r n a l A i d O f f i c e , Government o f Canada t h r o u g h a s t u d e n t s c h o l a r s h i p and t h e N a t i o n a l R e s e a r c h C o u n c i l t h r o u g h G r a n t s - i n - A i d o f Res e a r c h t o Dr. K.C. Mann. -1- CHAPTER I INTRODUCTION The d e s c r i p t i o n o f a n u c l e u s . i s e s s e n t i a l l y a c o m p l i c a t e d many-body problem w h i c h has not reached any p r e c i s e s o l u t i o n . To s i m p l i f y t h i s problem., s e v e r a l phenomeno- l o g i c a l models have been p r o p o s e d . The commonly known one i s 1) th e ' s i n g l e - p a r t i c l e s h e l l model 1 , w h i c h views each n u c l e o n ( p r o t o n o r n e u t r o n ) i n a n u c l e u s t o be moving under t h e a c t i o n o f an average p o t e n t i a l c o n t r i b u t e d by t h e o t h e r n u c l e o n s . As a quantum-mechanical consequence, t h e n u c l e o n s s h o u l d be moving i n d e f i n i t e ' s h e l l s ' s i m i l a r t o t h e e l e c t r o n s i n an atom. The number of p r o t o n s Z or n e u t r o n s N w h i c h completes a g i v e n number o f s h e l l s i s c a l l e d a magic number. T h i s model p r e d i c t s s u c c e s s f u l l y t h e s p i n s and p a r i t i e s o f most n u c l e i at t h e ground s t a t e . F o r n u c l e i whose Z and N v a l u e s a r e c l o s e t o t h e magic numbers, good q u a n t i - t a t i v e agreement i n l o w - l y i n g energy l e v e l s w i t h e x p e r i m e n t s can be o b t a i n e d . However, t h i s agreement d e t e r i o r a t e s as Z or N runs away from t h e magic numbers. I t i s even worse when one c o n s i d e r s heavy even-even n u c l e i whose mass numbers A are w i t h i n t h e range 1 5 0 - 1 9 0 o r g r e a t e r t h a n 228..'.In t h i s -2 - c a s e , t h e i n d i v i d u a l n u c l e o n i c motion g i v e s way t o t h e more predominent motions of t h e n u c l e u s as a whole, i . e . t h e c o l l e c t i v e r o t a t i o n and v i b r a t i o n . A c o l l e c t i v e model based 2) on t h e • l i q u i d - d r o p model was proposed by Bohr . Thus t h e s u r f a c e o s c i l l a t i o n or v i b r a t i o n o f t h e n u c l e u s i s a c counted f o r by t h e hydrodynamic b e h a v i o u r of a l i q u i d d r o p . A l s o because o f t h e i n t e r a c t i o n o f s i n g l e p a r t i c l e and c l o s e d s h e l l s , d e f o r m a t i o n i n t h e e q u i l i b r i u m shape of t h e n u c l e u s from 3) s p h e r i c a l symmetry becomes p o s s i b l e . T h i s d e f o r m a t i o n g i v e s r i s e t o t h e c o l l e c t i v e r o t a t i o n o f t h e n u c l e u s . C o n s e q u e n t l y , t h e energy l e v e l scheme o f t h e n u c l e u s c o n s i s t s o f v i b r a t i o n a l l e v e l s w h i c h a r e f u r t h e r s p l i t i n t o r o t a t i o n a l bands. On t h e o t h e r hand, t h e n u c l e u s can be c o n s i d e r e d as a r i g i d r o t a t o r , w h i c h g i v e s r i s e t o pure r o t a t i o n a l l e v e l s . The r o t a t o r i s t h e n s o f t e n e d t o y i e l d s u r f a c e v i b r a t i o n s , and t h e r e f o r e , v i b r a t i o n a l l e v e l s . The shape o f t h e r i g i d r o t a t o r i s the e q u i l i b r i u m shape, t h a t I s t h e shape a t z e r o v i b r a t i o n . The c o l l e c t i v e model d e s c r i b e d above has been under g r e a t t h e o r e t i c a l development i n t h e p a s t few y e a r s , n o t a b l y ; by A. F a e s s l e r , W. G r e i n e r , R.K. S h e l i n e , A.S. Davydov and . 4)-16) J.P. D a v i d s o n . The c u r r e n t i n t e r e s t l i e s i n t h e d e t e r m i n a t i o n of the form and.magnitude o f t h e r o t a t i o n - v i b r a t i o n i n t e r a c t i o n w h i c h a c c o u n t s f o r t h e d i s c r e p a n c y '•between-energy l e v e l c a l c u l a t i o n s , and e x p e r i m e n t a l measure- - -3- ments. T h i s d i s c r e p a n c y i s expected to be more pronounced f o r n u c l e i h a v i n g n u c l e a r masses l y i n g near the ends of the A ranges mentioned above, and Gadolinium 154 i s one of the t y p i c a l examples. The e x c i t e d s t a t e s of Gd 154 are o f t e n o b t a i n e d from the b e t a decay of'Europium 1 5 4 , the l a t t e r i s o t o p e b e i n g f i r s t produced by Sc h e i c h e n b e r g e r u s i n g n e u t r o n - c a p t u r e p r o c e s s . Intense i n v e s t i g a t i o n on the decay scheme was s t a r t e d i n 1 9 5 7 - The f i r s t d e t a i l e d decay scheme was e s t a b l i s h e d i n d e p e n d e n t l y by J.M. Cork et a l " * " ^ and F.S- Stephens et a l " ^ , u s i n g b e t a s p e c t r a l a n a l y s i s and gamma-gamma c o i n c i d e n c e work. S i m i l a r i n v e s t i g a t i o n s have been done by B.S. Dzelepov^"^ , B.V. B o b i l i n 2 0 ) and 0. Nathan et a l 2 1 ^ . The t r a n s i t i o n a l e n e r g i e s determined by the above a u t h o r s vary a p p r e c i a b l y , and t h e i r i n t e n s i t i e s have wide ranges of u n c e r t a i n t y . The reason f o r these can be e a s i l y a p p r e c i a t e d when c o n s i d e r i n g the complexity of the decay scheme, and the presence of Eu 152' im p u r i t y which has a decay scheme not l e s s c o m p l i c a t e d than t h a t of Eu 1 5 4 - I t sh o u l d a l s o be noted t h a t the e l e c t r o n c o n v e r s i o n peaks of Eu 152 are s i m i l a r i n energy and i n t e n s i t y to those of Eu 1 5 4 , and t h a t the ne u t r o n - c a p t u r e process f a v o u r s the p r o d u c t i o n of Eu 152 over Eu 1 5 4 - Other methods of source p r o d u c t i o n have so f a r been unable to e l i m i n a t e a l l i m p u r i t i e s . Beta-gamma and gamma-gamma c o r r e l a t i o n methods have s i n c e t h e n been employed i n t h e i n v e s t i g a t i o n by s e v e r a l 2 2 ) - 3 0 ) a u t h o r s , a i m i n g at l ) t o c o n f i r m o r improve t h e e s t a b l i s h e d decay scheme, 2 ) t o determine more p r e c i s e l y t h e reduced gamma t r a n s i t i o n p r o b a b i l i t i e s , and 3 ) t o f i n d t h e f o r b i d d e n n e s s o f each b e t a t r a n s i t i o n i n t h e decay energy continuum. These are e s s e n t i a l f o r v e r i f y i n g any proposed n u c l e a r model and f o r f i n d i n g t h e m a t r i x elements o f t h e be t a t r a n s i t i o n s . Other methods such as l i f e - t i m e measurements 3D f o r s p e c i f i c gamma t r a n s i t i o n s , 4 / |-counting f o r K- Y 32 ) c o i n c i d e n c e work , i n v e s t i g a t i o n o f t h e decay o f s h o r t - 33 ) l i v e d Tb 154 t o Gd 154 , and Coulomb e x c i t a t i o n f o r p r o d u c i n g 3 4 ) , 3 5 ) h i g h e r e x c i t e d l e v e l s o f Gd 154 have been e x p l o i t e d . However, a l l e x p e r i m e n t s performed t o date s u f f e r from poor r e s o l u t i o n o f t h e gamma d e t e c t o r s ( N a l s c i n t i l l a t o r s ) , w h i c h s e v e r e l y h i n d e r s t h e a n a l y s i s o f a c o m p l i c a t e d gamma spectrum. A l t h o u g h t h e use o f c o i n c i d e n c e methods may h e l p i n such an a n a l y s i s , i t i s o n l y p r a c t i c a b l e when d e a l i n g w i t h r e l a t i v e l y 36 ) s t r o n g gamma peaks. F i n a l l y , e x t e r n a l b e t a c o n v e r s i o n method (the p h o t o e l e c t r o n p r o c e s s ) has been used. I t improves the r e s o l u t i o n , but a g a i n s u f f e r s from l a c k of i n t e n s i t y . . . . - W i t h t h e newly d e v e l o p e d L i t h i u m - d r i f t e d Germanium d e t e c t o r s i n the l a b o r a t o r y o f the P h y s i c s Department ,U..B .C ., a . r e - i n v e s t i g a t i o n o f t h e decay of Eu 154 becomes more p r o m i s i n g , s i n c e t h e r e s o l u t i o n o f t h e s e d e t e c t o r s i s t e n t i m e s b e t t e r t h a n t h a t o f t h e u s u a l N a l s c i n t i l l a t o r s . I n the p r e s e n t work, t h e a u t h o r a p p l i e d t h i s new t o o l t o g e t h e r w i t h an i n t e r m e d i a t e - i m a g e b e t a s p e c t r o m e t e r t o o b t a i n more a c c u r a t e energy and i n t e n s i t y d a t a f o r t h e gamma t r a n s i t i o n s i n t h e decay o f Eu 1 5 4 . These d a t a were t h e n used t o check t h e v a l i d i t y o f t h e c o l l e c t i v e model proposed and developed 1 0 ) - 1 6 ) by Davydov, F i l i p p o v , and D a v i d s o n . The r e s u l t s , as w i l l be shown l a t e r , proved f r u i t f u l . CHAPTER I I THEORY §1. The C o l l e c t i v e Models. 2 ) Bohr's hydrodynamical model , which borrowed i t s concept from the l i q u i d - d r o p model, forms the b a s i s of the present t h e o r y . By c o n s i d e r i n g a nucleus t o be a drop of charged l i q u i d , the f o l l o w i n g assumptions immediately apply: 1 ) the n u c l e a r f l u i d i s i n c o m p r e s s i b l e and has constant mass d e n s i t y . Consequently, the n u c l e a r volume i s an i n v a r i a n t ; 2 ) the nucleus i s capable of s u r f a c e o s c i l l a t i o n s which can be d e s c r i b e d as s m a l l simple harmonic motions; and 3) the r e s t o r i n g f o r c e s c o n t r i b u t i n g to the o s c i l l a t i o n are the s u r f a c e t e n s i o n and the Coulomb r e p u l s i o n . The surface, of the nucleus can be w r i t t e n as an expansion i n s p h e r i c a l harmonics as shown, R(8,^,t) = R (1 +5, Q ( t ) A Y A (8,$) (1) where R Q i s the n u c l e a r r a d i u s when i n . s p h e r i c a l c o n f i g u r a t i o n and a{t)\^l are the d i s t o r t i o n s from s p h e r i c a l symmetry. It can be e a s i l y seen that a ( t ) ^ ^ r e p r e s e n t the dimension- l e s s d i s t a n c e v a r i a b l e s ; and from e x p r e s s i o n s of simple harmonic motion, the p o t e n t i a l and k i n e t i c e n e r g i e s become, (2a) V = ±2 C- — 2 •>ti T = B. A K A ( 2 b ) r e s p e c t i v e l y , where Bx Is the mass c o e f f i c i e n t and C\ , the constant f o r r e s t o r i n g f o r c e s . 3) I t was shown by Rainwater that a s i n g l e p a r t i c l e moving i n a p o t e n t i a l w e l l had a lower energy i f the w e l l was deformed than i f i t was s p h e r i c a l . T h i s ( ' s i n g l e - p a r t i c l e - 11 s h e l l e f f e c t makes i t p o s s i b l e f o r the ' l i q u i d drop' t o be n o n - s p h e r i c a l at e q u i l i b r i u m . Hence we can assume t h a t a permanently deformed ( e l l i p s o i d a l ) shape e x i s t s i n the n u c l e u s . Subsequently, we can a t t a c h . a new set of c o o r d i n a t e axes along the t h r e e p r i n c i p l e axes of the deformed body. T h i s new co o r d i n a t e system S' can be r e l a t e d t o the l a b o r a t o r y c o o r d i n a t e system S by E u l e r i a n angles, 6^,9 2,83, such that z ' - a x i s i n S 1 = z 1 (9 n ,9 2 ) i n "S and z - a x i s i n S = z (0 , v-6 ) i n S' . The v a r i a b l e s i n system S' can then be r e l a t e d t o the corresponding 37), v a r i a b l e s i n system S by a u n i t a r y r o t a t i o n matrix as shown 38) V = I 1 ^ ' ( 8 i } = ( e i ' 8 2 ' e 3 ) ( 3 ) I t should be noted t h a t the assignment of system S 1 i s not unique. R e s t r i c t i n g t o right-handed systems, t h e r e are 24 ways of choosing system S ! w i t h i t s axes along the p r i n c i p l e axes, of the n u c l e u s . T h i s w i l l be d i s c u s s e d l a t e r (§2). C o n s i d e r i n g only the quadrupole case ( i . e . X = 2 ) , f o r the time being, and dropping the s u b s c r i p t A., e q u a t i o n ( l ) becomes, Z •. - R - R o ( l . V (Ma) o r i n C a r t e s i a n c o o r d i n a t e s , R •= R (1+o-xx ,^+ ayy 4 + Q z z ± f c +2a Xy ^+2°-yz ^ t + 2 a z x =-^i) w i t h t h e r e l a t i o n s , O-yy + O-zz = 0 2]I ( axx - 15 ayy + 2ia-xy) 8 T r fa-zx + 15 ia-yz) a = ° K C2 azz - 45 a-xx - a y y) F o r t h e system t t t a y z = a z x = 0 T h e r e f o r e , we can w r i t e t T a = a = 2 -2 P sinT Q» _ Q' z/2 ' 1 1 = °' T I o (6) whereP ,y a r e newly d e f i n e d v a r i a b l e s i n d i c a t i n g t he t o t a l d e f o r m a t i o n o f t h e n u c l e u s and t h e d e v i a t i o n from a x i a l symmetry r e s p e c t i v e l y . From t h e e q u a t i o n s (2a),(2b) and (3 ) / and making use the o r t h o n o r m a l and ti m e d e r i v a t i v e p r o p e r t i e s o f D^v>(0_.) •.( see r e f . 37JP73) t h e p o t e n t i a l and k i n e t i c e n e r g i e s become:. A . (7) T = l B 2 ^ _ | ^ | 2 = | B 2 Z ||,- (^D*„(8.) + ^b*„ (9,)) 2 IB '(P2+ P 2 y 2 ) + ± B „ L 4 P 2 s i n 2 ( y - k 2 g 2 . 8 2 v i b r o t (8). -9- where j , k = 1,2,3 are t h e s u b s c r i p t s f o r c o o r d i n a t e a x e s , and Q k =2.̂  6j i s t h e a n g u l a r v e l o c i t y component a l o n g t h e p r i n c i p l e a x i s k ( s e e ' r e f . 2,p.12). A l s o note t h a t t h e f i r s t t e r m o f T i s t h e v i b r a t i o n a l p a r t and t h e second t e r m , t h e r o t a t i o n a l p a r t . The n e x t s t e p i s t o f i n d t h e H a m i l t o n i a n o p e r a t o r , f o r 39) w h i c h P a u l i ' s method i s used as f o l l o w s : L e t ( i ^ p = (P,y ,6^ ,0 2 , 0 3 ) be t h e 5 - d i m e n s i o n a l c u r v i l i n e a r space; and I R = L r B 2 P 2 s i n 2 ( y - 2 T r k / 3 ) , (9). w h i c h from (8) I s j u s t t h e k-component o f moment o f i n e r t i a Then t h e square of t h e d i f f e r e n t i a l i n t e r v a l o f a c t i o n i s d s 2 =2. G..„ dl i„dfl u = 2Tdt' and from (8) = B 2 d P 2 + B 2 P 2 d Y 2 + 2 I k ^ q g i d B 2 k 7 J J T h e r e f o r e , G = B 2 B 2 P ' , , 2 0 o ? The d e t e r m i n a n t , V 3 ^ 3 j | G | = 4 3 B 2 P 8 s i n 2 ( y - 2 T r / 3 ) s i n 2 ( T - 4 T T / 3 ) . s i n 2 ( 7 - 2 7 7 ) 0 ( 8 ^ = 4 B ^ 8 s i n 2 3 Y Q ( B ± ) (10) (11) (12) where Q(0i) -10- The H a m i l t o n i a n can t h e n be f o u n d . n = . + V = - | H > _ M L ^ + y ( 1 3) The p o t e n t i a l energy o p e r a t o r , V - l C 2 P 2 (14) The v i b r a t i o n a l energy o p e r a t o r , 2 * 2B (P*3f3 ^p p l S i n 3 y 37 *y ) J 2 The r o t a t i o n a l energy o p e r a t o r can be s i m p l y e x p r e s s e d as f o l l o w s w i t h o u t u s i n g e q u a t i o n ( 1 3 ) , T = £ _ J = + - ^ ^ . _ 2 = 7 JS (16) r 0 t U l x 2 I 3 1 8B 2P 2 £ J sin 2-(Y-2irk/3) where t h e component a n g u l a r momentum o p e r a t o r , i . e . moment o f i n e r t i a X a n g u l a r v e l o c i t y , c . f . (8) and (9)• Hence t h e S c h r o d i n g e r e q u a t i o n becomes, ( T v. b + T r o t + v )^(P,y,e i) = EcJr(P,y,e.) (is) I t s s o l u t i o n i s d e f e r r e d t o § 2 . So f a r , we have o n l y c o n s i d e r e d A = 2 c a s e . A = 1 g i v e s no 14). c o n t r i b u t i o n , w h i l e A= 3 has been, t r e a t e d by D a v i d s o n , wh i c h w i l l be o u t l i n e d i n |3- No e v i d e n c e e x i s t s f o r any l e v e l c o r r e s p o n d i n g t o A ? 3 . F u r t h e r development i n t h e c o l l e c t i v e model can be 4)-9). s e p a r a t e d i n t o two b r a n c h e s . F a e s s l e r and coworkers c o n s i d e r - ed t h e deformed n u c l e u s t o be an. a x i a l l y symmetric e l l i p s o i d , . -11- • : i o ) - i 6 ) w h i l e Davydov and coworkers t r e a t e d i t as a x i a l l y a s y m m e t r i c . Only t h e l a t t e r w i l l be d i s c u s s e d , as i t i s a g e n e r a l case and r e p r e s e n t s t h e l a t e s t development. §2. The Asymmetric R o t a t o r Model.. The asymmetric r o t a t o r model was proposed by Davydov 10) and F i l i p p o v , and developed by Davydov, D a v i d s o n and many 11)-16) o t h e r s . I t i s a c o n t i n u a t i o n of Bohr's model. The d i f f e r e n c e i n concept l i e s on t h e r e c o g n i t i o n o f a f i x e d a x i a l l y asymmetric n u c l e a r shape. T h i s i m p l i e s t h a t t h e shape parameter V i s no l o n g e r a v a r i a b l e . Hence, i n f i n d i n g t h e H a m i l t o n i a n o p e r a t o r as shown p r e v i o u s l y ( f o r A= 2 ) , we need o n l y a 4 - d i m e n s i o n a l c u r v i l i n e a r space, i . e . (fl) r: (p,8 ,0 ,0 ) . From i L e i e q u a t i o n (13), i t f o l l o w s t h a t t h e v i b r a t i o n a l energy o p e r a t o r i s s i m p l y , V I B 2 B 2 P 2(3 r P(3 (19) Note t h a t G = B 2 T *5 2 h f q i j O O i 2 2 q 2 j ? I 3 Z q 3 j ( 2 0 ) The r o t a t i o n a l energy o p e r a t o r i s s t i l l t he same as i n e q u a t i o n ( l 6 ) ; but t h e p o t e n t i a l energy o p e r a t o r i s s l i g h t l y a l t e r e d t o t a k e i n t o account o f t h e d e f o r m a t i o n from s p h e r i c a l e q u i l i b r i u m shape, i . e . V = 1 C 2 (P - P Q ) 2 ' ,• (21) where t h e c o n s t a n t P Q i s t h e t o t a l d e f o r m a t i o n parameter when th e n u c l e u s i s not v i b r a t i n g ( i . e . i n pure r o t a t i o n a l s t a t e s ) . C o n s e q u e n t l y , t h e S c h r o d i n g e r e q u a t i o n becomes ( 2 f l 3 / J \ ^ L £ ^ ^ 2B = E Tj"(P,8.) (22) S i n c e o n l y t h e o p e r a t o r s L k are f u n c t i o n s o f t h e E u l e r i a n a n g l e s 9 i , i = 1 , 2 , 3 , t h e above e q u a t i o n i s s e p a r a b l e . L e t - f L ( P , 8 i ) = $ u ( 8 ± ) eP u(P) (23) t h e n , i 2 , ? L k . - £(L)1 -4(9.) = 0 (24) fcSin2(y-2Trk/3) J I and r 2 <2 L M_ I f -fp 3 -^-) + |C„(P-P ) 2 + X £( L) - E r 1 c^(P) = 0 L 2B 2 P 3 ^PV J&J 2 ' o ; t+B 2P 2 L j ^ (25) where £(L) g i v e s r o t a t i o n a l e n e r g i e s o f t h e asymmetric r o t a t o r i n u n i t s o f K 2/(4B 2 p 2 ) . To s o l v e e q u a t i o n ( 2 4 ) , one needs t o choose a s e t o f b a s i s v e c t o r s , t h e s i m p l e s t of w h i c h i s t h a t o f n L (8 } , t h e MK i r o t a t i o n m a t r i c e s , because ;:::-v.- l ? DMK^i.5 = L ^ L + L ) D S K C 8 ± ) (26a) K D M K ^ = M D M K ^ ; (26b) t3 0 ^ ( 8 . ) • K i r ^ C H . ) (26c) ,where the s u b s c r i p t z r e f e r s t o S system and 3 - z' r e f e r s t o S.' system (see r e f . 33 p.64). -13- S i n c e t h e b a s i s vectors|LMK> = D J ^ C ^ ) . a r e e x p l i c i t l y known and so a r e t h e o p e r a t o r s L f j , t h e m a t r i x e l e m e n t s , • <XMK I L?|LMK')> , f o r a g i v e n v a l u e o f L and o f M can be c a l c u l a t e d . C o n s e q u e n t l y , f o r a g i v e n v a l u e o f t h e shape parameter y , A A < L M K I L? 1LMK' > <LMK |H r o t|LMK'> = !£, . 2 . . ^ can be c a l c u l a t e d . However, s i n c e t h e n u c l e u s i s not a x i a l l y symmetric, K I s not a good quantum number. Hence, t h e s t a t e v e c t o r s o f t h e n u c l e u s have t o be m i x t u r e s o f t h e b a s i s v e c t o r s , i . e . L |LM > = 2 i A j L M K > (28) What i s now l e f t i s t o det e r m i n e t h e c o e f f i c i e n t s A^ and t h e e i g e n v a l u e s i^(J-d i n (24). The e i g e n v a l u e s can be found A by d i a g o n a l i z i n g t h e m a t r i x ^ r o t • But b e f o r e d o i n g t h a t , t h e m a t r i x d i m e n s i o n can be reduced a p p r e c i a b l y by c o n s i d e r i n g the symmetry p r o p e r t y o f t h e c o e f f i c i e n t s A R . As was p o i n t e d out i n | l t h a t t h e r e a r e 24 ways o f a s s i g n i n g t h e system S' t o t h e n u c l e u s so t h a t t h e c o o r d i n a t e axes, o f S' c o i n c i d e w i t h t h e p r i n c i p l e axes o f t h e n u c l e u s . The wave f u n c t i o n o f t h e n u c l e u s s h o u l d be independent o f t h e as s i g n m e n t . T h e r e f o r e , we expect some symmetry r e l a t i o n s among t h e A 1 s , whi c h can be found K as f o l l o w s : The 24 ways o f a s s i g n i n g S' can be i n t e r r e l a t e d by t h r e e r o t a t i o n o p e r a t o r s , P L , P 2 , P 3 , such t h a t produces a r o t a t i o n of-rr about y ' - a x i s ; P , a - r o t a t i o n , o f it/2 about z 1 - a x i s ; . and P 3 , a r o t a t i o n o f 2TT/3 about t h e a x i s e q u i d i s t a n t a n g u l a r l y from t h e t h r e e axes ( r e f . 40; ,. p.110). A p p l y P^,P 2 on DMK ( (V = 1 LMK-> 1 > w e h a v e P1|LMK> = exp i-rr(L+K) | LM-K> (29a) P 2JLMK> = exp(iTrK) | LMK> (29b) As L and K a r e i n t e g e r s , a p p l y i n g on|LM> g i v e s r i s e t o f o u r c a s e s : 1) P 1|LM> = +|LM> , Pg\LM> = +|LM> 2) P1|LM> =-lLM> , P2|LM> = + |LM > 3) P 1ILM> = +|LM> , P 2|LM> =-lLM> 4) P 1)LM> = -]LM> , P?|LM> = -|LM> These f o u r c ases b e l o n g t o t h e T o u r i r r e d u c i b l e r e p r e s e n t a t i o n s o f a D 2 group, each t o each, and t h e r e f o r e cannot be mixed t o g e t h e r . F o r case l ) , f r o m (29b), K must.be even and from (28), (29a), A K - (-1) L A_ K - C K (31) I t f o l l o w s , f o r L=0: K=0, A Q= +AQ=C0 ,. dimension of H r b t ,N=1, | LM > = CCJLM0> f o r L=1: K=0, A Q= -AQ=0, N=0, 1LM>=0 f o r L=2: K=0,2, A Q= +A 0=C Q j A 2= +A2=C2,.'N=2', . \LM> = Co|LM0> + C 2(|LM2> + I LM-2 > ) /J2 e t c . (31a) -15- . S i m i l a r l y , i t f o l l o w s f o r cases 2 ) , 3 ) and 4 ) . However, from t h e l e v e l s t r u c t u r e o f even-even n u c l e i , o n l y cases l ) and 2) a p p l y , i . e . l ) f o r t h e quadrupole case '( A = 2 ), and 2 ) f o r t h e o c t u p o l e case ( \ = 3 ). Now t h e e i g e n v a l u e s f N ( L ) can be c a l c u l a t e d . Then by s u b s t i t u t i n g £ m back i n t o t h e m a t r i x e q u a t i o n , t h e N c o e f f i c i e n t s C„ can be d e t e r m i n e d . The s o l u t i o n o f e q u a t i o n ( 24 ) I s t h u s c o m p l e t e d . (The c o m p u t a t i o n s above and what f o l l o w s were done by . t h e IBM 7040 computer.) To s o l v e e q u a t i o n ( 2 5 ) f o r t h e v i b r a t i o n energy l e v e l s , t h e s o l e t e c h n i q u e i s t o t r a n s f o r m t h e e q u a t i o n t o a s i m p l e r s t a n d a r d d i f f e r e n t i a l e q u a t i o n by changing t h e d i f f e r e n t v a r i a b l e s and c o n s t a n t s i n t h e e q u a t i o n . T h i s was done i n r e f . 12 and 1 5 . I t proceeds as f o l l o w s : Then ( 2 5 ) i s reduced t o T~o + W r M C P ) - E r u l U r ^ 1 3 ) = 0 (33) 2B ^ P 2 L N LN J LN • w i t h boundary c o n d i t i o n U (0) = 0 , and t h e p o t e n t i a l energy 1_/N o p e r a t o r , W (P) = | C (P-P ) 2 + J l L i (L) + - 3 ^ L (34) LN 2 o 4B 2 P^ N ; 8B 2 P 2 L e t PQ be t h e v a l u e o f P when W L N ( P ) i s a minimum, i . e . ->w ( P ) o r ' 'o = C 2 ( P ; - P O ) - (f N(L) + 3 / 2 ) = 0 P = P : 2 B 2 P O 2 P o = P o + L ( f M ( L ) + V 2 ) (35) 2 B 2 C 2 P J 3 Then P Q i s a new t o t a l d e f o r m a t i o n parameter at e q u i l i b r i u m . I t d i f f e r s from P Q by ^2(£N(L) + 3 / 2 ) / ( 2 B 2 C 2 P Q 3 ) which i s o b v i o u s l y due t o t h e r o t a t i o n - v i b r a t i o n i n t e r a c t i o n . F u r t h e r , d e f i n e . ^ = t2 / ( B 2 C 2 P J ) (36) and z = P; /(P Q f O ( 3 7 ) (35). becomes - I Z 3 _ (£ ( L ) + 3 / 2 ) / 2 =0 ( 3 8 ) The p a r a m e t e r ^ measures t h e s t i f f n e s s o f t h e n u c l e u s a g a i n s t v i b r a t i o n , and i s c h a r a c t e r i s t i c o f a n u c l e u s . A f t e r c h o o s i n g a s u i t a b l e v a l u e f o r ̂  , ( 3 8 ) can be s o l v e d n u m e r i c a l l y f o r Z. A l s o , i n t r o d u c i n g z l = ̂  + | + 3 / 2 ) • C 3 9) y = z L ( P - P ^ ) / P i -,(i«o (4~2 y) = u L N ( P ) ( 4 1 ) t h e e q u a t i o n ( 33 ) i s reduced t o a s t a n d a r d form, d2Du (J2 y) , . \ V V  2 + (2V> + 1 _ . Y 2 ) D J > (|2 y) = 0 ( 4 2 ) dy where v> =v> (Z,) i s a quantum number determined by the. n nK I' boundary c o n d i t i o n U L N ( 0 ) = 0 or. (-\2 Zj-) .= 0 . . . ( 4 3 ) ' - 1 7 - Th e e i g e n v a l u e s f o r (42) are , (10+3/2 E L N n = J L 0 { ( P n + 1) ( Z l/Z) 2 + f N - ( L ) + 3 / 2 ' [ l + £N MZ 2 ^ 2 Z 2 (MM) where w 0 = J C 2 / B 2 The v a l u e s \) f o r n = 1 and f o r n = 2 were computed and n t a b u l a t e d as f u n c t i o n s o f Z^ I n r e f s . 14 and 4 l . Here n = 1 r e f e r s t o _ a l l t h e l e v e l s b e l o n g i n g t o t h e ground s t a t e b e t a band, and n = 2, t o .'the l e v e l s i n t h e f i r s t e x c i t e d b eta band. I t i s a l s o , c l e a r t h a t N i s t h e l e v e l o r d e r f o r a g i v e n L. The l e v e l s c o r r e s p o n d i n g t o N ? 2 and n = 1 are o f t e n c a l l e d 9 ) t h e gamma v i b r a t i o n a l l e v e l s i n another, model . The e i g e n v a l u e s ELNn c a l c u l a t e d a r e i n a r b i t r a r y energy s c a l e . T h e r e f o r e , i n th e p r e s e n t c a l c u l a t i o n , t h e f o l l o w i n g r a t i o was chosen f o r each l e v e l LNn } E - E LNn O i l E 2 1 1 " E 0 1 1 |3 • The O c t u p o l e Case i n t h e Asymmetric R o t a t o r Model. The t r e a t m e n t o f t h e o c t u p o l e case ( \ = 3 ) i n t h e asymmetric r o t a t o r model i s c o m p l e t e l y i n p a r a l l e l w i t h t h e quadrupole case ( \ = 2 ) . There are o n l y two p o i n t s w h i c h g i v e r i s e t o d i f f e r e n t m a t h e m a t i c a l e x p r e s s i o n s : a) I n s t e a d of t h e e x p r e s s i o n s f o r =-2,-1,0,1,2) g i v e n i n e q u a t i o n ( 6 ) o f ̂ 1 , we have a ± 1 = Q ± 3 = 0, a Q = P cosY a ± 2 = ( p y J 2 . ] s i . r i Y . (MB) T h e r e f o r e , t h e t h r e e moments of i n e r t i a become ti Tt O 2 " J l S TT TT O p 11 11 = 4 B 3 (' S i n 7 ~~2 5 3 1 1 1 7 C O s Y + i C O S 7 ̂ TT TT p p TT fl C Tt TT ^ p TT 1 2 = MB 3P ( s i n 7 - i | s in7 cos7 + |cos 7 ) (46) ti TTO TT 1 3 = 4B 3 P sln7 and t h e r o t a t i o n a l energy o p e r a t o r , • b) As mentioned i n § 2 , t h e symmetry c o n d i t i o n o f t h e c o e f f i c i e n t s A 1 s i n o c t u p o l e case i s d e r i v e d from t h e case K 2) o f e q u a t i o n (30). Hence, from e q u a t i o n s (28), (29a), (29b) a g a i n , K must be even and A-K = (-VL+1 A K ™ The forms o f t h e p o t e n t i a l and v i b r a t i o n a l energy o p e r a t o r s ar e t h e same as i n e q u a t i o n s (19) and ( 2 l ) , i . e . ^ , t? „ " p V = \ C 3 ( P - P Q ) ^ (49) \ i b 2B 3 p"3 ^ 1 P ( S 0 ) The methods o f c a l c u l a t i o n f o l l o w i n g t h i s a r e e x a c t l y t h e same as i n §2 . F i n a l l y , i t s h o u l d be noted t h a t t h e shape parameter 7 " and the s t i f f n e s s parameter y." = ^ T ^ P ^ B ^ Q ^ J -1 are. i n g e n e r a l d i f f e r e n t i n v a l u e s from 7 and .in t h e quad r u p o l e .case, as t h e s e two'cases a re q u i t e u n r e l a t e d . A l s o t h e p a r i t i e s o f t h e q u a d r u p o l e and o c t u p o l e cases a re n e c e s s a r i l y p o s i t i v e and n e g a t i v e r e s p e c t i v e l y . £ 4 . C a l c u l a t i o n s of Reduced E 2 T r a n s i t i o n P r o b a b i l i t i e s . S i n c e we are c o n s i d e r i n g deformed even-even n u c l e i , l a r g e q u a d r u p o l e moments are t o be e x p e c t e d . T h i s s h o u l d l e a d t o v e r y f a v o u r a b l e e l e c t r i c q u adrupole ( E 2 ) t r a n s i t i o n s between t h e v a r i o u s energy l e v e l s . The r e s u l t s o f t h e s e ' c a l c u l a t i o n s when compared w i t h e x p e r i m e n t a l d a t a s h o u l d p r o v i d e a s e n s i t i v e t e s t o f t h e v a l i d i t y o f t h i s model. The g e n e r a l e x p r e s s i o n f o r t h e gamma t r a n s i t i o n p r o b a b i l i t y p e r u n i t - t i m e i s 2J+1 T U ) = SvU+l) . /«\ BC f f L . - * L J - (51) i - i f iJ{{2i+Y))\]H l c / where t h e e m i t t e d photon has energy and a n g u l a r momentum X j t h e a n g u l a r momentum o f t h e i n i t i a l and f i n a l l e v e l s are g i v e n by L.. and L f r e s p e c t i v e l y ; and B(j ,1, ->> L f ) w h i c h I s energy independent ".Is c a l l e d t h e reduced t r a n s i t i o n p r o b a b i l i t y F o r E 2 t r a n s i t i o n s due t o t h e quad r u p o l e moment Q 2 ^ from a s t a t e |LMNn> t o a s t a t e jL'M'N'n 1> , B(E2;L,MNn-> L TM TN'n') ' = |^L tM fN ,n ,'| Q 2^jLMNn> | 2 Summing ov e r a l l f i n a l s t a t e s w i t h r e s p e c t t o M' and a v e r a g i n g t h e i n i t i a l s t a t e s w i t h r e s p e c t t o M, i n o r d e r t o omit p o l a r i s a t i o n , B(E2;LNn —> L'N'n') = __L^> j/LTM'N <n.' | Q 2 | LMNn> | 2 (52) L + J » , A 1 / - 2 0 - The e l e c t r i c quadrupole moment Q 2 [ 7 s h o u l d be i n the l a b o r a t o r y system ( S - s y s t e m ) , but i t t a k e s a s i m p l e r form i n the body- f i x e d system ( S ' - s y s t e m ) , the t r a n s f o r m a t i o n from S 1 to S b e i n g as u s u a l •Q 2 p= D * , (a) (53) (c.f» e q u a t i o n ( 3 ) ) « Nov/ assuming t h a t the n u c l e a r charge d e n s i t y i s a c o n s t a n t i n the n u c l e u s , i . e . ^ = ze/(L\rcR^)/')), then the quadrupole moment i n the S'-system i s j u s t = c o n s t a n t J 5 ^ 1 YZy,(Q • , 0 •) s i n 0 ' d9' d#' where R ' ( 9',^',t) = R 0[_l+ ^ a ^ ( t ) Y 2 V ( 6 ' , 0 » ) ( 5 ^ ) ( c . f . e q u a t i o n ( l ) ) . T h e r e f o r e , n e g l e c t i n g h i g h e r o r d e r terms o f a£y(t) than the f i r s t , v/e o b t a i n and from ( 6 ) _3_ cos r To 0 . f o r i > = 1 ±1 ( 5 5 ) sin ^ 2 j ±2 Prom ( 5 3 ) t h e r e f o r e , ^ = R o ? [ ^ o c o s V + + D * _ 2 ) . s i n X/z] S u b t i t u t i n g i n t o ( 5 2 ) , v/e have B(E2: LNn —> L ' N 1 n ) ,2.2 mt^L,,/o ^ / t « . ( f ) ! p | c P M ( p ) > < I ' M ' " ' ! y « l M # (57) where the l a s t two f a c t o r s r e p r e s e n t the v i b r a t i o n a l and the - 2 1 - r o t a t i o n a l p a r t s r e s p e c t i v e l y . Prom e q u a t i o n s (31a) 3 we have | B W > . C ™ + g O f ( D ^ + C -1) L D £ K > / / ? (58) Hence the r o t a t i o n a l p a r t can be c a l c u l a t e d . The e x p r e s s i o n i n terms o f Clebsch-Gordan c o e f f i c i e n t s ^ ( j j j g j ^ > m-^rr^m^) v/hen p r o p e r l y n o r m a l i s e d i s as f o l l o w s < L 'M ' N 1 1 ( V)| 1MN^> = C (L2L •; M^M 1 ) J^-±.1. | [ C o ' N , C o N C(L2L';000) + fcc^'c™ C(L2L ' ,-KOK)] cos V + i [ ( l + (-1) 1') C^' N IC^ N C(L2L':2 S~2,0) + (l+(-l)L)c£Nc£ ' W 6(L2L;02« +/2>~\ O ^ J C^C(L2L';K,2,K+2)4-/2 ^ 5 C^ NC(L2L«;K-2,K-2 j l s i n J T ^ 2 ^ ' k Ife4 k " 2 K J (59) F o r the v i b r a t i o n a l p a r t , we must e v a l u a t e ^ ) , n , \p\$LS) = x. ( I S ) S^/p i n the n o t a t i o n o f Da v i d s o n D (37), (40) and ( 4 1 ) , we can w r i t e "3/2 R e c a l l i n g e q u a t i o n s (32), ^ L N W -P~J/\(^y) and <J> , (/>) = / T 3 / % , ( ^ ' ) where y = Z-^/3/u.j^Z - 1) and y' = Z1«(/3^|iZ» - l ) . Thus, ^ ^ ^ / ^ ( M - Z - J ^ - ^ ^ ( ^ z ^ and ( p L , N , =p-3/2 D j | /[/2( x - Z * ) ] w i t h x ^ Z ^ / l ^ Z ' T h e r e f o r e , the m a t r i x element <C(PL IW I ((3)|pj ̂ L N ( | S ) ^ = where (h2dfi i s the volume element, and the f u n c t i o n (60) (61) (62) (63) =f\[w* - nd * - z ^ d x ( 6 i ° •Jo 1 The n o r m a l i z i n g c o n s t a n t s N,., and N v a r e d e f i n e d from N 2 J D 2 , (/2y)d^ = ^ Z / Z i ) / D 2 ( / 2 y ) d y = 1 Thus, N 2, = ( Z p ^ Z I J (65) w i t h I „ = J D 2 p ( / 2 y ) d y (66) Hence ^' ' K ^ L ' N ' C P J I H ^ L N ^ ) ) ! 2 = ( Z i ^ / Z ' Z ) ^ ^ ! ) ^ ^ = ( j u p o ) 2 ( Z ! / z ) ( Z ' / z i ) 3 i 2 ^ (67) The e x p l i c i t e x p r e s s i o n s f o r 1 ^ and I ̂  were worked ou t by D a v i d s o n as shown below and programmed •to = [z^+v'}JK / e x p { - i ( x 2 + R ^ x + Z ^ - Z - ^ 2 (x+Z-^XyCx). ~ z' X 2 / ;(R z(x+Z 1)-Z-[) dx (68) where Rz = Z 1Z'/ZZ-[ , 0 0 a n d X (x) = I X (-D k j ( k - i Q ( 2 x ) k and X p U ; r ( _ i i , ) r i ( 1 _ L ; ) I V ( Z 1 ) = ^ e + *yS-Ici+l) + i J f [ H ( 1 2 ^ ) - H C l + ^ 2 ) ] / ^R-i>) (69) where H(x) - d / d x ( l n R x ) ) and I V E = expj-ZjC^ T x r ^ ) X ( Z ^ - X Q - ^ J -Z l ^ T C ^ _ f , 72^t°±.^ 2 v 2 , Thus, r e t u r n i n g to e q u a t i o n (57)» the r a t i o o f two 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 computed. Of c o u r s e , t h i s i s o n l y a p p l i c a b l e to E2 t r a n s i t i o n s , c o r r e s p o n d i n g to the y\ - Z c a s e . For the /\ = 3 c a s e , d i s c u s s i o n i s o m i t t e d on the ground t h a t no t r a n s i t i o n between 7\-- 3 s t a t e s i s observed i n • the p r e s e n t e x p e r i m e n t . 5 5 - Other Forms of E l e c t r o m a g n e t i c T r a n s i t i o n s . Two p o s s i b l e forms of e l e c t r o m a g n e t i c t r a n s i t i o n s t h a t can compete wi t h E 2 t r a n s i t i o n are the Ml and EO. I t was shown 10) by Davydov et a l t h a t Ml t r a n s i t i o n was f o r b i d d e n i n a symmetric r o t a t o r ( i . e . when y = O ) J but not i n an asymmetric 42)-44) r o t a t o r . The l a t t e r was then p o i n t e d out by Tamura et a l t o be i n c o r r e c t , t h a t i s both cases are f o r b i d d e n . T h e r e f o r e , o n l y EO t r a n s i t i o n needs t o be c o n s i d e r e d . An EO t r a n s i t i o n i s o n l y p o s s i b l e between two s t a t e s of the same s p i n L. S ince no photon c a r r i e s an angular momentum zer o , the EO t r a n s i t i o n only works through the i n t e r n a l e l e c t r o n c o n v e r s i o n p r o c e s s . The a b s o l u t e t r a n s i t i o n p r o b a b i l i t y per 45) u n i t time was g i v e n by Church et a l as T(E0) = J l ^ (70) where fl i s the e l e c t r o n i c f a c t o r i n v o l v e d i n the t r a n s i t i o n and ^ the n u c l e a r f a c t o r . Only the K - c o n v e r s i o n i s important i n t h i s case, and hence i l was p l o t t e d a g a i n s t the t r a n s i t i o n K energy by the above a u t h o r s . ^ i s j u s t the m a t r i x element . • * c o r r e s p o n d i n g t o the v i b r a t i o n a l part of the E 2 t r a n s i t i o n (no r o t a t i o n ) . For EO t r a n s i t i o n from a beta band ( i . e . the f i r s t e x c i t e d s t a t e , n= 2) to a ground r o t a t i o n a l s t a t e (n= l ) , (see r e f . 16) •_ • f • ^ L N n ' C ' P ) | P 2 l g ' L N o ( P ) > % Ql) * Only c o n s i d e r t r a n s i t i o n s from beta v i b r a t i o n a l band. -2.4- wliere z = a t o m i c number. Thus f = ( 3 V 4 r r ^ ( p L , , T , n , ( p ) ^ ^ L N n ( ^ ) / 3 3 ¥ o oo • - ( 3 2 A r c ) N A ^ [ | 2 ( ^ - Z i ) ] f 2 D „ [ / 2 ( M _ - Z ^ d p and w i t h the same s u b s t i t u t i o n s w h i c h l e d to e q u a t i o n (67) but w i t h Z = Z', and Z-j_ = Z-£, we o b t a i n ^ = ( 3 z A r c ) ^ p O Z / Z 1 ) ^ y i / D ^ ^ X - Z - L ) ) X 2 D ^ ( X - Z x ) ] dx or j > 2 = ( 3 z A r c ) 2 . C ^ Z / Z ^ Y ^ M O ) ( ? 2 ) The o v e r l a p i n t e g r a l 1 ^ ( 0 ) = / D y j / 2 ( x - Z 1 ) J x 2 D ^ C x - Z - ^ J d x = r - 2 2 ^ + ^ ' ) J T C j f ( x + Z ) 2 x 2 ( x ) d x ( c . f . e q u a t i o n (68). F u n c t i o n s 1^(0) and I v ( 0 ) a r e g i v e n i n (69). The monopole t r a n s i t i o n p r o b a b i l i t y T(.EO) i s u s u a l l y compared w i t h the E2 t r a n s i t i o n p r o b a b i l i t y from the same s t a t e , T (E2; 0 •(- -»2 + ). From (51) 8rc. 3 VK<o~ T ( E 2 ) = 2 ( 5 o a ) ^ ^ B ( E 2 j 0+ -»2+) = —^TT—c— %l B(E2; 012 O i l ) 75K 6c5 r \\\ \\\ LNn L'Nh' where Ej, i s the energy o f the e m i t t e d photon. W i t h E ^ i n Mev and w i t h e q u a t i o n s (57), (67), and (72), we can w r i t e T i l ) = M x T ^ W " ? ( z / z 1 ) 5 ( z i / z ' P _ i y > ( 2 ) i ^ ( Q ) r r^2) 2 . 5 3 x l 0 ^ V 3 E r 5 I w ( 0 ) l 2 v ( 2 ) P r o t (78) v/here P r 0 - t i s the r o t a t i o n a l p a r t o f the t r a n s i t i o n p r o b a b i l i t y computed by (59). S i n c e EO t r a n s i t i o n s may a l s o o c c u r between any two s t a t e s o f the same s p i n and p a r i t y , e q u a t i o n (78) may e a s i l y be a l t e r e d t o a p p l y t o t h e s e . F o r example, f o r t r a n s i t i o n s between s t a t e s o f the f i r s t b e t a band and s i m i l a r s p i n s t a t e s o f the ground s t a t e band, we can w r i t e f o r the r a t i o o f the t r a n s i t i o n p r o b a b i l i t i e s beWeen the same s t a t e s , i l b ' J * b 2 .53x l09 A V3E f 12,(2) P r o f c (see r e f e r e n c e (16)). (78a) A l t h o u g h s e v e r a l t r a n s i t i o n s from the n e g a t i v e p a r i t y l e v e l s 3) t o p o s i t i v e p a r i t y l e v e l s (?\ = 2) have been o b s e r v e d , no t h e o r e t i c a l t r a n s i t i o n p r o b a b i l i t i e s have so f a r been worked o u t to a c c o u n t f o r t h e s e . -26- CHAPTER I I I THE DESIGN OF EXPERIMENTS I n n u c l e a r s p e c t r o s c o p y , th e t y p e s of problems t h a t a r e commonly i n v o l v e d a r e : t o c o n s t r u c t t h e n u c l e a r decay scheme of a r a d i o a c t i v e i s o t o p e , t o d e t e r m i n e mechanisms o f t r a n s i t i o n s from one n u c l e a r s t a t e t o a n o t h e r , and c o n s e q u e n t l y t o u n d e r s t a n d t h e n u c l e u s by model f i t t i n g . The energy l e v e l s i n t h e decay scheme of a n u c l e u s cannot be measured d i r e c t l y . They can o n l y be d e t e r m i n e d by.making use of t h e energy t r a n s f e r i n t r a n s i t i o n s between s t a t e s . The p h y s i c a l o b s e r v a b l e s i n v o l v e d i n a t r a n s i t i o n , w h i c h are u s u a l l y measured, a r e t h e k i n e t i c e n e r g i e s of t h e e m i t t e d p a r t i c l e s d u r i n g t h e t r a n s i t i o n s , t h e I n t e n s i t i e s o f e m i s s i o n of t h e p a r t i c l e s e i t h e r i n p o l a r i s e d or u n p o l a r i s e d c o n d i t i o n s , and t h e t ime c o r r e l a t i o n o r d i r e c t i o n a l c o r r e l a t i o n between a p a i r o f e m i t t e d p a r t i c l e s . The p a r t i c l e s r e f e r r e d t o here are a l p h a - p a r t i c l e s , b e t a - p a r t i c l e s ( e l e c t r o n s and p o s i t r o n s ) , n e u t r i n o s and p h o t o n s . . I n t h e 'present e x p e r i m e n t , we a r e concerned w i t h t h e decay o f Eu 1 5 ^ from I t s ground s t a t e t o t h e e x c i t e d s t a t e s o f t h e d aughter n u c l e u s , Gd 1 5 ^ . D u r i n g each t r a n s i t i o n i n t h e decay, an e l e c t r o n and a n e u t r i n o a r e e m i t t e d . The de- e x c i t a t l o n of each e x c i t e d s t a t e so formed may r e s u l t , i n t h e e m i s s i o n o f a photon, o r an e l e c t r o n t h r o u g h an i n t e r n a l c o n v e r s i o n p r o c e s s (see ^2 , C h a p t e r 6), o r a p o s i t r o n - e l e c t r o n p a i r i f t h e energy t r a n s f e r i s g r e a t e r than. 1.022 M.ev. S i n c e t h e n e u t r i n o c r o s s - s e c t i o n o f n u c l e o n s i s next t o z e r o (~10 cm ), th e o n l y measurable p a r t i c l e s u s i n g c o n v e n t i o n a l t e c h n i q u e s a r e t h e b e t a s and t h e gammas ( p h o t o n s ) . The methods f o r i n v e s t i g a t i n g t h e b e t a and gamma t r a n s i t i o n s v a r y f rom one experiment t o a n o t h e r . The d e t e r m i n - i n g f a c t o r s f o r u s i n g the d i f f e r e n t methods l i e p r i m a r i l y i n th e n a t u r e o f t h e t r a n s i t i o n s o f t h e chosen i s o t o p e ( e . g . t h e e n e r g i e s o f t h e e m i t t e d p a r t i c l e s ) , t he s p e c i f i c need f o r f u r t h e r e x a m i n a t i o n o f t h e i s o t o p e , and t h e t e c h n i c a l l i m i t - a t i o n s such as e x i s t on t h e e f f i c i e n c i e s and r e s o l u t i o n s of th e d e t e c t o r s a v a i l a b l e and on t h e speed o f t h e e l e c t r o n i c system. S t r o n g emphasis has t o be p l a c e d a t t h e l a s t p o i n t , because s p e c t r o s c o p i c work r e l i e s e s s e n t i a l l y on t h e p r e c i s i o n o f measurement. As s t a t e d i n t h e I n t r o d u c t i o n , t h e decay o f Eu 154 has been i n v e s t i g a t e d by s e v e r a l w o r k e r s , and c o n s e q u e n t l y a rough s k e l e t o n o f t h e decay scheme has. been e s t a b l i s h e d f o r some t i m e . The problems l e f t o v e r now a r e : l ) t o determine the e n e r g i e s and i n t e n s i t i e s o f a l l t h e t r a n s i t i o n s a c c u r a t e l y enough so as to,make. a- m e a n i n g f u l i d e n t i f i c a t i o n w i t h an a p p r o p r i a t e t h e o r e t i c a l model. -28- 2) t o s e a r c h f o r new weak t r a n s i t i o n s t h a t have not been found b e f o r e , and, i f any, t o a s s i g n them t o t h e i r p r o p e r p o s i t i o n s i n t h e decay scheme; and 3 ) t o check t h o s e p a r t s o f t h e decay i n w h i c h t h e r e a r e d i s a g r e e m e n t s o r u n c e r t a i n t i e s i n e a r l i e r i n v e s t i g a t i o n s . W i t h t h e above c o n s i d e r a t i o n s i n mind, t h r e e methods of i n v e s t i g a t i o n were employed f o r t h e p r e s e n t work, t h e gamma s i n g l e s s p e c t r o s c o p y , gamma-gamma c o i n c i d e n c e work, and b e t a s p e c t r o s c o p y . They a re s e p a r a t e l y d i s c u s s e d i n t h e f o l l o w i n g t h r e e c h a p t e r s . CHAPTER IV THE GAMMA SPECTROSCOPY § 1 . G e n e r a l C o n s i d e r a t i o n s . I t was mentioned i n t h e p r e v i o u s c h a p t e r t h a t t h e de- e x c i t a t i o n o f an e x c i t e d s t a t e o f Gd 154 t o a l o w e r s t a t e may be c a r r i e d "out by t h e d i r e c t e m i s s i o n o f a photon, or by an i n t e r n a l c o n v e r s i o n p r o c e s s , o r by i n t e r n a l p a i r p r o d u c t i o n . I n t h i s c h a p t e r , o n l y t h e d i r e c t gamma e m i s s i o n w i l l be t r e a t e d . The o t h e r two p r o c e s s e s w i l l be c o n s i d e r e d a l o n g w i t h b e t a t r a n s i t i o n s i n C h a p t e r 6. The change o f s t a t e s i n a n u c l e u s i n t h e p r o c e s s o f d e - e x c i t a t i o n c o r r e s p o n d s t o t h e sudden a l t e r a t i o n o f t h e c h a r g e - c u r r e n t d i s t r i b u t i o n o f t h e n u c l e u s i n o r d e r t o a c q u i r e a l o w e r p o t e n t i a l energy. I n g e n e r a l , t h i s a l t e r a t i o n i s e q u i v a l e n t t o sudden s w i t c h i n g on and o f f o f a c o m b i n a t i o n o f e l e c t r o m a g n e t i c o s c i l l a t o r s , and t h u s s e n d i n g out a s e r i e s o f e l e c t r o m a g n e t i c waves w i t h v a r i o u s ; . m u l t i p o l e o r d e r s . These waves o r r a d i a t i o n s can be s e p a r a t e d i n t o two g r o u p s , t h e e l e c t r i c m u l t i p o l e s (EL) and t h e magnetic m u l t i p o l e s (ML) .'" The m u l t i p o l e o r d e r L i s j u s t t h e a n g u l a r momentum i n u n i t s K c a r r i e d away by each quantum o f r a d i a t i o n (a p h o t o n ) . The. p a r i t y o f an e l e c t r i c m u l t i p o l e r a d i a t i o n , . i s • d e f i n e d as E L V -('*) . From M a x w e l l ' s e q u a t i o n , V ( r ) x E ( r ) = - -^-H(r) and V ( - r ) x E ( - r ) = - £ H ( - r ) , (79) and s i n c e Y ( - r ) = - - V ( r ) / i t i m p l i e s t h a t f o r t h e same L, t h e e l e c t r i c f i e l d and t h e magnetic f i e l d a r e o f o p p o s i t e p a r i t y . Hence, t h e p a r i t y o f a magnetic m u l t i p o l e r a d i a t i o n i s 7T M = ' ( - 1 ) L Not a l l t h e components o f t h e m u l t i p o l e r a d i a t i o n s are e q u a l l y p r e f e r r e d i n each t r a n s i t i o n . T h e i r p r e s ence i s r e s t r i c t e d by a few s e l e c t i o n r u l e s as shown below: 1. I n o r d e r t o c o n s e r v e a n g u l a r momentum, th e f o l l o w i n g t r i a n g u l a r r u l e must h o l d , | i i - I f | ^ L < I f ] (80) where 1^, I f a r e t h e t o t a l a n g u l a r momenta i n u n i t s H o f t h e i n i t i a l and f i n a l l e v e l s i n t h e t r a n s i t i o n r e s p e c t i v e l y . 2. C o n s e r v a t i o n o f p a r i t y d u r i n g t h e t r a n s i t i o n must be observed . 3. From t h e e x p r e s s i o n f o r t r a n s i t i o n p r o b a b i l i t i e s w i t h m u l t i p o l e o r d e r L ( c . f . e q u a t i o n s ( 5 l ) and ( 56 ) i n C h a p t e r 2 ) , t h e f o l l o w i n g f a c t o r can be e x t r a c t e d , -, 2L (81) Ui 2L RL" 2 V 0 Ic. where / V i s t h e wave l e n g t h o f t h e e m i t t e d r a d i a t i o n . S i n c e the r a t i o R D/A i s v e r y s m a l l , even f o r s e v e r a l Mev t r a n s f e r o f energy, o n l y t h e term w i t h l o w e s t o r d e r o f L i s s i g n i f i c a n t i n each t r a n s i t i o n . 4. A g a i n from e q u a t i o n (51), when L = 0, t h e t r a n s i t i o n p r o b a b i l i t y , T (L) becomes i n f i n i t e , w h i c h i s i m p o s s i b l e , i - f Hence, no e l e c t r o m a g n e t i c r a d i a t i o n can be expected w i t h z e r o m u l t i p o l e o r d e r . ^ ' 5. 'For t h e same L, i t can be shown t h a t t h e magnetic r a d i a t i o n i s weaker t h a n t h e e l e c t r i c r a d i a t i o n by a' f a c t o r o f (v/c) (see r e f .47 p.592), where v is t h e speed of m o t i o n o f t h e charges i n t h e n u c l e u s . I n c o l l e c t i v e models, a n o t h e r s e l e c t i o n r u l e due t o r o t a t i o n a l quantum number K i s added, l , e . L > \K± - K f (82) However, i n asymmetric r o t a t o r model, s i n c e K i s not a good quantum number, t h i s K - f o r b i d d e n n e s s o n l y h i n d e r s t h e t r a n s i t i o n but does not f o r b i d it.The h i n d r a n c e i s e x p r e s s e d a s , - L (83) A c c o r d i n g t o t h e asymmetric r o t a t o r model d e s c r i b e d i n Ch a p t e r 2, t h e predominant m u l t i p o l e r a d i a t i o n s i n t h e gamma t r a n s i t i o n s of Gd 154 are a g a i n l i m i t e d t o E2, c o n s i s t e n t w i t h t h e above s e l e c t i o n r u l e s . E x p e r i m e n t a l d e t e r m i n a t i o n o f t h e t y p e s o f m u l t i p o l e r a d i a t i o n r e q u i r e s t h e knowledge o f i n t e r n a l c o n v e r s i o n d a t a , and hence w i l l be t r e a t e d i n Chapter 6. K i ~ K f Meanwhile, we w i l l proceed t o d e a l w i t h t h e means o f measure. Ing t h e e n e r g i e s and i n t e n s i t i e s o f t h e s e gamma r a y s . § 2 . I n t e r a c t i o n between Gamma Rays and t h e D e t e c t o r s . When a photon e n t e r s a d e t e c t o r , s e v e r a l t h i n g s can happen. The photon energy may be c o m p l e t e l y absorbed by an e l e c t r o n i n t h e d e t e c t o r . T h i s e l e c t r o n t h e n moves about i n t h e d e t e c t o r p r o d u c i n g i o n p a i r s o r l u m i n e s c e n c e u n t i l i t comes t o r e s t w i t h i t s energy s p e n t . The i o n p a i r s i f c o l l e c t e d by a p a i r o f e l e c t r o d e s w i l l g i v e a charge p u l s e whose magnitude i s l i n e a r l y p r o p o r t i o n a l t o t h e e l e c t r o n energy. S i m i l a r l y , t he lu m i n e s c e n c e i f c o l l e c t e d by a p h o t o m u l t i p l i e r w i l l g i v e a p u l s e p r o p o r t i o n a l t o t h e l u m i n i s c e n t energy. T h i s p r o c e s s o f complete energy t r a n s f e r from a photon t o a d e t e c t o r i s c a l l e d p h o t o - a b s o r p t i o n . The peaks i n an energy spectrum o b t a i n e d from t h i s p r o c e s s a r e t h u s named p h o t o - a b s o r p t i o n peaks. I f t h e gamma r a y s a r e mo n o - e n e r g e t i c , a s i n g l e peak s h o u l d be observed w h i c h i s i d e a l l y G a u s s i a n i n shape. On t h e o t h e r hand, i f a photon i n t e r a c t s w i t h an e l e c t r o n and i s i t s e l f s c a t t e r e d out o f t h e d e t e c t o r , t h e n t h e energy of t h e photon absorbed by t h e e l e c t r o n i s p a r t i a l . The amount of t h i s p a r t i a l energy ( i . e . t h e e l e c t r o n r e c o i l energy, E e ) 43 ) v a r i e s w i t h t h e s c a t t e r i n g a n g l e 9 as g i v e n i n t h e e q u a t i o n , - 3 3 - E e ( e ) = E [ i - 1/(1 + l l ( l - c o s e ) ) ] (84) mc2 where E ^ i s the i n i t i a l photon energy and 9 i s defined as shown below. -* • E y / ( s c a t t e r e d photon) The r e c o i l e l e c t r o n t h e n meets t h e same f a t e as t h a t d e s c r i b e d i n t h e p r e v i o u s p a r a g r a p h . T h i s p r o c e s s o f p a r t i a l t r a n s f e r o f energy i s c a l l e d Compton s c a t t e r i n g . S i n c e 0 can be any v a l u e between 0 ° and l 8 0 ° , t h e energy spectrum t h u s o b t a i n e d f o r mono-energetic i n c i d e n t gamma r a y s i s known as t h e Compton continuum. T h i s continuum extends from E e ( 0 ° ) - O t o E e ( l 8 0 ° ) . Hence, t h e Compton edge (upper edge o f t h e continuum) c o r r e s p o n d s t o t h e case i n w h i c h t h e photons a r e b a c k - s c a t t e r e d . Another p r o c e s s which has been mentioned b e f o r e i s p a i r p r o d u c t i o n . When a photon w i t h energy g r e a t e r t h a n two e l e c t r o n mass e n t e r s the E M - f i e l d of a n u c l e u s i n t h e d e t e c t o r , t h e energy may be c o n v e r t e d i n t o m a t t e r by l i f t i n g an e l e c t r o n from a n e g a t i v e energy s t a t e t o a p o s i t i v e energy s t a t e and l e a v i n g a 'hole' o r p o s i t r o n b e h i n d . Thus an e l e c t r o n - p o s i t r o n p a i r i s c r e a t e d . The p o s i t r o n i s o f t e n stopped and a n n i h i l a t e d w i t h an e l e c t r o n i n t h e d e t e c t o r y i e l d i n g a p a i r o f photons of energy 0 . 5 1 1 Mev each. T h e r e f o r e , a double-escape peak o f energy, -34- E - = ( E y - 1 . 0 2 2 ) Mev ( 85 ) can be o b t a i n e d , i f b o t h photons escape from t h e d e t e c t o r . However, i f one o f them i s r e - a b s o r b e d i n t h e d e t e c t o r , a s i n g l e - e s c a p e peak o f energy, i s formed \ § 3 . Gamma-ray D e t e c t i o n A s s e m b l i e s . The f i r s t gamma-ray d e t e c t i o n assembly c o n s t r u c t e d and i n t e n d e d f o r t h e p r e s e n t work i s shown i n f i g u r e 1 . I t makes use o f t h e p r i n c i p l e of Compton b a c k - s c a t t e r i n g . Gamma r a y s from t h e sour c e S were c o l l i m a t e d by t h e c y l i n d r i c a l l e a d b l o c k s A and B, and t r a v e l l e d t h r o u g h t h e alu m i n i u m t u b i n g t o a L i t h i u m - d r i f t e d S i l i c o n d e t e c t o r w h i c h has a d e p l e t i o n depth of 3 mm. and an a c t i v e volume o f 0.15,. c . c . Some o f t h e photons were stopped by t h e d e t e c t o r and b a c k - s c a t t e r e d t o t h e b l o c k o f p l a s t i c s c i n t i l l a t o r molded i n t h e shape o f a c y l i n d e r . The S i l i c o n d e t e c t o r was c o o l e d by a copper b r u s h dipped i n a DeWar of l i q u i d n i t r o g e n so as to. a c h i e v e optimum r e s o l u t i o n . The p l a s t i c s c i n t i l l a t o r was viewed by f o u r p h o t o m u l t i p l i e r s w h i c h were a d j u s t e d t o y i e l d t h e same.charge m u l t i p l i c a t i o n f a c t o r . The o u t p u t s of t h e p h o t o m u l t i p l i e r s were t i e d t o one cathode f o l l o w e r stage as shown I n f i g u r e 2 . Each event, was d e f i n e d by t h e c o i n c i d e n c e between a p u l s e . f r o m t h e d e t e c t o r . E ( E - - 0 . 5 1 1 ) Mev S 6 * ( 8 6 )  -36- - P l a s t i c S c i n t i l l a t o r P h o t o m u l t i p l i e r i o 9 9 9 0 l i - D S i D e t e c t o r Lov;-noise Preamp. Cathode F o l l o w e r Cathode F o l l o w e r \2h 21 B.H.T. -1100 v. D r i v e r D r i v e r F a s t C o i n . V a r i a b l e D e l a y gate K i c k S o r t e r i n n u t Low-noise A m p l i f i e r F i g . 2 E l e c t r o n i c c i r c u i t f o r t h e gamma s p e c t r o m e t e r . -37- • and a p u l s e from t h e p h o t o m u l t i p l i e r s . The output from t h e d e t e c t o r c o r r e s p o n d s t o t h e r e c o i l e n e r g i e s o f t h e e l e c t r o n s i n t h e d e p l e t i o n r e g i o n . T h i s output was s t o r e d i n a . 1 2 8 - c h a n n e l k i c k s o r t e r a f t e r b e i n g gated by t h e c o i n c i d e n c e p u l s e s . T h e r e f o r e , each count r e c o r d e d by t h e k i c k s o r t e r c o r r e s p o n d s t o a b a c k - s c a t t e r i n g e v e n t , t h e • b a c k - s c a t t e r i n g o _ o a n g l e b e i n g l i m i t e d t o a range 1 5 7 - 1 8 0 by t h e cone i n t h e l e a d b l o c k C. A spectrum o f Cs 134 was t h e n t a k e n as shown i n f i g u r e 3 . Prom § 2 , t h e peak p o s i t i o n s o f t h e spectrum a r e almost at t h e p o s i t i o n s o f . t h e o r i g i n a l Compton edges. I t can be seen from t h e spectrum t h a t t h e r e s t o f t h e Compton continuum i s h i g h l y suppressed by t h e c o i n c i d e n c e system, w h i c h i s t h e beauty o f t h i s assembly. The r e s o l u t i o n as quoted on t h e f i g u r e i s f a i r l y good. I t i s a c h i e v e d because i n t h e range o f back- s c a t t e r i n g a n g l e s a c c e p t e d , t h e energy o f s c a t t e r e d e l e c t r o n i s almost independent".of s c a t t e r i n g a n g l e . The o n l y drawback i n t h i s assembly i s low e f f i c i e n c y . By t h e ti m e t h e above assembly was t e s t e d , L i t h i u m - d r i f t e d Germanium d e t e c t o r s were a v a i l a b l e i n t h i s l a b o r a t o r y . S i n c e t h e l a t t e r f a r exceed t h e former i n r e s o l u t i o n and e f f i c i e n c y , t h e gamma e x p e r i m e n t s were t h e n performed by u s i n g the Germanium d e t e c t o r s i n s t e a d . However, i t i s i n t e r e s t i n g t o note t h a t t h e above assembly p r o v i d e s a method o f gamma -38- 20 18 |6 I f a CO 10 o H O o 563 Kev 569 Kev 605 Kev / / j I" Cs 134 FWHM = 11.6 Kev (e r e c o i l energy) 797 Kev 803 Kev 2% 38 62 Channel Number 28 101 F i g . 3 Cs 134.spectrum t a k e n from t h e gamma-spectrometer assembly. -39- d e t e c t i o n based on a q u i t e d i f f e r e n t p r i n c i p l e . The Germanium d e t e c t o r assembly i s shown i n f i g u r e 4. Two p l a n a r - t y p e d e t e c t o r s p r e p a r e d and mounted by D.A. D a l b y have been used one a f t e r t h e o t h e r . The f i r s t d e t e c t o r has a d e p l e t i o n d e pth of 5 mm. and a c t i v e volume, 1 . 5 c . c . , w h i l e t h e second one i s much b i g g e r , h a v i n g a d e p l e t i o n depthtof:.. 7.5.mm. and a c t i v e volume, 5 c . c . As u s u a l , each d e t e c t o r was mounted i n a vacuum chamber and c o o l e d by a c o l d f i n g e r . I n t h i s c a s e , because of t h e s p e c i a l preamplifier c i r c u i t used, t h e d e t e c t o r b i a s had t o be n e g a t i v e . Thus t h e P s u r f a c e o f t h e d e t e c t o r r e s t i n g on t h e c o l d f i n g e r was e l e c t r i c a l l y i n s u l a t e d from t h e l a t t e r by a t h i n sheet o f n y l o n . The N s u r f a c e ( i . e . t h e L i s u r f a c e ) was i n spot c o n t a c t w i t h t h e g a t e t e r m i n a l o f a f i e l d e f f e c t t r a n s i s t o r ( 2N3823 ) and a f e e d b a c k l e a d t h r o u g h a 500 M A r e s i s t o r as shown i n f i g u r e 5 . T h i s f i g u r e p r e s e n t s t h e f i r s t s t age o f t h e l o w - n o i s e preamplifier used. The s u p e r - h i g h i n p u t irnpedence p r o v i d e d by t h e f i e l d e f f e c t t r a n s i s t o r s i g n i f i c a n t l y i n c r e a s e d t h e peak-to-rnoise r a t i o when compared w i t h o t h e r l o w - n o i s e p r e a m p l i f i e r s u s i n g cathode f o l l o w e r i n p u t s t a g e s ( e . g . O r t e c 101XL and Simtec P-10). The p r e a m p l i f i e r o u t p u t was connected t o a Time C o n s t a n t Box w i t h 1 ^ s e c . r i s e t i m e and 10 f-sec. decay t i m e , and t h e n t o a l o w - n o i s e a m p l i f i e r and a 1024-channel k i c k s o r t e r . U s i n g a d e t e c t o r b i a s of - 6 0 0 v. -40- Dewar Rough purap L i q u i d N i t r o g e n ' r Id I o n pump L i - d ^ i f t e d Ge S u p p o r t s D e t e c t o r A l Window C o l d f i n g e r F i g . 4 The Germanium d e t e c t o r a s s e m b l y . + 24 v +12 v O.lHf -24 v F i g . 5 Input stage o f the l o w - n o i s e p r e a m p l i f i e r connected t o t h e Germanium d e t e c t o r . f o r t h e f i r s t d e t e c t o r , we o b t a i n e d a r e s o l u t i o n o f 4 Kev a t about 1.3 Mev o f energy o r below; w h i l e w i t h a b i a s o f - 1 0 0 0 v. f o r t h e second d e t e c t o r , t h e r e s o l u t i o n was 3 . 5 Kev i n t h e same energy r a n g e . These a r e I l l u s t r a t e d i n . f i g u r e s 6 and 7 . . I t i s a l s o c l e a r t h a t t h e second d e t e c t o r h a v i n g a l a r g e r a c t i v e volume gave a much b e t t e r r a t i o o f p h o t o - a b s o r p t i o n peak t o Compton continuum. % 4 . Source P r e p a r a t i o n and M o u n t i n g . The Eu 154 s o u r c e was p r e p a r e d from 2 m i l l i g r a m s o f Europium i n o x i d e form, w h i c h was e n r i c h e d t o 9 8 . 7 6 $ o f Eu 1 5 3 - The o x i d e was s e a l e d i n a q u a r t z c a p s u l e and i r r a d i a t e d f o r 7 days i n t h e Oak Ridge N a t i o n a l L a b o r a t o r y r e a c t o r t o y i e l d about 5 m i l l i c u r i e s o f Eu 154 by n e u t r o n - c a p t u r e p r o c e s s . A s m a l l q u a n t i t y of t h e i r r a d i a t e d s o u r c e was i n t r o d u c e d i n t o a m i n i a t u r e beaker and a few drops o f pure c o n c e n t r a t e d h y d r o c h l o r i c a c i d were added t o o b t a i n a c h l o r i d e s o l u t i o n . The s o l u t i o n was e v a p o r a t e d t o d r y n e s s under a t u n g s t e n lamp t o remove t h e e x c e s s a c i d , and when, c o o l t h e c h l o r i d e was d i s s o l v e d i n d i s t i l l e d w a t e r . I t was r e - e v a p o r a t e d and t h e n d i s s o l v e d i n d i s t i l l e d w ater a g a i n . The purpose of changing t h e i n s o l u b l e - o x i d e i n t o t h e s o l u b l e c h o r i d e i s m a i n l y f o r p r e p a r i n g t h e b e t a s o u r c e s . 40 h Channel Number F i g . 6 Co 60 gamma spectrum o b t a i n e d : from the 1.5 c.c. Ge d e t e c t o r . F i g . 7 Co 60 gamma spectrum o b t a i n e d from the S e c . Ge D e t e c t o r . -45-' But i t i s a l s o c o n v e n i e n t t o p r e p a r e gamma s o u r c e s from l i q u i d f orm, because t h e r a d i o a c t i v e s t r e n g t h can be e a s i l y c o n t r o l l e d i n t h i s way.' A drop o f t h e l i q u i d was d r i e d on an IBM c a r d cut i n t o a c i r c u l a r d i s c of 1 i n c h d i a m e t e r w i t h t h e drop a t t h e c e n t r e . The s o u r c e was t h e n s e a l e d w i t h s c o t c h t a p e and mounted on a The o t h e r s o u r c e s used f o r ° energy c a l i b r a t i o n were a l s o p r e p a r e d i n t h e s i m i l a r , way. ^5- E x p e r i m e n t a l P r o c e d u r e s . The e x p e r i m e n t s were c a r r i e d out a t t h r e e s e p a r a t e t i m e s r u n was t a k e n t o o b t a i n t h e gamma spectrum o f Eu 154 i n a 1024-channel k i c k s o r t e r . This'was f o l l o w e d by 10-minute r u n s f o r v a r i o u s c a l i b r a t i o n s o u r c e s i n c l u d i n g Co 57, Co 60, Cs 137; Na 22, Mn 54, Ba 133, Cs 134, Y 88, RdTh, Hg 203, and Am 2 4 l . The p o s i t i o n o f t h e sour c e h o l d e r r e l a t i v e t o t h e d e t e c t o r was f i x e d on an aluminium frame, so t h a t e v e r y source c o u l d be p l a c e d at e x a c t l y t h e same p o s i t i o n . Hence, no c o r r e c t i o n f o r t h e d e t e c t o r geometry was n e c e s s a r y . ( A c t u a l l y , t h e r e i s were p r e p a r e d w i t h v a r i o u s s t r e n g t h s . l u c i t e r i n g as shown. S e v e r a l s o u r c e s u s i n g t h e Germanium d e t e c t o r s d e s c r i b e d i n | 3 , and t h e gamma so u r c e s p r e p a r e d as d e s c r i b e d i n § 4. At each t i m e , a 40-minute -46- no way t o do t h i s , as ev e r y Germanium d e t e c t o r has i t s own p e c u l i a r e f f e c t i v e geometry.) Then, i n o r d e r t o o b t a i n b e t t e r i n f o r m a t i o n on t h e weak peaks, an o v e r - n i g h t r u n o f t h e Eu 154 spectrum was repeated., and so a l s o a l o n g e r - p e r i o d r u n f o r each o f t h e weaker c a l i b r a t i o n s o u r c e s . From t h e b e g i n n i n g t o t h e end, t h e c o n d i t i o n s o f t h e e l e c t r o n i c system such as t h e a m p l i f i c a t i o n , t h r e s h o l d and b i a s v o l t a g e were kept c o n s t a n t . The l o s s p e r c e n t a g e i n d i c a t e d on t h e k i c k s o r t e r was not a l l o w e d t o exceed 5 i n a l l t h e r u n s . I f i t d i d , a new source p o s i t i o n had t o be l o c a t e d . S p e c i a l c a r e was t a k e n t o ensure no t i m e s h i f t i n t h e e l e c t r o n i c system when t h e s h o r t - p e r i o d r u n s were t a k i n g p l a c e . T h i s was done by u s i n g a s u i t a b l e c a l i b r a t i o n s o urce as a pro b e . (Na 22 was chosen f o r t h i s purpose.) S p e c t r a o f t h i s 'probe' were t a k e n a t t h e b e g i n n i n g and t h e end of t h e s h o r t - p e r i o d r u n s and a l s o b e f o r e t h e 40-minute r u n o f Eu 1 5 4 . Any s h i f t i n t h e two Na 22 peaks ( i . e . t h e 511.0 Kev and 1 2 7 4 . 6 Kev) would i n d i c a t e i n s t a b i l i t y i n t h e system and t h e s p e c t r a t h e n had t o be r e - t a k e n . The o u t p u t data from t h e k i c k s o r t e r were photographed i n p o l a r o i d f i l m s f o r immediate i n s p e c t i o n , and punched out i n paper t a p e s f o r f u r t h e r p r o c e s s i n g . The f i r s t experiment was done i n O c t o b e r , 1 9 6 6 , i n . w h i c h t h e Eu 154 spectrum was t a k e n i n two p o r t i o n s by means o f a b i a s a m p l i f i e r . Each c h a n n e l o f t h e k i c k s o r t e r t h e n c o r r e s p o n d s -47- • t o s l i g h t l y l e s s t h a n 1 Kev. These s p e c t r a gave a f i n e p i c t u r e o f t h e number and l o c a t i o n s o f t h e peaks t o be e x p e c t e d . A l s o s i m i l a r s p e c t r a o f Eu 152 were t a k e n t o check f o r t h e i m p u r i t y o f t h i s i s o t o p e I n Eu 154. The peaks b e l o n g i n g t o Eu 152 were soon s o r t e d o u t . U n f o r t u n a t e l y , t h e s m a l l e r d e t e c t o r (1.5 c . c . • • \ • \ . • • • e f f e c t i v e volume) was used i n t h i s c a s e , so t h a t t h e i n t e n s i t y measurement was not v e r y r e l i a b l e . . . I n t h e second and t h i r d e x p e r i m e n t s w h i c h were done i n December, 1966 and A p r i l , 19^7 r e s p e c t i v e l y , t h e . b i g g e r d e t e c t o r (5 c . c . e f f e c t i v e volume) was employed, and much b e t t e r r e s u l t s were o b t a i n e d . F i g u r e 8 shows a t y p i c a l Eu 154 spectrum on l o g a r i t h m i c p l o t . I n t h i s c a s e , each c h a n n e l o f t h e k i c k s o r t e r c o r r e s p o n d s t o about 1.7 Kev o f energy. I t can be seen from t h e f i g u r e t h a t t h e t h r e s h o l d o f t h e k i c k s o r t e r was s e t a t a f a i r l y h i g h l e v e l . T h i s was done so as t o be a b l e to e l i m i n a t e the v e r y h i g h c o u n t i n g r a t e o f the low energy p u l s e s . I n o r d e r t o be f r e e - from any p o s s i b l e d i s t o r t i o n i n energy and i n t e n s i t y a t t h e low-energy peaks due t o t h e t h r e s h o l d s e t t i n g , t h e lower p o r t i o n o f t h e spectrum.was r e c a l i b r a t e d i n a 400- c h a n n e l k i c k s o r t e r as shown i n f i g u r e 9, and t h e i n t e n s i t i e s were n o r m a l i s e d t o the main spectrum. • . The s t a n d a r d s o u r c e s f o r i n t e n s i t y c a l i b r a t i o n were o b t a i n e d from the I n t e r n a t i o n a l Atomic Energy Agency, V i e n n a . -.000 a • o a a ro r°" a a a « I oo 2 : C—- *C i - j C a CD rn ID C?5 S3 •1 y CO O cf pi 3 5 a cn CD' O a a a • CD • b a a S-4 » o a a LULriiNunotn ur LUUINISJ 2.000 4.000 6.000 • ^ — ^ J 1  ++++++++ 8.000 _ J 10.000 12.000 86.86 Kev 105 .32 Kev 122.93 K e v . ( E u l 5 4 +Eul'32) 247.63 K ev (Hul54 +3Sul52) 343.63 Kev ( E u l 5 2 ) 444.02 Kev 557.96 Kev 582.11 Kev 591.61 Kev 6'92.02 Kev 722.90 Kev 756.71 Kev -815.02 Kev 872.62 Kev 892.74 Kev 903.60 Kev 964.09 Kev ( E u l 5 2 ) 995.94 Kev 1004.50 Kev 1085.47 Kev ( E u l 5 2 ) 1111.98 Kev (Eu'152) 1246.16 Kev ( ? ) 1274.43 Kev •1408.16 Kev ( E u l 5 2 ) 1460.88 Kev ( ? ) 1493.68 Kev ( ? ) 1536.64 Kev ( ? ) 1595.87 Kev -817- -49- lt - 122.9 3Kc.-v 16 • IZ O # 105.32Kev c O 86.86Kev 4 Z i • i i i i < 1 1— 1 1 1 1 1 — i — €0 70 30 10 100 I/O UO 130 IfO ISO ISO 170 l$0 If0 ZOO Channel Number . , Low-energy gamma peaks o f Eu 154. . ' -50- • They i n c l u d e Am 2 4 1 , Hg 2 0 3 , Co 5 7 , Na 2 2 , Cs 1 3 7 , Mn 5 4 , C o .60, and Y 8 8 , c o v e r i n g an energy range from 5 9 . 5 7 Kev t o l 8 4 l Kev. They were a l l spot s o u r c e s , and, when t h e c a l i b r a t i o n was b e i n g performed, t h e s e s o u r c e s were a g a i n p l a c e d at e x a c t l y t h e same p o s i t i o n as t h e Eu 154 s o u r c e . One i m p o r t a n t r e a s o n f o r p e r f o r m i n g t h e e x p e r i m e n t s at t h r e e s e p a r a t e t i m e s has not y e t been mentioned. By examining t h e Eu 1 5 4 s p e c t r a t a k e n at t h e t h r e e d i f f e r e n t p e r i o d s , we found t h a t some of t h e peaks were s h r i n k i n g w i t h r e s p e c t t o t h e o t h e r s , i n d i c a t i n g t h e p r e s e n c e o f some s h o r t - l i v e d i m p u r i t i e s . These peaks, o f c o u r s e , had t o be e x c l u d e d . The a n a l y s i s o f t h e s p e c t r a t a k e n w i l l be d i s c u s s e d i n the next s e c t i o n . § 6 . R e s u l t s and A n a l y s i s . A f t e r t h e v a s t amount o f s p e c t r a l d ata were p l o t t e d out by t h e IBM computer, t h e peak p o s i t i o n s and t h e peak counts were e s t i m a t e d by g r a p h i c a l methods. I t s h o u l d be noted t h a t t h e peak shapes were not G a u s s i a n , so t h a t t h e s t a n d a r d G a u s s i a n f i t t i n g c o u l d not be a p p l i e d i n the hope.of o b t a i n i n g more a c c u r a t e r e s u l t s . I n s p i t e o f t h e . o n l y 3 . 5 Kev f u l l w i d t h . at h a l f maximum, a l o n g t a i l e x i s t e d at t h e lower energy s i d e of each peak as shown i n f i g u r e 7 i n £ 5 . T h i s was p r o b a b l y due • •-51- . t o d i s l o c a t i o n s o r i m p u r i t i e s i n t h e Germanium c r y s t a l , w hich o c c a s i o n a l l y t r a p p e d some e l e c t r o n s c a u s i n g i n c o m p l e t e c o l l e c t i o n o f charges i n each e v e n t . These t a i l s gave some d i f f i c u l t y i n t h e i n t e n s i t y e s t i m a t i o n . However, t h e coun t s i n a t a i l a r e o n l y about 5 per cent o f t h e c o u n t s under the r e l e v a n t peak. Assuming the t a i l c o unts are p r o p o r t i o n a l t o t h e peak c o u n t s , t h e e r r o r s h o u l d not be t o o s e r i o u s even i f p a r t o f t h e t a i l i s n e g l e c t e d . A n o t h e r p o i n t t o be mentioned i s t h a t , s i n c e t h e r e a r e so many peaks over t h e e n t i r e Eu 154 spectrum,- i t i s q u i t e p o s s i b l e t h a t some of t h e s e peaks might s i t on some Compton edges, o r s i n g l e o r double escape peaks. F o r t h i s , a l l t h e p o s i t i o n s o f t h e Compton edges, s i n g l e and double escape peaks r e l a t e d t o t h o s e prominant peaks were computed by u s i n g the s i m p l e e q u a t i o n s (84), (85) , and (86) g i v e n , i n f 2 . Care was t a k e n i n a n a l y z i n g t h o s e few peaks i n t h e v i c i n i t y o f t h e mentioned p o s i t i o n s . F o r t h e energy c a l i b r a t i o n , t h e known-energy peaks used are l i s t e d i n t a b l e I . From f i g u r e 10, wh i c h shows one c a l i b r a t i o n c u r v e f o r t h e Eu 154 spectrum, we see t h a t t h e • •. e l e c t r o n i c system i s f a i r l y l i n e a r . However, we d i d not assume any s i m p l e f u n c t i o n a l dependence o f t h e energy on the c h a n n e l number. S i n c e the c a l i b r a t i o n c u r v e i s f a i r l y l i n e a r , t h e - 5 2 - R a d i o n u c l i d e E n e r g y ( K e v ) R a d i o n u c l i d e E n e r g y ( K e v ) Am 241 59.57 Cs 134 569.0 Hg 203 73.0 RdTh 583.0 Ba 133 81.0 Cs 134 604.65 Co 57 122.0 Cs 137 661.59 Co 57 136.4 RdTh 727.0 Hg 203 279.1 Cs 154 796.0 RdTh 238.6 ' r-Tn 54 835.0 Ba 133 ' 276.0 RdTh 860.0 Ba 133 302.0 Y 88 897.5 Ba 133 355 .0 Co 60 1173.3 Ba 133 383.0 Na 22 1274.6 RdTh 511.0 Co 60 1333.0 Na 22 511.0 RdTh 1592.4 Cs 134 563.0 Y S8 1841.0 T a b l e 1 Peaks used f o r e n e r g y c a l l b r a t i o n - ( o b t a i n e d f rom r e f . 49 and o t h e r s o u r c e s ) . F i g . 1 0 ENERGY ( Ke*) Gamma energy c a l i b r a t i o n c urve f o l l o w i n g method o f l i n e a r i n t e r p o l a t i o n was c o n s i d e r e d t o be the b e s t way: L e t A,B,C,D be t h e known energy p o i n t s and X, t h e p o i n t t o be c a l i b r a t e d . L i n e a r i n t e r p o l a t i o n s were computed u s i n g t h e p a i r s o f known energy p o i n t s , ( B , C ) , (A,C) and (B,D), and t h e s e gave t h e r e s u l t s f o r X as X ( l ) , X(2) and X(3) r e s p e c t i v e l y . I f t h e s e t h r e e v a l u e s f o r X a g r e e t t o w i t h i n 1 Kev, t h e n X = X ( l ) . I f o t h e r w i s e , t h a t s e c t i o n o f th e c u r v e was expanded i n a graph paper and X was determined by c u r v e f i t t i n g . The above method, o f c o u r s e , depends c o n s i d e r a b l y on the a c c u r a c y o f t h e i n d i v i d u a l c a l i b r a t i o n p e a ks. However, because so many known energy peaks were b e i n g used, i t was not d i f f i c u l t t o check whether any i n d i v i d u a l peak v a l u e was up t o t h e s t a n d a r d o r n o t . No p u l s e r was used i n t h e p r e s e n t c a s e , as b e t t e r a c c u r a c y was not expected from i t . . P r o v i d e d t h a t t h e e n e r g i e s l i s t e d i n t a b l e I a r e c o r r e c t t p w i t h i n 0.5 Kev, t h e peaks c a l i b r a t e d i n t h i s way s h o u l d be w i t h i n 1 Kev. The e n e r g i e s o f t h o s e w e l l - d e f i n e d peaks i n each , 40-minute spectrum o f Eu 154 were t h u s c a l i b r a t e d . As f o r t h e -55- weak peaks, c a l i b r a t i o n had t o be done on t h e o v e r - n i g h t - r u n s p e c t r a . I n t h i s c a s e , t h e s t r o n g peaks o f t h e same spectrum a c t e d as s u b s t a n d a r d s . C o n s e q u e n t l y , any ti m e s h i f t would not a f f e c t t h e c a l i b r a t i o n , s i n c e t h e whole spectrum would have s h i f t e d a l t o g e t h e r . The c h a r a c t e r i s t i c s of t h e s t a n d a r d s o u r c e s f o r i n t e n s i t y c a l i b r a t i o n are g i v e n i n t a b l e I I , w h i c h were c a l i b r a t e d at z e r o hour GMT, J a n u a r y 1, 19^7• The r e l a t i v e s t r e n g t h o f each source at t h e ti m e when i t s spectrum was h a l f t a k e n was c a l c u l a t e d , and so were t h e r e l a t i v e i n t e n s i t i e s c o r r e s p o n d i n g t o i t s gamma e n e r g i e s . The observed i n t e n s i t i e s o f t h e gamma peaks were d i r e c t l y measured from each spectrum. The r a t i o s o f r e l a t i v e i n t e n s i t y t o observed i n t e n s i t y were t h e n p l o t t e d as a f u n c t i o n o f gamma energy as shown i n f i g u r e 11*. The cur v e i s f a i r l y smooth and i s j u s t t h e i n v e r s e o f t h e e f f i c i e n c y c u r v e . The window e f f e c t s e t s i n a t about 80 Kev. I t i s due t o t h e o b s t r u c t i o n o f t h e N l a y e r o f t h e d e t e c t o r (about 0.5 mm. t h i c k ) and t h e al u m i n i u m window o f the "vacuum chamber (0.25 mm. t h i c k ) . U s i n g t h e gra p h p l o t t e d . , * The i n t e n s i t y r a t i o at 8 l .0 Kev was o b t a i n e d by t a k i n g a Ba 133 spectrum. The r e l a t i v e . i n t e n s i t y o f 355 Kev o f Ba. 133 was found from t h e g r a p h . Then we m u l t i p l i e d i t by 0.5 2, (see r e f , Ab ) t o o b t a i n the r e l a t i v e i n t e n s i t y o f t h e 8 l Kev peak and hence i t s i n t e n s i t y r a t i o . - I s o t o p e S t r e n g t h .(uc) H a l f - l i f e Y-energy (Kev) Y-ray p e r d i s i n t e g r a t - i o n ($>) Am 241 10.66 485.110.5 y e a r s 59.5710.02 35.910.6 Co 57 10.78 271.6+0.5 days 122.0 85 .311 • 5 Hg 203 21.77 46.57+0.03 days 279.110.05 81.5510.15 Na 22 11.46 2.60310.005 511.0 179.710.8 y e a r s 1274.610.3 99.94 Cs 137 10.68 29.8210.11 y e a r s 661.59 10.076 84.610.6 Mn 54 10.70 313 11 days 835.010.3 100 Co 60 10.87 5.26310.003 1173.310.3 10010.012 y e a r s 1333.010.3 iooio.oo Y 88 10.64 106.610.1 897.510.5 92 days 1836.2 0.3 100 . T a b l e I I Peaks used f o r i n t e n s i t y c a l i b r a t i o n . Energy (Kev) t h e r e l a t i v e i n t e n s i t i e s f o r t h e c o r r e s p o n d i n g Eu 15+ spectrum were found by m u l t i p l y i n g t h e observed i n t e n s i t i e s t o t h e c o r r e s p o n d i n g r a t i o s i n t h e g r a p h . The c a l i b r a t e d e n e r g i e s and t h e r e l a t i v e i n t e n s i t i e s w i t h e r r o r l i m i t s were t h e n p r e s e n t e d i n t a b l e I I I . The -en e r g i e s g i v e n are a c c u r a t e t o w i t h i n 1 Kev. T h i s a c c u r a c y i s r e v e a l e d i n C h a p t e r 7 when c o n s t r u c t i n g t h e decay scheme. The r e l a t i v e i n t e n s i t i e s d etermined a r e f a r more complete t h a n t h o s e of p r e v i o u s w o r k e r s . The a c c u r a c i e s o f t h e energy measurements compare v e r y f a v o u r a b l y w i t h t h o s e from c o n v e r s i o n l i n e s measured w i t h h i g h r e s o l u t i o n s p e c t r o m e t e r s . S c a n n i n g t h r o u g h t a b l e I I I , I n a d d i t i o n t o t h e w e l l - e s t a b l i s h e d s t r o n g peaks, we f i n d t h a t t h e r e a re a few p a r t i a l l y f a m i l i a r peaks, i . e . 86.86 Kev, IO5.32 Kev, 444.02 Kev, 557-96 Kev, 692.02 Kev, 815.02 Kev, and 892.74 Kev. Among them, t h e 557.96 Kev and 892.74 Kev peaks have been observed by Harmatz 33) et a l i n t h e decay o f Tb 154 t o Gd 154, but have never been observed i n t h e decay of Eu 154. The gamma i n t e n s i t y o f the.' 36) 692.02 Kev was b a r e l y measured by H a m i l t o n e t . a l u s i n g the- e x t e r n a l c o n v e r s i o n method. The r e s t o f t h e t r a n s i t i o n s . w e r e 20),36) known from t h e i n t e r n a l c o n v e r s i o n data •In a d d i t i o n t o the above, t h e r e a r e c o m p l e t e l y u n f a m i l i a r peaks, i . e . 582.11 Kev, 903.60 Kev, 1246.16 Kev, 1460 .88 Kev and 1493.68 Kev. I t i s q u i t e . i n t e r e s t i n g . t o f i n d -58- y-energy (Kev) R e l a t i v e I n t e n s i t y Remark 86.86 15.42 ± 1.31 * 105.32 9.70 i 0 . 8 4 * 122.93 100.00 ±2.44 E u l 5 2 I n t f s u b t r a c t e d 247..63 15.86 ±0.72 E u l 5 2 I n t . s u b t r a c t e d 343.63 3.76 ±0 . 2 9 E.ul52 444.02 ••1.56 ±0.14 557.96 0.867±0.163 582.11 1 . 7 3 ±0.16 591.61 10.51 ±0.54. 692.02 3.80 ±0.29 722 . 9 0 .47 .30 ±2.05 756.71 10.36 ±0.60 815.02 1. 31 t0.22 872.62 29 . 3 8 ±1.36 892.74 1.23 ±0.20 903.60 2.04 ±0.23 964 . 0 9 1.82 ±0.25 E u l 5 2 995.94 24.69 ±1.12 1004 . 5 0 43.85 ±1.92 1085.47 1.67 ±0.22 E u l 5 2 1111 . 9 8 2.40 ±0.24 E u l 5 2 1246.16 2.27 ±0.21 •** 1274.43 . 92.00 ±4.13 1408.16 3.29 ±0.20 E u l 5 2 1460.88 0.386±0.052 #- * . 1493.68 1.71 ±0.11 #* 1536.64 0.125±0.022 * * 1595.87 4.67 ±0.22 I T r a n s i t i o n s -known to be b e l o n g i n g to. t h e decay o f E u l 5 4 2 0 ^ , but cannot be f i t t e d i n t o the decay scheme. Weak peaks w i t h unknown o r i g i n . . T a b l e I I I E n e r g i e s and I n t e n s i t i e s o f E u l 5 4 Spectrum. (The second f i g u r e a f t e r each d e c i m a l i n column one i s p h y s i c a l l y i n s i g n i f i c a n t . ) '-•59-. ,. • t h a t t h e f i r s t two peaks f i t p e r f e c t l y i n t o t h e decay scheme i n C h a p t e r 7. The o t h e r s s t i l l cannot be f i t t e d t o t h e known l e v e l s . Among the v e r y weak peaks, 4 4 4 . 0 2 Kev i s shown d i s t i n c t l y i n f i g u r e 8 , § 5 . The o t h e r s were p l o t t e d a g a i n i n an e n l a r g e d s c a l e as shown i n \ f i g u r e . - j l 2 . They .are a l l w e l l above t h e s t a t i s t i c a l f l u c t u a t i o n . I t was noted i n t a b l e I I I t h a t a few Eu 152 peaks were p r e s e n t due t o a s m a l l p e r c e n t a g e of t h i s I m p u r i t y . Comparison 4 9 ) o f t h e i r i n t e n s i t i e s w i t h t h o s e g i v e n i n N u c l e a r Data Sheets i s shown i n table'.'IV. They agree f a i r l y w e l l . We a l s o expected a s m a l l i m p u r i t y m i x i n g i n t h e peaks 1 2 2 . 9 3 Kev and 247.63 Kev due t o t h e 1 2 1 . 8 Kev and' 2 4 4 . 7 Kev peaks of Eu 1 5 2 . The c o n t r i b u t i o n t o t h e i n t e n s i t y by t h i s i m p u r i t y i n each peak has a l r e a d y been s u b t r a c t e d . T h i s was done by u s i n g i n t e r n a l c o n v e r s i o n d a t a c a l c u l a t e d i n C hapter 6 ( s i n c e t h e 1 2 1 . 8 K-1 peak of Eu 152 was s e p a r a b l e from t h e 1 2 2 . 9 3 K: peak i n t h e b e t a s p e c t r u m ) . -60- X C O % I ax 40 557.96 Kev 582.11 Kev A \ \ 3X0 "33* W> Channel Number 486 Channel Number I7S 170 i«4 (60 CN IS5 CO O o 150 145 /40 5 * 8 903.6 Kev 892.74 Kev \ 538 548 Channel Number P i g . 12 Weak gamma peaks i n t h e Eu ^ s p e c t r u m (see f i g Gamma-energy (Kev) R e l . I n t e n s i t y o b t a i n e d R e l . I n t e n s i t y from r e f . 4 9 3+3 .63 3 . 7 6 ± 0 . 2 9 ( 2 9 $ ) 24$ 9 6 4 . 0 9 '. - I . 8 2 i 0 . 2 5 (14$) . 14$ 1 0 8 5 . 4 7 1 . 6 7 ± 0 . 2 2 ( 1 3 $ ) 1 1 $ I I I I . 9 8 2 . 4 0 i 0 . 2 4 ( 1 8 $ ) ; 1 5$ . • 1 4 0 8 . 1 6 3 . 2 9 * 0 . 2 0 ( 2 6 $ ) 2 5 $ T a b l e . I V . Gamma peaks b e l o n g i n g t o Eu 152 i m p u r i t y . -62- CHAPTER V GAMMA-GAMMA COINCIDENCE SPECTROSCOPY § 1 . G e n e r a l C o n s i d e r a t i o n s . The r e s u l t s from t h e l a s t c h a p t e r p r o v i d e many i n t e r e s t - i n g a s p e c t s w h i c h r e q u i r e f u r t h e r i n v e s t i g a t i o n . They can be s t a t e d as f o l l o w s , 1) The 9 9 5 . 9 4 Kev and 1004.50 Kev peaks w h i c h have never been s e p a r a t e d by p r e v i o u s w o r k e r s a re w e l l r e s o l v e d . T h e r e f o r e , i f gamma-gamma c o i n c i d e n c e s h o u l d be performed a g a i n , we expect t o get c o n c l u s i v e r e s u l t s r e g a r d i n g t h e p r o p e r l o c a t i o n s o f t h e s e two t r a n s i t i o n s I n t h e decay scheme. 2) New peaks such as 9 0 3 . 6 0 Kev and 5 8 2 . 1 1 Kev were f o u n d , w h i c h , as w i l l be shown l a t e r , have s u i t a b l e p l a c e s i n t he decay scheme. But t h e y need t o be c o n f i r m e d . 3) New peaks such as 1246 . 1 6 Kev, 1 4 6 0 . 8 8 Kev and 1493-68 Kev were fou n d , but t h e i r o r i g i n s a r e unknown. 4) Weak peaks such as 8 7 2 . 6 2 Kev, 815.02 Kev and 444.02 Kev w h i c h have been r e p o r t e d from b e t a s p e c t r o s c o p i c measurements ( e . g . r e f s . 20 and 3 6 ) , h a v e a l s o been seen i n t h i s gamma spectrum. T h e i r p o s i t i o n s i n t h e decay scheme need t o be c o n f i r m e d . A l l t h e above p o i n t s can be examined by gamma-gamma c o i n c i d e n c e at l e a s t i n p r i n c i p l e . However, i n p r a c t i c e . . . -63- •. one r e q u i r e s much s o p h i s t i c a t i o n i n t h e d e t e c t i o n and e l e c t r o n i c systems such as an i n c r e a s e i n t h e a c t i v e volume o f t h e Germanium d e t e c t o r s , t h e use of m u l t i p a r a m e t e r k i c k s o r t e r s e t c . I n view o f t h e time consumption I n d o i n g gamma-gamma c o i n c i d e n c e work and t h e present equipment a v a i l a b l e , we have f o r t h e t i m e b e i n g l i m i t e d our c o i n c i d e n c e e x p e r i m e n t s t o the f i r s t o f t h e above f o u r p o i n t s . R e s u l t s o b t a i n e d a r e q u i t e c o n c l u s i v e . The experiment s w i l l , be d e s c r i b e d i n t h e next s e c t i o n s . The i d e a o f gamma-gamma c o i n c i d e n c e i s s i m p l e and s t r a i g h t - f o r w a r d . Suppose t h e r e a r e two gamma t r a n s i t i o n s i n cascade as shown i n f i g u r e 13a, and t h e d i r e c t i o n s of ^ c F i g u r e 13. e m i s s i o n o f t h e s e gammas are r e l a t e d by t h e a n g l e 6 as i n f i g u r e 13b. Now i f . w e p l a c e two c o u n t e r s o r d e t e c t o r s at t h e p o s i t i o n s R and S r e s p e c t i v e l y , t h e two gammas w i l l be re c o r d e d e i t h e r s i m u l t a n e o u s l y o r i n a s m a l l f i x e d I n t e r v a l , of t i m e . However, t h e most p r o b a b l e a n g l e o f 0 v a r i e s .. w i t h d i f f e r e n t p a i r s ^ and <(t , so t h a t t h e p o s i t i o n of S : r e l a t i v e t o R has t o be determined i n o r d e r t o g a t h e r a"' maximum number of p a i r s i n a g i v e n p e r i o d o f t i m e . I f t h e two gammas were u n c o r r e l a t e d , t h e n any p o s i t i o n o f t h e c o u n t e r S -64- r e l a t i v e t o R w i l l g i v e e q u a l p r o b a b i l i t y i n c o u n t i n g the p a i r s . In the c o r r e l a t e d c a s e , the p r o b a b i l i t y i s g i v e n by where A 2 n a r e c o n s t a n t c o e f f i c i e n t s , and. P 2 n ( c o s 9) are the Legendre p o l y n o m i a l s , g i v e n e x p l i c i t l y by P 0 ( c o s 0) = 1 P 2 ( c o s 0) = i-(3cps. 2e' - .1) P^(cos Q) = (35cos-^e - 30cos29- + 3)/8 e t c . T h e o r e t i c a l e v a l u a t i o n o f the t r u e c o u n t i n g r a t e s i s n o t a problem i n t h i s i n v e s t i g a t i o n , because no v a r i a t i o n o f the c o r r e l a t i o n a n g l e 9 i s i n v o l v e d i n the e x p e r i m e n t , and i n any c a s e , the r e s u l t s t h a t w i l l be p r e s e n t e d l a t e r a re so unambiguous t h a t r e l i a n c e upon a t h e o r e t i c a l a n a l y s i s i s ^ e n t i r e l y u n n e c e s s a r y . 2. The C o i n c i d e n c e System. The e x p e r i m e n t a l arrangements are shown i n f i g u r e 14. The source was p l a c e d between a Germanium-Lithium d e t e c t o r and a l X l i - i n . d i a m e t e r N a l ( T l ) s c i n t i l l a t o r . The 1.5 cc. Ge d e t e c t o r was used i n t h i s c a s e . ( I t would have been p r e f e r a b l e t o use the 5 cc d e t e c t o r , e x c e p t t h a t i t . was b e i n g used i n o t h e r N n=0 (87) -65- L i q u i d N i t r o g e n Ge D e t e c t o r - •Ion Pump ^rTrv- N a l P h oto- M u l t i p l i e r Low-noise Preamp. Time Co n s t a n t Box v Source- F a s t Preamp F a s t D i s c r i m - i n a t o r F a s t D i s c r i m - i n a t o r A B V a r i a b l e D e l a y s & F a s t C o i n . U n i t Low-Noise A m p l i f i e r F a s t L i n e a r A m p l i f i e r D e l a y S . C . A a 1. Slow C o i n . U n i t K i c k S o r t e r Gate input? (. P u l s e Shaper S c a l e r F i g . 14'. The gamma-gamma c o i n c i d e n c e system, • -66- e x p e r i m e n t s . ) As u s u a l , t h e s c i n t i l l a t o r was i n photo c o n t a c t w i t h a p h o t o m u l t i p l i e r (RCA 5 8 1 9 ) which.was b i a s e d a t a v o l t a g e o f - 1 1 0 0 v o l t s . Outputs from t h e p h o t o m u l t i p l i e r were o b t a i n e d from t h e anode and t h e eighth•dynode as shown i n f i g u r e 1 5 . The r e a s o n s f o r u s i n g t h e e i g h t h dynode i n s t e a d o f t h e l a s t dynode a r e t o have t h e output p u l s e h e i g h t comparable t o t h e c o r r e s p o n d i n g one from t h e anode output and t o a c h i e v e b e t t e r l i n e a r t y . The n e g a t i v e output from the. anode was used f o r t h e purpose o f f a s t c o i n c i d e n c e . I t was connected t o a cascade e m i t t e r f o l l o w e r i n o r d e r t o a c q u i r e enough power t o d r i v e t h e f a s t d i s c r i m i n a t o r i n t h e f o l l o w i n g s t a g e . T h i s e m i t t e r f o l l o w e r does not need good l i n e a r t y , a l l t h a t was demanded of i t was a f a s t r i s e t i m e ( - ^50 nsec.) and a low impedance o u t p u t . The p o s i t i v e o u t p u t from t h e e i g h t h dynode was f e d t o a w h i t e cathode f o l l o w e r , w h i c h has a l i n e a r i t y b e t t e r than' 1%. W i t h t h e g i v e n i n p u t R C - c o u p l i n g , t h e r i s e t i m e and decay time were found t o be 0.2jK-sec. and 30 psec . r e s p e c t i v e l y . T h i s c i r c u i t a c c e p t s b o t h p o s i t i v e and n e g a t i v e p u l s e s e q u a l l y w e l l , and hence any o v e r s h o o t w i l l not cause cut o f f or o t h e r d i s t o r t i o n at t h e o u t p u t . The o u t p u t p u l s e s were t h e n a m p l i f i e d by a f a s t l i n e a r a m p l i f i e r w i t h d o u b l e - d e l a y - l i n e c l i p p i n g . These p u l s e s were c l i p p e d t o 1 j^sec. i n w i d t h and were t h e n f e d t o an anti-walk s i n g l e c h a n n e l a n a l y s e r .(S .C .A:.) / w h i c h -67- s e l e c t s t h e p u l s e s c o r r e s p o n d i n g t o t h e d e s i r e d energy i n t h e spectrum t a k e n by t h e s c i n t i l l a t o r . The f a s t d i s c r i m i n a t o r connected t o t h e cascade e m i t t e r f o l l o w e r o u t p u t i s shown i n f i g u r e 16. The n e g a t i v e i n p u t p u l s e was a m p l i f i e d by t h e f i r s t two t r a n s i s t o r s t a g e s . The d i s c r i m i n a t i o n , i s c o n t r o l l e d b y ' t h e 2.5 K i l p o t e n t i o m e t e r . The r e s u l t a n t c u r r e n t t r i g g e r e d t h e t u n n e l d i o d e ( lN37l6).and brought about a square p u l s e o f r i s e t i m e l e s s t h a n 10 n s e c . The low impedance output was t h e n o b t a i n e d from t h e two e m i t t e r f o l l o w e r s i n s e r i e s . The Zenor d i o d e 1N752A was used t o l i m i t t h e p u l s e h e i g h t i n o r d e r t o match t h e i n p u t r e q u i r e m e n t of t h e f a s t c o i n c i d e n c e u n i t . The l o w - n o i s e p r e a m p l i f i e r a t t a c h e d t o t h e Germanium d e t e c t o r assembly i s t h e same as t h a t d e s c r i b e d , i n Ch a p t e r 4. The p u l s e s f o r f a s t c o i n c i d e n c e on the d e t e c t o r s i d e were o b t a i n e d d i r e c t l y from t h e p r e a m p l i f i e r o utput b e f o r e b e i n g shaped by t h e t i m e c o n s t a n t box. These p u l s e s b e i n g p o s i t i v e , an i n v e r t e r s tage was i n s t a l l e d a t the i n p u t o f t h e f o l l o w i n g f a s t d i s c r i m i n a t o r . The shaped p u l s e s from t h e t i m e c o n s t a n t box were f e d t o a 128-channel k i c k s o r t e r v i a a l o w - n o i s e a m p l i f i e r . The r e s t o f t h e u n i t s i n f i g u r e 14 c o n s t i t u t e a f a s t - , slow c o i n c i d e n c e system, w h i c h chooses the gat e pulses, f o r t h e k i c k s o r t e r . .. ''. +24v +12v Ov P i g . 16 The t u n n e l d i o d e d i s c r i m i n a t o r . §3. E x p e r i m e n t a l p r o c e d u r e s . A s o u r c e o f Eu 154 w i t h s u i t a b l e s t r e n g t h was s e l e c t e d from among t h o s e p r e p a r e d e a r l i e r , and mounted on a l u c i t e s u p p o r t . The d i s t a n c e s o f t h e sour c e from t h e Germanium d e t e c t o r and t h e s c i n t i l l a t o r were chosen by t a k i n g t h e s i n g l e count r a t e s from t h e d e t e c t o r and t h e s c i n t i l l a t o r r e s p e c t i v e l y . W i t h t h e sour c e c l o s e t o t h e alu m i n i u m window o f t h e d e t e c t o r assembly and a t a d i s t a n c e o f 5 cm. from t h e s c i n t i l l a t o r , t h e s i n g l e count r a t e s from t h e d e t e c t o r and t h e s c i n t i l l a t o r were 0.7 x 10^ cpm and 1.1 x 10^ cpm r e s p e c t i v e l y . These count r a t e s were about t h e maximum t h e system can t o l e r a t e . H i g h e r t h a n t h e s e would r e s u l t i n poor r e s o l u t i o n on b o t h s i d e s . The p o t e n t i o m e t e r o f each f a s t d i s c r i m i n a t o r was a d j u s t e d t o e l i m i n a t e most of t h e base l i n e f l u c t u a t i o n s w i t h t h e h e l p of an o s c i l l o s c o p e . The c o i n c i d e n c e p u l s e w i d t h o f t h e f a s t c o i n c i d e n c e u n i t was s e t a t 50 n s e c . W i t h c h a n n e l 2 i n p u t o f t h e slow c o i n c i d e n c e u n i t s w i t c h o f f , t h e d e l a y s i n the f a s t c o i n c i d e n c e u n i t were v a r i e d u n t i l a maximum c o u n t i n g r a t e was o b t a i n e d i n t h e s c a l e r . Then t h e c h a n n e l 2 i n p u t was s w i t c h e d on a g a i n , w h i l e t h e c h a n n e l A i n p u t o f t h e f a s t c o i n c i d e n c e u n i t was s w i t c h e d o f f . A l s o t h e output o f the f a s t l i n e a r a m p l i f i e r was connected t o . t h e k i c k s o r t e r , i n p u t . i n p l a c e o f t h e l o w - n o i s e a m p l i f i e r . W ith t h i s arrangement, t h e r e q u i r e d energy peak from the s c i n t i l l a t o r t o be used as t h e k i c k s o r t e r g a t e c o n t r o l ( h e r e a f t e r r e f e r r e d as t h e g a t e peak) c o u l d be l o c a t e d . T h i s was done by v a r y i n g t h e base l i n e ( f r o m z e r o up) o f t h e S.C.A. and a t t h e same ti m e w a t c h i n g t h e d i s p l a y i n t h e k i c k s o r t e r , u n t i l t h e d e s i r e d peak p o s i t i o n i s r e a c h e d . Then t h e window o f S.C.A. was narrowed down t o about 20 Kev i n r w i d t h and t h e base l i n e was a g a i n a d j u s t e d t o a c q u i r e t h e peak p o s i t i o n and t o o b t a i n maximum s c a l e r c o u n t s . F i n a l l y , t h e c o n n e c t i o n s were r e s t o r e d t o t h a t shown i n f i g u r e 14 and t h e experiment was s e t g o i n g . The system was a l l o w e d t o r u n . f o r 24 hours a day, and a l l t o g e t h e r f o u r r u n s were done c o r r e s p o n d i n g t o d i f f e r e n t g a t e s e t t i n g s . The t o t a l t i m e t a k e n was a p p r o x i m a t e l y 300 h o u r s . I t was checked once i n a w h i l e f o r any t i m e s h i f t by c o u n t i n g t h e f a s t c o i n c i d e n c e output and t h e S.C.A. output, and by p r i n t i n g out t h e k i c k s o r t e r d a t a . I f t i m e s h i f t t o o k p l a c e , t h e v a r i a b l e d e l a y s i n the f a s t c o i n c i d e n c e u n i t o r t h e base l i n e o f S.C.A. would have t o be a d j u s t e d . However, t h e a m p l i f i c a t i o n s , b i a s v o l t a g e s and t h e k i c k s o r t e r t h r e s h o l d , never were a l t e r e d t h r o u g h o u t t h e f o u r r u n s , $4. R e s u l t s . R e s u l t s o f t h e f o u r r u n s a r e shown i n t h e f i g u r e s 17a,b,c,d. F i g u r e 17a used 722.90 Kev peak as t h e g a t e peak, and t h e spectrum*, shows c l e a r l y t h a t 872.62 Kev and 995.94 Kev were i n c o i n c i d e n c e w i t h 722.90 Kev. The t i m e f o r t h i s r u n was 77 h r s . 26 mins. When t h e gate s e t t i n g was brought down t o t h e base o f the 722.90 Kev peak on t h e lower energy s i d e , we got t h e spectrum .shown i n f i g u r e 17b i n 6 l h r s . 33 mins. T h i s background spectrum was composed of. t h e a c c i d e n t a l c o u n t s p l u s t h e counts i n c o i n c i d e n c e w i t h t h e Compton e v e n t s . S i m i l a r l y , t h e spectrum i n f i g u r e 17c c o r r e s p o n d s t o th e gate peak o f 591-61 Kev r u n f o r 85 h r s . 2 mins., and t h a t i n f i g u r e 17d c o r r e s p o n d s t o i t s background spectrum r u n f o r 67 h r s . 37 mins. I t l e a v e s no doubt t h a t t h e 1004.50 Kev peak i n t h e spectrum i s i n c o i n c i d e n c e w i t h t h e 591.61 Kev peak. 872.62 Kev 995.94 Kev ( a) gat e peak 722,90Kev <i 26 36 *6 56 66 76 g6 96 4 00 F i g . 17. The gamma- gamma coincidence s p e c t r a (see t e x t ) . w >6 *6 J6 +S S6 i6 76 41 Hi 1004.50 Kev (c) gate peak 591-6lKev i£ »S 35 +6 S£ 66 76 %6 l£ •(a) ii >-6 36 +6 S6 66 76 86 f£~ Channel Number CHAPTER V I THE BETA SPECTROSCOPY £l. G e n e r a l C o n s i d e r a t i o n s The t h e o r y 1 p r e s e n t e d i n Ch a p t e r 2 d i d not i n c l u d e b e t a t r a n s i t i o n s . The r e a s o n s f o r t h i s a r e t w o - f o l d . F i r s t l y , t h e measurements made w i t h t h e be t a s p e c t r o m e t e r g i v e i n f o r m a t i o n onoboth t h e p r i m a r y b e t a r a d i a t i o n s between p a r e n t and daughter n u c l e i and t h e I n t e r n a l c o n v e r s i o n e l e c t r o n s . We a r e m a i n l y concerned w i t h t h e i n t e r n a l c o n v e r s i o n e l e c t r o n peaks. E v a l u a t i o n o f t h e e n e r g i e s and i n t e n s i t i e s from t h e b e t a continuum a r e o n l y f o r t h e purpose o f e s t a b l i s h i n g t h e decay scheme and as a check upon t h e t r a n s i t i o n i n t e n s i t i e s . No attempt has been made t o de t e r m i n e t h e t r a n s i t i o n m a t r i x elements i n t h e be t a decay, s i n c e t h i s r e q u i r e s d i r e c t i o n a l c o r r e l a t i o n work as. w e l l . S e c o n d l y , t h e be t a t r a n s i t i o n s i n t h i s case a re from an odd-odd n u c l e u s (Eu 154) t o an even- even n u c l e u s , w h i l e t h e gamma t r a n s i t i o n s d i s c u s s e d i n Ch a p t e r 2 u s i n g t h e Asymmetric R o t a t o r Model are concerned w i t h an even-even n u c l e u s o n l y (Gd 154).. The two cases a re not t h e same. I n t h i s s e c t i o n , we w i l l o u t l i n e some o f t h e f e a t u r e s of t h e b e t a t r a n s i t i o n s o f an odd-odd p a r e n t n u c l e u s and th e n . - 7 5 - pass t o t h e d i s c u s s i o n of t h e i n t e r n a l c o n v e r s i o n p r o c e s s . S i n c e Eu 154 i s a l s o a deformed body, t h e s e l e c t i o n r u l e s g i v e n i n Ch a p t e r 4,£l a l s o a p p l y . I n a d d i t i o n , we have t o t a k e i n t o account an odd p r o t o n and an odd n e u t r o n . Because o f t h i s , t h e N i l s s o n Model f o r i n d i v i d u a l n u c l e o n s i n s t r o n g l y \ 5 1 ) deformed n u c l e i i s r e q u i r e d . I n t h i s model, N i l s s o n c o n s i d e r s t h e H a m i l t o n i a n f o r a s i n g l e n u c l e o n i n a deformed n u c l e u s t o be H = H Q + Cl . s + D l 2 (88) where T / 2 / M 2 t H = - ^ r r /\ + ~(ao X + co .Y + GO Z ) (89) no 2M 2 V x T y T z' 7 v J i s t h e o s c i l l a t o r H a m i l t o n i a n , and t h e o t h e r two terms a r e the s p i n - o r b i t and o r b i t - o r b i t c o u p l i n g t e r m s . As a crude a p p r o x i m a t i o n , c o n s i d e r t h e def o r m a t i o n , t o be a x i a l l y symmetric, i . e . u . - u ; = u (1 + kt) x' y T oK 2 J (90) co = co (1- 2£/3) z' o where £ i s a d e f o r m a t i o n p a r ameter. The. v a r i a b l e s a re t h e n changed t o (X",Y",Z") = (X' Mco T Mco . I t f o l l o w s t h a t H = H „ + H „ + H ' (91) o x" y" z" K J W h 6 r e . H x„ = i t f « v ( - J ^ •+ X " 2 ) , e t c . (91a) Hence H i s d i a g o n a l i n t h e r e p r e s e n t a t i o n , !n.>|nA|n^\ o I V \ 2'\ 3 ' such t h a t H x ?,|n L)= ( n 1 + i ) K c o x t ,etc. (92) •'• -76- C o n s e q u e n t l y H q |n]>|n2>|n3> = E q |n]>|n2>|n3> . (93) W i t h E q = ( n 3 > !)tfco z, + ( n L + n 2 + 1 ) ^ , (94a) D e f i n e N = n L + n 2 + n 3 , n L + n 2 , n z, T=n 3 and from (90) E Q = fa ((N+3/2) + £ ( n x - 2nz„) /3)] (94b) T h i s s o l u t i o n i s known as t h e a s y m p t o t i c s o l u t i o n i n t h e l i m i t o f s t r o n g d e f o r m a t i o n , and i t i s ob v i o u s t h a t t h e energy l e v e l s r e l y on t h e quantum numbers N,nj_, and n z, t f o r a g i v e n deform- a t i o n parameter £ . Now l e t A be t h e z"-component o f t h e o r b i t a l quantum number, t h e n A = nj_,n x-2, ... ,-nL+2,-n_t (9 5) Thus f o r an odd-A n u c l e u s , we expect t h a t some s e l e c t i o n r u l e s on t h e quantum numbers N , A and would appear. T h i s i s Indeed t h e case,' and t h e s e l e c t i o n r u l e s were t a b u l a t e d by Al a g a f o r t h e m a t r i x elements o f t e n used i n c a l c u l a t i n g t h e f S - t r a n s i t i o n p r o b a b i l i t i e s as shown i n r e f e r e n c e 52. F o r an odd-odd n u c l e u s , t h e s e l e c t i o n r u l e s mentioned a p p l y t o b o t h t h e odd p r o t o n and odd n e u t r o n . I n a d d i t i o n , the. c o u p l i n g r e l a t i o n s between t h e s e two odd n u c l e o n s i n t h e i n i t i a l and. f i n a l s t a t e s would a l s o g i v e r i s e t o new s e l e c t i o n ,53) r u l e s . The d e t a i l s were g i v e n by G a l l a g h e r However, i f one compares t h e reduced t r a n s i t i o n p r o b a b i l i t i e s o f t w o - t r a n s i t i o n s from the same i n i t i a l s t a t e t o d i f f e r e n t members of a r o t a t i o n a l f a m i l y , t h e n t h e . I n t r i n s i c ,wave f u n c t i o n s o f t h e odd n u c l e a n s a re c a n c e l l e d , out i n t h e r a t i o shown below, and hence t h e s e l e c t i o n r u l e s i n v o l v i n g N, A, and nx do not e n t e r . Thus ( r e f . 5 4 ) , B C L . I ^ I f ) B ( L , I 1 - > I f , j C C l i L I f . ; % , % - % , % ) C ( I L I f ,;K.,K f ,-K.,Kf ,).. 2 (96) T h i s e q u a t i o n i s f o r a x i a l l y symmetric n u c l e i . F o r t h e asymmetric c a s e , m i x t u r e s o f K terms s h o u l d be i n c l u d e d , i . e . B i L j I t ^ I f . ) • | . A K m C ( l 1 L I f m ; K 1 , V K . , K m ) ] 2, A K n C d i L I f n j K ! , ^ -K t,K n ) J I t i s .well-known t h a t t h e energy E 0 o f each b e t a t r a n s i t i o n i s shared between t h e e m i t t e d e l e c t r o n and n e u t r i n o i n a l l p o s s i b l e ways. As a r e s u l t , t h e b e t a spectrum f o r a s i n g l e b e t a t r a n s i t i o n i s a continuum w i t h a d e f i n i t e shape and an energy ra n g e , 0 — E . F o r more t h a n one t r a n s i t i o n , t h e spectrum i s a s u p e r p o s i t i o n o f a l l t h e c o n t i n u a . E x p e r i m e n t a l d e t e r m i n a t i o n o f E 0 i s u s u a l l y done by t h e method o f K u r i e p l o t ( c . f . r e f . 5 5 ) • From t h e K u r i e p l o t , t h e component c o n t i n u a can a l s o be r e s o l v e d . Hence t h e t r a n s i t i o n i n t e n s i t i e s can be found, ^ 2 . The I n t e r n a l C o n v e r s i o n and P a i r P r o d u c t i o n . I n C h a p t e r 3, we have d i s c u s s e d t h e p r o c e s s e s o f de- e x c i t a t i o n , w h i c h i n c l u d e i n t e r n a l c o n v e r s i o n and i n t e r n a l p a i r p r o d u c t i o n . The i n t e r n a l c o n v e r s i o n p r o c e s s i n v o l v e s t h e t r a n s f e r o f energy from t h e n u c l e u s t o an e x t r a n u c l e a r e l e c t r o n by d i r e c t i n t e r a c t i o n between t h e n u c l e a r charge and t h e e l e c t r o m a g n e t i c f i e l d o f t h e e l e c t r o n (Coulomb i n t e r a c t i o n ) . -78- \; : 56) . . T h i s was shown by T a y l o r and Mott by c a l c u l a t i o n , t h a t t h e p r o b a b i l i t y f o r i n t e r n a l c o n v e r s i o n b y a p h o t o e l e c t r i c e f f e c t ( i . e . by e m i s s i o n and a b s o r p t i o n o f a photon) i s v e r y s m a l l compared t o t h e p r o b a b i l i t y f o r i n t e r n a l c o n v e r s i o n by d i r e c t energy t r a n s f e r . I t can a l s o be v i s u a l i z e d from t h e pr e s e n c e " • A o f e EO t r a n s i t i o n s i n t h e c o n v e r s i o n spectrum, as i n t h i s case t h e r e i s no gamma c o u n t e r p a r t . C o n s e q u e n t l y , we may con c l u d e t h a t d i r e c t gamma e m i s s i o n and i n t e r n a l c o n v e r s i o n a r e two independent p r o c e s s e s o f d e - e x c i t a t i o n . The energy c a r r i e d by t h e e m i t t e d e l e c t r o n i n i n t e r n a l c o n v e r s i o n i s r e l a t e d t o the : d e - e x c i t a t i o n energy, W by E e = ¥ - B x (98) where B^ i s t h e e l e c t r o n b i n d i n g energy f o r o r b i t X from w h i c h t h e e l e c t r o n was e j e c t e d . S i n c e i s d i f f e r e n t f o r d i f f e r e n t X, t h e r e i s more t h a n one v a l u e o f E e f o r a g i v e n ¥. T h e r e f o r e , t h e c o n v e r s i o n peaks i n an energy spectrum c o r r e s p o n d i n g t o one ¥ a r e c l a s s i f i e d i n t o X = K,L,M,N,-etc. A l s o s i n c e each of the L,M,N, e t c has more t h a n one e l e c t r o n o r b i t , X may be r e d e f i n e d as X = K,L1,L2,L3,M1, e t c . The r a t i o o f t h e e m i s s i o n r a t e o f t h e c o n v e r s i o n e l e c t r o n s t o t h a t of th e gamma photons i n a. g i v e n energy t r a n s i t i o n i s c a l l e d t h e i n t e r n a l c o n v e r s i o n c o e f f i c i e n t d. , which may be expanded i n terms o f X's as below o( . 4 K + c< L 1 + . * i 2 + 4 L 3 + * M 1 + - ' ' (99) / -79- A l s o , s i n c e t h e t r a n s i t i o n s depend on t h e a n g u l a r momentum L c a r r i e d away and t h e change o f p a r i t y T T , o< can be exp r e s s e d as a l i n e a r c o m b i n a t i o n o f t h e terms a r i s i n g from d i f f e r e n t e l e c t r i c m u l t i p o l e s EL and magnetic m u l t i p o l e s ML as shown, . * s 2sfa)24 x(L) + 2 $2(L)]L ( 3 X ( L ) (100) where c< x(L)and ^ X ( L ) a r e t h e c o n v e r s i o n c o e f f i c i e n t s r e f e r r e d t o EL and ML r e s p e c t i v e l y , and t h e £ 's are t h e r e l a t i v e c o n t r i b u t i o n s c o r r e s p o n d i n g t o t h e r e s p e c t i v e EL's and ML's. • The c o e f f i c i e n t s # v ( L ) and/S v(L) , w h i c h a r e f u n c t i o n s A I X 57) of energy, were c a l c u l a t e d and t a b u l a t e d by Rose , and S l i v 58) • et a l f o r t h e f i r s t few v a l u e s o f X and L. Rose's c a l c u l a t i o n was based on t h e a s s u m p t i o n o f a p o i n t n u c l e u s t a k i n g i n t o account t h e e f f e c t o f s c r e e n i n g by t h e atomic e l e c t r o n c l o u d , w h i l e i n t h e case o f S l i v et a l , a f i n i t e - s i z e d n u c l e u s w i t h m o d i f i c a t i o n s on t h e i n i t i a l and f i n a l e l e c t r o n wave f u n c t i o n s were adopted. Thus t h e second c a l c u l a t i o n i n c l u d e d t h e p e n e t r a t i o n e f f e c t ( t h a t i s t h e i n t e r a c t i o n when t h e e l e c t r o n i s i n s i d e t h e charge d i s t r i b u t i o n of t h e n u c l e u s ) , and was \ c o n s i d e r e d t o be more a c c u r a t e . I n g e n e r a l , i t agrees w i t h e x p e r i m e n t a l data t o w i t h i n a few per c e n t . E x p e r i m e n t a l e v a l u a t i o n o f i n t e r n a l c o n v e r s i o n c o e f f - ' - . . . 59) c i e n t s can be done i n s e v e r a l ways . I n . t h e p r e s e n t .work, we used t h e s o - c a l l e d n o r m a l i z e d peak t o gamma'method . From • ' - 8 o - t h e gamma s i n g l e spectrum and thejSspectrum, a s u i t a b l e gamma- peak ( e . g . 122.93 Kev) and a c o r r e s p o n d i n g b e t a c o n v e r s i o n peak were chosen as s t a n d a r d s . L e t ( l y . ) t and ( l e x ) ' s t b e t h e i r r e s p e c t i v e r e l a t i v e i n t e n s i t i e s and (°fx^st ^ e ^ e c o n v e r s i ° n c o e f f i c i e n t . U s i n g t h e t a b l e s ' o f t h e o r e t i c a l v a l u e s of oLx , (^x^st c ^ n ^ e o b t a i n e d by i n t e r p o l a t i o n . Then t h e e x p e r i m e n t a l i n t e r n a l c o n v e r s i o n c o e f f i c i e n t f o r any o t h e r t r a n s i t i o n may be c a l c u l a t e d f r om > I e X ' ^ r ^ s t . , . ' , . where I and l y a r e the : r e l a t i v e i n t e n s i t i e s of t h e p a i r . eX ' i A f t e r a K - o r b i t e l e c t r o n i s i n t e r n a l l y c o n v e r t e d , t h e unoccupied o r b i t must be f i l l e d up e v e n t u a l l y . T h i s i s done by d r o p p i n g a n o t h e r e l e c t r o n f r om a f r e e o r bound s t a t e down t o the K - o r b i t . The r a d i a t i o n t h u s r e l e a s e d i s c a l l e d t h e K x - r a y . T h e r e f o r e , a knowledge of t h e K x - r a y i n t e n s i t y t o g e t h e r w i t h t h e g a m m a . i n t e n s i t y o f f e r s a method o f a b s o l u t e d e t e r m i n a t i o n - 32) o f t h e i n t e r n a l c o n v e r s i o n c o e f f i c i e n t s . However, not a l l K - s h e l l v a c a n c i e s a r e f i l l e d by e m i s s i o n o f K x - r a y s . A s m a l l f r a c t i o n o f t h e eve n t s goes t h r o u g h a d i f f e r e n t c h a n n e l . The energy r e l e a s e d , i n s t e a d o f i n t h e form o f a K x-photon, may be used t o e j e c t a n o t h e r e l e c t r o n from a h i g h e r o r b i t , t h u s e m i t t i n g a s o - c a l l e d Auger e l e c t r o n . The f r a c t i o n o f t h e eve n t s - 8 1 - g o i n g t h r o u g h t h e x - r a y c h a n n e l (known as t h e f l u o r e s c e n t y i e l d ) I s a c o n s t a n t f o r a g i v e n atom and can be e v a l u a t e d . There a r e , o f c o u r s e , o t h e r x - r a y s , L,M,N, e t c . , but t h e y a r e much, l o w e r i n energy and i n t e n s i t y . I n C h a p t e r 4, we have d e s c r i b e d p a i r p r o d u c t i o n i n a d e t e c t o r . The p r o c e s s o f i n t e r n a l p a i r p r o d u c t i o n f o l l o w s t h e same p r i n c i p l e as t h e p r o c e s s o f i n t e r n a l c o n v e r s i o n . The b a s i c d i f f e r e n c e i s t h a t i n t h e second c a s e , t h e n u c l e a r energy i s t r a n s f e r r e d d i r e c t l y t o a bound atomic e l e c t r o n , w h i l e i n th e f i r s t . p r o c e s s , t h e energy i s t r a n s f e r r e d t o an e l e c t r o n i n a ' n e g a t i v e energy' s t a t e . However, s i m i l a r t o t h e i n t e r n a l . c o n v e r s i o n c o e f f i c i e n t s , t h e e m i s s i o n r a t e o f t h e i n t e r n a l p a i r p r o d u c t i o n i s a l s o e x p r e s s e d i n r a t i o w i t h t h a t o f t h e gamma photons, and i s known as t h e p a i r p r o d u c t i o n c o e f f i c i e n t s , T(L) . P o r t r a n s i t i o n e n e r g i e s e x c e e d i n g s e v e r a l Mev, t h i s p r o c e s s s h o u l d be t a k e n i n t o a c c o u n t . However, t h e t r a n s i t i o n e n e r g i e s i n t h e p r e s e n t i n v e s t i g a t i o n a r e a l l below 2 Mev, and 60 ) t h e c o r r e s p o n d i n g T ( L ) a r e l e s s t h a n 5 x 1 0 - ^ . Hence, t h e y are w i t h i n t h e e x p e r i m e n t a l e r r o r and can be n e g l e c t e d . F o r ' an energy l e s s t h a n 1 . 022 Mev, such p r o c e s s e s cannot even o c c u r . •;:.- . £3 . The B e t a S p e c t r o m e t e r . An i n t e r m e d i a t e image b e t a s p e c t r o m e t e r ( a l s o known as a d o u b l e - l e n s s p e c t r o m e t e r ) was used i n t h e p r e s e n t work. As shown i n f i g u r e 18/ i t c o n s i s t s o f two w a t e r - c o o l e d magnetic l e n s e s , a c y l i n d r i c a l vacuum chamber, b a f f l e s A,B,C, and e x t e r n a l l y a d j u s t a b l e h o l d e r s f o r t h e s o u r c e and t h e d e t e c t o r . The magnetic l e n s e s , as t h e name i m p l i e s , f o c u s t h e b e t a p a r t i c l e s w i t h an a p p r o p r i a t e momentum from t h e source onto t h e d e t e c t o r . The a p p r o p r i a t e momentum r e f e r r e d t o i s d i r e c t l y p r o p o r t i o n a l t o the. magnetic f i e l d s t r e n g t h i n t h e vacuum chamber, w h i c h i s i n t u r n p r o p o r t i o n a l t o t h e c u r r e n t i n t h e l e n s e s . The c u r r e n t was s u p p l i e d by a 150 v o l t d.c. g e n e r a t o r and c o n t r o l l e d by a c u r r e n t r e g u l a t o r . The l a t t e r c o n s i s t s o f two t r a y s of 6AS7 t r i o d e s , a s t a n d a r d r e s i s t o r o f low t e m p e r a t u r e c o e f f i c i e n t and a f e e d b a c k b i a s c o n t r o l . system ( f i g u r e 19) w i t h a h i g h p r e c i s i o n p o t e n t i o m e t e r f o r v a r y i n g t h e d.c. c u r r e n t . Thus t h e momenta of t h e b e t a p a r t i c l e s can be e x p r e s s e d i n terms o f t h e p o t e n t i o m e t e r s e t t i n g . To a v o i d t h e e f f e c t o f t h e e a r t h magnetic f i e l d , t h e . s p e c t r o m e t e r was p l a c e d w i t h i t s a x i s a l o n g t h e magnetic m e r i d i a n and between two compensating c o i l s t o reduce t h e v e r t i c a l component o f t h e f i e l d . The sou r c e p o s i t i o n t o g e t h e r w i t h t h a t o f b a f f l e A can be v a r i e d i n t h e p l a n e p e r p e n d i c u l a r t o t h e chamber a x i s by Detector : . B i a s Power Supply Detector P o s i t i o n i n g Rod / . Low Noise Preamp. T Time Constant :. Box A m p l i f i e r Disc Output Spot Source J. Vacuum Gauge t =jyn \ PUTT Delay & Shaper 150 v o l t d.c A n t i - c o i n . U n i t Bias C o n t r o l C i r c u i t S c a l e r High P r e c i s i o n Potentiometer Fig.1 8 B e t a s p e c t r o m e t e r assembly, i .P Source- . \C e n t e r i n g 'Control ump > r Magnet Current Standard R e s i s t o r r CO 00 Fig.19 Magnet c u r r e n t c o n t r o l c i r c u i t .. -85- means o f t h e two c e n t e r i n g d i a l s , w h i l e t h e d e t e c t o r i s movable a l o n g t h e chamber a x i s by t h e p o s i t i o n i n g r o d . The a n n u l a r s l i t I n b a f f l e A d e f i n e s t h e i n i t i a l a n g l e o f t h e b e t a t r a c k s and l i m i t s t h e b e t a i n t e n s i t y t o t h e d e t e c t o r . The c e n t r a l b a f f l e B c o n t r o l s t h e momentum spread o f t h e p a s s i n g b e t a p a r t i c l e s . The d e t e c t o r b a f f l e C p r o t e c t s t h e d e t e c t o r f rom t h o s e b e t a s not f o l l o w i n g t h e p r o p e r p a t h s . The r e s o l u t i o n o f t h i s s p e c t r o m e t e r depends on t h e c u r v a t u r e o f t h e b e t a t r a c k s and on t h e d.c. c u r r e n t s t a b i l i t y . The former i s determined by magnetic f i e l d s t r e n g t h , and t h e l a t t e r , by t h e s e n s i t i v i t y o f t h e c u r r e n t r e g u l a t o r . The d e t e c t o r mentioned above i s a t h i n s u r f a c e b a r r i e r :• type w i t h s u r f a c e d i a m e t e r o f 1cm. The use o f t h i s t y p e o f d e t e c t o r i n t h e p r e s e n t case i s p a r t i c u l a r l y advantageous, i f one compares i t w i t h t h e c o n v e n t i o n a l s c i n t i l l a t o r s o r g a s - f i l l e d c o u n t e r s . F i r s t l y , because of t h e t h i n d e p l e t i o n l a y e r o f t h e d e t e c t o r , i t i s p r a c t i c a l l y i n s e n s i t i v e t o gamma r a d i a t i o n o r i g i n a t i n g e i t h e r i n t h e s o u r c e o r i n t h e background. T h e r e - f o r e , no l e a d s h i e l d i n g i n t h e chamber i s n e c e s s a r y . S e c o n d l y , t h e s u r f a c e b a r r i e r d e t e c t o r i s u n a f f e c t e d by t h e magnetic f i e l d i n t h e chamber, whereas i n t h e case of a p h o t o m u l t i p l i e r w hich must accompany a s c i n t i l l a t o r , t h e p r e s ence o f t h i s : ..strong f i e l d would be i n t o l e r a b l e . The s i g n a l o utput of t h e -86- d e t e c t o r is,.however> r e l a t i v e l y s m a l l . T h e r e f o r e , a l o w - n o i s e p r e a m p l i f i e r w i t h a t i m e c o n s t a n t box was r e q u i r e d t o i n c r e a s e t h e p e a k - t o - n o i s e r a t i o . The i n t r o d u c t i o n o f an a n t i - c o i n c i d e n c e u n i t and a feedback d e v i c e shown i n f i g u r e 18 was o n l y f o r t h e sake o f m i n i m i z i n g t h e e f f e c t o f n o i s y s u r r o u n d i n g s . Sudden b u r s t s o f p u l s e s o c c a s i o n a l l y were obse r v e d i n t h e m o n i t o r o s c i l l o s c o p e . Each o f t h e s e b u r s t s o f p u l s e s , a f t e r e n t e r i n g t h e a n t i - c o i n - c i d e n c e u n i t , were reduced t o j u s t one l e a d i n g p u l s e . C o n s e q u e n t l y , t h e e f f e c t became i n s i g n i f i c a n t when c o n s i d e r i n g t h e h i g h e r b e t a c o u n t i n g r a t e . The d e l a y and shaper u n i t produced t h e r e q u i r e d b l o c k i n g p u l s e f o r t h e a n t i - c o i n c i d e n c e u n i t . ^4. P r e p a r a t i o n o f B e t a S o u r c e s . The p r e p a r a t i o n o f a spot s o u r c e f o r b e t a s p e c t r o s c o p y . w i t h minimum p o s s i b l e s o u r c e s c a t t e r i n g but w i t h maximum p o s s i b l e r a d i o a c t i v e s t r e n g t h i s a c h a l l e n g i n g t a s k . S e v e r a l methods have been t r i e d by p r e v i o u s w o r k e r s , such as vacuum e v a p o r a t i o n , m o l e c u l a r d e p o s i t i o n , e l e c t r o s t a t i c s p r a y i n g , 61)-64) e l e c t r o p l a t i n g , l i q u i d drop d e p o s i t i o n e t c . Each method has i t s own advantages and d i s a d v a n t a g e s . But by f a r , the l i q u i d drop d e p o s i t i o n method i s t h e s i m p l e s t and most f r e q u e n t l y used among them a l l . I t has t h e d i s a d v a n t a g e s o f l i m i t e d s t r e n g t h and c o m p a r a t i v e l y poor s u r f a c e u n i f o r m i t y . B u t , i n a d d i t i o n t o b e i n g easy t o p r e p a r e , i t a c c e p t s almost any k i n d o f t h i n b a c k i n g . T h e r e f o r e , h a v i n g t r i e d some o t h e r methods w i t h o u t s a t i s f a c t o r y r e s u l t s , t h i s method was f i n a l l y • \ chosen. • B e f o r e s t a r t i n g t h e so u r c e p r e p a r a t i o n , a t h i n b a c k i n g had t o be p r e p a r e d f i r s t . V i n y l f i l m s were s e l e c t e d f o r t h i s p u r p o s e . About 10 gms. o f B a k e l i t e v i n y l r e s i n powder ( c a l l e d VYNS) were mixed w i t h 100 m l . o f cyclohexanone s o l u t i o n i n a b o t t l e and s t i r r e d u n t i l most o f t h e powder had d i s s o l v e d . I t was l e f t f o r a few days w i t h o c c a s i o n a l s t i r r i n g . When a l l t h e powder had d i s a p p e a r e d , a s m a l l q u a n t i t y o f t h e s o l u t i o n was d i l u t e d by an equal'.amount o f cycl o h e x a n o n e on a watch g l a s s . By u s i n g a g l a s s r o d , a drop o f t h e s o l u t i o n was i n t r o d u c e d t o t h e s u r f a c e o f a t r a y o f c l e a n w a t e r . The s o l u t i o n q u i c k l y spread i n t o a tough t h i n f i l m . The u n i f o r m p a r t ( j u d g i n g from the r e f l e c t i n g c o l o u r s ) was p i c k e d up by a copper w i r e l o o p and p l a c e d on an aluminium r i n g . The f i l m t h u s p r e p a r e d was e s t i m a t e d t o be l e s s t h a n 10 pg/cm^- t h i c k . When t h e f i l m was d r y , a t r a c e o f alu m i n i u m was e v a p o r a t e d i n vacuum onto t h e f i l m t o s e r v e as a charge c o n d u c t i n g l a y e r . Great c a r e was '~ t a k e n not t o overheat? t h e f i l m d u r i n g e v a p o r a t i o n . S e v e r a l . -88- b a c k i n g s were p r e p a r e d i n t h i s way. To p r e p a r e t h e s o u r c e , a s m a l l g l a s s j e t w i t h a c l e a n and p l a n e - c u t n o z z l e was connected t o a system such t h a t t h e I n t e r n a l p r e s s u r e o f t h e j e t c o u l d be v a r i e d c o n v e n i e n t l y . A t i n y q u a n t i t y o f t h e c h l o r i d e s o l u t i o n o f Eu 154 w i t h s u i t a b l e c o n c e n t r a t i o n was sucked i n t o t h e j e t . A s o u r c e b a c k i n g was t h e n p l a c e d under t h e n o z z l e on an a d j u s t a b l e b a s e . By c a r e f u l l y c o n t r o l l i n g t h e p r e s s u r e , a s m a l l w e l l - d e f i n e d spot s o u r c e c o u l d be d e p o s i t e d onto t h e c e n t r e o f t h e v i n y l f i l m . T h i s was done w i t h r e p e a t e d t r i a l s , and a f a i r l y i n t e n s e and u n i f o r m s o u r c e was f i n a l l y o b t a i n e d . The sou r c e was t h e n d r i e d i n a d e s i c c a t o r ( s i n c e Europium C h l o r i d e i s a h y g r o s c o p i c compound). Then a v e r y d i l u t e s o l u t i o n of c o l l o d i o n i n dry e t h e r was p r e p a r e d , and a drop o f i t was i n t r o d u c e d onto t h e s u r f a c e o f t h e d r i e d s o u r c e t o p r o t e c t t h e sou r c e from f l a k i n g o f f . The sou r c e was a g a i n r e p l a c e d i n t h e d e s i c c a t o r , r e a d y . t o be mounted i n . t h e vacuum chamber. ^5. E x p e r i m e n t a l P r o c e d u r e s . . P r e l i m i n a r y a d j u s t m e n t s t o t h e s p e c t r o m e t e r c o n s i s t e d o f changing b a f f l e s , and r e p e a t e d v a r i a t i o n o f t h e sour c e and d e t e c t o r p o s i t i o n s as w e l l as t h e o r i e n t a t i o n o f t h e chamber, u n t i l optimum i n t e n s i t y w i t h b e s t p o s s i b l e r e s o l u t i o n - w a s o b t a i n e d . A b e t a s o u r c e o f Cs 137 was used f o r . t h i s p u r p o s e . -89- •• ••/•}^'-:-:-:-'./\ D e t a i l s o f t h e a d j u s t m e n t s and c a l i b r a t i o n o f t h e s p e c t r o m e t e r a r e g i v e n i n r e f . 65. The b e s t r e s o l u t i o n a c h i e v e d was 0.7 $ i n terms o f p o t e n t i o m e t e r s e t t i n g o r momenta w i t h 0.96$ t r a n s m i s s i o n . •The Cs 137 s o u r c e was t h e n r e p l a c e d by a be t a s o u r c e o f Eu 154 chosen from among t h o s e p r e p a r e d , and t h e chamber was c o n t i n u o u s l y pumped down t o keep away t h e wa t e r vapour. ("Unfortunately, i n t h e l a t e r r u n s , because o f r e p e a t e d removal and r e p l a c e m e n t o f t h e s o u r c e , a s m a l l q u a n t i t y o f water vapour was absorbed by t h e s o u r c e and t r a p p e d i n t h e c o l l o d i o n f i l m . T h i s caused d e t e r i o r a t i o n o f r e s o l u t i o n i n t h e low energy p o r t i o n o f t h e spectrum, but d i d not a f f e c t t h e h i g h e r energy p a r t . ) , I n each r u n o f t h e e x p e r i m e n t , t h e p r e s s u r e o f t h e chamber was kept at about 10 mm. of Hg. The p o t e n t i o m e t e r r e f e r e n c e v o l t a g e was c a l i b r a t e d a g a i n s t a s t a n d a r d c e l l e v e r y f i v e o r t e n m i n u t e s . The shape of t h e ou t p u t p u l s e s from the t ime c o n s t a n t box was observed c o n s t a n t l y w i t h an o s c i l l o s c o p e . The c o u n t i n g t i m e f o r each p o t e n t i o m e t e r s e t t i n g v a r i e d from h a l f a minute t p e i g h t minutes depending on the c o u n t i n g r a t e . Ore s e c t i o n o f t h e spectrum was t a k e n . e a c h t i m e w i t h r e p e a t e d r u n s , u n t i l enough cou n t s were accumulated such t h a t the s t a t i s t i c s f o r ' e a c h d a t a p o i n t was w i t h i n t h e • • - 9 0 - r e q u i r e d l i m i t s ( i . e . 1 % f o r t h e energy continuum and l e s s f o r t h e p e a k s ) . Three e x p e r i m e n t s have been performed a t d i f f e r e n t p e r i o d s o f t i m e . The f i r s t two e x p e r i m e n t s were m a i n l y concerned w i t h t h e i n t e r n a l c o n v e r s i o n peaks. A t y p i c a l spectrum was p l o t t e d out i n two p o r t i o n s as shown i n f i g u r e s 20a,b. The t h i r d experiment was des i g n e d t o i n v e s t i g a t e t h e beta continuum near t h e h i g h energy end. I n t h i s e x p e r i m e n t , a s t r o n g e r b e t a source was used t o o b t a i n a g r e a t e r c o u n t i n g r a t e and b e t t e r s t a t i s t i c s . The s p e c t r o m e t e r was s e t up t o use a l a r g e r s o u r c e - d e t e c t o r d i s t a n c e and s m a l l e r i n i t i a l t r a j e c t o r y a n g l e s . T h i s was n e c e s s a r y i n o r d e r t o r e a c h e n e r g i e s near t h e end p o i n t of t h e Eu 154 spectrum w i t h t h e maximum a v a i l a b l e magnetic c u r r e n t . The spectrum f o r t h e b e t a continuum was shown i n f i g u r e 20c .(Note t h a t t h e counts a r e d i v i d e d by t h e momentum.) ^6. R e s u l t s and A n a l y s i s . The b e t a spectrum shown p l o t t e d i n f i g u r e s 20a,b i n the p r e v i o u s s e c t i o n was o b t a i n e d a f t e r a l l s h o r t - l i v e d peaks had decayed t o n e g l i g i b l e s i z e . They were p l o t t e d i n l o g a r i t h - mic v a l u e s i n o r d e r t o show as much as. p o s s i b l e o f t h e f e a t u r e s o f a l l t h e c o n v e r s i o n peaks. S i n c e t h e beta s p e c t r o m e t e r was f i r s t c a l i b r a t e d u s i n g a ,Cs 137 s o u r c e , t h e energy c o r r e s p o n d e n c e o f each p o t e n t i o m e t e r CM r-IVC Lf\ C\l C\l CO CO O rH rH i H (Al CM CM CM i—! rH CM r-c-- •"3" vt- CM CM 4-4- • .1811 .226 .268 .310 .352 P O T E N T I O M E T E R S E T T I N G .394 .136 .1478 F i g . 2 0 a B e t a s p e c t r u m o f E u 154, l o w - e n e r g y p a r t . i n m i n Lf 5 " CD CO ID CO I— 2 : ZD 2 Oco ^ c V o f + + + + +.. «—> o -"S cn Ui cn LP. ^ O cn CM t-- cn VO vo cn O O C~- cn • • • • • C\J CM C\J VO C\J CM cn cn LT\ CM r— vo vo c-- f - Ui vo • CM co VO * CM co * " " " " I I H I I I H + I Ui Ui • • LP. "td-cn o cno o o o .500 ,542 .584 T _ _ _ . R , — 1 ,BZ6 .B58 .710 .752 POTENTIOMETER S E T T I N G .794 .836 F i g . 2 0 b B e t a s p e c t r u m o f Eu 154, h i g h - e n e r g y p a r t . 6 CM E 3 QJ E o co +-> 3 C 3 3 O CJ I I 0 I Z 3 Momentum P ( i n mc ) F i g . 2 0 c Continuum f o r b e t a t r a n s i t i o n s o f Eu 154. s e t t i n g was roughly.known. Hence, th e c o n s p i c u o u s c o n v e r s i o n peaks i n t h e Eu 154 spectrum were soon r e c o g n i z e d . The 722.90K c o n v e r s i o n peak was t h e n s e l e c t e d as a s t a n d a r d t o c a l i b r a t e t h e e l e c t r o n e n e r g i e s o f a l l t h e o t h e r c o n v e r s i o n p e aks. The i n t e n s i t y measurement was done by e s t i m a t i n g t h e a r e a under each peak i n an e n l a r g e d l i n e a r p l o t a f t e r t h e continuum was s u b t r a c t e d , and t h e n d i v i d i n g t h e a r e a by t h e momentum o r p o t e n t i o m e t e r s e t t i n g ' a t t h a t peak. The f u l l w i d t h a t h a l f maximum was a l s o determined g r a p h i c a l l y i n each c a s e . The p a r t i c u l a r s f o r t h e c o n v e r s i o n peaks a r e p r e s e n t e d i n t a b l e V. F i g u r e 20a shows t h a t t h e l o w e r p o r t i o n o f t h e b e t a spectrum i s dominated by t h e 122.9 Kev c o n v e r s i o n p e a k s . The t h e asymmetry o f t h e peak shape i n d i c a t e s s l i g h t s o u r c e s c a t t e r i n g i n t h i s energy r a n g e . The t a i l s at t h e l o w e r energy s i d e o f t h e s e s t r o n g peaks d i d i n t e r f e r e w i t h t h e i n t e n s i t y measurement o f t h e weaker peaks between them as w e l l as t h e b e t a continuum beneath them. However, s o u r c e s c a t t e r i n g b e g i n s t o * Column 1 o f t h e t a b l e g i v e s t h e e n e r g i e s o f t h e t r a n s i t i o n s as determined by t h e gamma-ray measurements t o g e t h e r w i t h t h e atomic s h e l l s . Column 5 g i v e s t h e t r a n s i t i o n e n e r g i e s c a l c u l a t e d by a d d i n g Column 2 t o t h e a p p r o p r i a t e s h e l l b i n d i n g e n e r g i e s B x ( i . e . B R = 50.22 Kev e t c f o r Eu 154,and B K - 46.85 e t c f o r Eu .152). Column 6 compares t h e t r a n s i t i o n energies, from, gamma and c o n v e r s i o n e l e c t r o n d a t a . •""•'/"...' -95- Peak Name ( f r o m Y) E l e c t r o n E n e rgy (Kev) R e l a t i v e I n t e n s i t y FWHM Tran s Energy ': (Kev) Y-energy D e v i a t i o n 86.9K 37.28 ' 1.4 . 8 7 . 5 0.69- 105.3K 54.54 10.5 ±0.4 1.21 104.8 0.48 122.9K 72.49 260.0±2.6 1.0 122.7. 0.16 121.8K 74.6 10.7 ±2.1 1.0 121 .5 0.25 •86.9L 77.85 1.90 ±0.22 1.0 85.7 1.4 86.9M 83.05 0.37 ±0.08 1.0 84.6 2.6 105.3L 96.18 1.21 ±0.25 1.45 104.0 1.2 122.9L 115.20 170.313.5 1.0 123-0 . 0.081 122.9M 121.30 48.8 ±1.8 1.0 122.8 0.081 247.6K 196.56 5.71 ±0.12 0.7 246.8 0.32 247.6L 239 .33 1.46 ±0.15 0.77 247.2 0.16 247.6M 245.78 0.30 ±o.03 0.74 247.3 0.12 343.6K 293.94 0.58 ±0.02 0.67 340.8 0.82 591.7K 540.57 0.26 ±0.03 0.78 590.8 0.15 679.4K 629-2 0.13510.014 0.73 679.4 — 692.OK 642.1 0.839±0.017 0.67 692 .3 0.04 722.9K 672.68 0.47710.019 0.66 722 .9 0. 692.OL 684 .5 0.127±0.025 0.80 •69-2.3 0.04 692.0M 690.9 0.09710.019 0.80 692 .4 0.058 756.7K 706.57 0.23810.020 .0.67 756.8 . 0.013 .722.9L 718.0 0.04810.010 0.67 725.8 0.40 872.6K 824.0 0.40810.018 0.70 874.2 " 0.18 872. 61 868.0 0.08410.017 0.67 875.8 0.57 995.9K 945 .0 0.23410.047 0.71 995 .2 0.07 1004.5K 953.2 0.39310.080 0.66 1003.4 0.11 12J4,4K 1227.9 0 .299 ± 0.070 1.64 1278,1. 0.29 T a b l e V D a t a o f P C o n v e r s i o n Peaks i n f i g u r e s 20a,b, ( E x p l a n a t i o n g i v e n . i n the f o o t note *, p. 9 4 ) . - 9 6 - : ; . d i s a p p e a r when t h e energy i s above 121.30 Kev ( i . e . above t h e 122.9M p e a k ) , and a l l t h e c o n v e r s i o n peaks h a v i n g e n e r g i e s g r e a t e r t h a n t h i s a r e f a i r l y s y m m e t r i c a l . T h i s can a l s o be seen from t h e v a l u e s o f t h e FWHM p r e s e n t e d i n t a b l e V. The i n t e n s i t y o f t h e 86.9K peak c o u l d not be e s t i m a t e d , because i t i s b a r e l y above t h e n o i s e l e v e l and t h e t a i l due t o s c a t t e r i n g c e r t a i n l y e x t e n d s below t h e d i s c r i m i n t o r l e v e l o f t h e a m p l i f i e r . The two humps between t h e 86.9K and IO5.3K peaks a r e s u s p e c t e d t o be Auger e l e c t r o n l i n e s but have not been p o s i t i v e l y i d e n t i f i e d . I t i s i n t e r e s t i n g t o note t h a t t h e 121.8K peak b e l o n g i n g t o Eu-152 i m p u r i t y i s s e p a r a t e d from t h e 122.9K peak o f Eu. 154, and t h a t t h e fo r m e r i s o n l y 4.12 % of t h e l a t t e r . S i n c e t h e s e peaks a r e r e s p e c t i v e l y t h e s t r o n g e s t peaks i n Eu 152 and Eu 154, t h e p e r c e n t a g e r a t i o was made use o f i n c a l c u l a t i n g a l l t h e o t h e r Eul52 peak i n t e n s i t i e s p r e s e n t i n t h e spectrum.'. F o r example, t h e i n t e n s i t y o f t h e 244.7K of Eul52 expected t o be p r e s e n t i n t h e 247.6K peak o f Eu 154 was c a l c u l a t e d . T h i s i n t e n s i t y was s u b t r a c t e d f r om t h a t of t h e l a t t e r peak i n o r d e r t o f i n d t h e e x p e r i m e n t a l v a l u e f o r t h e i n t e r n a l c o n v e r s i o n c o e f f i c i e n t . The p r o c e d u r e was a l s o a p p l i e d t o t h e gamma peaks 122.93 Kev and 247.63 Kev as mentioned p r e v i o u s l y . From f i g u r e 20b, t h e main i n t e r e s t l i e s i n t h e group o f peaks from 679.4K t o 722.9L shown i n an expanded s c a l e . . : ' '• • • -97- 36) i n f i g u r e 20d. A c c o r d i n g t o H a m i l t o n et a l , two c o n v e r s i o n peaks namely 6 7 8 K and 6 8 2 K were found l y i n g c l o s e t o each o t h e r . I n t h i s spectrum, we o n l y found a s i n g l e peak l a b e l l e d 679.4K and FWHM of 0.73 %. I f t h e r e a r e i n f a c t two peaks as r e p o r t e d , t h e peak w i d t h would have been much l a r g e r t h a n t h o s e o f t h e n e i g h b o u r i n g p e aks. T h i s i s not t h e c a s e . F u r t h e r d i s c u s s i o n w i l l be g i v e n i n t h e next c h a p t e r . The next p o i n t t h a t needs t o be mentioned i s t h a t we have not found any gamma or b e t a c o n v e r s i o n peak c o r r e s p o n d i n g t o t h e 6 2 6 Kev t r a n s i t i o n g i v e n i n t h e same r e f e r e n c e . F i n a l l y , i t s h o u l d be noted t h a t t h e 1274.4K peak g i v e n I n t a b l e V was not I n c l u d e d i n t h e f i g u r e s 20a,b,d, because t h i s peak was o b t a i n e d i n t h e t h i r d r u n o f t h e b e t a e x p e r i m e n t s , w h i l e t h e above f i g u r e s were from t h e second r u n . From t h e l a s t column o f t a b l e V, t h e agreement f o r t h e K peaks o f Eu 154 i s good. The r e l a t i v e i n t e n s i t i e s i n the.' same t a b l e have not been c o r r e c t e d f o r t h e Eu 152 i m p u r i t y . The c o r r e c t i o n was done l a t e r o n l y f o r t h e K peaks i n o r d e r " t o f i n d t h e K - c o n v e r s i o n c o e f f i c i e n t s . • To f i n d t h e K - c o n v e r s i o n c o e f f i c i e n t s , t h e 1 2 2 . 9 3 Key t r a n s i t i o n , . w h i c h was c o n s i d e r e d t o be p u r e l y E2, was chosen as t h e s t a n d a r d . From t h e i n t e n s i t y d a t a g i v e n i n t a b l e s I I I 58) and V, and t h e t a b l e o f S l i v e t a l . , we have from e q u a t i o n . ( 1 0 1 ) , 7 • '• i .  - 9 9 - (from T a b l e I I I ) (from T a b l e V) (E2 c o n v e r s i o n - 1 2 2 . 9 Kev) Wi t h the.se v a l u e s and e q u a t i o n ( 1 0 1 ) , the e x p e r i m e n t a l re- c o n v e r s i o n c o e f f i c i e n t s were c a l c u l a t e d , and are l i s t e d i n Table VI t o g e t h e r w i t h the t h e o r e t i c a l v a l u e s f o r E l , M l , and E2 t r a n s i t i o n s . The d a t a i n T a b l e VI c o n f i r m s the expected E2. n a t u r e o f a l l but one o f the t r a n s i t i o n s between p o s i t i v e p a r i t y s t a t e s The one e x c e p t i o n i s the t r a n s i t i o n o f energy 692 Kev, w h i c h has a c o n v e r s i o n c o e f f i c i e n t t en t i m e s the t h e o r e t i c a l E2 v a l u e . T h i s s u g g e s t s an EO component. The magnitude o f t h i s component ( c a l c u l a t e d on the a s s u m p t i o n t h a t the S2 c o n v e r s i o n c o e f f i c i e n t i s indeed 0 . 0 0 5 2 ) i s a p p r o x i m a t e l y 6 p e r c e n t o f the t o t a l EO + E2 t r a n s i t i o n p r o b a b i l i t y . The 591.7 Kev gamma-ray has an DC^ whose l i m i t s o f u n c e r t a i n t y do not q u i t e encompass the t h e o r e t i c a l E2 v a l u e , a l t h o u g h M l and E l can be r u l e d o u t . T h i s c o n v e r s i o n peak r e c e i v e d a l o t o f a t t e n t i o n e x p e r i m e n t a l l y , and many counts were accumulated i n an e f f o r t t o a t t a i n good s t a t i s t i c s . I t i s p o s s i b l e o f c o u r s e , t h a t the e r r o r l i m i t s were somewhat u n d e r e s t i m a t e d . The 7 2 2 . 9 Kev and the 1 2 7 4 . 4 Kev t r a n s i t i o n s b o t h i n v o l v e n e g a t i v e p a r i t y l e v e l s , and a r e most p r o b a b l y E l , assignments t h a t are c o n s i s t e n t w i t h the decay scheme shown i n F i g u r e 2 2 . The 1 0 5 * 3 Kev t r a n s i t i o n has n o t been f i t t e d i n t o the decay scheme, but i t appears a l s o to be E l o X = K <Vst = 1 0 0 - 0 0 (Wst = 2 6 0 '° (%) Q 1- = 0.652 -100- Peak Name K- I n t e r n a l Convers i o n C o e f f i c i e n t s E x p e r i m e n t a l (E2) (Ml) ( E l ) 105.3K 0.272 ± 0 . 0 3 3 1.002 1.469 0.216 122.9K 0.652 ± 0.022 0.652 0.941 0.142 24-7. 6K 0.085 i 0.006 0.0815 0.135 0.0218 591.7K 0.0065 ± 0.0011 0.00803 0.0140 0.00281 692.OK 0.056 i 0.0055 0.00519 0.00954 0.00201 722.9K 0.00254+0.00021 0.00471 0.00857 0.00183 756.7K 0.0058 +0.0010 0.00426 0.00766 0.00167 872.6K 0.00347i0.00031 0.00314 0.00542 0.00127 995.9K 0.00238±0.00058 0.00238 0.00395 0.000988 1004.5K 0.0022510.00056 0.00234 0.00388 0.000971 1274.4K 0.0007li0.00023 0.00145 0.00219 0.000631 T a b l e VI Comparison o f K - I n t e r n a l C o n v e r s i o n C o e f f i c i e n t s w i t h the T h e o r e t i c a l V a l u e s f o r E l , M l , and E2 t r a n s i t i o n s t a k e n from r e f e r e n c e ( 5 8 ) . -101- The a n a l y s i s on t h e be t a continuum was done by u s i n g K u r i e - p l o t method (see f i g u r e 2 l ) , and t h e r e s u l t s a r e p r e s e n t e d I n t a b l e V I I . ( F o r d e t a i l s o f t h e a n a l y s i s , see r e f e r e n c e 65.) B e t a Energy (Mev) T r a n s i t i o n I n t e n s i t y {%) . 1.866+.012 10.8 ±0.12 1.1 98 ±.060 0.67±0.49 0.976 + .030 4.6 ± 3 . 8 0.843+ .015 17-0 ±3.9 0 .579 + .005 37-8 ±3.5 0.274 ± .010 29.1± 2.5 T a b l e V I I . E n e r g i e s and r e l a t i v e i n t e n s i t i e s o f t h e be t a t r a n s i t i o n s . -102- P i g . 102 The K u r i e p l o t s N=counts/min. p=momentum(mc) f= r e d u c e d F e r m i f u n c t i o n 6 = c o r r e c t i o n f a c t o r (see r e f . 55) CfN/EKtjr (MEV) - 1 0 3 - CHAPTER V I I .. THE DECAY SCHEME AND MODEL FITTING •$1. The Decay Scheme. Summing a l l t h e r e s u l t s o b t a i n e d so f a r from t h e b e t a - and gamma-spectroscopic work as w e l l as t h e gamma-gamma c o i n c i d e n c e i n v e s t i g a t i o n d e s c r i b e d i n t h e p r e v i o u s t h r e e c h a p t e r s , t h e decay scheme o f Eu 154 t o Gd 154 was c o n s t r u c t e d , and t h e e x c i t e d s t a t e s of Gd 154 r e s u l t i n g f r om t h i s decay areshown i n f i g u r e 22. The r e l a t i v e i n p u t and output t r a n s i t i o n a l i n t e n s i t i e s w i t h r e s p e c t t o each l e v e l a r e p r o v i d e d . i n t a b l e VHT. The l e v e l s t r u c t u r e p r e s e n t e d i n t h e f i g u r e i s as a whole I n agreement w i t h t h o s e c o n s t r u c t e d by t h e p r e v i o u s 36) w o r k e r s , i n p a r t i c u l a r by H a m i l t o n et a l , a l t h o u g h t h e r e a r e i m p o r t a n t d i f f e r e n c e s . I n g e n e r a l , t h e r e i s a marked improvement i n t h e a c c u r a c y o f t h e l e v e l e n e r g i e s , w h i c h can . be e a s i l y p e r c e i v e d from t h e f a c t t h a t a l l t h e . e x p e r i m e n t a l l y determined v a l u e s f o r t h e gamma t r a n s i t i o n a l e n e r g i e s f i t i n t o t h e decay scheme w i t h energy d e v i a t i o n s l e s s t h a n 1 Kev. The. two new weak t r a n s i t i o n s d i s c o v e r e d , i . e . 903.60 Kev and 532.11 Kev, were a s s i g n e d t o t h e t r a n s i t i o n s from t h e • l e v e l s 1718.80 Kev and 1397-36 Kev t o t h e l e v e l '814.77 Kev . r e s p e c t i v e l y . (These l e v e l s were, a l l a s s i g n e d , from other, more .. C22JL Gd 154 [211] 722 126 3 .3 (4+) 1127.4 (3+) 99 5.8 (2+) F i g . 2 2 The e x c i t e d s t a t e s o f Gdi54 o b t a i n e d from the decay o f E u l 5 4 . (The l e v e l and t r a n s i t i o n s given i n dotted l i n e s 626 are obtained from r e f . • 36.) 995 .0 C211] [Oil] 591 L90 61 I42JQ 872. 94 1004 h2 756 50 I3JJ1 I22J1 892. 71 247 122. 74 90! 1274 63 C212] 60 582 [012] 43 679 93 557 4 815 96 11- 1595 692 02 1444 .02 02 1718.8 (2-) 1397.4 (2-) 87 f - 1049 .0 (4+) 678 ̂ 0 i 814.8 (2+) 680.1 (0+) A. 370.6 (4+) 122.93(2+) 0.0 (0+) i M O -t" I -105- T r a n s i t i o n a l I n t e n s i t i e s ( R e l a t i v e ) L e v e l Input Output D i f f e r e n c e Beta from Name y + C E . Y + C.E. ( i n % ) Continuum (Kev) (%) [212] " 1718.8 64.72+3.06 64.72+3.06 (26.33%) 29.1+2.5 [211]- 1397.4 93.80+4.30 93.80+4.30 (38.10%) 37.8+3.5 [421] + 1263.3 1.23+0.20 1.23+0.20 (0.50%) [311] + 1127.4 10.58+0.55 54.3112.04 43.73+2.59 (17.80%) 17.0+3.9 [221] + 995.8 47.43+2.06 54.25+2.50 6.82+4.56 (2.77%) 4.6+3.8 [411] + 370.6 13.75+0.95 17.73±0.80 3.98+1.75 (1.65%) . [211] + 122.93 192.85+8.93 220.014.44 27.15+13.37 (11.07%) 10.8+0.12 [212] + 814.8 3.77+0.39 6.9810.88 3. 21+1.27 (1.31%) 0.67±0.49 [012] + 680.10 0.0 0.9010.17 0.90+0.17 (0.37%) Table VUI T r a n s i t i o n a l i n t e n s i t i e s f o r gammas, conversion e l e c t r o n s K and betas. L e v e l name n o t a t i o n , [LNnj . -106- . I n t e n s e gamma-rays.) The energy d e v i a t i o n s a r e l e s s t h a n f- Kev. T h i s energy agreement i s e x c e l l e n t . I n a d d i t i o n , t h e s e t r a n s i t - i o n s a r e p r e d i c t e d t o have no change o f a n g u l a r momentum but o n l y a change o f p a r i t y ( E l ? ) . F o r t h e s e , t h e b e t a c o n v e r s i o n peaks s h o u l d be much weaker I n i n t e n s i t y t h a n t h e gamma peaks. T h i s i s t h e case i n t h e p r e s e n t i n v e s t i g a t i o n . A l t h o u g h t h e gamma t r a n s i t i o n s have been d e t e c t e d , none o f t h e c o n v e r s i o n peaks have been f o u n d . From t h e low output i n t e n s i t y o f t h e l e v e l 8l4.77 Kev g i v e n i n t a b l e VI3I, i t i s o b v i o u s t h a t t h e s e two t r a n s i t i o n s a r e n e c e s s a r i l y weak, wh i c h i s t h e r e a s o n t h a t t h e y have not been obse r v e d b e f o r e . C o n s e q u e n t l y , t h e s e two t r a n s i t i o n s c o n t r i b u t e t h e major p o r t i o n o f t h e p o p u l a t i o n o f th e l e v e l 8l4.77 Kev. 36) H a m i l t o n et a l suggested a l e v e l o f 1049 Kev on th e b a s i s o n l y of t h e e x i s t e n c e o f t h e 678K b e t a c o n v e r s i o n peak. I n t h e p r e s e n t work, no such peak was found e i t h e r i n the b e t a c o n v e r s i o n spectrum o r i n t h e gamma spectrum. A l s o . we can f i n d no o t h e r t r a n s i t i o n f r om t h i s l e v e l t o any o t h e r l e v e l o r v i c e v e r s a . A l t h o u g h t h e 1049 Kev l e v e l was w e l l - 33) e s t a b l i s h e d i n t h e decay o f Tb 154 t o Gd 154 . , we have r e a s o n s t o doubt i t s presence i n t h e decay of Eu 154. On the o t h e r hand, a n o t h e r 4+ l e v e l o f energy 1263.3 Kev was found due t o t h e presence o f 892.74 Kev.gamma t r a n s i t i o n . -107- . " As w i l l be seen i n t h e next s e c t i o n , t h i s l e v e l was p r e d i c t e d by t h e Asymmetric R o t a t o r Model. The l a s t p o i n t o f d i f f e r e n c e 36) from t h e scheme of H a m i l t o n et a l i s t h e absence of t h e 626 Kev t r a n s i t i o n . I n t a b l e VTH, t h e sum o f t r a n s i t i o n a l i n t e n s i t i e s • • - \ . •, V o f gammas p l u s c o n v e r s i o n e l e c t r o n s t o and from each l e v e l were g i v e n . A f t e r a l l o w i n g f o r t h e e x p e r i m e n t a l e r r o r , t h e d i f f e r e n c e s h o u l d be c o n t r i b u t e d by a b e t a t r a n s i t i o n from t h e ground s t a t e o f Eu 154 t o t h a t l e v e l . These d i f f e r e n c e s are a l s o e x p r e s s e d i n p e r c e n t a g e so as t o compare them w i t h t h e e x p e r i m e n t a l v a l u e s f o r t h e b e t a t r a n s i t i o n s g i v e n i n t h e l a s t column. The r e s u l t o f t h i s c o m parison shows c l e a r l y t h a t a l l t h e d a t a a r e q u i t e c o n s i s t e n t . |2. Model F i t t i n g . • The: t h e o r y f o r c a l c u l a t i n g t h e gamma t r a n s i t i o n a l e n e r g i e s and t h e reduced t r a n s i t i o n p r o b a b i l i t i e s base on th e Asymmetric R o t a t o r Model was g i v e n i n C h a p t e r 2. To proceed t o t h e a c t u a l c a l c u l a t i o n , we made use o f f i v e b a s i c 41) programs w r i t t e n by D a v i d s o n . . The f i r s t program c a l c u l a t e s t h e m a t r i x elements o f the a n g u l a r momentum components g i v e n e x p l i c i t l y as f o l l o w s , •>2, (L(L+1) - K 2 ) /2 t f o r K' = K <LMKf L H L M K ' > = < - i l i t ( L ^ K - L ) (L^K) (L+K+l) (L±K+2)^j 2 . f o r K'=K+2 <LMK|L 2 |LMK'> = ( ^ L + l ^ ' ^ / 2 > f ° r K ' = K t t ( ( L + K - l ) (L+K) (L+K+l) (L+K+2)J ^, f o r K'=K+2 <LMK/b3|LMK'> = ^ ^ K K ' and t h u s c a l c u l a t e s t he m a t r i x elements o f the r o t a t i o n a l H a m i l t o n i a n (see e q u a t i o n (27)) f o r a g i v e n y . Then, t h e l a t t e r m a t r i x i s d i a g o n a l i z e d by u s i n g t h e J a c o b i a n method. The e i g e n v a l u e s £ N ( L ) as w e l l as t h e c o e f f i c i e n t s CK are found i n t h i s way. - The second program s o l v e s e q u a t i o n (38) f o r a g i v e n p. by. i t e r a t i o n p r o c e s s and c a l c u l a t e s Z, from e q u a t i o n (39) •• . 41) The quantum number )>{ i s a v a i l a b l e i n t a b u l a r form by l i n e a r i n t e r p o l a t i o n . Hence, t h e t h e o r e t i c a l r a t i o s o f each s t a t e i n t h e ground s t a t e r o t a t i o n a l band t o t h e f i r s t 2+-. l e v e l energy ( E 2 n ^ a r e c a l c u l a t e d by means o f e q u a t i o n (44) • ' • ' v • -109- . and (44a). The t h i r d program i s t h e same as t h e second except t h a t t h e quantum number i s r e p l a c e d by ^ , w h i c h i s . o b t a i n e d from 41) a n o t h e r t a b l e . T h i s g i v e s t h e e n e r g i e s o f t h e f i r s t e x c i t e d b e t a band. The f o u r t h program j u s t c a l c u l a t e s t h e r o t a t i o n a l p a r t o f t h e E2 t r a n s i t i o n p r o b a b i l i t i e s . T h i s i s done by u s i n g e q u a t i o n (59) w i t h t h e c o e f f i c i e n t s C^N and y known and w i t h a C l e b s c h - G o r d a n C o e f f i c i e n t s s u b r o u t i n e . The l a s t program t h e n c a l c u l a t e s t h e v i b r a t i o n a l p a r t of t h e p r o b a b i l i t y . T h i s program c o n t a i n s a l l t h e s u b r o u t i n e s n e c e s s a r y f o r s o l v i n g e q u a t i o n s (68) and (69). Note t h a t t h e i n t e g r a t i o n i n (68) i s done.by d i v i d i n g t h e i n t e g r a l range i n t o 20 i n c r e m e n t s . A l l t h e above programs a p p l y t o t h e q u a d r u p o l e case...' ( A = 2 ) and t h e o c t u p o l e case ( A = 3 ) . I n t h e p r e s e n t c a l c u l a t i o n , t h e f i r s t t h r e e programs were combined t o g e t h e r t o y i e l d a l l t h e l e v e l e n e r g i e s f o r a g i v e n p a i r o f 7 and . The e x p e r i m e n t a l v a l u e s o f a l l t h e l e v e l e n e r g i e s a r e a l s o r e a d i n . The root-mean-square d e v i a t i o n o f t h e c a l c u l a t e d l e v e l e n e r g i e s from the e x p e r i m e n t - a l ones i s found i n p e r c e n t a g e f o r m . I n t h i s c a l c u l a t i o n , t h o s e l e v e l s h a v i n g no e x p e r i m e n t a l c o r r e s p o n d e n c e a r e o m i t t e d .' Then ••.the "two parameters y and \K. a r e v a r i e d w i t h i n s u i t a b l e ranges . w h i c h e n c l o s e a minimum root-mean-square d e v i a t i o n of t h e l e v e l e n e r g i e s . F i n a l l y , t h i s minimum i s determined by i t e r a t i o n , and so a l s o the c o r r e s p o n d i n g l e v e l e n e r g i e s . By a p p l y i n g t h e l a s t two programs, the r a t i o s o f the reduced t r a n s i t i o n p r o b a b i l i t i e s a r e a l s o found. The r e s u l t s o f the energy f i t t i n g s i n the quadrupole case a r e p r e s e n t e d I n t a b l e IX. The root-mean-square d e v i a t i o n i n t h i s case i s d e f i n e d as f o l l o w s , fy ,„Th ^ E x p ^ U ~ = l ^ E L N n m -LNn > J ( 1 Q 2 ) where the summations a r e c a r r i e d out o v e r the l a s t s i x energy - l e v e l s i n t a b l e IX, - E ? ^ a r e the e x p e r i m e n t a l l e v e l e n e r g i e s ( i n Kev) determined, and the f i t t e d t h e o r e t i c a l l e v e l e n e r g i e s . Note t h a t the a r e i n an a r b i t r a r y energy s c a l e , and t h a t the e q u a t i o n (103) i s Th. Exo Th Exp o b t a i n e d under the r e s t r i c t i o n o f E Q - ^ = ^QJJ_ and E 0 ^ = E ^ i i • The purpose o f t h i s r e s t r i c t i o n i s to o b t a i n the same energy . s c a l e - f o r b o t h E?i? and E ^ P . I t s h o u l d a l s o be mentioned t h a t j_iNn L N n t h i s method o f f i t t i n g i s d i f f e r e n t f r o m t h e s t a n d a r d l e a s t - , square f i t . We b e l i e v e t h a t t h e a p p l i c a t i o n o f the l a t t e r method w i l l meet w i t h g r e a t c o m p u t a t i o n a l d i f f i c u l t i e s * " :; The RMS d e v i a t i o n D-r^jg r e s u l t i n g f r o m t h e v a l u e s i n . t a b l e .IX i s 1.503 per c e n t , and the c o r r e s p o n d i n g v a l u e s f o r the asymmetry parameter T and the s t i f f n e s s JU. a r e r e s p e c t i v e l y 11.52 degrees and 0.402. ' S i m i l a r ( u n p u b l i s h e d ) c a l c u l a t i o n s have. been.done by. 67) Davidson u s i n g a n o t h e r s e t o f e x p e r i m e n t a l d a t a . The r e s u l t s To f o l l o w page 110. '. . . ., o b t a i n e d f o r T and a r e 11.62 degrees and 0.401 r e s p e c t i v e l y ; i n good agreement w i t h o u r s . A v e r y r e c e n t p u b l i c a t i o n by A i s e n b e r g e t a l 6 8 ^ u s i n g the method o f Davydov and C h a b a n 1 2 ^ g i v e s T = 11.5 and Y =0.8. The e x p e r i m e n t a l d a t a i n t h i s 34) p u b l i c a t i o n have been determined by Yoshizawa et a l by means o f C o u l o m b . e x c i t a t i o n . Experimental E n e r § y ESn (Kev) T h e o r e t i c a l Energy E ^ n (Kev) D e v i a t i o n (%) L N n 0.00 0.00 0 1 1 122.93 122.93 2 1 1 995.75 1052.73 5.41 2 2 1 1127.35 1121.31 0.54 3 1 1 370.56 365.54 1.37. 4 1 1 1263.30 1211.96 4.24 4 2 1 680.10 676.49 0.53 0 1 2 814.77 831.85 2.05 2 1 2 Table IX Comparison of the experimental and t h e o r e t i c a l energies i n the quadrupole case (^=2, p o s i t i v e p a r i t y ) . _ " •'_ .• .. -111- To f i n d t h e r a t i o s o f t h e reduced t r a n s i t i o n p r o b a b i l i t i e s from t h e e x p e r i m e n t a l d a t a , we made use o f e q u a t i o n (51). Only- f o u r r a t i o s were c a l c u l a t e d , each o f whic h c o n s i s t s of two t r a n s i t i o n s from t h e same i n i t i a l s t a t e t o d i f f e r e n t l e v e l s o f t h e ground s t a t e b eta band. Assuming a l l t h e s e t r a n s i t i o n s a r e E2, t h e n from e q u a t i o n ( 5 l ) , / = 2 ; and hence B(E2,L-r -> L n ) = (E72) 5 Ti (E2) B(E2 , L i - ^ » L f 2 ) ( E n ) 5 T 2(E2) where Ey = fa • , t h e gamma energy. S u b s t i t u t i n g t h e experiment- a l r e l a t i v e i n t e n s i t i e s f o r T and T 2 and t h e c o r r e s p o n d i n g gamma e n e r g i e s , t h e r a t i o s B ( E 2 > Li L f i ) were found as B(E2 ,L i Lf2) below i n t a b l e X t o g e t h e r w i t h t h e t h e o r e t i c a l v a l u e s . Energy R a t i o Name E x p t . V a l u e Theo. V a l u e 995.94 872.62 [221] [bit! [22LJ -> [211] 0.43410.040 0.443 444.02 692.02 (212] (411} (212] - » [2113 3.790+0.629 4.352 815.02 692.02 [212] Con] [212] — 1211] 0.152+0.014 0.373 1004.5 756.71 [31.1] - f e l l ] [311] -* £411) 1.026+0.104 1.004 :Table X The b r a n c h i n g r a t i o s o f gamma t r a n s i t i o n s " between p o s i t i v e - p a r i t y l e v e l s . - 1 1 2 - Three o f the four, c a l c u l a t e d r a t i o s i n T a b l e X agree with- the measured v a l u e s w i t h i n the e x p e r i m e n t a l u n c e r t a i n t i e s . The t h i r d r a t i o 815/ 6 9 2 i s l e s s than h a l f the v a l u e p r e d i c t e d . T h i s s u g g e s t s t h a t i f the 815 Kev t r a n s i t i o n i s pure E2 w h i c h seems l i k e l y from the s p i n a ssignment o f the l e v e l s i n v o l v e d , then the 692 Kev t r a n s i t i o n has a s t r o n g EO component. The. c o n v e r s i o n c o e f f i c i e n t d a t a i n d i c a t e d t h i s , but p r e d i c t e d t h a t i t was o n l y 6 p e r c e n t . To acc o u n t f o r the low 8 15/692 r a t i o i n T a b l e X on t h i s b a s i s a l o n e , the EO component would have t o e q u a l about 60 p e r c e n t o f the t o t a l 692 Kev t r a n s i t i o n i n t e n s i t y . The 692 Kev t r a n s i t i o n i s i n v o l v e d i n one o t h e r r a t i o , 444 / 6 9 2 . W h i l e t h e o r y and e x p e r i m e n t agree here w i t h i n the e r r o r l i m i t s , the t h e o r e t i c a l v a l u e i s on the h i g h s i d e . I f a g a i n t h i s i s caused by the 692 Kev EO component, i n t h i s case i t o n l y r e q u i r e s . i t t o be about 12 p e r c e n t f o r the mean e x p e r i m e n t a l v a l u e to match the t h e o r e t i c a l p r e d i c t i o n . So i t i s not l i k e l y t h a t the low 8 15/692 r a t i o can be e x p l a i n e d i n t h i s way. Por the o c t u p o l e c a s e , s i n c e we have o n l y two n e g a t i v e p a r i t y l e v e l s ( 1 7 1 8 . 8 and 1 3 9 7 . 4 Kev) b o t h w i t h s p i n 2 , we a s s i g n e d them to be {~212]~ and ^ 2 1 l ] ~ r e s p e c t i v e l y . W i t h t h e s e T i t and.the s t i f f n e s s p-" were found t o be 4 . 6 0 6 degrees and 0 , 4 9 7 2 5 . No gamma t r a n s i t i o n was found beWeen them, a l t h o u g h t h e r e a r e s i x t r a n s i t i o n s l i n k i n g them to p o s i t i v e p a r i t y l e v e l s . The monopole t r a n s i t i o n p r o b a b i l i t y T(E0) f o r the- t r a n s i t i o n (0 + —>Q± n rj) was c a l c u l a t e d from e q u a t i o n ( 7 8 ) . The -113- f u n c t i o n s 1 ^ ( 0 ) , I p , ^ ( 2 ) , I y , ( 0 ) and I y / ( 2 ) were e v a l u a t e d v / i t h D a v i d s o n ' s s u b r o u t i n e s . The n u m e r i c a l v a l u e s o f the n e c e s s a r y parameters f o l l o w ; - E = 0 . 5 5 7 9 6 Mev. fl = 0 . 3 3 5 x 1 0 1 1 s e c " 1 p. = 0 . 4 0 2 1 5 8 p r o t = °«964775 f>0 = 0 . 3 0 3 z = 2 . 5 3 2 7 5 z-, = 2 . 5 6 6 6 8 ( r e f . ( Z f 5 > ) Z-f = 2 . 7 5 5 5 5 ( r e f . (16) Z' = 2.64444 1^(0) =. 1.726.0 1^(2) = 1.76-84 1 ^ ( 0 ) = 6.. 3418 . 1 ^ ( 2 ) = 1.5334 From these d a t a , T ( E 0 ) T ( E 2 ) v > (0; Ognd) = °«085 from ( 7 8 ) = 0 . 0 3 9 ± 0 . 0 1 2 ( e x p e r i m e n t a l ) I t thus appears t h a t the p r e d i c t i o n s o f the Asymmetric R o t a t o r model, w h i l e s u c c e s s f u l f o r the E2 r a t i o s , a r e n o t r e l i a b l e f o r monopole t r a n s i t i o n s . We n e x t programmed e q u a t i o n (78a) f o r the t r a n s i t i o n 692 Kev. The v a l u e s o f the parameters used were E = 0 . 6 9 2 0 2 Mev Z = fl = O.3.5 x: 1 0 1 1 s e c " 1 |JL = 0 . 4 0 2 1 5 8 p r o t = 0 . 2 7 1 4 B0 = 0 . 3 0 3 ° T i E O j . ( 2 + - - > 2 j n d ) = 0 . 1 5 8 Thence T(E2) P* Zx = 2.7 5 5 5 1 ^ ( 0 ) = 6 . 8 5 5 1 ^ 2 ) = 1 .236 from w h i c h the p r e d i c t e d E0 component i s a p p r o x i m a t e l y 13 per c e n t o f the t o t a l 692 t r a n s i t i o n . Assuming i t i s about t w i c e too l a r g e (as a b o v e ) , i t i s c o n s i s t e n t v / i t h the c o n v e r s i o n d a t a r e s u l t s . -114- CHAPTER ¥111 CONCLUSIONS • The i n f o r m a t i o n deduced from the p r e s e n t e x p e r i m e n t a l d a t a as w e l l as from t h a t o f the o t h e r w o r k e r s l e a d s t o a f a i r l y c omplete l e v e l s t r u c t u r e o f Gd 154 from the decay o f Eu 154. The gamma t r a n s i t i o n s from o n e - l e v e l t o a n o t h e r have been e x h a u s t i v e l y s o r t e d o u t . S h o u l d t h e r e be any new gamma t r a n s i t i o n s , t h e y must be e x t r e m e l y weak i n i n t e n s i t y . I t i s no t e x p e c t e d t h a t t h e r e w i l l be f u r t h e r m o d i f i c a t i o n t o the e n e r g i e s o f t h e l e v e l s t o any a p p r e c i a b l e e x t e n t . Because o f the p r e s e n c e o f some o f the weaker t r a n s i t i o n s shown i n t a b l e I I I , w h i c h a p p a r e n t l y have no p l a c e i n the decay scheme, i t i s hoped t h a t new l e v e l s w i l l be fo u n d i n the f u t u r e t o i n c l u d e t h e s e t r a n s i t i o n s . Comparison o f the e n e r g i e s o f the l e v e l s and the . gamma t r a n s i t i o n p r o b a b i l i t i e s w i t h the t h e o r e t i c a l v a l u e s . based on the Asymmetric R o t a t o r M odel d e m o n s t r a t e s as a whole the v a l i d i t y of t h i s model i n the p r e s e n t c h osen even- •-. even n u c l e u s (Gd 1 5 4 ) . The c l o s e f i t s i n most c a s e s a re r e m a r k a b l e . The e r r o r l i m i t o f the o +—>o + monopole t r a n - s i t i o n i s r e l a t i v e l y l a r g e . . E x p e r i m e n t a l l y , r e - i n v e s t i g a t i o n -115- o f the monopole t r a n s i t i o n s i n t h i s n u c l e u s might be b e s t c a r r i e d o ut by means o f Coulomb e x c i t a t i o n , because the b e t a e x c i t e d s t a t e s i n the p r e s e n t i n v e s t i g a t i o n a r e w e a k l y pop- u l a t e d . Thus the t r a n s i t i o n i n t e n s i t i e s were e s t i m a t e d w i t h g r e a t d i f f i c u l t y . As has been shov/n i n the s e c t i o n on model f i t t i n g , ( Chapter 7 ), the d e t e r m i n a t i o n o f the asymmetry parameter Y and the s t i f f n e s s parameter JJL i n v o l v e s the assignment o f the t h e o r e t i c a l e n e r g i e s o f the two l o w e s t energy l e v e l s t o be e q u a l t o the c o r r e s p o n d i n g e x p e r i m e n t a l l y determined e n e r g i e s . In t h i s method, we have o n l y two parameters ( i . e . and ) to v a r y i n o r d e r to a c h i e v e a minimum RMS d e v i a t i o n . An a l t e r n a t i v e method -would be t o r e l a x the c o n d i t i o n o f such an a s s i g n m e n t . In consequence, Wo a d d i t i o n a l a d j u s t a b l e parameters would have t o be v a r i e d i n o r d e r to m i n i m i z e the RMS d e v i a t i o n . Computation by t h i s method would c e r t a i n l y be more complex. One c o u l d , o f c o u r s e , i n c l u d e the RKS v a l u e s o f the reduced t r a n s i t i o n p r o b a b i l i t i e s i n o r d e r to e v a l u a t e y and JX . However, the u n c e r t a i n t y l i m i t s on these r a t i o s a r e i n g e n e r a l much l a r g e r than those o f the l e v e l e n e r g i e s so t h a t the a c c u r a c y o f the method c o u l d be reduced over the p r e s e n t a p p r o a c h . F i n a l l y , i t i s u r g e n t l y to be hoped t h a t the f u r t h e r development o f t h i s model o f the n u c l e u s v / i l l i n c l u d e the p r e d i c t i o n o f the t r a n s i t i o n p r o b a b i l i t i e s between n e g a t i v e . p a r i t y and p o s i t i v e p a r i t y l e v e l s . There a r e a s u f f i c i e n t -116- number o f such t r a n s i t i o n s i n even-even n u c l e i to make such c a l c u l a t i o n s b o t h i n t e r e s t i n g and u s e f u l . -117- REPERENCES • 1. K. Sle g b a h n , A l p h a - , Beta-and Gamma-ray S p e c t r o s c o p y , p.557 2. A. Bohr, Mat.Fys.Medd.Dan.Vid.Selsk 26, No . l 4 (1952). 3..- J . R a i n w a t e r , Phys. Rev. 79, 432 (1950).. 4. A. F a e s s l e r & ¥. G r e i n e r , Z. P h y s i k 168, 425 (.1962) . 5. A. F a e s s l e r & W. G r e i n e r , Z. P h y s i k 170, 105 (1962). 6. A. F a e s s l e r & W. G r e i n e r , Z. P h y s i k 177, 190 (1964). 7. A. F a e s s l e r , W. G r e i n e r & R.K. S h e l i n e , P h y s i c s Dept., U n i . M a r y l a n d , TR No. 345 (1963). . 8. A. F a e s s l e r , W. G r e i n e r & R.K. S h e l i n e , P h y s i c s D e p t . , U n i . Mary l a n d , TR No. 372 (1964). 9. R.K. S h e l i n e , Rev. Mod. Phys. 3_2, 1 (i960) . 10. A.S. Davydov & G .F. F i l i p p o v , - Nu. Phys. 8, 237 (1958). 11. A.S. Davydov & V.S. R o s t o v s k y , Nu. Phys. 12, 58 (1959). 12. A.S. Davydov &A.A. Chahan, Nu. Phys. 20_, 499 ( i960). 12a. A.S. Davydov , Nu. Phys. 20, 682(1961) . 13. A.S. Davydov, V.S. R o s t o v s k y & A.A. Chaban, Nu. Phys. 27, 134 (1961). 14. S.A. W i l l i a m s & J.P. Davidson,. Can. J . Phys. 40, 1423(1962) 15. J.P. D a v i d s o n & M.G. D a v i d s o n , Phys. Rev. 138, B3l6 (1964). 16. J.P. D a v i d s o n , Nu. Phys. 86_, 561 (1966). 17. J.M. Cork, M.K. B r i c e , R.G. Helmer & D.E. Sara son, Phys. • Rev. 107, 1621 (1957). -118- ' 18. J.O..Juliano & P.S. Stephens, Phys. Rev. 108, 3 4 1 (1957). 19. B.S. 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