Spin assignments in the transitional nuclei 215Po, 219Rn and 223Ra from alpha-gamma directional correlation measurements

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SPIN ASSIGNMENTS IN

THE TRANSITIONAL NUCLEI ^^^?o, ^^^Rn

AND " 3 Ra FROM ALPHA-GAMMA

DIRECTIONAL CORRELATION MEASUREMENTS

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SPIN ASSIGNMENTS IN

THE TRANSITIONAL NUCLEI ^'=Po, ^''Rn

AND " 3 Ra FROM ALPHA-GAMMA

DIRECTIONAL CORRELATION MEASUREMENTS

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SPIN ASSIGNMENTS IN

THE TRANSITIONAL NUCLEI ^''Po, ^ " R n

AND " ' Ra FROM ALPHA-GAMMA

DIRECTIONAL CORRELATION MEASUREMENTS

PROEFSCHRIFT

ter verkrijging van de graad van doctor in de technische wetenschappen

aan de Technische Hogeschool Delft, op gezag van de Rector Magnificus ir. H. R. van Nauta Lemke, hoogleraar in de Afdeling der Elektrotechniek, voor een Commissie aangewezen door het College van

Dekanen te verdedigen op donderdag 28 September te 14.00 uur

door

WILHELMUS HENDRIKUS ARNOLDUS HESSELINK geboren te Wisch

€S./ L

1972

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Dit proefschrift is goedgekeurd door de promotor prof. dr. A. H. Wapstra.

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Aan Irmgard, Martijn en Mayke

Aan mijn ouders.

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CONTENTS page I GEHERAL INTRODUCTION 9 II METHODS 12 1 1 . 1 I n t r o d u c t i o n 12 1 1 . 2 Alpha-gamma d i r e c t i o n a l c o r r e l a t i o n 13 1 1 . 3 P e r t u r b a t i o n s o f t h e d i r e c t i o n a l c o r r e l a t i o n IT II. 3.1 Perturbations by extra-nualear effeats IT

II. 3. 2 Finite solid angle aorreations 18

I I I EXPERIMENTAL ARRANGEMENTS 21 1 1 1 . 1 D e t e c t i o n and a n a l y s i s 21 1 1 1 . 2 D i r e c t i o n a l c o r r e l a t i o n s e t - u p 25 III. 2.1 Turn-table 25 III. 2. 2 Automation 26 1 1 1 . 3 A r r a n g e m e n t f o r a d e c o u p l i n g e x p e r i m e n t 2T

III. 3.1 The liquid helium oryostat 2T III. 3.2 Superconductive magnet 30

IV THE DECAY OF 2 19^^ AND ^2 3 ^ ^ 3h

I V . 1 I n t r o d u c t i o n 3^ I V . 2 Alpha-gamma c o i n c i d e n c e s 34

I V . 3 Alpha-gamma d i r e c t i o n a l c o r r e l a t i o n s ^ 0 IV.lt C o n v e r s i o n e l e c t r o n m e a s u r e m e n t s h2 IV. 5 S p i n a s s i g n m e n t s i n 215pQ ^^^ 219RJJ I48

IV. 5.1 Directional correlations in the decay of ^^'^Rn k8

IV. 6.2 The ground state spin of ^^^Ra 51 IV. 6. 3 The spin of levels in ^"^^Rn 51

I V . 6 C o n c l u s i o n 3^

V THE DECAY OF ^ZV^h 56 V.1 I n t r o d u c t i o n 56 V.2 Alpha-gamma c o i n c i d e n c e s 56

V . 3 Alpha-gamma d i r e c t i o n a l c o r r e l a t i o n s 6 8 V. 3.1 Instriments and source preparation 6 8

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CONTENTS (continued)

page

V. 3. 2 Experimental results 69

V. 1* Spin assignments in 223^3^ T3

V.4.1 The ground state spin of ^^''Ac and ^^'^Th T3

V.4.2 The spin of levels in ^^^Ra T3

V. 5 Band assignments in 223^3^ yQ

VI PERTURBATIONS OF ALPHA-GAMMA DIRECTIONAL CORRELATIONS IN

THE DECAY OF 2 3 0u AND 22 6Th 82

VI.1 Introduction 82 VI.2 Instruments and source preparation 82

VI.3 Measurements and results 83

VI. 1* Discussion 85

SUMMARY 8 T

SAMENVATTING 88

NAWOORD 89

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CHAPTER I GENERAL INTRODUCTION The n u c l e a r s h e l l model d e s c r i b e s t h e n u c l e u s i n t e r m s o f t h e m o t i o n o f t h e i n d i v i d u a l n u c l e o n s i n an i s o t r o p i c a v e r a g e d p o t e n t i a l ^ > ^ ) . A g r e a t v a r i e t y o f e x p e r i m e n t a l d a t a h a s b e e n e x p l a i n e d on b a s i s o f t h i s m o d e l . D i s c o n t i n u i t i e s i n n u c l e a r q u a n t i t i e s s u c h a s n u c l e a r m a s s , a - d e c a y e n e r g y and S - d e c a y e n e r g y , o c c u r r i n g a t t h e "magic n u m b e r s " caji be u n d e r s t o o d i f a s p i n - o r b i t c o u p l i n g f o r t h e n u c l e o n s i s a s s u m e d . N e a r t h e c l o s e d s h e l l n u c l e i , i . e . n e a r t h e " m a g i c n u m b e r s " , t h e n u c l e a r l e v e l s c h e m e s a r e s u c c e s s f u l l y i n t e r p r e t e d b y t h e s h e l l m o d e l .

When t h e nxomber o f n u c l e o n s d i f f e r s s t r o n g l y from t h a t o f t h e c l o s e d s h e l l s , t h e a s s u m p t i o n o f an i s o t r o p i c p o t e n t i a l i s n o t l o n g e r v a l i d and n u c l e a r d e f o r m a t i o n s s h o u l d be t a k e n i n t o a c c o u n t . C o l l e c t i v e m o t i o n o f t h e n u c l e u s h a s t h e n a l s o t o be c o n s i d e r e d . The N i l s s o n model d e s c r i b e s t h e m o t i o n of t h e l a s t odd n u c l e o n i n t h e f i e l d o f a d e f o r m e d r o t a t i n g n u c l e a r c o r e ' ^ ) . The s i n g l e p a r t i c l e s t a t e s o f d e f o r m e d n u c l e i a r e l a b e l e d b y t h e c o m b i n a t i o n o f t h e N i l s s o n quantum n u m b e r s K [N, n , A ] . K i s t h e p r o j e c -t i o n of -t h e p a r -t i c l e a n g u l a r momen-tum on -t h e n u c l e a r symme-try a x i s . T h i s quantum n u m b e r r e p l a c e s t h e t o t a l a n g u l a r momentum q u a n t u m number J o f t h e p a r t i c l e s i n a s p h e r i c a l n u c l e u s . The ( 2 J + 1 ) f o l d d e g e n e r a t e s t a t e w i t h s p i n J i s s p l i t up i n t o ( 2 J + l ) / 2 s t a t e s , e a c h t w o f o l d d e g e n e r a t e . N r e p r e -s e n t -s t h e t o t a l number o f o -s c i l l a t i o n -s o f t h e wave f u n c t i o n and n t h e

z

number of o s c i l l a t o r q u a n t a a l o n g t h e symmetry a x i s . The component o f t h e t o t a l o r b i t a l a n g u l a r momentum on t h e symmetry a x i s i s r e p r e s e n t e d b y A. The r o t a t i o n of t h e n u c l e u s a r o u n d an a x i s p e r p e n d i c u l a r t o t h e symme-t r y a x i s g e n e r a symme-t e s a number o f e x c i symme-t e d s symme-t a symme-t e s w i symme-t h i n c r e a s i n g s p i n , f o r m i n g a r o t a t i o n a l b a n d . The p r o j e c t i o n of t h e s p i n on t h e symmetry a x i s i s c o n -s e r v e d f o r t h e member-s o f a r o t a t i o n a l b a n d . The e n e r g i e -s o f t h e l e v e l -s f o r m i n g s u c h a b a n d can be w r i t t e n a s E ( J ) = E(j + I Y {J (J+1) + a (-l)-^""^ ( J + n &^^,_} E i s a c o n s t a n t depending on t h e n u c l e a r s t r u c t u r e . I i s t h e e f f e c t i v e moment of i n e r t i a . The l a s t term i n the expression for E(J) i s a c o r r e c t i o n

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t e r m , which i s only important for K = 1/2 bands. 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 of t r a n s i t i o n s t o d i f f e r e n t l e v e l s of a r o t a t i o n a l band can be expressed by Clebsoh-Gordan c o e f f i c i e n t s , t h e 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 very useful m determining t h e s t a t e s which belong t o a r o t a t i o n a l band. The i s o t o p e s 215pQ ^ 219pj^ g^j^^ 223pg^ g^j.^ n u c l e i of t h e t r a n s i t i o n r e g i o n between n u c l e i which can be adequately d e s c r i b e d by t h e s h e l l model and n u c l e i which are s u c c e s s f u l l y explained by t h e Nilsson model. The neutron number of 215pQ -^g 5 h i g h e r than t h a t of t h e closed s h e l l nucleus •^^^P'b. The s h e l l model p r e d i c t s a 2g . o r b i t for the l a s t added neutron i n ^ P o . Thus, t h e ground s t a t e spin of 215pg should be 9/2 i f t h e s h e l l model p r e d i c t i o n s are v a l i d . However, m e a r l i e r s t u d i e s a spin of 7/2 was t e n t a t i v e -l y a s s i g n e d t o t h e ground s t a t e of 215pQ ( r e f s . h-6). An attempt i s made in t h i s study t o s e t t l e t h i s q u e s t i o n .

The nucleus 223j^^^ having 9 a d d i t i o n a l n e u t r o n s a s compared t o " ^ P b may a l r e a d y have a s t a b l e n o n - s p h e r i c a l p o t e n t i a l m i t s ground s t a t e . A

1/2 [6U0] ground s t a t e r o t a t i o n a l band has been p o s t u l a t e d , based on t h e r e s u l t s of a - p a r t i c l e and conversion e l e c t r o n s p e c t r o s c o p y ' ) . The occur-rence of o t h e r proposed b a n d s , though, i s much l e s s e v i d e n t . More d e f i n i t e spin assignments are needed for a b e t t e r u n d e r s t a n d i n g of the l e v e l scheme of t h i s n u c l e u s . P r e d i c t i o n s can hardly be made for t h e spins of l e v e l s in 2'5Rn. The a p p l i c a b i l i t y of t h e s h e l l model i s here v e r y doubtful, but well developed r o t a t i o n a l bands can a l s o h a r d l y be expected.

Knowledge of s p i n s of n u c l e a r l e v e l s i s e s s e n t i a l f o r the i n t e r p r e -t a -t i o n of l e v e l schemes. D i r e c -t i o n a l c o r r e l a -t i o n measuremen-ts a r e a very v a l u a b l e t o o l in o r d e r t o assign spins t o n u c l e a r l e v e l s . In t h e p r e s e n t work, d i r e c t i o n a l c o r r e l a t i o n s have been s t u d i e d for a l a r g e number of a-Y cascades in t h e decay of ' ^Rn, 223fjg^ ^j^^j 227r]ij^_ D e t a i l e d information about t h e numerous y - r a y t r a n s i t i o n s in t h e s e n u c l e i was required f o r the c o r r e c t i n t e r p r e t a t i o n of t h e measured c o r r e l a t i o n s . This information has been o b t a i n e d by performing a-y coincidence measurements.

D i r e c t i o n a l c o r r e l a t i o n s may be s t r o n g l y p e r t u r b e d due to i n t e r a c t i o n s of t h e nucleus w i t h i t s environment. In even-even n u c l e i , a-y c a s c a d e s with well known d i r e c t i o n a l c o r r e l a t i o n p a t t e r n s occur and can be used f o r a study of p e r t u r b a t i o n s . Such a study has been made f o r some cascades in the decay of 226^^ and ^^^U.

In i s o l a t e d atoms p e r t u r b a t i o n s a r e caused by coupling of t h e nuclear

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spin to the total angular momentum of the atomic electrons. The influence of this type of perturbations can be removed if a-y directional correlation experiments are performed in an external magnetic field, applied in the direction of emission of the a-particles. A system using a superconductive magnet has been designed for this type of experiments.

Chapter II is devoted to the description of theoretical and experimen-tal aspects of the a-y directional correlation method. A description of the experimental arrangements is presented in chapter III. The measurements and their interpretation are described in chapters IV, V and VI. The contents of these chapters consists of the complete manuscripts of publications 2)

References

1) E.K. Hyde, I. Perlman and G.T. Seaborg, The Nuclear Properties of the Heavy Elements, part II, Englewood Cliffs I96U

2) M. Goeppert Mayer, J.H.D. Jensen and D. Kurath, a-, 8-, y-Ray Spectros-copy, Vol. I, K. Siegbahn ed., North Holland Amsterdam (I965)

3) 0. Nathan and S.G. Nilsson, a-, S-, y-Ray Spectroscopy, Vol. I, K. Sieg-bahn ed., North Holland Amsterdam (I965)

1+) R.C. Pilger, University of California, Radiation Lab. Rept. UCRL 38TT (1957)

5) W.F. Davidson and R.D. Connor, Nucl. Phys. All+9 (1970) 363

6) K. Krien, C. Gunther, J.D. Bowman and B. Klemme, Nucl. Phys. Ali+l (1970) 75

7) C. Vieu, Thesis Paris (I966)

8) W.F. Davidson and R.D. Connor, Nucl. Phys. AII6 (1968) 3I+2 9) Ch. Brian(;on, Thesis Paris (1970)

10) W.H.A. Hesselink, J.G. Kromme, A.H. Wapstra, K.E.M. Dijkman and J. Schipper, to be published

11) W.H.A. Hesselink, A.H. Wapstra, J.G. Kromme, E.J. Haighton, M. van Kampen, W. Hutjes and K.E.M. Dijkman, accepted for publication in Nuclear Physics

12) W.H.A. Hesselink and M. van Kampen, Z. Phys. 2l+7 (I97l) I6I.

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CHAPTER I I METHODS I I . 1 I n t r o d u c t i o n The l e v e l s c h e m e s o f d a u g h t e r n u c l e i of a d e c a y i n g i s o t o p e s a r e p r i -m a r i l y c o n s t r u c t e d fro-m t h e r e s u l t s o f a - p a r t i c l e s p e c t r o s c o p y . Fro-m y - r a y and c o n v e r s i o n e l e c t r o n s p e c t r o s c o p y i n f o r m a t i o n i s o b t a i n e d on t h e d e -e x c i t a t i o n o f -e x c i t -e d l -e v -e l s . T h -e s -e s i n g l -e m -e a s u r -e m -e n t s g i v -e m o s t l y no c o m p l e t e u n d e r s t a n d i n g o f t h e complex d e c a y s c h e m e s . More i n f o r m a t i o n on t h e d e c a y o f an e x c i t e d s t a t e can b e o b t a i n e d by m e a s u r i n g t h e y r a y s p e c -t r u m i n c o i n c i d e n c e w i -t h -t h e a - p a r -t i c l e s f e e d i n g -t h a -t l e v e l . I n -t h i s way one may s e l e c t t r a n s i t i o n s w h i c h d e c a y from a p a r t i c u l a r n u c l e a r s t a t e .

The a p a r t i c l e s e m i t t e d b y a r a d i o a c t i v e n u c l e u s c a r r y away an a n g u -l a r momentum L ( u n i t s h ) . The p a r i t y o f t h e e m i t t e d a - w a v e s i s IT = ( - 1 ) . 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 i n a n u c l e u s a r e a l s o c l a s s i f i e d a c c o r d i n g t h e i r a n g u l a r momentum and p a r i t y . The p a r i t i e s o f e l e c t r i c and m a g n e t i c m u l t i -p o l e s h a v i n g a n g u l a r momentum L a r e ( - 1 ) a n d ( - 1 ) , r e s -p e c t i v e l y . The p o s s i b l e a - p a r t i c l e s and y - r a y s a r e l i m i t e d by s e l e c t i o n r u l e s a r i s i n g

from t h e c o n s e r v a t i o n o f a n g u l a r momentum a n d p a r i t y . The s e l e c t i o n r u l e s f o r t r a n s i t i o n s b e t w e e n two s t a t e s h a v i n g s p i n J - and J and p a r i t i e s TT. and TT a r e l ^ i - J f I 4 L i | J - + J f l ( I I . 1 ) 11. Tt = ( - 1 ) f o r a - w a v e s "^ L = ( - 1 ) f o r e l e c t r i c m u l t i p o l e s ( I I . 2 ) , > L+ 1 • 1 ; f o r m a g n e t i c m u l t i p o l e s The 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 l e c t r o m a g n e t i c r a d i a t i o n d e c r e a s e s s t r o n g l y w i t h i n c r e a s i n g L. T h e r e f o r e , t h e l o w e s t m u l t i p o l e L = | j . - J | m o s t l y s t r o n g l y p r e d o m i n a t e s , t h o u g h a m i x t u r e o f t h e two l o w e s t m u l t i -p o l e s L and L+1 may o c c u r . I n a - d e c a y t h e t r a n s i t i o n -p r o b a b i l i t y d e c r e a s e s f a r l e s s s t r o n g l y w i t h i n c r e a s i n g a n g u l a r momentum L o f t h e e m i t t e d a p a r -t i c l e s . An a n g u l a r momen-tum L+2 i s o f -t e n f o u n d i n c o m b i n a -t i o n w i -t h -t h e l o w e s t v a l u e L. 12

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Instead o f e m i t t i n g a yray a nucleus in an e x c i t e d s t a t e can t r a n s -f e r energy t o an o r b i t a l e l e c t r o n , which r e s u l t s in t h e emission o-f an atomic e l e c t r o n . This p r o c e s s i s c a l l e d i n t e r n a l conversion. The conversion e l e c t r o n s are d i s t i n g u i s h e d in K, L , L , L , M , e t c . e l e c t r o n s a c c o r -ding t o t h e i r o r i g i n from d i f f e r e n t e l e c t r o n s h e l l s . The i n t e n s i t y r a t i o s of t h e d i f f e r e n t conversion e l e c t r o n s a r e r e p r e s e n t a t i v e for t h e m u l t i -p o l a r i t y of a n u c l e a r t r a n s i t i o n . Thus, conversion e l e c t r o n measurements can give information on t h e m u l t i p o l a r i t i e s of t h e e m i t t e d y - r a y s .

Information on n u c l e a r spins and m u l t i p o l a r i t i e s of e m i t t e d r a d i a t i o n can be obtained by study of t h e d i r e c t i o n a l d i s t r i b u t i o n of y - r a y s e m i t t e d by o r i e n t e d n u c l e i . Normally, t h e n u c l e i a r e rajidomly o r i e n t e d in space and t h e r a d i a t i o n e m i t t e d from a r a d i o a c t i v e sample i s i s o t r o p i c . I f n u c l e i decay through s u c c e s s i v e emission of two r a d i a t i o n s , an ensemble of o r i e n -t e d n u c l e i can be o b -t a i n e d by d e -t e c -t i n g -t h e primary r a d i a -t i o n in a fixed d i r e c t i o n . Then, t h e succeeding r a d i a t i o n g e n e r a l l y has a non i s o t r o p i c d i r e c t i o n a l d i s t r i b u t i o n with r e s p e c t t o t h e d i r e c t i o n of emission of t h e primary r a d i a t i o n . I t i s assumed t h a t t h e n u c l e a r spin d i r e c t i o n remains unchanged in t h e i n t e r m e d i a t e s t a t e between t h e s u c c e s s i v e r a d i a t i o n s . This assumption holds i f t h e l i f e - t i m e of t h e i n t e r m e d i a t e s t a t e i s s h o r t

(T < 10~^1 s . ) . When t h e l i f e - t i m e i s l o n g e r , r e o r i e n t a t i o n of t h e n u c l e a r spin due t o i n t e r a c t i o n of t h e nucleus with i t s environment can p e r t u r b t h e d i r e c t i o n a l c o r r e l a t i o n p a t t e r n .

I I . 2 Alpha-gamma d i r e c t i o n a l c o r r e l a t i o n

The p r o b a b i l i t y of emission of two u n p o l a r i z e d r a d i a t i o n s as a func-t i o n of func-the angle 6 befunc-tween func-t h e r a d i a func-t i o n s , W ( 9 ) , can be expressed in Legendre p o l y n o m i a l s ^ ' ):

W (6) = S A ' ^ ^ P^ (COS e) ( I I . 3 ) k=even

The a n i s o t r o p y c o e f f i c i e n t s A are i n d i c a t e d by dashed symbols t o d i s t i n -guish them from t h e normalized values which a r e i n t r o d u c e d l a t e r . Since p a r i t y i s conserved i n a - p a r t i c l e and y - r a y decay A^ = 0 for odd k v a l u e s and summation i s only over even i n t e g e r s . The A c o e f f i c i e n t s can be e x -p r e s s e d as a -product A^ ( l ) A ( 2 ) , in which t h e two f a c t o r s de-pend only

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F i g . I I . 1. Quantum numbers i n v o l v e d in t h e a-y d i r e c t i o n a l c o r r e l a t i o n

on t h e p r o p e r t i e s of t h e f i r s t and second r a d i a t i o n , r e s p e c t i v e l y . For a a-y cascade having parameters as defined in f i g . I I . 1 the A (a) and A^ (y) c o e f f i c i e n t s are given by t h e e x p r e s s i o n s ' ' 2 ) :

A^ (a) = I ^ (-1) ^ cj^o (LiLla) W ( J J L i L ) ; k J . ) < J | | Lj LiL _1^1 < J J. > 1 J . > 1 ( I I . M T o • .1.

A|^ (y) = I , (-1) Cj^g (L2L2y) W (JJL2L2;kJ^) < J II L2 II J^ >" L2L2

< J

•^f ^ ( I I . 5 )

The Racah c o e f f i c i e n t s W ( j J L j L j j k J . ) and W (JJL2L2 ;kJ ) a r i s e s from summa-t i o n of m a summa-t r i x elemensumma-ts d e s c r i b i n g summa-t r a n s i summa-t i o n s besumma-tween magnesumma-tic sublevels having quantum numbers J. m. , J m and J m . The r a d i a t i o n parameters c, (LiLia) and c, (LoLoy) a r e r e l a t e d t o t h e d i r e c t i o n a l d i s t r i b u t i o n

ko M '^° ^ ^ ' '

f u n c t i o n s Fl (9) of a- and y - r a d i a t i o n s having a n g u l a r momentum quantum L

number L and magnetic quantum number M. The m a t r i x elements of t h e form < J i J2 > give t h e amplitudes for r a d i a t i o n s having d i f f e r e n t angular momentum. The mixing r a t i o S of t h e s e amplitudes can be defined

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< J l I I L I I J >

6 = ^— ( I I . 6 ) < Ji II L ' I I J^ >

The phase between the amplitudes i s e i t h e r 0 or 180 for reasons of time r e v e r s a l i n v a r i a n c e ; t h u s 6 can be e i t h e r p o s i t i v e or n e g a t i v e . Then, t h e r a t i o of t h e i n t e n s i t i e s of t h e r a d i a t i o n s i s equal t o <S2 .

The r a d i a t i o n parameters for a - p a r t i c l e s and y - r a y s a r e given by t h e e x p r e s s i o n s :

1 L i I , 1

Cj^^(LiLia) = (-1) C(LiLik;00) [ (2Li+1 ) (2Li + 1 )] ' (11-7)

=J^O(L2L2Y) = (-1) ^"^ C(L2L2k;1-l) [ (2L2+1 ) (2L2+I )] ' ( I I . 8 )

The c o e f f i c i e n t s C (LiLik;00) and C (L2L2k;1-l) a r e Clebsch-Gordan

c o e f f i c i e n t s . After n o r m a l i s a t i o n (A (a) = 1 and A (y) = l ) and combination o o

of Racah and Clebsch-Gordan c o e f f i c i e n t s i n t o F c o e f f i c i e n t s , which a r e t a b u l a t e d for a l l cases of i n t e r e s t (see r e f . 3 ) , t h e following expression i s found for t h e normalized A (y)

K

F (L2L2J„J) + 26 F (L2L2J.J) + 6^F, (L2L2 J„J)

A^(y)=^^ ^^ ^^ ^~ (II.9)

^ 1 + 62 Y

An analogous formulae can be obtained for A^(a) if L j^ 0. The F coeffi-cients have only to be multiplied by the particle parameters defined as

\ ^ (LlLia)

\ ^^1^1") = c' (LiLly) ("•^°)

ko '• ^

I n t r o d u c t i o n of t h e p a r t i c l e parameters as defined above means t h a t t h e y - r a d i a t i o n parameters a r e taken as s t a n d a r d s . Expansion of t h e Clebsch-Gordan c o e f f i c i e n t s shows t h a t t h e a - p a r t i c l e parameters can be w r i t t e n as

2 [ L i ( L i + l ) h[ ( L j + l ) ] ^

^ ( L i L l a ) = L i ( L i + l ) + L 1 ( L ; + 1 ) - k ( k + l ) =°^ ^"h^'^Ll ' " ' " ^

cos {a -a ) i s a phase s h i f t f a c t o r , which i s only s l i g h t l y d i f f e r e n t from

Lj Lj

one, caused by t h e d i s t o r t i o n of t h e outgoing a-waves by t h e screened Cou-lomb f i e l d of t h e n u c l e u s .

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F i n a l l y , t h e normalized d i r e c t i o n a l c o r r e l a t i o n function W (9) i s given by t h e expression

W (9) = 1 + X A (a) A (y) P (cos 9) (11.12) k=even

S i n c e , t h e Clebsch-Gordan and Racah c o e f f i c i e n t s vanish i f k > L + L and t h e l a t t e r a l s o i f k > 2J i t i s u s u a l l y not n e c e s s a r y t o proceed t o higher values than h for k.

The y - r a y s always c a r r y away a non zero angular momentum. T h e r e f o r e , t h e p a r t i c l e parameters and F c o e f f i c i e n t s are meaningless i f L = 0. On t h e c o n t r a r y , L = 0 waves do occur i n adecay. In t h a t case t h e A (a) c o e f f i -c i e n t s have t o be -c a l -c u l a t e d d i r e -c t l y from eq. ( l l . l * ) . Su-ch a -computation of t h e n e c e s s a r y A2 (a) c o e f f i c i e n t for c o r r e l a t i o n s of cascades having i n i t i a l spin J . and i n t e r m e d i a t e spin J g i v e s t h e following r e s u l t

1 1

5^ll+6 W(JJ02;2J.) cos ( o n - a , ) - 5 . ll+^'^W(JJ22;2J. )

A2 (a) = ^ i : i - (11.13) TW(JJOO;OJ.) + 5 ^ 7 6 2 w ( J J 2 2 ; 0 J . )

1 a 1

The Clebsch-Gordan c o e f f i c i e n t s , used in t h i s c a l c u l a t i o n , have been taken from t h e t a b l e s of Inoue ( r e f . It). The n e c e s s a r y Racah c o e f f i c i e n t s are t a b u l a t e d in the t a b l e s of Rotenberg ( r e f . 5 ) .

The t h e o r e t i c a l a n i s o t r o p y c o e f f i c i e n t s have been c a l c u l a t e d for a g r e a t number of a-y c a s c a d e s , using eq. ( I I . 9 ) , ( I I . I I ) and ( I I . I 3 ) . For each cascade t h e c a l c u l a t i o n s were c a r r i e d out for s e v e r a l mixing r a t i o s of t h e a - p a r t i c l e and y-ray angular momenta. A computer program in Algol has been developed for t h i s purpose.

Since W (9) can be w r i t t e n as a s e r i e s of Legendre polynomials A P (cos 9 ) , t h e A c o e f f i c i e n t s can be found experimentally by p e r f o r

-K.K. K. -K.K.

ming coincidence measurements at n angles between the detectors (n is the number of coefficients to be measured). Normally, angles at 90 , 135 and 180 have been chosen for a measurement of A22 and Ai,i,. For reasons of symmetry, coincidences have also been measured at the negative angles. The coincidence counting rate at different angles has to be corrected for background radiation and accidental coincidences. In order to calculate the

experimental anisotropy coefficients from the coincidence counting rates, 16

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t h e l a t t e r have t o be normalized t o t h e t o t a l number of d e s i n t e g r a t i o n s . Normalization i s p r e f e r a b l y performed by d i v i d i n g t h e coincidence counting r a t e s by the c o u n t i n g r a t e s i n t h e y - r a y d e t e c t o r . This procedure has t h e advantage t h a t t h e coincidence counting r a t e s a r e independent of t h e s o l i d a n g l e s of the y r a y d e t e c t o r , t h e p o s i t i o n of which v a r i e s during t h e e x -p e r i m e n t . A s l i g h t maladjustment of t h e source causes s l i g h t l y d i f f e r e n t a n g l e s .

I I . 3 P e r t u r b a t i o n s of d i r e c t i o n a l c o r r e l a t i o n s

J J . 3.1 Perturbations by extra-nualear effects

In the deduction of t h e A, , c o e f f i c i e n t s i t i s assumed t h a t t h e l i f e kk

time of the i n t e r m e d i a t e s t a t e i s so short t h a t t h e o r i e n t a t i o n of t h e n u c l e a r spin remains unchanged i n t h e i n t e r m e d i a t e s t a t e . This can be e x p e c t e d i f the l i f e time x 4 1 0 " ' ' s . I f t h e l i f e time i s l o n g e r , i n t e r a c -t i o n of -the n u c l e u s wi-th i -t s environmen-t may cause r e o r i e n -t a -t i o n of -t h e n u c l e a r spin.

Two kinds of i n t e r a c t i o n can be d i s t i n g u i s h e d , namely t h e i n t e r a c t i o n of t h e nuclear magnetic moment with an e x t r a - n u c l e a r magnetic f i e l d and t h e i n t e r a c t i o n of t h e n u c l e a r quadrupole moment with ain e x t r a n u c l e a r e l e c -t r i c f i e l d g r a d i e n -t . These i n -t e r a c -t i o n s cause a changing popula-tion balance of n u c l e a r s t a t e s having d i f f e r e n t magnetic quantum numbers ( m - s t a t e s ) . A s t a t i c f i e l d cannot a f f e c t t h e d i s t r i b u t i o n over m - s t a t e s with r e s p e c t t o t h e d i r e c t i o n of t h e f i e l d . This i m p l i e s t h a t a s t a t i c i n t e r a c t i o n , even i n t h e case of randomly o r i e n t e d f i e l d s , cannot completely d i s t u r b a d i r e c t i o n a l c o r r e l a t i o n p a t t e r n . As a s p e c i a l consequence, an e x t e r n a l mag-n e t i c f i e l d , a p p l i e d imag-n t h e d i r e c t i o mag-n of emissiomag-n of t h e f i r s t - r a d i a t i o mag-n , w i l l not i n f l u e n c e a d i r e c t i o n a l c o r r e l a t i o n . On t h e o t h e r hand, a time dependent f i e l d can completely d e s t r o y a n i s o t r o p i e s , depending on t h e r e -l a x a t i o n time of t h e f i e -l d as compared t o t h e -l i f e - t i m e of t h e nuc-leus i n t h e i n t e r m e d i a t e s t a t e .

I f the i n t e r a c t i o n s are caused by randomly o r i e n t e d f i e l d s , t h e form of t h e angular c o r r e l a t i o n p a t t e r n i s not changed by t h e p e r t u r b a t i o n s . Then, t h e d i r e c t i o n a l c o r r e l a t i o n f u n c t i o n for a time i n t e g r a t e d measure-ment can be e x p r e s s e d as"> )

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W (6) = 1 + X A, (a) A (y) G P (cos 9) ( I I . l U ) exp , k k k k

k=even

The r e s o l v i n g time of t h e coincidence c i r c u i t i s assumed t o be long as compared t o t h e l i f e t i m e of t h e i n t e r m e d i a t e s t a t e . For a s t a t i c i n t e r a c t i o n G can only have v a l u e s above "the hard core v a l u e " , which i s i n d e -pendent of t h e i n t e r a c t i o n frequency.

When d i r e c t i o n a l c o r r e l a t i o n s are measured for cascades i n v o l v i n g p a r t i c l e e m i s s i o n , p e r t u r b a t i o n s caused by " a f t e r e f f e c t s " a r e extremely i m p o r t a n t . "After e f f e c t s " can be d e s c r i b e d as d i s t u r b a t i o n s of t h e e l e c -t r o n c o n f i g u r a -t i o n a f -t e r n u c l e a r d e s i n -t e g r a -t i o n ° ) . In a - p a r -t i c l e decay, t h e daughter n u c l e u s , r e c e i v i n g a r e c o i l energy of around 100 keV, w i l l be e j e c t e d from t h e s o u r c e . The y - r a y s e m i t t e d by daughter n u c l e i r e c o i l i n g e i t h e r i n t o or from t h e backing m a t e r i a l can be s e l e c t e d by measuring them in coincidence with a - p a r t i c l e s emitted in t h e o p p o s i t e d i r e c t i o n .

I f t h e daughter n u c l e i r e c o i l i n t o vacuum t h e p e r t u r b a t i o n s may be s e v e r e . They can be d e s c r i b e d as a magnetic I - J coupling ( l i s t h e spin of t h e nucleus and J i s t h e spin of t h e e l e c t r o n c o n f i g u r a t i o n ) between t h e nucleus and t h e e l e c t r o n c o n f i g u r a t i o n , which i s i n an e x c i t e d o r i o n i z e d s t a t e due t o t h e proceeding a-decay. The i n f l u e n c e of such p e r t u r b a t i o n s can be removed by performing a d i r e c t i o n a l c o r r e l a t i o n experiment in an e x t e r n a l magnetic f i e l d . This f i e l d can decouple t h e nuclear s p i n and t h e angular momentum of t h e atomic e l e c t r o n s . As d i s c u s s e d b e f o r e , a magnetic f i e l d a p p l i e d i n t h e d i r e c t i o n of emission of t h e primary r a d i a t i o n does not a f f e c t t h e d i r e c t i o n a l c o r r e l a t i o n p a t t e r n .

P e r t u r b a t i o n s of d i r e c t i o n a l c o r r e l a t i o n s i n v o l v i n g n u c l e i r e c o i l i n g i n t o metals are s m a l l e r but can g e n e r a l l y not be removed by an e x t e r -n a l mag-netic f i e l d . The p e r t u r b i -n g f i e l d s a r e p r o b a b l y predomi-na-ntly of e l e c t r i c o r i g i n and t h e i n t e r a c t i o n s s t r o n g l y depend on t h e r e c o v e r y and r e l a x a t i o n times of t h e e l e c t r o n i c s h e l l s in t h e d i f f e r e n t m a t e r i a l s .

II. 3. 2 Finite solid angle corrections

The source and d e t e c t o r s are normally not small as compared t o t h e d i s t a n c e s between t h e source and t h e d e t e c t o r s . As a consequence, t h e e x

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p e r i m e n t a l a n g u l a r c o r r e l a t i o n i s always more or l e s s a t t e n u a t e d . To compare t h e experimental r e s u l t s with t h e t h e o r e t i c a l p r e d i c t i o n s , c o r r e c -t i o n s have -t o be made for -t h e f i n i -t e s i z e of -t h e source and -t h e d e -t e c -t o r s . The Ge (Li) d e t e c t o r and t h e s i l i c o n s u r f a c e - b a r r i e r d e t e c t o r , used f o r t h e d e t e c t i o n of the y - r a y s and t h e a - p a r t i c l e s , are c y l i n d r i c a l l y symme-t r i c ; symme-t h e i r symmesymme-try axes are d i r e c symme-t e d symme-towards symme-t h e c e n symme-t r e of symme-t h e s o u r c e . The f i n i t e s o l i d angle c o r r e c t i o n s can then be taken i n t o account as f o l l o w s S ' l " ) :

"exp (9) = 1 + X \ '"^ \ '"^ \ ^^^ \ ^^' \ ^k ''""^ '^^ (11-15) k=even

The c o n t r i b u t i o n of t h e source s i z e t o (1 (y) i s n e g l i g i b l e , since t h e diameter of t h e source i s small as compared t o t h e diameter of t h e Ge (Li) d e t e c t o r . A c o a x i a l Ge (Li) d e t e c t o r normally c o n s i s t s of a s e n s i t i v e cy-l i n d e r around a n o n - s e n s i t i v e c o r e . The d e t e c t i o n e f f i c i e n c y of y - r a y s in t h e s e n s i t i v e volume depends on t h e angle of i n c i d e n c e of t h e y - r a y s . Theref o r e , t h e c a l c u l a t i o n s oTheref t h e a t t e n u a t i o n c o e Theref Theref i c i e n t s Therefor a Ge (Li) d e t e c -t o r become so complex -t h a -t compu-ter c a l c u l a -t i o n s a r e r e q u i r e d .

The mean range of a p a r t i c l e s i n Si i s small as compared t o t h e d e -t e c -t o r -t h i c k n e s s . T h e r e f o r e , -t h e a - p a r -t i c l e d e -t e c -t o r may be assumed -t o have

100^ d e t e c t i o n e f f i c i e n c y . Neglecting t h e source s i z e , t h e c o e f f i c i e n t s <! (a) can then be expressed as

^ 9 J P (cos 9) sin e d9

Q ^ ( a ) = ^ ^ (11.16) J s i n 9 de

o

For a circular a-detector of radius r, placed at a distance h from the source, the correction factors are given by the expressions^J

The author is indebted to dr. D.C. Camp for performing the & calcula-tions for the detector used in the present experiment.

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Q2 (a) = 1/2 cos 9 (1 + cos 9)

Qi, (a) = 1/8 cos 9 ( 1 + cos 9) (7 cos2 9 - 3 ) (11.17)

e = t a n " ' ( r / h )

In t h e decoupling experiment t h e s i z e of t h e source has t o be of t h e same order of magnitude as t h e s i z e of the a - p a r t i c l e d e t e c t o r . The c o e f f i c i e n t s 0 (a) have been o b t a i n e d by averaging t h e above e x p r e s s i o n s over t h e source a r e a .

References

1) L.C. Biederharn and M.E. Rose, Rev. Mod. Phys. 25 (1953) 729

2) H. Frauenfelder and R.M. Steffen i n a - , 6 - , y-Ray Spectroscopy, Vol. I I K. Siegbahn ed. North-Holland Amsterdam (1965)

3) M. Ferentz and N. Rosenzweig, Argonne National Laboratory Report 5321* (195I+)

1+) T. I n c u e , Table of Clebsch-Gordan C o e f f i c i e n t s , Tokio (1966) 5) Rotenberg, The 3-j and 6-j symbols, Techn. P r e s s Cambridge 1959 6) R.M. Steffen and H. F r a u e n f e l d e r , P e r t u r b e d Angular C o r r e l a t i o n s ,

Karlsson e . a . e d s . North-Holland Amsterdam (196**) 7) A. Abragam and R.V. Pound, Phys. Rev. 92 (1953) 9**3

8) J . E . Thun, Angular C o r r e l a t i o n s i n Nuclear D e s i n t e g r a t i o n , B. van Nooijen e . a . e d s . , Wolters-Noordhoff Groningen (1971)

9) A.M. Feingold and S. F r a n k e l , Phys. Rev. 97 (1955) 1025 10) J . L . Black and W. Gruhle, Nucl. I n s t r . and Meth. 1*6 (I967) 213.

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CHAPTER I I I EXPERIMENTAL ARRANGEMENTS I I I . 1 D e t e c t i o n a n d a n a l y s i s S i l i c o n s u r f a c e - b a r r i e r a n d Ge ( L i ) d e t e c t o r s h a v e b e e n u s e d f o r t h e d e t e c t i o n o f a - p a r t i c l e s a n d y - r a y s , r e s p e c t i v e l y . The e l e c t r o n i c a r r a n g e m e n t s f o r t h e c o i n c i d e n c e and d i r e c t i o n a l c o r r e l a t i o n e x p e r i m e n t s a r e shown i n f i g . I I I . 1 a n d f i g . I I I . 2 . The a - y c o i n c i d e n c e m e a s u r e m e n t s h a v e b e e n p e r f o r m e d a s o n - l i n e e x p e r i m e n t s u s i n g a PDP-9 c o m p u t e r , w h e r e a s t h e d i r e c t i o n a l c o r r e l a t i o n d a t a w e r e r e c o r d e d by a m u l t i c h a n n e l a n a l y z e r (Laben U 0 9 6 ) . A m p l i f i e r s and c o i n c i d e n c e s y s -t e m w e r e -t h e same i n b o -t h -t y p e s o f e x p e r i m e n -t s . The o - p a r -t i c l e d e -t e c -t o r p r e a m p l i f i e r p r e a m p l i f i e r a - d e t e c t o r y - r a y d e t e c t o r a m p l i f i e r d o u b l e d i f -f e r e n t i a t i o n z e r o s t r o b e f a s t c o i n c i d e n c e c i r c u i t a n a l o g u e t o d i g i t a l c o n v e r t e r PDP-9 c o m p u t e r 2l*K, 18 b i t s m a g n e t i c t a p e a m p l i f i e r d o u b l e d i f -f e r e n t i a t i o n analogue to digital converter linear amplifier

F i g . I I I . l . Block diagram of t h e e l e c t r o n i c system for two-dimensional coincidence measurements

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I— p r e a m p l i f i e r a m p l i f i e r double d i f -f e r e n t i a t i o n s i n g l e channel analyzer s c a l e r p r e a m p l i f i e r a - d e t e c t o r y-ray d e t e c t o r

1

a m p l i f i e r double di f-f e r e n t i a t i o n zero s t r o b e f a s t coincidence c i r c u i t single channel analyzer scaler

'

routing system scaler s e r i a l read-out s c a l e r s p r i n t e r _{p e r f o r a t o r}papertape l i n e a r a m p l i f i e r analogue t o d i g i t a l c o n v e r t e r m u l t i channel a n a l y z e r Laben 1*096 automation t u r n - t a b l e

F i g . XXI.2. Block diagram of t h e e l e c t r o n i c system for d i r e c t i o n a l c o r r e -l a t i o n measurements.

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was connected t o a TC 130 and the y - r a y d e t e c t o r t o a TC 135 p r e a m p l i f i e r . F u r t h e r a m p l i f i c a t i o n of t h e s i g n a l s was performed by two l i n e a r a m p l i f i e r s

(CI Il*20), used i n t h e double delay l i n e mode, and by a s p e c t r o s c o p i c am-p l i f i e r (CI 11*17). The coincidence system was connected t o t h e b i am-p o l a r o u t p u t s of t h e l i n e a r a j n p l i f i e r s ; t h e a-spectrum p u l s e s were taken from t h e u n i p o l a r o u t p u t . The coincidence arrangement c o n s i s t e d of two zero

strobe u n i t s (CI ll*20) and a f a s t coincidence c i r c u i t (CI ll*l*0). The time r e s o l u t i o n of t h i s system was 2T ^ 100 n s . The r a t i o of t r u e t o a c c i d e n t a l coincidences was l a r g e r than 10 i n a l l experiments.

In order t o measure twodimensional coincidence s p e c t r a , t h e s p e c -trum p u l s e s were s u p p l i e d t o two analogue t o d i g i t a l c o n v e r t e r s (ADC; Laben CD 60/1*096). The d a t a obtained i n t h e ^^"^Th and 22 3^^^ experiments were analyzed in a d i f f e r e n t way. In the case of t h e 22 7r]nj^ measurements, t h e a - p a r t i c l e spectrum was divided i n t o 12 g r o u p s , each c o n t a i n i n g around

15 c h a n n e l s . The y - r a y s p e c t r a c o i n c i d e n t with t h e d i f f e r e n t a-groups were s t o r e d in p a r t s of t h e core memory, each c o n t a i n i n g 1021* c h a n n e l s . The a-y coincidence measurements i n t h e decay of Ra were performed as a twodimensional 256 ( a c h a n n e l s ) x 1021* ( y c h a n n e l s ) experiment. The c o i n -c i d e n t a - p a r t i -c l e and y - r a y spe-ctrum p u l s e s were temporary s t o r e d in a memory b u f f e r . The coincidences were subsequently recorded on magnetic t a p e in 256 b l o c k s , each c o n t a i n i n g t h e y - r a y spectrum c o i n c i d e n t with one a - c h a n n e l . This was achieved by s u c c e s s i v e r e a d i n g of t h e s e 256 s p e c t r a i n t o a data b u f f e r , followed by t r a n s f e r of c o i n c i d e n c e s , i d e n t i f i e d by t h e achannel number, from the memory b u f f e r t o t h e data buffer and r e -w r i t i n g of t h e s p e c t r a on magnetic t a p e . After t e r m i n a t i o n of a c y c l e , t h e magnetic t a p e was rewinded and t h e next cycle was s t a r t e d . The n e c e s s a r y computer programs were developed by J . Kromme and are d e s c r i b e d in an i n -t e r n a l r e p o r -t ).

In order t o perform d i r e c t i o n a l c o r r e l a t i o n measurements on cascades i n v o l v i n g d i f f e r e n t a - g r o u p s , a r o u t i n g system was employed t o address t h e c o i n c i d e n t y - r a y s p e c t r a i n t h e m u l t i c h a n n e l a n a l y z e r ( f i g . I I I . 2 ) . The r e l e v a n t p a r t s of t h e a-spectrum were s e l e c t e d by s i n g l e channel a n a l y z e r s (CI 11*30). The f i r s t subgroup of t h e m u l t i c h a n n e l a n a l y z e r , c o n s i s t i n g of 512 or I02I* c h a n n e l s , always contained t h e y - r a y spectrum not c o i n c i d e n t with a p a r t i c l e s s e l e c t e d by t h e s i n g l e channel a n a l y z e r s . The o t h e r s u b groups were a v a i l a b l e for y r a y s p e c t r a c o i n c i d e n t with t h e d i f f e r e n t a -groups. The counting r a t e s in t h e coincidence c i r c u i t and in t h e s i n g l e

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channel a n a l y z e r s were c o n t r o l l e d by s c a l e r s which were a u t o m a t i c a l l y read-out a f t e r each measuring c y c l e .

Fig. I I I . 3. Top view of t h e d i r e c t i o n a l c o r r e l a t i o n s e t - u p

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Ge(Li ) d e t e c t o r m i c r o -s w i t c h e -s b r a s s -p r o j e c t i o n F i g . I I I . l * . Cross s e c t i o n of t h e d i r e c t i o n a l c o r r e l a t i o n s e t - u p I I I . 2 Normal d i r e c t i o n a l c o r r e l a t i o n s e t - u p III. 2.1 Turn-table

The normal d i r e c t i o n a l c o r r e l a t i o n s e t - u p c o n s i s t s of a vacuum chamber mounted on t h e movable arm of a t u r n - t a b l e ( f i g . I I I . 3 and f i g . I I I . l * ) . The r o t a t i o n of t h i s arm i s achieved by a P h i l i p s s t e p p i n g motor (AU 5050) with r e d u c t i o n gear (125 : l ) . The motor i s connected t o t h e r o t a t i o n axis of t h e movable arm using g e a r w h e e l s . A number of b r a s s p r o -j e c t i o n s can be mounted on t h e t u r n - t a b l e a t a n g l e s of 90 , 135 , I80 , 225° and 270° w i t h r e s p e c t t o t h e d i r e c t i o n of t h e y - r a y d e t e c t o r , which i s f i x e d t o the t u r n - t a b l e ( f i g . I I I . 3 ) . The vacuum chamber c o n t a i n s source and o p a r t i c i e d e t e c t o r . The a p a r t i c l e d e t e c t o r can be p o s i t i o n e d at d i s -t a n c e s of 2 - 10 cm from -t h e s o u r c e . In a l l experimen-ts -t h e symme-try axes of t h e source and a - p a r t i c l e d e t e c t o r were p o s i t i o n e d a t an angle of 1*5 in

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o r d e r t o avoid y - r a y a b s o r p t i o n in t h e source a t t h e 90 and 270 p o s i t i o n s .

III. 2. 2 Automation

The automation of t h e a-y d i r e c t i o n a l c o r r e l a t i o n arrangement i s based on t h e system designed by W. Lourens employing a Nuclear Data ND 130A a n a l y z e r ( r e f . 2 ) . The e l e c t r o n i c block diagram i s p r e s e n t e d i n f i g . I I I . 5 . The measurements are always s t a r t e d i n t h e 90 or 270 p o s i t i o n . To minimize decay c o r r e c t i o n s as well as t h e i n f l u e n c e of long time d r i f t s , t h e mea-surements a r e t o be c a r r i e d out i n t h e sequence of p o s i t i o n s 90 , 135 , 180°, 180°, 2 2 5 ° , 2 7 0 ° , 2 7 0 ° , 2 2 5 ° , l 8 o ° , l 8 o ° , 1 3 5 ° , 90°.

Five micro-switches a r e mounted on t h e backside of the, moving arm ( f i g . I I I . 3 ) . I f switch s i s c l o s e d , t h e r o t a t i n g arm comes t o stop when-ever t h e pen of one of t h e switches h i t s a p r o j e c t i o n . The o p e r a t i o n of t h e switches can be understood from f i g . 111.5- The micro-switches 1 - 5 a r e r e l a t e d t o t h e d i f f e r e n t p o s i t i o n s and a c t i v a t e t h e r e l a i s A - E. When t h e r e l a i s A and E ( p o s i t i o n s 90 and 270 ) a r e a c t i v a t e d t h e d i r e c t i o n of r o t a t i o n of t h e motor i s r e v e r s e d by means of t h e r e l a i s X and Y. The func-t i o n of r e l a i s Z, which comes i n func-t o a c func-t i o n i f one of func-t h e swifunc-tches a , c , e i s c l o s e d , w i l l be d i s c u s s e d l a t e r . stop-ar,olyse°VF 330D relais A B C 0 E msw 1 2 3 4 5 |3k9V position 90° 135° 1«0° 225° 270°

F i g . I I I . 5 . Block diagram of t h e automized d i r e c t i o n a l c o r r e l a t i o n s e t - u p

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The electronical driver (Philips 2P72786) of the stepping motor receives pulses from a double phase rectifier, which supplies 100 c/s pulses. These pulses have to pass through a gate G2 which is controlled by the bistable multivibrator B2 and the gate Gj. When the motor comes to stop one of the switches b, d, z is closed and the gate Gj stops pulses to pass gate G2. The stop pulse, supplied by the timer of the Laben analyzer after each measuring time, switches the output of Gj and opens G2. This stop pulse is stretched by means of the monostable multivibrator M2 in order to open the gate Gj as long as one of the switches b, d, z is still closed.

Bj comes into action if switch z is closed. If z is closed the stop pulse of the timer switches Bj from its "set" to "reset" position and the gate G2 is closed before it is opened by Gj. This is accomplished by introducing a delay by means of the monostable multivibrator M j . After re-ceiving a second pulse Bj returns to its original position and G2 can be opened by G|. Thus, the system is allowed to stay two measuring cycles in the 90 , 180 and 270 positions. By means of switch s the supply of the

100 c/spulses to the electronical driver can be stopped. Normally one of the switches x and y is closed. If both switches are open, 100 c/s pulses can be supplied directly to the motor driver if switch s is closed. In this operation mode the arm can be moved to the 90 or 270 position when a new measurement is started.

The motor of the Tally puncher is started and stopped by relais H, using the stop and start pulses of the timer, which are supplied to the bistable multivibrator B2.

III.3 Arrangement for a decoupling experiment

III. 3.1 The liquid helium aryostat

The influence of perturbations on a-y directional correlations can be removed if the measurements are performed in a magnetic field, applied in the direction of emission of the a-particles. Yet, effective decoupling from the internal fields has only been observed in cases where the daugh-ter nuclei have escaped from the source and the backing madaugh-terial before emitting y-rays. A system with a superconductive magnet has been designed for this type of measurements.

The system consists of a rotating cryostat containing magnet,

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Fig. III.6. Cross section of the liquid helium cryostat and superconduc-tive magnet

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F i g . I I I . 6 : 1. 2 . 3 . 1*. 5. 6. 7. 8. 9. 1 0 . 11. l i q u i d helium r e s e r v o i r l i q u i d n i t r o g e n r e s e r v o i r high vacuum c r y o s t a t t a i l aluminum window

source and d e t e c t o r space magnet space superconductive magnet source a - p a r t i c l e d e t e c t o r l i q u i d helium f i l l 12. 13. 11*. 15. 16. 17-18. 19-2 0 . 2 1 . l i q u i d n i t r o g e n f i l l t o helium recovery system t e r m i n a l for c u r r e n t l e a d t o o i l d i f f u s i o n pump t o ion g e t t e r pump connector for l e v e l i n d i c a t o r mounting flange c r y o s t a t support b r a s s p r o j e c t i o n m i c r o - s w i t c h e s

s o u r c e , and a - p a r t i c l e d e t e c t o r . F i g . I I I . 6 and f i g . V.8 show t h e c r y o s t a t and t h e magnet. The c r y o s t a t i s movable around i t s symmetry a x i s and can be stopped a t t h e 90 , 180 and 270 p o s i t i o n s of t h e a - p a r t i c l e d e t e c t o r with respect t o t h e y - r a y d e t e c t o r . The r o t a t i o n i s achieved by a P h i l i p s

s t e p p i n g motor (AU 5050) with r e d u c t i o n gear (125 : l ) - The motor i s coup-l e d t o the mounting fcoup-lange of t h e c r y o s t a t . The coup-l a t t e r i s mounted on t h e support flange by a b a l l b e a r i n g system. The automation of t h i s a r r a n g e -ment i s the same as t h a t designed for t h e o r d i n a r y s e t - u p (§ I I I . 2 . 2 ) . The micro-switches a r e fixed t o t h e underside of t h e mounting flange of t h e

c r y o s t a t . The b r a s s p r o j e c t i o n s can be p o s i t i o n e d on t h e support f l a n g e . The main p a r t s of the c r y o s t a t , t h e l i q u i d helium r e s e r v o i r , t h e l i q u i d n i t r o g e n r e s e r v o i r and t h e o u t e r v e s s e l , are made of b r a s s . The volume of t h e helium r e s e r v o i r i s 6 dm^. The magnet i s f i x e d by b r a s s s t r i p s in t h e t a i l of t h e helium r e s e r v o i r . A thermal r a d i a t i o n s h i e l d , connected t o t h e nitrogen r e s e r v o i r , surrounds t h e t a i l of t h e helium r e s e r v o i r . The helium and n i t r o g e n r e s e r v o i r s are supported by and i n s u l a t e d from t h e o u t e r v e s s e l by t e f l o n b l o c k s .

Access t o t h e c e n t r e of t h e magnet, t o p o s i t i o n t h e source and t h e a - d e t e c t o r , i s achieved by a tube of s t a i n l e s s s t e e l , which i s removably connected t o t h e helium r e s e r v o i r by an indium s e a l . The source and a d e -t e c -t o r h o l d e r , having -t h e same symme-try a x i s as -t h e magne-t, i s moun-ted on-to t h e thermal r a d i a t i o n s h i e l d in order t o obtain optimum use of t h e a v a i l -a b l e sp-ace.

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Opposite t h e magnet p o r t s t h e wall of t h e helium c r y o s t a t has been made l o c a l l y t h i n n e r , in order t o minimize a b s o r p t i o n of y - r a y s . For the same p u r p o s e , t h e thermal r a d i a t i o n s h i e l d c o n t a i n s holes and t h e t a i l of t h e o u t e r v e s s e l i s p r o v i d e d with aluminum windows.

The t r a n s f e r t u b e s for helium and n i t r o g e n a r e of s t a i n l e s s s t e e l . The helium t r a n s f e r t u b e s are a l s o used as s u p p o r t s for the e l e c t r i c a l l e a d s . These copper l e a d s c o n s i s t of four wires ( t o t a l cross s e c t i o n 2 mm ) which are s p i r a l l e d i n t h e t r a n s f e r t u b e s in o r d e r t o i n c r e a s e t h e thermal r e s i s t a n c e . A system c o n s i s t i n g of four carbon r e s i s t o r s serves as an i n d i -c a t o r of t h e l i q u i d helium l e v e l . The -c r y o s t a t i s -covered by two flanges having feed-throughs (provided with "O" r i n g s ) for t h e helium and n i t r o g e n t r a n s f e r t u b e s . On t h e t o p flange t h e r e are two vacuum f l a n g e s , p o r t s for t h e helium f i l l and r e c o v e r y , two t e r m i n a l s for t h e magnet c u r r e n t leads and a four-way e l e c t r i c a l connector for t h e l e v e l i n d i c a t o r . The c r y o s t a t i s evacuated by an o i l d i f f u s i o n pump and an ion g e t t e r pump (Vacion 8 d m V s ) .

III. 3. 2 Superconductive magnet

The magnet i s of t h e s p l i t - c o i l t y p e . The symmetry a x i s of the c o i l s i s in t h e h o r i z o n t a l p l a n e . The a x i a l access t o t h e magnet has a minimum diameter of 22 mm. The four r a d i a l access p o r t s have a p e r t u r e s of 21* t a n -g e n t i a l t o a 1* ram c i r c l e in t h e plane p e r p e n d i c u l a r t o the windin-g a x i s . About 2800 m Nb - 33^ Zr wire has been used for t h e c o i l , which contains approximately 12000 windings. The wire has a d i a m e t e r of O.25I* mm and i s covered with 0.025 mm e l e c t r o l y t i c copper and 0.025 mm formvar i n s u l a t i o n . The magnet design allows a maximum f i e l d of about 1* T e s l a , which i s

achieved at a magnet c u r r e n t of 25 A. The f i e l d a t s e v e r a l p o s i t i o n s of t h e source as well as in t h e d i r e c t environment of t h e source has been calcu-l a t e d from t h e formucalcu-lae for t h e f i e calcu-l d of a c u r r e n t I in a c i r c u calcu-l a r wire of r a d i u s p i n t h e plane z = 0 around t h e c e n t r e of t h e coordinate s y s t e m ' ) :

P r ( r - p ) + z^

B. ( - . e , z ) ^ ^ - , ^ f ^ [ K + f - f - f E]

P r ( r - p ) + z^

( I I I . l )

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The c o n s t a n t y i s t h e magnetic p e r m e a b i l i t y , K and E a r e complete e l l i p t i c i n t e g r a l s . An Algol procedure has been used f o r t h e n u m e r i c a l c a l c u l a t i o n of t h e s e i n t e g r a l s ( r e f . 1*).

The formulae f o r t h e i n t e g r a l f i e l d of t h e c o i l a r e d e r i v e d a s s u -ming a c o n s t a n t c u r r e n t d e n s i t y NX/A i n t h e c o i l . N i s t h e t o t a l number of w i n d i n g s , A i s h a l f t h e a r e a of a c r o s s s e c t i o n through t h e c o i l in a p l a n e t h r o u g h t h e a x i s . The f i e l d components a r e given by t h e e x p r e s s i o n s

f^U)

f i ( c ) p fv 0 , 1 - li™. f [ ' ^ ( z - C ) r ^ , r 2 + p2 + ( z - ; ) 2 , •" o r ( r - o + ( z - C ) f^{K) -' •" D r r-D ) + z-C f j ( c ) I n t e g r a t i o n i s o v e r b o t h r a n d ±z r a n g i n g from 1.2 cm t o 1*.8 cm. F o r e a c h v a l u e o f z , t h e p o s s i b l e r - v a l u e s i n t h e c o i l r a n g e from f . ( z ) t o f , ( z ) . A c o m p u t e r p r o g r a m h a s b e e n d e v e l o p e d , u s i n g an a v a i l a b l e Simpson a p p r o x i -m a t i o n p r o c e d u r e i n A l g o l l a n g u a g e , f o r t h e i n t e g r a t i o n . T a b l e I I I . l shows B i n s e v e r a l p o i n t s o f t h e a r e a w h e r e y - r a y e m i s s i o n from r e c o i l i n g n u c l e i may b e e x p e c t e d . The r e c o i l e n e r g y i s a b o u t 100 keV. The l i f e t i m e o f t h e i n t e r m e d i a t e s t a t e i s m o s t l y < 1 n s . T h e r e f o r e , t h e n u c l e u s c a n d u r i n g i t s l i f e t i m e c o v e r a t most a d i s t a n c e o f 0 . 2 mm. The r e c o i l i n g n u c l e i e s c a p e from a s o u r c e o f 8 mm d i a m e t e r , p o s i t i o n e d a t a 1*5 a n g l e w i t h r e s p e c t t o t h e symmetry a x i s o f t h e c o i l . Only t h e a x i a l component o f t h e f i e l d B i s t a b u l a t e d s i n c e t h e r a d i a l component i s s m a l -l e r t h a n 0 . 3 ^ o f B a t Ei-l-l p o s i t i o n s . The v a -l u e s o f B ( r , z ) a r e n o r m a -l i z e d z z t o B ( 0 , 0 ) . T a b l e I I I . l i n d i c a t e s t h a t t h e h o m o g e n e t y o f t h e f i e l d o v e r z t h e s o u r c e a r e a i s b e t t e r t h a n 3%-The f i e l d a t t h e c e n t r e o f t h e s o u r c e i s m e a s u r e d a s a f u n c t i o n o f t h e magnet c u r r e n t b y a H a l l g e n e r a t o r . The r e s u l t s ( f i g . I I I . 7 ) a g r e e w i t h t h e c a l c u l a t i o n s . 31

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Table I I I . 1 Normalized v a l u e s of B ( r , z ) z 1* mm 2 mm 0 mm 1.035 I.Oll* 1.000 0 mm 1.030 1.009 0.99** 2 mm 1.021 1.000 0.981* 1* mm 0.5

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References

1) J.G. Kromme, Internal Report Lab. Tech. Nat. University of Technology Delft, October 1971

2) W. Lourens and P.M.H. van Baren, Nucl. Instr. and Meth. 5I* (1967) 311 3) G. Wendt in Handbuch der Physik, Vol. XVI, S. Fliigge ed. , Springer

Ver-lag, Berlin (1958)

1+) D.J. Hofsommer and R.P. van de Riet, Report TW 9I* (I962), Mathematical Centre Amsterdam.

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CHAPTER IV

THE DECAY OF 2 19Rn AND 2 2 3 ^ ^

I V . 1 I n t r o d u c t i o n The r e s u l t s of p r e v i o u s s t u d i e s on t h e s p i n o f l e v e l s i n 2 19pj^ g^^g, 215pQ were t e n t a t i v e i n t e r p r e t e d a s i n d i c a t i n g a 3 / 2 a n d 7/2 a s s i g n m e n t f o r t h e s p i n of t h e g r o u n d s t a t e o f b o t h i s o t o p e s , r e s p e c t i v e l y ' " ^ ) . I n a p r e v i o u s s h o r t c o m m u n i c a t i o n ^ ) we r e p o r t e d o u r c o n v e r s i o n l i n e and a y d i r e c -t i o n a l c o r r e l a -t i o n m e a s u r e m e n -t s on -t h e s e i s o -t o p e s a n d c o n c l u d e d -t o s p i n v a l u e s 5 / 2 and 9 / 2 . Two f u r t h e r s t u d i e s however p r e f e r t h e e a r l i e r s p i n a s s i g n m e n t s ^ ' 5 ) . We t h e r e f o r e e x t e n d e d o u r e a r l i e r e x p e r i m e n t s w i t h a d d i t i o n a l a y d i r e c t i o n a l c o r r e l a t i o n m e a s u r e m e n t s a n d c o n v e r s i o n l i n e m e a s u r e m e n t s on t h e t r a n s i t i o n s c o n n e c t i n g t h e t h r e e l o w e s t l e v e l s i n ^^^Bn. M o r e -o v e r , we made d e t a i l e d a - y c -o i n c i d e n c e m e a s u r e m e n t s t -o c -o m p l e t e t h e d a t a o b t a i n e d from G e ( L i ) y - r a y s p e c t r a ^ ' ^ ) . The p r e s e n t p a p e r d i s c u s s e s a l l t h e s e r e s u l t s and a l s o new m e a s u r e m e n t s on a - y l i n e a r p o l a r i z a t i o n and y - y d i r e c t i o n a l c o r r e l a t i o n s " ) .

XV.2 Alpha-gamma c o i n c i d e n c e m e a s u r e m e n t s

T h i n s o u r c e s o f Ra f o r good r e s o l u t i o n i n t h e a - p a r t i c l e s p e c t r u m w e r e made by e v a p o r a t i o n o f t h e a c t i v i t y on Al f o i l s . The y - r a y s w e r e d e t e c t e d w i t h a G e ( L i ) d e t e c t o r , h a v i n g a r e s o l u t i o n o f 1.8 keV a t 120 keV and k% e f f i c i e n c y ( c o m p a r e d w i t h 7 . 5 cm x 7 . 5 cm N a l ) . The a - p a r t i c l e d e t e c t o r was a s i l i c o n s u r f a c e b a r r i e r d e t e c t o r w i t h a s e n s i t i v e a r e a of 2 cm2 and a r e -s o l u t i o n o f 30 keV. A t i m e r e -s o l u t i o n o f 90 n -s wa-s -s u f f i c i e n t t o o b t a i n a g o o d r a t i o o f t r u e t o a c c i d e n t a l c o i n c i d e n c e s .

The y - r a y s p e c t r u m up t o 700 keV was m e a s u r e d i n 1021* c h a n n e l s , t h e a - p a r t i c l e s p e c t r u m i n 2 5 6 c h a n n e l s . C o i n c i d e n c e s w e r e a n a l y z e d u s i n g a PDP-9 c o m p u t e r and s t o r e d d i r e c t l y on m a g n e t i c t a p e i n 256 b l o c k s , e a c h c o n t a i n i n g t h e c o i n c i d e n t s p e c t r u m w i t h o n e o f t h e a - c h a n n e l s . F i g . IV. 1 shows t h e c o i n c i d e n t y - r a y s p e c t r u m w i t h a - p a r t i c l e s of e n e r g i e s 1*.5 - 5 . 9 MeV. The s p e c t r a d i s p l a y e d in f i g . IV.2-1* a r e y - r a y s p e c t r a c o i n c i d e n t w i t h d i f f e r e n t p a r t s of t h e a - p a r t i c l e spectrum. These s p e c t r a can r e a d i l y be o b t a i n e d by summing t h e c o n t e n t s of d i f f e r e n t b l o c k s from t h e magnetic t a p e .

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± + ± + O.OI+ 0.01+ 0 . 2 0 . 3 0 . 7 1 . 1 O . I I * O.oi* O.oi* 0 . 0 6 0.1* 3 0 . 0 7 0 . 8 0 . 1 0 . 0 8 O.T 0 . 1 2 0 . 0 5 0 . 1 0 0 . 5 0 . 1 0 0 . 1 0 0 . 0 5 O . O l l * 1.1 0 . 0 6 36

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Table IV.1 ( c o n t i n u e d ) Energy (keV) 1+88.0 ± 527.0 ± 598.8 + 609.0 + 632 ^) 0 . 8 0.6 1.0 1.0 t h i s work ) 0. 11 ± 0.06 0.61+ + 0. 15 0.90 ± 0.18 0.1+1 ± 0.15 < 0.05 Davidson "- 0. 15 0.7 + O.II+ 0.93 ± 0.15 0.63 ± 0.09 0.3 ± 0.1 Krien ^) 0.13 ± 0.06 0.73 ± 0.07 I.OI+ ± 1.0 0.73 ± 0.66 < 0.1 ^) The i n t e n s i t i e s were c a l c u l a t e d from t h e coincidence s p e c t r a . I^) See ref. 8.

= ) See ref. 9.

E n e r g i e s and i n t e n s i t i e s of a l l d e t e c t e d y - r a y s have been summarized in t a b l e IV. 1. The y - r a y i n t e n s i t i e s were c a l c u l a t e d per thousand 22 3^,^ decays a c c o r d i n g t o Davidson^).

The coincidence d a t a were f i t t e d i n t h e decay scheme c o n s t r u c t e d from a s p e c t r a , as measured by R. W a l e n " ) . No s i g n i f i c a n t information was o b -t a i n e d from y - r a y s p e c -t r a c o i n c i d e n -t wi-th a-groups feeding l e v e l s higher t h a n 73I+ keV. The y - r a y spectrum measured i n coincidence with o , and

731+ keV "712 keV ^^°^^ '*'"° t r a n s i t i o n s at 368.8 and 391-0 keV, which are disappeared in t h e spectrum c o i n c i d e n t with a^j^g j^ ^^^ and a^ ^ ^^^ ( f i g . I V . 2 ) . They a r e t h e r e f o r e a s s i g n e d t o d i r e c t decay from t h e corresponding l e v e l s . The y - r a y s at 1 3 6 . 1 , 193.0, 221.0 and 373.3 keV, assigned by Davidson^) or Krien^) as decaying from t h e s e l e v e l s , have not been d e t e c t e d h e r e . The

counts counts 50 (7> • L • CO 1 f n CM cn CM m . L CO CM 4 1 r

1

_t J - 1 m m

•

"ft <y 1 1 1 ' , '1 [^ H 0 • &H CLH o r - . i n ; i n o ^ C^.CM CM 1 a> COiT> 1 • • t—t C O H 0 uar^ J-OTTO . . 1

Mli

-" M B (y^ M l * * MR ^ <T^ J J

-I-'' V ••

^f\WWW..,4^100 -1+00 F i g . 500 600

channel number channel number XV.2a, b . The y r a y s 3001+50 keV, in coincidence with a p a r

-t i c l e s feeding -t h e 731++712 keV and 61+6.1++623.6 keV l e v e l s .

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2 2 1 . 0 keV t r a n s i t i o n i s f o u n d t o be c o i n c i d e n t w i t h a „ „ „ „ , ,,. An u p p e r 5 9 9 . 0 keV - -^-^ l i m i t f o r t h e i n t e n s i t y o f t h e o t h e r t h r e e t r a n s i t i o n s ( i n a l l c a s e s l e s s t h a n 2 0 ^ o f t h e p u b l i s h e d v a l u e s ) i s g i v e n i n t a b l e I V . 1 . The l o w i n t e n s i t i e s of t h e 3 6 8 . 8 and 3 9 1 . 0 keV y r a y s c o m p a r e d w i t h t h e a f e e d i n g s i n d i -c a t e t h a t o t h e r t r a n s i t i o n s , p r o b a b l y h i g h l y -c o n v e r t e d , a -c -c o i m t f o r t h e m a j o r i t y o f t h e d e c a y s o f t h e p r i m a r y l e v e l s . T h r e e a d d i t i o n a l y r a y s a t 1 3 1 . 2 , 199.1* a n d 2l*5.2 keV f o u n d i n c o i n c i -d e n c e w i t h a,-, ^ I , „ a n -d a ^ „ . ^ , ,, ( f i g . I V . 3 ) c o u l -d be p l a c e -d i n t h e 61*6.1* keV 6 2 3 . 6 keV d e c a y o f t h e c o r r e s p o n d i n g l e v e l s . An u p p e r l i m i t o f 0 . 0 0 5 ? i s p l a c e d on t h e i n t e n s i t y o f t h e 6 3 2 . 0 keV t r a n s i t i o n i n t h i s s p e c t r u m . By c o m p a r i n g f i g s . IV. 3b and IV. 3c i t i s c l e a r t h a t y - r a y s a t 2 2 0 . 6 , 2 5 5 . 6 a n d 2 6 0 . 5 keV a r e i n c o i n c i d e n c e w i t h a^^, „ , „ a n d a ^ „ „ „ , „ a s w e l l a s t h e 2 5 1 . 1

591*. 0 keV 5 9 9 - 0 keV

keV y - r a y w h i c h h a s b e e n a s s i g n e d e a r l i e r t o t h e d e c a y of t h e 59l*.0 keV l e v e l . The 2 2 0 . 6 keV t r a n s i t i o n i s p l a c e d b e t w e e n t h e 599-0 keV l e v e l and a l e v e l we p o s t u l a t e d a t 3 7 8 . 9 keV f o r r e a s o n s d i s c u s s e d l a t e r . A y - r a y of 2 5 1 . 8 keV w h i c h i s a s s i g n e d t o t h e d e c a y o f t h e l a t t e r l e v e l w i l l a l s o c o n t r i b u t e t o t h e i n t e n s i t y o f t h e 2 5 1 . 1 keV y - r a y m e a s u r e d i n c o i n c i d e n c e w i t h a , n w V "'"^^ i n t e n s i t y o f t h e 2 5 1 - 8 keV y - r a y can b e d e t e r m i n e d d i r e c t l y from t h e y - r a y s p e c t r u m c o i n c i d e n t w i t h a^„/- o v u ' '^^^ i n t e n s i t y of t h e 2 5 1 . 1 keV y - r a y can b e d e r i v e d from t h e i n t e n s i t y o f t h e c o m b i n a t i o n of t h e s e y - r a y s i n t h e t o t a l c o i n c i d e n c e s p e c t r u m . The main d e c a y of t h e 59I+.O keV l e v e l , f e d by 0 . 2 ? o f t h e t o t a l number a - p a r t i c l e s , i s n o t y e t c l e a r , b e c a u s e o n l y two weak y - r a y s a t 2 5 1 . 1 a n d 2 5 5 - 6 keV a r e a s s i g n e d t o i t s d e c a y h e r e . The 1+39.9 keV t r a n s i t i o n w h i c h was p l a c e d b e t w e e n t h e 5 9 9 . 0 and 1 5 8 . 6 keV l e v e l ^ ) h a s n o t b e e n d e t e c t e d . T h i s i n d i c a t e s t h a t t h e i n t e n s i t y of t h i s y - r a y i s l e s s t h a n 0 . 0 0 3 ? . A y - r a y a t III+.5 k e V , o n l y f o u n d i n c o i n c i d e n c e w i t h a^, , /- , „ and a ^ , _ _ , ,, ( f i g . I V . 3 c ) c o u l d n o t

51+1.6 keV 5 1 3 . 3 keV

b e p l a c e d i n t h e d e c a y s c h e m e . The t r a n s i t i o n of 3 8 8 . 0 keV c o u l d be a d d e d t o t h e d e c a y o f t h e 5 1 3 . 3 keV l e v e l . The 177 keV y r a y i s d o u b l e , as p r o -p o s e d by K r i e n ^ ) . The i n t e n s i t y of t h i s y - r a y i n f i g . I V . 3 d i s s l i g h t l y more t h a n t h e i n t e n s i t y o f t h e 175-5 keV y - r a y i n t h i s s p e c t r u m , w h e r e a s i n f i g . I V . 3 c t h e i n t e n s i t y r a t i o of t h e s e y - r a y s i s (3 ± 0 . 5 ) . From t h e c o i n c i d e n c e s p e c t r u m w i t h a, , ^ n , ,, and a, , , _ , ,, ( f i g . I V . 3 d ) a d d i t i o n a l

1+1+6.8 keV I+I+I+.9 keV ^

t r a n s i t i o n s of 1 0 3 . 7 keV and 1+30.5 keV c o u l d be a s s i g n e d t o t h e d e c a y o f t h e s e l e v e l s . The 1 0 3 . 7 keV y - r a y h a s t o e x p l a i n a l m o s t c o m p l e t e l y t h e f e e d i n g of t h e 31+2.9 keV l e v e l . B a s e d on t h e a p p e a r a n c e of t h e 3 2 8 . 5 keV

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counts counts 250 CM J -i n CM r-CM m 11 1 J -c n c n t o o CM CM

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J -cn i-H CM i n CM • • • | i r ) 0 LO ILOLO J - SNCM 100 200 300 250 ' " u n i n on UJJ- CM

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CM J d -in ID ^ CM

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100 200 300 1000 CTl r-l CM (N

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250 m (—1 o o , j \ into [^ ".•V.-iT'^v 100 200 1000 300 channel number o - n -i-~ • ^ CM i n LOn-CJi 'V'^''»->»**' I X > ^ V 100 200 250 <n J -J - cn o J - . UD . \ ODJ- . J - m . CO _ cn m e n LO LO UD .-1 300 channel number

Fig. IV. 1+. Alpha spectrum in c o i n -cidence with t h e 3I+2.5 keV gamma-ray t r a n s i t i o n .

100 200 300

chajinel number

Fig. IV. 3 a , b , c , d , e . The y - r a y s 100-270 keV, in coincidence with a-p a r t i c l e s feeding t h e 61+6.0+623.6 keV, 599.0+ + 59I+.O keV, 5I+I.6+515.3 keV and 1+1+6.8+1+1+)+.9 and 378.9+376.3 keV l e v e l s .