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UBC Theses and Dissertations

Spectroscopic determination of the nuclear moments of bismuth Shipley, George 1968

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A SPECTROSCOPIC DETERMINATION OF THE NUCLEAR MOMENTS OF BISMUTH by GEORGE SHIPLEY A . B . , U n i v e r s i t y o f C a l i f o r n i a , 1961 M . S c , U n i v e r s i t y o f A l b e r t a , 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department o f PHYSICS We a c c e p t t h i s t h e s i s as conforming t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1968 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his represen-tatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of P h y s i c s The University of Brit ish Columbia Vancouver 8, Canada Date A p r i l , 1968 v i ABSTRACT The n u c l e a r magnet i c moment jx, and the n u c l e a r e l e c t r o -s t a t i c q u a d r u p o l e moment Q, were de termined from the o p t i c a l h y p e r f i n e s t r u c t u r e s o f B i . The magnet ic moment was c a l c u l -a t e d f o r 8 c o n f i g u r a t i o n s and 14 l e v e l s . The quadrupo le moment was c a l c u l a t e d f o r 4 c o n f i g u r a t i o n s and 6 l e v e l s . The v a l u e s o f ji t h a t were o b t a i n e d from o n e - e l e c t r o n s p e c t r a showed good agreement w i t h more p r e c i s e resonance measurements The agreement f o r Q was n o t q u i t e so good . Good measurements 9 were made f o r the 5d 6p c o n f i g u r a t i o n , b u t there i s no r e a d i l y a v a i l a b l e t h e o r y from which to c a l c u l a t e Q f o r t h i s c o n f i g -u r a t i o n . The l i g h t source used i n t h i s i n v e s t i g a t i o n was a "condensed" e l e c t r o d e l e s s d i s c h a r g e , and the spec trograms were taken on a 9 .1 metre concave g r a t i n g s p e c t r o g r a p h . Q was found t o be - . 5 ( 1 ) b a r n s . U s i n g v a l u e s o f p. t h a t employed i n f o r m a t i o n from o n e - e l e c t r o n s p e c t r a , p. was found to be 4 .1(1) n u c l e a r magnetons. i i TABLE OF CONTENTS A b s t r a c t v i Acknowledgements . . . . . . . . . . v i i I n t r o d u c t i o n . . . . 1 C h a p t e r I . T h e o r y 4 The H y p e r f i n e - M u l t i p l e t . . . . . . . 5 D e p a r t u r e s from the I n t e r v a l Rule . . . . . . . 7 S i n g l e E l e c t r o n L e v e l s . . . . 8 Two E l e c t r o n , s C o n f i g u r a t i o n s . 9 P e r t u r b a t i o n s .• 10 C h a p t e r I I . E x p e r i m e n t a l 12 L i g h t Sources 12 S p e c t r o g r a p h s 16 C o m p a r a t o r . . 18 C h a p t e r I I I . D a t a R e d u c t i o n . 20 D i s p e r s i o n T a b l e s 20 E n e r g y D i f f e r e n c e s i n an H f s . 21 I n t e n s i t i e s 30 C h a p t e r I V . R e s u l t s 32 N u c l e a r Moments from B i I I . . . 32 N u c l e a r Moments from B i I I I 36 N u c l e a r Moments from B i IV _ 38 M a g n e t i c Moment from B i V 46 Summary o f R e s u l t s 46 i i i C o n c l u s i o n and Comments 49 B i b l i o g r a p h y 51 Appendix I : L i n e L i s t 53 Appendix I I : U n c l a s s i f i e d L i n e s . . . . . 6 4 Appendix I I I : Energy D i f f e r e n c e s . . 65 i v LIST OF TABLES I . F a c t o r s f o r quadrupo le energy d i f f e r e n c e s . . . . 29 I I . A and B f o r l e v e l s o f B i I I 34 I I I . M a g n e t i c moment from B i I I I . 36 I V . A and B f o r l e v e l s o f B i I I I . 37 V . A and B f o r . l e v e l s o f B i I V . . 41 V I . Summary o f R e s u l t s 46 V I I . xx, c a l c u l a t e d from a", from s J_ c o n f i g u r a t i o n s . . 49 V I I I . L i n e L i s t . 5 3 V L I S T OF FIGURES 1. Schema o f p u l s e d h o l l o w cathode d i s c h a r g e t u b e . , . . 14 2. Schema of condensed e l e c t r o d e l e s s d i s c h a r g e t u b e . . 15 v i i ACKNOWLEDGEMENTS P r o f e s s o r A . M . C r o o k e r , my r e s e a r c h s u p e r v i s o r , sugges ted t h i s p r o j e c t , was r e s p o n s i b l e f o r the p e r s o n a l c o n t a c t s a t the Argonne N a t i o n a l L a b o r a t o r y , and was a s o u r c e o f h e l p f u l and i n t e r e s t i n g d i s c u s s i o n s . Thanks are due a l s o to D r s . F . S . Tomkins and M . F r e d f o r so g e n e r o u s l y a l l o w i n g me to use t h e i r . s p e c t r o g r a p h , and t o D r . A . G ia^che t t i and M r . B . E r c o l i f o r a s s i s t a n c e i n t a k i n g the Argonne e x p o s u r e s . A t U . B . C . , M e s s r s . E . P r i c e , J . L e e s , and A . F r a s e r p r o v i d e d me w i t h e x p e r t t e c h n i c a l h e l p and s u g g e s t i o n s . A number o f o thers - m a c h i n i s t s , s t u d e n t s , and f a c u l t y -made v a l u a b l e c r i t i c i s m s and s u g g e s t i o n s . And I am i n d e b t e d to the N a t i o n a l Research C o u n c i l f o r p r o v i d i n g f i n a n c i a l a s s i s t a n c e d u r i n g the course o f my r e s e a r c h . INTRODUCTION I f the nuc l eus o f a f r e e atom has a magnet ic moment, the n u c l e u s can e x i s t o n l y i n a f i n i t e number o f o r i e n t a t i o n s w i t h r e s p e c t to the o r b i t a l e l e c t r o n s ' magnet ic f i e l d . The energy o f i n t e r a c t i o n i s W=-yuHcos (£i ,H) , where p. i s the n u c l e a r magnet i c moment, and H i s the magnet ic f i e l d a t the n u c l e u s , produced by the e l e c t r o n s . S i n c e the n u c l e a r o r i e n t a t i o n i s q u a n t i z e d , c o s\ ja,B) has a f i n i t e number o f v a l u e s . F o r each e l e c t r o n i c energy l e v e l , a group of c l o s e l y spaced energy l e v e l s e x i s t s . T h i s group i s c a l l an hfm ( h y p e r f i n e m u l t i p l e t ) . When e l e c t r o n i c t r a n s i t i o n s o c c u r , an h f s ( h y p e r f i n e s t r u c t u r e ) i s e m i t t e d . From b o t h an a n a l y s i s o f the hfm and a l s o i n f o r -mat ion about the e l e c t r o n i c c o n f i g u r a t i o n t h a t i n c l u d e s the hfm, the n u c l e a r magnet ic moment can be o b t a i n e d . H y p e r f i n e r e f e r s to e l e c t r o n - n u c l e a r i n t e r a c t i o n s . H i s t o r i c a l l y , h y p e r f i n e meant the e n e r g i e s i n v o l v e d were much s m a l l e r than f i n e - s t r u c t u r e e n e r g i e s . F i n e s t r u c t u r e e n e r g i e s are on the o r d e r o f 1000cm"' ; h y p e r f i n e e n e r g i e s are seldom g r e a t e r than a few c m - ' . An h f s w i l l a l s o be observed i f t h e r i s more than one i s o t o p e i n a sample . So i f one uses a sample o f say , n a t u r a l l y o c c u r r i n g i n d i u m , the h y p e r f i n e s t r u c t u r e s would r e s u l t from two e f f e c t s . The i s o t o p i c spectrum and n u c l e a r moment spectrum would o v e r l a p , and the r e s u l t i n g h y p e r f i n e s t r u c t u r e s would be d i f f i c u l t t o a n a l y z e . The spectrum o f b i smuth i s w e l l s u i t e d to a n a l y s i s . I t has a l a r g e magnet ic moment, and there i s on ly one s t a b l e i s o t o p e . T h e r e f o r e , the h y p e r f i n e s t r u c t u r e s are l a r g e and one does n o t have t o be t r o u b l e d w i t h s e p a r a t e d - i s o t o p e samples . When d o i n g h f s e x p e r i m e n t s , Q, the n u c l e a r e l e c t r o s t a t i c q u a d r u p o l e moment, can a l s o be de termined from the h f s d a t a . C o n s i d e r i n g the n u c l e u s to be an e l l i p s o i d , the p h y s i c a l s i g -n i f i c a n c e o f Q i s i l l u s t r a t e d as Q < 0 Q = 0 Q > 0 The r e f e r e n c e a x i s i s the s p i n v e c t o r I, and the shape i n d i -ca tes the charge d i s t r i b u t i o n . The energy o f i n t e r a c t i o n , W^, i s p r o p o r t i o n a l to ?jj(0)Q, where <Pjj(0) i s the time average o f the g r a d i e n t o f the e l e c t r o s t a t i c f i e l d o f the e l e c t r o n s ; the g r a d i e n t i s e v a l u a t e d a t the n u c l e u s . In B i , W i s - .01W • 209 The n u c l e u s o f B i has a magic number o f neutrons 8 3 and one more than a magic number o f p r o t o n s . A magic number of nuc leons c o n s t i t u t e s a c l o s e d s h e l l , or c o r e , t h a t has z e r o s p i n . When 1^0, ju=0 and Q=0. T h e r e f o r e , i n B i ji and Q are produced by a s i n g l e p r o t o n o u t s i d e a c l o s e d s h e l l . In t h i s t h e s i s , the n u c l e a r moments o f b i smuth were o b t a i n e d from the o p t i c a l s p e c t r u m . O p t i c a l s p e c t r o s c o p y i s not the o n l y method o f o b t a i n i n g n u c l e a r moments. Resonance t echn ique namely r a d i o f r e q u e n c y and a tomic beam t e c h n i q u e s , y i e l d more p r e c i s e measurements than o p t i c a l s p e c t r o s c o p y . However, a t o m i c beams g i v e i n f o r m a t i o n o n l y on the ground s t a t e o f the atom. R a d i o f r e q u e n c y t echn iques are u s u a l l y l i m i t e d to s t a t e s which b e l o n g to the n e u t r a l atom. A d i s c u s s i o n o f r a d i o f r e -quency t e c h n i q u e s i s g i v e n by K a s t l e r (1967) . Kopfermann (1958) d i s c u s s e s a t o m i c beam s t u d i e s . O p t i c a l s p e c t r o s c o p y makes a v a i l a b l e f o r s t u d y many more s t a t e s than do the resonance t e c h n i q u e s . The r e s u l t s from a tomic s p e c t r o s c o p y are more a c c u r a t e than much o f the t h e o r y from which n u c l e a r moments are c a l c u l a t e d . The purpose o f these exper iments then , was t o p r o v i d e a t e s t o f the t h e o r i e s t h a t d e a l w i t h n u c l e a r moments. In some c a s e s , the t h e o r y a p p l i e d to the spec trum o f B i y i e l d s moments t h a t a r e i n agreement w i t h each o t h e r and w i t h the r e s u l t s o f resonance e x p e r i m e n t s . In o t h e r c a s e s , the c a l c u l a t i o n s y i e l d moments t h a t do not agree a t a l l w i t h a c c e p t e d v a l u e s . In t h i s t h e s i s , the n o t a t i o n and trea tment o f n u c l e a r moments f o l l o w s t h a t g i v e n by Kopfermann (1958) . CHAPTER I THEORY I n the f o l l o w i n g , the d i r e c t i o n o f the magnet ic moment i s assumed t o be t h a t o f the n u c l e a r s p i n v e c t o r I , and H to be a n t i p a r a l l e l t o J . V e c t o r i a l l y , I_+J= F , and cos {I,J) = - c o s ( y,H) = ( F 2 - I 2 - J 2 ) / 2 I J . Quantum m e c h a n i c a l l y , F 2 2 2 i s r e p l a c e d by F ( F + 1 ) , J i s r e p l a c e d by J ( J + 1 ) , and I i s r e p l a c e d by 1(1+1), so W = U H ( F ( F + 1 ) - I ( I + 1 ) - J ( J + 1 ) ) / 2 U . F o r c o n v e n i e n c e , l e t A = pH/U and C = F ( F + 1 ) - I ( I + 1) -J(J+1) , so W becomes W = A C / 2 . E x p e r i m e n t a l l y , AW = w (F)-W ( F - l ) i s needed. A w i s g i v e n by the Lande i n t e r v a l r u l e , t W = AF S i n c e we have assumed H i s a n t i p a r a l l e l to J , cos(2J,H) = - c o s ( ^ , J ) . In some c a s e s , H i s p a r a l l e l t o J , the the A f a c t o r i s n e g a t i v e , and the m u l t i p l e t i s s a i d t o be i n v e r t e d . T h i s p a r a l l e l i s m a r i s e s , f o r example, when two e l e c t r o n s have t h e i r s p i n p a r a l l e l , b u t o p p o s i t e l y d i r e c t e d t o the o r b i t a l a n g u l a r momentum v e c t o r L . F o r example, i n a two e l e c t r o n , si. c o n f i g u r a t i o n , A ( ^ L ^ _ ^ ) i s n e g a t i v e . I n d e s c r i b i n g , the quadrupo le i n t e r a c t i o n , the f o l l o w i n g 5 assumpt ions a r e i n v o l v e d . The e l c t r o n i c c l o u d d i s t r i b u t i o n i s c y l i n d r i c a l l y s y m m e t r i c a l about the J a x i s , and the n u c l e a r charge i s c y l i n d r i c a l l y s y m m e t r i c a l about the I a x i s . <p + ( 0 ) J J i s the g r a d i e n t o f the e l e c t r o n s ' e l e c t r i c f i e l d , e v a l u a t e d a t the n u c l e u s . IjT (0) i s the time average o f <p ( 0 ) . The energy J J J J o f i n t e r a c t i o n , from a v e c t o r mode l , i s e q u a l to. 2 eQcpjjtO) (3/2 cos ( I , J ) - ^ ) . Quantum m e c h a n i c a l l y , t h i s becomes (3 /2C(C + l ) - 2 1 ( 1 + 1) J (J+l) W^= ^eQtpjj tO)^ 1(21-1) J ( 2 J - 1 ) As b e f o r e , C=F (F + l ) - I (1 + 1) - J ( J+l) . F o r c o n v e n i e n c e , W q w i l l be s h o r t e n e d to W Q = ^ B G ' w h e r e B = e Q ? j j ( ° ) ' and G i s the e x p r e s s i o n i n c u r l y b r a c k e t s . In many o f the e a r l i e r p a p e r s , ( i n c l u d i n g B r i x (1952)) , W Q was g i v e n by WQ=B 1 (C (C+l) -41 (1 + 1) J ( J + l ) / 3 , where B 1 = 3 B / 8 1 ( 2 1 - 1 ) J ( 2 J - 1 ) ) . To compare my work w i t h the v a l u e s i n B r i x (1952), I was s e t e q u a l to 9 /2 , and the f o l l o w i n g t a b l e u s e d . J 1 2 3 4 ih b / b ' 96 576 1440 2688 288 960 Whenever v a l u e s o f B„ . have been used or quoted i n t h i s B r i x ^ t h e s i s , they have been c o n v e r t e d u s i n g the above t a b l e . The H y p e r f i n e M u l t i p l e t The energy o f each l e v e l i n an hfm i s g i v e n by W = WU+WQ ' or W=AC/2+BG/4. A and B are c o n s t a n t f o r each e l e c t r o n i c energy l e v e l , and C and G depend on the quantum numbers I , J , and F . I f 1=0, then ^i=0 and t h e r e would be o n l y one energy l e v e l f o r each e l e c t r o n i c energy l e v e l , i . e . W and WQ would always be z e r o . F o r B i , 1=9/2. When J=0, W and WQ. s t i l l e q u a l z e r o . But f o r example , when J = l , the f o l l o w i n g energy scheme r e s u l t s . F = l l / 2 -F=9/2 -F=7/2 -10A-.2083B 9 /2A-1 .1250B 11/2A+.9167B 9 /2A-1 .1250B The f i r s t v a l u e s on the r i g h t hand s i d e o f the above energy d iagram are c a l c u l a t e d from W=AC/2+BG/4. E x p e r i m e n t a l l y , the energy d i f f e r e n c e s a r e wanted, and these are g i v e n by the second s e t o f v a l u e s . When t r a n s i t i o n s between two h y p e r f i n e m u l t i p l e t s o c c u r , the s e l e c t i o n r u l e s g o v e r n i n g the t r a n s i t i o n s are A J=0,+1; &(jL i-l ~ +1, i . e . the t r a n s i t i o n s must be from an even to odd (or v i c e ver sa ) e l e c t r o n i c s t a t e ; and A F=0,+1, and F=0->-F=0 i s f o r b i d d e n . F o r example, i f the t r a n s i t i o n i s from a J = l to a J = l s t a t e , the d e s c r i p t i o n o f the r e s u l t i n g h f s c o u l d be drawn as f o l l o w s . F 11/2. 9/2_ 7/2. 7/2. 9/2-11/2. ) > • I n t h i s d i a g r a m , the lower A v a l u e i s n e g a t i v e , or i n v e r t e d , and i s g r e a t e r than the A o f the upper l e v e l ; the upper A i s p o s i t i v e . Below the ' t r a n s i t i o n scheme a r e shown what the h f s would look l i k e on a s p e c t r o g r a m , and the t h e o r e t i c a l i n t e n -s i t i e s ; the h e i g h t s o f the l i n e s are p r o p o r t i o n a l to the i n t e n -s i t i e s . These v a l u e s o f i n t e n s i t y are taken from T a b l e 2 o f Kopfermann(1958) . Wavelengths are shown i n c r e a s i n g to the r i g h t . The i n t e n s i t i e s can be v e r y h e l p f u l when a n a l y z i n g an h f s ; a l m o s t a l l o f the B i h y p e r f i n e s t r u c t u r e s s t u d i e d f o l -lowed the t h e o r e t i c a l i n t e n s i t i e s . D e p a r t u r e s From the I n t e r v a l Rule I f , i n some n u c l e u s , Q=0, the d i f f e r e n c e i n energy between one l e v e l and the next i s p r o p o r t i o n a l to the upper F v a l u e . So i n the d iagram on p .6 / the r a t i o o f the energy d i f f e r e n c e s would be 11:9 . When the e x p e r i m e n t a l d i f f e r e n c e s form r a t i o s t h a t e q u a l the r a t i o s o f the F v a l u e s , the hfm i s s a i d to s a t i s f y the i n t e r v a l r u l e . The i n t e r v a l r u l e w i l l not be s a t i s f i e d i f 1) there i s a n o n - z e r o quadrupo le moment o r 2) i f the hfm i s p e r t u r b e d by a n e i g h b o u r i n g m u l t i p l e t . The o n l y way to t e l l f o r sure i f the d e p a r t u r e i s due to 1) i s to c a l c u l a t e Q from d i f f e r e n t m u l t i p l e t s . In p r a c t i c e , Q can be c a l c u l a t e d f o r v e r y few m u l t i p l e t s , because t h e o r e t i c a l e x p r e s s i o n s have been d e r i v e d o n l y f o r a few c o n f i g u r a t i o n s ; f u r t h e r m o r e , the e l e c t r o n i c c o n f i g u r a t i o n must be u n p e r t u r b e d . A l s o , the o n l y h f s components 8 t h a t can be used are ones t h a t are c o m p l e t e l y r e s o l v e d . I f the e l e c t r o n i c energy l e v e l s are u n p e r t u r b e d , p. can be o b t a i n e d from A , and Q. from B . When d e a l i n g w i t h two-e l e c t r o n c o n f i g u r a t i o n s , A and B w i l l be used to denote the i n t e r a c t i o n c o n s t a n t s ; a and b w i l l be used f o r o n e - e l e c t r o n c o n f i g u r a t i o n s . F o l l o w i n g the n o t a t i o n o f Kopfermann (1958) , the i n t e r a c t i o n c o n s t a n t s a r e : S i n g l e E l e c t r o n L e v e l s s e l e c t r o n s S h c R ^ Z ^ U - d c / d n ) ( l - £ ) F r m e u a s = : — T U 3 n a m p I p i s i n n u c l e a r magnetons. b=0; t h e r e i s no i n t e r a c t i o n between a s p h e r i c a l e l e c t r o n c l o u d and Q. p , d e l e c t r o n s a. J i a p I j ( j + l ) b e 2 Q ( 2 j - i ) R . r - 3 D > h K e 2 ( j + l ) -3 r i s g i v e n by ? Sw r - J = 2 4 2 K m ^ B U ^ ) Z i H r cr = the quantum d e f e c t n .= p r i n c i p a l quantum number n = n - C, n i s the e f f e c t i v e quantum number a a Z_^ = Z f o r s e l e c t r o n s , Z - 4 f o r p e l e c t r o n s , and Z - l l f o r d e l e c t r o n s . Z = 1 f o r n e u t r a l atoms, 2 f o r s i n g l y - c h a r g e d i o n s , e t c . o SW =f ine s t r u c t u r e s p l i t t i n g , e . g . the d i f f e r e n c e between 2 p ^ a n d 2 P ^ F r , R r = r e l a t i v i t y c o r r e c t i o n s t a b u l a t e d i n Kopfermann(1958) $ = c o r r e c t i o n f o r the d i s t r i b u t i o n o f n u c l e a r charge £ = c o r r e c t i o n f o r the d i s t r i b u t i o n o f the magnet ic moment k =1.1126 4 x 1 0 " 1 0 c o u l o m b / v o l t metre e k m = p o / 4 T T - 1 0 _ v o l t s e c . / a m p metre jig=Bohr magneton Two E l e c t r o n , sj. C o n f i g u r a t i o n In the f o l l o w i n g , an JL e l e c t r o n i s d e f i n e d to be one w i t h o r b i t a l a n g u l a r momentum g r e a t e r than z e r o . I t has been found t h a t the i n f l u e n c e o f the s and the X. e l e c t r o n s can be cons idered i n d e p e n d e n t l y . T h i s i s r e a s o n a b l e s i n c e the s o r b i t i s f a r more p e n e t r a t i n g than the 1, o r b i t . The i n t e r a c t i o n c o n s t a n t s a r e : A ( 3 L i + | ) = a s / ( 2 ( l + l ) ) + ( 2 > l ) a i + ! s / ( 2 U + l ) ) 5 A ( 3 L 4 _ , ) = - a s / 2 +(2l + l)aj,_h/2£ 6 ={[{1+1)0%- c^ ]a s + ( 2 i + 3 ) C 2 a ' ? + ( 2 i - l ) ( | + l ) c 2 a " + 4 c 1 c 2 ( i ( i + l ) ) 1 ' 5 a " ']/{2jt{J[+l)) F o r A ( ^ L i ) , c i s r e p l a c e d by c , c i s r e p l a c e d by -c . c . A. 1 2 1 1 and c^ are d e f i n e d on p . 3 2 . I n e q u a t i o n s 5, 6, and 7, a =a o f e q . 1. s s a 1 1 1 i s g i v e n i n Kopfermann(1958) on p . 151. 10 To o b t a i n Q from an s c o n f i g u r a t i o n , e 2 Q2 7^ B ( 3 L « + 1 ) = 1 k e ( 2 | + 3 ) 3 e2Q2{f-l) ( 2 i - 3 ) R r P ^ B( L j _ x ) = ^ - I . ^ k e ^ ( 4 i 2 - l ) . e 2 Q f i U + 2 ) ( 2 i - l ) R ' c 2 B ( ° L ; ) •= { K KeU+h) [ ( i + D (2i+3) . 2 6 ( / ( i+1)) ^c c S ~) -il-DR" c , LULI r r 2 (2/+3) J 8 10 R r ' R r ' ' a n c ^ S r a r e r e l a t i v i s t i c c o r r e c t i o n s , and are t a b u l a t e d i n Kopfermann(1958) . r~ i s g i v e n by e q . 4, b u t now <Sw° i s 3 3 - 1 the energy d i f f e r e n c e , L / ^+i ~ L ^ ^« F o r B ( ' •'-n e c 3* c^and C2 a r e r e p l a c e d by c 2 and -c^ . A and B , or f o r the one e l e c t r o n s p e c t r a , a and b , are c a l c u l a t e d from the e x p e r i m e n t a l data by the method d e s c r i b e d on p . 2 6 . F o r a one e l e c t r o n c o n f i g u r a t i o n , u and Q are c a l -c u l a t e d from e q . 1 or 2, and 3. P e r t u r b a t i o n s C a l c u l a t i o n s f o r p e r t u r b a t i o n s o f a h f m u l t i p l e t have been made f o r o n l y a few s p e c i a l c a s e s . Kopfermann(19 58) 201 on page 29, d i s c u s s e s the case t h a t a p p l i e s to Hg ; h i s t r ea tment i s taken from Goudsmit and Bacher (1933) . McLay and C r a w f o r d (1933) a p p l i e d the same i d e a to the 6s7p c o n f i g -u r a t i o n o f B i I V . Kopfermann, on page 137, a l s o d i s c u s s e s p e r t u r b a t i o n s by s t a t e s w i t h the same J ; t h i s 11 d i s c u s s i o n i s q u a l i t a t i v e . L u r i o e t a l (1956) have g i v e n e x p r e s s i o n s f o r second o r d e r , i n t r a - c o n f i g u r a t i o n p e r t u r b a t i o n s , f o r an sp c o n f i g u r a t i o n . Based on t h i s p a p e r , a sample c a l c u l a t i o n was made f o r 6p7s o f B i I I . T h i s c a l c u l a t i o n was the 3 c o r r e c t i o n to the h f l e v e l s o f P 2 , due to the i n f l u e n c e o f 3 3 1 p l ' P 0 ' a n c ^ P l * These c o r r e c t i o n s , a long w i t h the quadrupo le c o n t r i b u t i o n s , a r e shown be low. 3 F 6.5 P e r t . / 0 J P 2 6p7s, B i I I j P e r t . = 0 Q = 0 Q = 0, P e r t u r b a t i o n = 0 . B = - . 0 4 cm" 1 ' ' i I row rois 5.5 4 . 5 3 .5 K 2.5 006 004 .002 013 .0006 016 The "5 and ^ t h a t appear i n L u r i o ' s paper was taken = 1. ( C a l c u l a t i o n s by Schwarz (1955) , page 389, show 1 to be a good 3 a p p r o x i m a t i o n . ) b - ^ was taken e q u a l to .1 B( P 2 ) . L u r i o ' s c a l c u l a t i o n s r e q u i r e c and c „ , t h e r e f o r e the c o n f i g u r a t i o n needs to be u n p e r t u r b e d . S i n c e these s e c o n d - o r d e r p e r t u r b a t i o n c a l c u l a t i o n s can not always be made, and are s m a l l compared to the quadrupo le i n t e r a c t i o n , o n l y t h i s one c a l c u l a t i o n was done. 12 CHAPTER I I EXPERIMENTAL L i g h t Sources 1. H o l l o w Cathode A few p i c t u r e s were taken u s i n g a h o l l o w cathode d i s c h a r g e t u b e . The cathode was o f molybdenum. A h o l e a p p r o x i m a t e l y 4" deep and \ " i n d iameter was d r i l l e d i n the molybdenum, and a p i e c e o f b i smuth p l a c e d i n the h o l e . The anode was a r i n g o f s t a i n l e s s s t e e l . S e v e r a l exposures were made w i t h a F a b r y - P e r o t i n t e r f e r o -m e t e r . The i n t e r f e r o m e t e r was c r o s s e d w i t h a l a r g e , L i t t r o w -mount, p r i s m s p e c t r o g r a p h . H e l i u m a t a p r e s s u r e o f a p p r o x i m a t e l y 7 t o r r was s l o w l y c i r c u l a t e d through the t u b e . W i t h a d . c . v o l t a g e o f 350 v o l t s and .180 amps, a good exposure was o b t a i n e d i n 15 m i n u t e s . The f u l l w i d t h a t h a l f maximum (FWHM) under these c o n d i t i o n s was e s t i m a t e d to be a t most .03 cm \ or . OlS . f o r the 5719A* B i I I l i n e . T h i s v a l u e was o b t a i n e d by c a l c u l a t i n g the d i s p e r s i o n between s u c c e s s i v e i n t e r f e r e n c e f r i n g e s , measur ing the FWHM as d i s p l a y e d by the comparator , and then m u l t i p l y i n g the d i s p e r s i o n by the d i s p l a y e d FWHM. 2. P u l s e d H o l l o w Cathode S i n c e the h f s spectrum o f B i I and II had a l r e a d y been s t u d i e d by S c h u l e r and Schmidt (1936), F i s h e r and Goudsmit (1931) and Mrowzosk i (1942), i t was d e s i r a b l e to o b t a i n a source that ' would produce s h a r p l i n e s o f the doub ly and 13 t r i p l y i o n i z e d atom. F o r t h i s purpose , the h o l l o w cathode was p u l s e d . A schema i s shown i n F i g . 1. The e x t e r n a l gap was s e t t o b r e a k down a t a p p r o x i m a t e l y 3500 v o l t s . T h i s method i s s i m i l a r to t h a t d e s c r i b e d by G a r t l e i n and G i b b s (1931) . I n the p r e s e n t work, the gap broke down a p p r o x i m a t e l y f i v e t imes p e r s e c o n d . E a c h breakdown was a s i n u s o i d o f 20yU.sec p e r i o d . The o s c i l l a t i o n s were h e a v i l y damped and l a s t e d o n l y 2 or 3 p e r i o d s . A f a i n t spectrum o f the m a t e r i a l o f the anode was p r o d u c e d , and h e a t i n g o f the anode a l s o o c c u r r e d . The h o l l o w cathode o p e r a t e d i n t h i s manner produced most o f the c l a s s i f i e d I I I and IV l i n e s , and many o f the I and I I l i n e s were a b s e n t t h a t i n the d . c . mode were p r e s e n t . A F a b r y - P e r o t p i c t u r e was t a k e n , and the l i n e s showed p o o r l y - r e s o l v e d h f s . 3 . Condensed E l e c t r o d e l e s s D i s c h a r g e . A schema of t h i s source i s shown i n F i g . 2. The gap was s e t t o break down a t a p p r o x i m a t e l y 50,000 v o l t s . To produce a d i s c h a r g e , the vapour p r e s s u r e o f the m a t e r i a l i n the q u a r t z tube has to be a p p r o x i m a t e l y 0.1 t o r r . F o r b i s m u t h , t h i s r e q u i r e d a temperature o f 8 0 0 ° C . The q u a r t z tube was 2 .5 cm. i n d i a m e t e r , 60 cm. l o n g , and had a q u a r t z window a t each e n d . The c o i l a s u r r o u n d i n g the tube had 9 t u r n s i n 10 c m . , and was o f 4 mm. d i a m e t e r copper w i r e . A d i s c u s s i o n o f t h i s source i s g i v e n by Minnhagen (1964) . A F a b r y - P e r o t p i c t u r e w i t h 1 cm. e t a Ions, was made w i t h the condensed e l e c t r o d e l e s s d i s c h a r g e . A l l t h r e e components o f the 5719 B i I I l i n e were r e s o l v e d , and the PULSED HOLLOW CATHODE GL 8020 v . 3 .5 kv A A / V — 2 k_n. 7 .5 juf -> ^ A i r Gap Anode D i s c h a rge Tube Cathode A i r Gap 5 kw 50 k v . T o t a l C = .05 pf "CONDENSED" ELECTRODELESS DISCHARGE X M e c h a n i c a l > Pump hrj Oven ' w to 16 FWHM e s t i m a t e d t o be .05 cm 1 or .015$. The FWHM due to D o p p l e r b r o a d e n i n g i s g i v e n by A\) = 7 x 10 \>0 (T/M) 2 . See , e . g . Kuhn (1962) , page 386. The m o l e c u l a r w e i g h t o f B i i s 209, the t e r m p e r a t u r e was a p p r o x i m a t e l y 1 0 0 0 ° K . Then Al) = 16 x 1 0 ~ 7T ) o . F o r 5719A3, V 0 = 17, 500 c m - 1 , so A l) = .03 cm - 1 . I f we a t t r i b u t e the t o t a l w i d t h t o D o p p l e r b r o a d e n i n g , the e f f e c t i v e temperature would be'~ 3 0 0 0 ° K . O r , i f the p r e s s u r e i n c r e a s e d c o n s i d e r a b l y d u r i n g o p e r a t i o n , the l i n e w i d t h might be e x p l a i n e d by p r e s s u r e b r o a d e n i n g . 4 . Microwave E l e c t r o d e l e s s D i s c h a r g e . T h i s s o u r c e c o n s i s t e d o f a s m a l l , s e a l e d q u a r t z tube i n t o which B i had been d i s t i l l e d . Neon, to a few t o r r p r e s s u r e , was i n c l u d e d as a c a r r i e r g a s . The tube was p l a c e d i n a r e s o n a n t c a v i t y , and the c a v i t y was powered by a 2450 M e g a c y c l e d i a t h e r m y u n i t . On the Argonne s p e c t r o g r a p h , the Zeeman s p e c t r a i n a f i e l d o f 24 K gauss was t a k e n , b u t o n l y the z e r o - f i e l d spectrum was measured i n t h i s work . The B i I spec trum was v e r y s t r o n g , B i I I was weak, and the. h i g h e r i o n i z e d s p e c t r a were a b s e n t a l t o g e t h e r . S p e c t r o g r a p h s 1. P r i s m . A l a r g e p r i s m s p e c t r o g r a p h was used f o r s e v e r a l d i f f e r e n t k i n d s o f e x p o s u r e s . In p r e p a r a t i o n f o r the Argonne p i c t u r e s , "survey" exposures were made w i t h the p r i s m s p e c t r o g r a p h . To i d e n t i f y the wave length and i o n i z a t i o n o f some o f the u n c l a s s i f i e d h f s t h a t appeared on the Argonne p l a t e s , spark -i n - h e l i u m p i c t u r e s were made w i t h the p r i s m i n s t r u m e n t . And the F a b r y - P e r o t i n t e r f e r o m e t e r was c r o s s e d w i t h the p r i s m s p e c t r o g r a p h . 17 T h i s i n s t r u m e n t was made by H i l g e r , was a L i t t r o w mount, and had e a s i l y i n t e r c h a n g e d g l a s s and q u a r t z o p t i c s . The f o c a l l e n g t h was 1.5m, and the -f/ number was 18. 2. F a b r y - P e r o t I n t e r f e r o m e t e r . The f l a t s were from Z e i s s , and coated w i t h a m u l t i l a y e r d i e l e c t r i c s a n d w i c h . The u s e f u l range o f the o o p l a t e s was from about 4000A to a t l e a s t 8500A. T h i s i n s t r u m e n t p r o v i d e d a measure o f the FWHM of the l i g h t o s o u r c e s , and a l s o a good s p e c t r o g r a m o f the 5719A hf s o f B i I I . T h i s h f s was a n a l y z e d a c c o r d i n g to the procedure d e s c r i b e d by M e i s s n e r (1941) . 3 . Argonne G r a t i n g S p e c t r o g r a p h The m a j o r i t y o f the i n f o r m a t i o n p r e s e n t e d i n t h i s t h e s i s was o t a i n e d w i t h a g r a t i n g s p e c t r o g r a p h a t the Argonne N a t i o n a l L a b o r a t o r y . T h i s s p e c t r o g r a p h i s a 9 .1 metre Rowland mount. The g r a t i n g used f o r t h i s work was d e s i g n a t e d by Tomkins and F r e d "G5", and i s an o r i g i n a l . I t i s r u l e d w i t h 15,000 l i n e s / i n c h , or 8 3 3 3 A / l i n e . o The d i s p e r s i o n ranged from about .8A/mm, i n the f i r s t o r d e r to about . 15A/mm. i n the f i f t h o r d e r . T h o r i u m , i n the form o f t h o r i u m i o d i d e and p i a c e d i n a 2450 M c / s c a v i t y , was used as the s t a n d a r d . The wavelengths o f the t h o r i u m l i n e s used as s t a n d a r d s were o b t a i n e d from the c o m p i l a t i o n o f Gia^chetti (1966) . The exposure t imes were: 1) condensed e l e c t r o d e l e s s d i s c h a r g e , 2 h o u r s ; 2) microwave e l e c t r o d e l e s s d i s c h a r g e ( z e r o - f i e l d ) , 4 minute s ; 3) Th s t a n d a r d s , 2^ to 10 m i n u t e s , 18 depending on the f i l t e r u s e d . When the exposures were t a k e n , the Th spec trum was p r o j e c t e d t h r o u g h , i . e . , a l o n g the a x i s o f , the B i d i s c h a r g e t u b e . A l l the p l a t e s were 18" x 2". The emuls ions used depended on the wave length c o v e r e d . The I l f o r d emuls ions used were Q2 and HP3; on Kodak' p l a t e s , the 103-0 e m u l s i o n was u s e d . A d i s c u s s i o n o f the Argonne s p e c t r o g r a p h i s g i v e n by Tomkins and F r e d (1963) . Comparator The comparator used i n t h i s work was b u i l t by G r a n t and used the d i s p l a y d e v i c e i n v e n t e d by Tomkins and F r e d (1951) . T h i s d e v i c e d i s p l a y s , on an o s c i l l o s c o p e s c r e e n , the d e n s i t y t r a c e o f a l i n e , as w e l l as the m i r r o r image o f the l i n e . I f a l i n e i s p e r f e c t l y s y m m e t r i c a l , the c e n t e r o f the l i n e i s reached when there appears to be o n l y one p r o f i l e . I f a l i n e i s a s y m m e t r i c a l , the maximum d e n s i t y o f the l i n e can q u i t e r e p r o d u c i b l y be measured. I t was found t h a t the c e n t r e o f s t r o n g , s y m m e t r i c a l l i n e s c o u l d be r e p r o d u c i b l y s e t t o - .005 o f the FWHM. The p o s i t i o n and t r a n s m i s s i o n o f the p l a t e a r e s t o r e d i n d i g i t a l form. By p r e s s i n g a s w i t c h , the i n f o r m a t i o n i s t r a n s f e r r e d t o , and punched onto cards by an IBM c a r d punch . The p o s i t i o n c h a r a c t e r s go from .000 to 252.000 m i l l i m e t r e s ; the t r a n s m i s s i o n goes from 000 to 999. A motor and gear t r a i n was c o n n e c t e d , v i a a c l u t c h , to the d r i v e o f the c o m p a r a t o r . The output o f the t r a n s m i s s i o n 19 p h o t o m u l t i p l i e r was fed i n t o a pen r e c o r d e r . When l i n e p r o f i l e s were t r a c e d , the m o t o r i z e d d r i v e and pen r e c o r d e r were u s e d . The r e s u l t i n g t r a c e was v e r y n e a r l y the same s i z e as the p r o f i l e t h a t appeared on the o s c i l l o s c o p e , and was a p p r o x i m a t e l y a 50x m a g n i f i c a t i o n o f what appeared on the p h o t o g r a p h i c p l a t e . The measurement o f l i n e s was done m a n u a l l y ; the gear t r a i n was d i s e n g a g e d , and the s tage advanced by h a n d . 20 CHAPTER I I I DATA REDUCTION D i s p e r s i o n T a b l e s F o r the Argonne p l a t e s , a t a b l e o f d i s p e r s i o n as a f u n c t i o n o f wave l ength was found to be v e r y u s e f u l . The d i s p e r s i o n formula i s d e r i v e d from the f o l l o w i n g f i g u r e and f o r m u l a e . S l i t R = r a d i u s o f the g r a t i n g , %R = r a d i u s o f the Rowland c i r c l e , n = b ( s i n i + s i n O ) ; n = o r d e r ; 0 i s p o s i t i v e i f on the same s i d e o f the n o r m a l as i , n e g a t i v e i f on the o p p o s i t e s i d e , s = d i s t a n c e a l o n g the Rowland c i r c l e . The p l a t e f a c t o r (sometimes r e f e r r e d t o as the d i s p e r s i o n ) D = ^ \ _ =])A_^o = i f 1 " (tlk ~ s i n i • )s 20 Rn / [ \q . , 21 A t . A r g o n n e , R, b , and i were measured to be R = 9143.3 mm., b = 8333.679$ and i = 5 2 ° 5 9 ' . ( E m p i r i c a l l y , i t was found t h a t b = 8333.700$ gave a b e t t e r f i t . ) A computer programme was w r i t t e n t h a t c a l c u l a t e d D o i n increments o f 10A and p r i n t e d the r e s u l t s i n t a b l e f o r m . T h i s was done f o r n = 1 , 2 , 3 , 4 and 5. I d e n t i f i c a t i o n Cards When t a k i n g the exposures o f B i , f i l t e r s were n o t u s e d . To a i d i n the i d e n t i f i c a t i o n o f o v e r l a p p i n g o r d e r s , cards w i t h t h e f o l l o w i n g appearance were made. When a p h o t o g r a p h i c p l a t e was p l a c e d on i t s c a r d , the p o s s i b l e wavelengths o f a l i n e were e a s i l y s e e n . 5528.5 11057 .0 3685.7 2764.3 2211.4 ' 1 cm. 65532.4 11064.7 3688 .2 j 2766.2 2212.9 5536.2 11072.5 3690.8 2768.1 2214.5 U s i n g the d i s p e r s i o n f o r m u l a , the computer c a l c u l a t e d the wavelengths f o r each c e n t i m e t r e . E n e r g y D i f f e r e n c e s i n an HFS The energy d i f f e r e n c e s between members o f an h f s a r e more i m p o r t a n t than the e n e r g i e s o f the i n d i v i d u a l members. The d i f f e r e n c e s between n o n - a d j a c e n t components was o f t e n needed. A programme was w r i t t e n t h a t 1) a l l o w e d s e v e r a l s c a n n i n g measurements to be taken o f a s i n g l e h f s , 2) f o r 22 each s c a n , c a l c u l a t e d the d i f f e r e n c e s between a l l members o f the h f s , 3) c a l c u l a t e d the average energy d i f f e r e n c e s and s t a n d a r d d e v i a t i o n from a l l the measurements and 4) p r i n t e d the average d i f f e r e n c e and s t a n d a r d d e v i a t i o n i n a format t h a t made i t easy to t e l l which components the v a l u e s b e l o n g e d t o . F i r s t , a l l the l i n e s on a p l a t e , B i and T h , were measured . To measure an h f s , the comparator s tage was s h i f t e d p e r p e n d i c u l a r to the long d imens ion o f the p l a t e . A measur ing scan was made. The s tage was s h i f t e d a g a i n and a n o t h e r s c a n was made. The average d i f f e r e n c e s and s t a n d a r d d e v i a t i o n o f the d i f f e r e n c e s were found t o be the same f o r t e n scans as f o r t h r e e s c a n s . T h e r e f o r e t h r e e scans were u s u a l l y made. • The Th l i n e s t h a t were used as s t a n d a r d s a r e those c t a b u l a t e d by Gia^che t t i (1967) . These were i n t e r f e r o m e c -t r i c a l l y d e t e r m i n e d , and a r e a c c u r a t e to a few t e n -thousandths o f an a n g s t r o m . The wave length and comparator r e a d i n g s o f a l l the s t a n d a r d Th l i n e s were f i t t e d by a l e a s t squares p r o c e d u r e to a f o u r t h degree p o l y n o m i a l . From the p o s i t i o n s o f the s t a n d a r d s and the q u a r t i c p o l y n o m i a l , a d e r i v e d s e t o f wavelengths was c a l c u l a t e d . The d i f f e r e n c e between the t r u e and d e r i v e d wave length was t a k e n , and the s t a n d a r d d e v i a t i o n o f a l l these d i f f e r e n c e s c a l c u l a t e d . I f the d i f f e r e n c e o f any one l i n e was more than twice the s t a n d a r d d e v i a t i o n , t h a t l i n e was omi t t ed and a new p o l y n o m i a l c a l c u l a t e d . A new s t a n d a r d d e v i a t i o n was found, and the i n d i v i d u a l d i f f e r e n c e s were f o u n d . T h i s proces s was r e p e a t e d u n t i l a l l the d i f f e r e n c e s were l e s s than twice the s t a n d a r d d e v i a t i o n . These c a l c u l a t i o n s were a l l done on the computer . S t a n d a r d d e v i a t i o n s ranged from 2 x 1 0 - 3 A5 t o 5 x 10 4 $ . On the low - nX p l a t e s , as many as 20 s t a n d a r d s o c c u r r e d i n 25 cm; on the h i g h - nX p l a t e s , as few as 8 s t a n d a r d s were a v a i l a b l e . Th l i n e s from o n l y one o r d e r were u s e d , b u t the wavelengths were c o n v e r t e d to n X . T h i s was o f t e n a n i n e - d i g i t number, and s i n g l e p r e c i s i o n o f t e n y i e l d s u n a c c e p t a b l e r o u n d - o f f e r r o r s . T h e r e f o r e , d o u b l e - p r e c i s i o n format was used i n a l l the c a l c u l a t i o n s , b u t f o r output t h a t was l e s s than 9 d i g i t s , the double p r e c i s i o n was changed to s i n g l e p r e c i s i o n . T h i s a l l o w e d more room f o r o u t p u t , and the r e s u l t s were e a s i e r to r e a d . C a l c u l a t i o n s f o r the wave numbers i n c l u d e d E d l e n ' s d i s p e r s i o n f o r a i r . No c o r r e c t i o n was made f o r n o n - s t a n d a r d a i r . As Tomkins and F r e d (1963) s t a t e d , these c o r r e c t i o n s g would amount t o a few p a r t s i n 10 ; f o r energy d i f f e r e n c e s c o v e r i n g an h f s , i . e . l e s s than 10 cm \ the c o r r e c t i o n would n o t be d e t e c t a b l e . To i l l u s t r a t e the method o f a n a l y s i s , the w e l l - r e s o l v e d 3012$ h f s o f B i IV w i l l be e x p l a i n e d . A p r i n t o f t h i s h f s i s shown on the n e x t page . 24 3012 R h f s o f B i 4— Scan 1 < Scan 2 See Page 28. Scan 3 I V The c l a s s i f i c a t i o n o f the 3012A hfs s t a t e s t h a t the upper l e v e l i s J = 2 and the lower l e v e l J = 1. From the appearance o f the h f s , the J = 1 l e v e l has the l a r g e r A f a c t o r . B r i x (1952) s t a t e s b o t h A ' s a r e p o s i t i v e . We can now draw the f o l l o w i n g d i a g r a m . F = 13/2 11/2 9/2 7/2 5/2 13/2 11/2 9/2 17 35, 51 46 22 8 TOO 3 5 8 '43 o Diagram f o r the 3012A hfs o f B i IV, The numbers a t the bottom are i n t e n s i t i e s , and are from T a b l e 2 o f Kopfermann (1958) . The numbers a t the top i n d i c a t e the o r d e r i n which the components would appear on a s p e c t r o g r a m . A d e n s i t o m e t e r t r a c e o f the observed h f s i s on page 27. When the s e p a r a t i o n s , d i r e c t i o n o f i n c r e a s i n g w a v e l e n g t h , and i n t e n s i t i e s a r e compared w i t h the d e n s i t o m e t e r t r a c e , we see t h a t b o t h A ' s a r e indeed p o s i t i v e . I f the i n t e r v a l r u l e were f o l l o w e d , the d i f f e r e n c e i n energy between components 1 -and 5 would e q u a l ( 9 / 2 ) A - ^ o w e r . F o r t h i s h f s , 2 d i f f e r e n c e s determine b o t h 9A^/2 and l l A ^ / 2 , and one d i f f e r e n c e 1 3 A 0 / 2 and 7 A l ) / 2 . S i n c e the e f f e c t o f the quadrupo le moment i s t o be taken i n t o a c c o u n t , the i n t e r v a l r u l e i s n o t e x a c t l y obeyed. The energy d i f f e r e n c e s , from the t a b l e on page 28, are F = 13/2 13A/2 + .5417B 11/2 9 / 2 1 1 A / 2 7 / 2 _____ 9A/2 - . 3125B 5/2 7A/2 - . 437 5B XL/2 11A/2 + .9167B 9/2 . 9/2A 1. 12 50B 7/2 26 To see how the e x p e r i m e n t a l energy d i f f e r e n c e s were d e t e r m i n e d , look a t page 28. On the f i r s t s c a n , the n i n e components were measured. T h e i r p o s i t i o n s and t r a n s m i s s i o n a r e p r i n t e d on the f i r s t l i n e . -The measurements from the .: second and t h i r d scans are p r i n t e d on the second and t h i r d l i n e s . F o r each s c a n , the computer c a l c u l a t e d the 36 p o s s i b l e d i f f e r e n c e s , a v e r a g e d each o f the 36 d i f f e r e n c e s , and found the s t a n d a r d d e v i a t i o n o f each o f the 36 d i f f e r e n c e s . These averages and s t a n d a r d d e v i a t i o n s a r e p r i n t e d i n the t r i a n g u l a r a r r a y . F o r example, the d i f f e r e n c e between the f i r s t and second component i s .8404 cm \ and the s t a n d a r d d e v i a t i o n o f t h r e e measurements i s .0019 cm \ From the d iagram on the p r e v i o u s page, the d i f f e r e n c e between the f i r s t and second component i s 9 A u / 2 . S i m i l a r l y , the d i f f e r e n c e between the 4 th and 8 t h component i s l l A u / 2 . A l l these p e r t i n e n t energy d i f f e r e n c e s a r e i d e n t i f i e d on the t r i a n g u l a r a r r a y . The w i d t h o f the output shee t l i m i t e d the h f s to 14 components. Hfs w i t h more members had to be done i n two g r o u p s . R e s o l v e d h f s components are e s s e n t i a l f o r q u a n t i t a t i v e r e s u l t s . T h e r e f o r e , a microphotometer t r a c e was made o f each h f s . When energy d i f f e r e n c e s were s e l e c t e d from the computer o u t p u t , the t r a c e was c o n s u l t e d to check t h a t the components were indeed r e s o l v e d . To o b t a i n A and B f o r an h f m u l t i p l e t , two d i f f e r e n c e s have to be known. Then two e q u a t i o n s a r e s o l v e d f o r the two o unknowns, A and B . F o r example, the 3012A l i n e o f B i IV HFS W L = 3 0 1 2 V B I 4 , FROM P L A T E C 1 3 1 2 1 3 . 7 5 5 436 3 0 1 1 . 4 5 5 2 2 1 4 . 1 9 1 213 3 0 1 1 . 5 3 1 2 3 3 1 9 6 . 8 6 4 3 3 1 9 6 . 0 2 5 2 1 4 . 5 2 7 2 1 6 . 8 4 4 2 1 7 . 3 8 7 171 148 158 3 0 1 1 . 5 8 9 8 3 0 1 1 . 9 9 4 1 3 0 1 2 . 0 8 8 8 3 3 1 9 5 . 3 7 9 3 3 1 9 0 . 9 2 4 3 3 1 8 9 . 8 8 0 2 1 7 . 8 2 4 2 2 0 . 6 4 1 2 2 1 . 2 9 6 3 37 092 214 3 0 1 2 . 1 6 5 1 3 0 1 2 . 6 5 66 3 0 1 2 . 7 7 0 9 3 3 1 8 9 . 0 4 0 3 3 1 8 3 . 6 2 6 3 3 1 3 2 . 3 6 7 22 1. 839 740 3 0 1 2 . 3 6 5 6 3 3 1 8 1 . 3 2 4 i HFS WL=3C12 , B I 4 , FROM P L A T E C 1 3 1 COMP 1 COMP 2 COMP 3 COKP 4 COMP 5 COMP 6 COMP 7 COMP 8 COMP 9 CQMP 2 1 3 . 755 2 1 4 . 1 9 1 2 1 4 . 527 2 1 6 . 8 4 4 2 1 7 . 3 8 7 2 1 7 . 824 2 2 0 . 6 4 1 22 1 . 2 9 6 221 . 83<J P o s i H o f l 436 213 171 148 158 337 092 214 740 2 1 3 . 7 6 6 2 1 4 . 2 0 3 2 1 4 . 539 2 1 6 . 858 2 1 7 . 4 0 1 2 1 7 . 839 2 2 0 . 6 5 7 22.1 . 3 1 2 221 . 8 6 0 44 5 213 172 149 161 34 5 091 218 7 32 2 1 3 . 7 6 9 2 1 4 . 207 2 1 4 . 542 2 1 6 . 862 2 1 7 . 4 0 5 2 1 7 . 844 2 2 0 . 6 6 1 221 . 3 1 7 221 . 8 6 2 Tl,/j\ StVt 445 217 17? 148 161 342 092 218 747 ' U M / t -%h 7/2 A, \ \\/Z L %h 13^ X (l/M, 0 .840% 0 . 6 4 5 5 4 . 4 5 8 3 1 . 0 4 3 9 0 . F 4 2 0 . 5 . 4 1 5 0 1 . 2 5 9 3 1 . 0 4 7 9 0 . C 0 1 9 0 . C 0 1 1 G . 0 G 2 9 O.COCO 0 . 0 0 1 9 0 . 0 0 1 1 0 . 0 0 1 1 0 . 0 0 4 8 \ / N 1 . 4 8 5 9 5 . 1039 5 . 5023 1 . 3859 6 . 2 5 7 1 6 . 6 7 4 4 2 . 3 0 7 2 op 0 . 0 0 1 1 C . 0 0 2 2 0 . 0 0 2 9 0 . 0 0 1 9 0 . 0 0 2 2 0 . 0 0 1 1 0 . 0 0 4 8 \ 5 . 9 4 4 3 6 . 1 4 78 6 . 3 4 43 7 . 3 0 1 0 7 . 5 1 6 4 7 . 7 2 2 3 0 . C 0 4 0 0 . O C 2 2 0 . 0 0 4 8 0 . 0 0 2 2 0 . 0 0 2 9 0 . 0 0 5 8 h % At \ A / i J* A / 6 . 9 8 8 2 6 . 9896 1 1 . 7 5 9 3 8 . 3 6 0 3 3 . 5 6 4 T  0 . C Q 4 U 0 . 0 0 4 0 0 . 0 0 5 1 0 . 0 0 2 9 0 . 0 0 6 9 7 . 3 3 0 2 1 2 . 4 0 4 8 1 3 . 0 1 8 7 9 . 6 0 8 2 G . 0 0 5 9 0 . 0 0 4 4 0 . 0 0 5 9 0 . 0 0 6 9 1 3 . 2 4 5 3 1 3 . 6 6 4 2 1 4 . 0 6 6 5  0 . G C 6 2 0 . 0 0 5 1 0 . 0 0 9 5 1 4 . 5 0 4 6 1 4 . 7 1 2 1 0 . 0 0 6 9 0 . 0 0 9 1 : 1 5 . 5525 : ; 0 . 0 1 0 6 shows i n t e r v a l s f o r 6 o f 6.9856 and 8.5702 cm . "From the f i g u r e on page 6, the two e q u a t i o n s are 4 .5A - 1.1250B = 6 . 9 8 9 0 5.5A + .9167B = 8 .5603 . (The 9/2 i n t e r v a l v a l u e i s an average o f the two v a l u e s , 6.9882 and 6.9898 c m - 1 . The 11/2 i n t e r v a l i s from the s t r o n g t r a n s i t i o n o n l y ; component 9 i s weak, and measurements i n v o l -v i n g t h i s component have a r e l a t i v e l y l a r g e u n c e r t a i n t y . ) From t h e s e , A = 1.5559 c m " 1 , B= .014 c m - 1 . When a n a l y z i n g the d a t a , i t was e s s e n t i a l t o know AWsW(F) - W ( F - l ) = AW - AW . AW = F A , and P Q P-AWQ = %B(G(F + 1) - G (F) ) = %BAG; G i s g i v e n on page 3. A s h o r t t a b l e o f AG/4 i s g i v e n be low. 8 7 6 5 4 3 2 1 .6667 - .2083 - . 6667 2H .4667 .07 50 - . 1667 - . 2833 - .3000 .3810 .1250 - 0476 - .1488 - . 1905 - . 1845 - . 1429 X 8h 7h eh 5h Ah 3h 2k 1*5 1 .9167 - 1 . 1250 2 .5417 0 - . 3125 - . 4 3 7 5 3 .4167 .1083 - .0917 - . 2 0 0 0 - .2333 - .2083 4 .3542 .1339 - . 0193 - . 1 1 4 6 - .1607 - .1667 .1414 - .0938 From each h f s t h a t was u s e d , A and B f o r each l e v e l was c a l c u l a t e d . F o r each l e v e l , i f components from s e v e r a l l e v e l s were r e s o l v e d , more than one v a l u e o f A and B were c a l c u l a t e d ; e . g . 12 p a i r s o f measured energy d i f f e r e n c e s were used to c a l c u l a t e A and B f o r trie 1 4 ° l e v e l o f B i I V . Three p a i r s were from the 3rd o r d e r l i n e o f 30 three from the 4 th o r d e r o f 3012$. F o r each l e v e l , a l l the A ' s and B ' s were a v e r a g e d , and the s t a n d a r d d e v i a t i o n s c a l c u l a t e d . I f an i n d i v i d u a l v a l u e d i f f e r e d from the average by more than twice the s t a n d a r d d e v i a t i o n , t h a t v a l u e was thrown out and a new average and s t a n d a r d d e v i a t i o n c a l c u l a t e d . I f the s i g n o f B was no t the same f o r the c a l c u l a t i o n s i n v o l v i n g energy d i f f e r e n c e s o f one hfm, then the d e v i a t i o n from the i n t e r v a l r u l e * i n t h a t m u l t i p l e t , was no t due to y the q u a d r u p o l e moment. O b i o u s l y , no B c o u l d be a s s i g n e d i n cases l i k e t h i s . I n t e n s i t i e s A s t e p wedge was no t used when making the B i e x p o s u r e s . An e f f o r t was made to c a l i b r a t e the Argonne p l a t e s by u s i n g a s t e p wedge on d i f f e r e n t p l a t e s o f the same e m u l s i o n . The r e s u l t s were n o t r e p r o d u c i b l e , and were p r a c t i c a l l y u s e l e s s f o r o b t a i n i n g h f s i n t e n s i t i e s . I t was no ted t h a t a l o g - l o g p l o t o f the measured t r a n s m i s s i o n v s . the t h e o r e t i c a l i n t e n s i t i e s o f the h f s components gave a s t r a i g h t l i n e w i t h n e g a t i v e s l o p e . A s s i g n i n g i n t e n s i t y I = 100 to the component o f minimum t r a n s m i s s i o n , T . , : , . , meant I = 100 (T . / T ) , and x i s the ' m i n ' m m V o f the e m u l s i o n . F o r each r e s o l v e d h f s , the s t r o n g e s t component was a s s i g n e d i n t e n s i t y 100, and the i n t e n s i t y o f the o t h e r components c a l c u l a t e d from the above e q u a t i o n f o r I . x was v a r i e d ' f r o m 1.0 to 2 . 1 , i n increments o f o . l . A programme was w r i t t e n to do the c a l c u l a t i o n s . The c a l c u l a t e d i n t e n s i t i e s were compared w i t h the t h e o r e t i c a l v a l u e s , and the v a l u e s o f x t h a t gave the b e s t agreement appea w i t h the wave lengths i n Appendix I . 32 CHAPTER IV RESULTS N u c l e a r Moments From B i I I comple te , c l a s s i f i e d There i s o n l y one A sX c o n f i g u r a t i o n i n B i I I , 6p7s. B e f o r e the magnet i c and quadrupo le moments a r e c a l c u l a t e d , the c o u p l i n g c o n s t a n t s c^ and c 2 w i l l be e v a l u a t e d . These c o n s t a n t s a r e d e f i n e d be low. These c o n s t a n t s a r e n e c e s s a r y f o r the e v a l u a t i o n o f n u c l e a r moments from the terms t h a t a r e 3 1 dependent on c o u p l i n g , L^£ , and L ^ . 465 1 3 i, d = Lij - L( , and £ = the f i In the above d iagram, d = L^ - L^ , and d = the f i n e 3 3 s t r u c t u r e s p l i t t i n g , Ln+ ^ - L ^ _ ^ . I f the t r i p l e t terms 3 obeyed the Land^ i n t e r v a l r u l e , the P-^  term would be a t the dashed l i n e . The "Lande* p o s i t i o n " i s g i v e n by ( 3 L . - 3 L . ) / ( 2 i + l ) ; f o r 6p7s o f B i I I , t h i s = 6545. A+ 1 X- 1 A i s the d i f f e r e n c e between the"Lande p o s i t i o n " and the 3 a c t u a l p o s i t i o n o f L ^ _ ^ . F o r t h i s c o n f i g u r a t i o n , A = 6545 - 465 = 6080. F o l l o w i n g Kopfermann's n o t a t i o n , c ; l = s i n ( 0 o - 0 ) , c 2 = cos ( 0 O - 0) , where © 0 = a r c t a n + 3 5 ° 16*. 0 = a r c s i n U / d ) ^ = 3 3 ° 11 c^ = - c ^ , and c | = c 2 ; thus ^ f c , = .0363 , (c' = .9993 x ( c 2 = .9993 / c £ =-.0363 M a g n e t i c Moment B e f o r e u s i n g e q u a t i o n s 5,6 and 7 to o b t a i n , e q . Z i s u sed to o b t a i n a ' 1 ' = , 0 3 3 a " , a ' = . 1 9 4 3 a " . F o r J[= 1, A ( 3 P ) = 0, so a " = a f / 3 . Then u s i n g the O a measured A ' s we have A ( 3 P 2 ) = .2761a $ = .1057 a § = .3828 3 A( P±) = .6633a s = .3905 a $ = .5887 A ^ P . ^ = - , 1 7 0 4 a s = - .0607 a $ = .3562 To o b t a i n p. from a s , e q . i i s u s e d . However, the f a c t o r s i n e q . l , and e s p e c i a l l y n a , r e f e r to the s e l e c t r o n a l o n e . T h e r e f o r e da ta from the ns sequence were needed, i . e . v a l u e s o f n a , Z a , and dcr/dn from B i I I I . F o r the 7s term of B i I I I , n ^ = 3 .981 , and d c / d n = - . 0 7 . The r i g h t hand s i d e o f e q . i i s .113^1. The average v a l u e o f a^ from 6p7s i s a s = . 44 . T h u s , .44 = . 113;i, or p. = 3.9 n u c l e a r magnetons. The v a l u e 3.9 n .m. i s no t too r e l i a b l e ; the u n c e r t a i n t y i s 27% or - 1 n . m . I t i s n o t known what causes the l a r g e s p r e a d i n v a l u e s . T h e . c l o s e s t c l a s s i f i e d l e v e l t h a t c o u l d p e r t u r b any o f the 6p7s l e v e l s i s 6000 cm ^ away. T h e r e f o r e , s t r o n g m i x i n g from o t h e r s t a t e s i s n o t e x p e c t e d . A n o t h e r f a c t t h a t argues a g a i n s t s i g n i f i c a n t m i x i n g i s t h a t the whole c o n f i g u r a t i o n i s u n p e r t u r b e d . 34 Quadrupole Moment F o r ease o f c a l c u l a t i n g Q from e q u a t i o n s 8 ,9 and 10, we note t h a t e 2 / ( k e k m » B 2 ) = 2.675 x 1 0 2 1 c m " 2 . E q . 8 g i v e s B =. .099Q; B = - . 0 3 8 , t h e r e f o r e Q = - . 3 8 b a r n s . 3 P F o r the P Q t erm, the quadrupo le i n t e r a c t i o n i s z e r o . F o r 3 P 1 # e q . 10 g i v e s B = Q ( 6 2 . 6 x 1 0 2 1 ) ( .0005 - .1011) = - Q ( 6 . 3 x 1 0 2 1 ) . B = .0035 c m " 1 , so 3 Q = - . 5 5 barns P 1 F o r 1 P 1 , S c h u l e r and Schmidt (1936) o b t a i n e d B = - . 022 c m - 1 , T h i s g i v e s 1 Q = - . 3 6 b a r n s . P 1 The average o f these v a l u e s i s Q = - . 4 3 b a r n s . B e f o r e the h f s were a n a l y z e d , they were i d e n t i f i e d a c c o r d i n g to the c l a s s i f i e d l i n e l i s t s . The s p e c t r a were d e s c r i b e d by the f o l l o w i n g p e o p l e : B i I Mrozowski (1942); B i I I C r a w f o r d and McLay (1934); and F i s h e r and Goudsmit (1931); B i I I I C r a w f o r d and McLay; B i IV McLay and C r a w f o r d (1933) A summary of the A ' s and B' s up to 1952 was p u b l i s h e d by B r i x (1952) . In the f o l l o w i n g t a b l e s , the l e v e l d e s i g n a t i o n i s from Moore (1958) . V a l u e s f o r A and B a r e i n c m - 1 . B i I I L e v e l A B r . x B ^ A B L i n e s 1 , 2X 4 2 D 2 ^ 6 p * ~ - 0 2 5 2368,2803 35 Leve 1 ° 3 B r i x B r i x B L i n e s 2 X - P x (6p7s) .39090 .0028 4 ° 5 S 2 (6s6p 3 ) .410 5 2 3 ° 2 < 6 P 6 d ) - 1 2 7 6 ° 3 D 1 (6p6d) - . 1 6 5 7 ° 3 F (6p6d) .099 2 2 (6p6d) .080 8 1 D x (6p7p) -(6p7p) .2697 10210 - .00077 10599 - . 0 3 5 9 2 " D 2 (6p7p) .1232 - . 0 0 2 9 - .06068 - . 022 9 ° 3 P (6p7s) 1 0 ° 1 P 1 (6p7s) 10 2 (6p5f) - . 0 0 8 12 (6p5f) - . 0 1 8 1 3 3 (6p5f) .065 .3905(3) .404(3) .14(1) .1736(3) .091 ,028( 1) .056(1) 003(2) 2530,5209, 5270, 5719 2503,3411 3654,3815, 3845 2746,3408, 3648 4301 0845(4) 4259 268(1) 4476,5818 1021(3) 5144,5270 1057(3) - . 0 4 ( 1 ) 4916, 5091 1234(1) - . 007 (3 ) 5209 3430,3815 3411 20' 14, 15-.124 (6p5f) .056 (6p8p) - . 0 3 6 or (6p7p) 36 L e v e l B r i x B r i x B L i n e s 21^ (6p7d) - . 0 8 5 or (6s6p ) 16-17. (6p7p) .012 (6p7p) - . 0 1 4 or (6p8p) 2 2 2 3 D 2 (6p8p) 18 1 Si (6p7p) 19, (6p7p) .03699 - .0013 or (6p8p) - .0793(2) .003(1) 4476 102(1) - . 068(1 ) 0351 - . 0 0 6 4 2 544 2501,2530 4916 3408 N u c l e a r Moments From B i I I I  M a g n e t i c Moment F o r the 7s and 8s l e v e l s , e q . 2 was used to c a l c u l a t e ;u; e q . 3 was used f o r the 7p l e v e l s . The f o l l o w i n g t a b l e was o b t a i n e d . n-_ l-do~/dn 7s 2 .981 1.07 8s 4 .025 1.009 1A 2 7 P n 5135 5135 S .47 2 .185 . 105 .017 V-4.18 4.27 4 .26 6.62 N e g l e c t i n g the l a s t v a l u e , • / i = 4 .24( .05) n . m . K e l l y a t a l (1950) d i s c u s s the p e r t u r b a t i o n a f f e c t i n g 7 p l X 37 Quadrupole Moment 2 From the 7p P , l e v e l , S c h u l e r and Schmidt (1936) o b t a i n e d Q = - . 4 4 b a r n s . In the p r e s e n t work, the o n l y l e v e l o f B i I I I from which i t was p o s s i b l e to c a l c u l a t e 2 B was 6s6p ^ B = - . 0 3 8 ( 3 ) . Q was n o t c a l c u l a t e d f o r t h i s t e r m . B i I I I L e v e l A „ . B „ . _ . . . A B L i n e s B r i x o 2 2 1 V (6p) s m a l l 4^ (6s6p 2 ) 2.00 B r i x l l h (6s6p ) 22V (6s6p 2 ) 50 50 5160(2) - . 038 (3 ) 2944 .503 3039 2Sx^ (7s) 2 "2 A12 .4704(2) 4561 10 , D' (6d) - . 082 - .0043 lh -L'2 l l 2 h B 2 h ( 6 d) 5^ (6s6p^) 6 n l (6s6p ) 3 2 i . (6s6p 2 ) o 2 o 4 ° , 2 P ° (7p, .10 .80 .17 .37 . 106 .0167 - . 0 0 1 1 140(2) 2855, 5079 076 370(2) 106(1) 017 3450 2499,4752 2944,4561 3^ 40 3848 38 L e v e l A B '. A B L i n e s B r i x B r i x 7 ] ^ (6s6p 2 ) - . 3 3 8, (6s6p 2 ) 2.062 2.030 3930 *i 2 \2V S (8s) .182 .185 3540 2 J_ N u c l e a r Moments From B i IV M a g n e t i c Moment a w i l l be o b t a i n e d from the da ta of B i I V , b u t to 6s c a l c u l a t e p, da ta from B i V were needed. The r i g h t hand s i d e o f e q . 2, a p p l i e d t o B i V , y i e l d s a 6 s = .591u . (For 5 d 1 0 6 s o f B i V , n 4 = 2 .464, and (1-da/dn) = 1.14.) 6s6d T h i s c o n f i g u r a t i o n i s p e r t u r b e d , b u t the two l e v e l s t h a t a r e independent o f c o u p l i n g y i e l d a v a l u e t h a t i s c o n s i s t e n t w i t h the v a l u e s from B i I I and I I I . U s i n g a ' = .4018a", A ( 3 D ) = .'16.67a- + .3348a" = .422 c m - 1 3 s A ( 3 D - . ) = - . 2 5 0 0 a o + 1.250a" = - .587 c m " 1 ; from t h e s e , a g = 2 .471 . T h i s = .591u, or p - 4 .18 n .m. 6s7p T h i s c o n f i g u r a t i o n has two terms whose s e p a r a t i o n i s the same o r d e r of magnitude as the h f e n e r g i e s . These terms have been d i s c u s s e d by C r a w f o r d and McLay (1933) . The c o n f i g u r a t i o n has the f o l l o w i n g a p p e a r a n c e . p i : ' \ 7 301 3 ' / p o , i Y 2 7 6s7p c o n f i g u r a t i o n o f B i IV 3 -1 From the r e s u l t s o f B i I I , A( P j = .2761a , = .517 cm . 2 s a 6 s = 1.87, and p = 1 . 8 7 / . 5 9 1 , p = 3.12 n .m. T h i s v a l u e i s c o n s i d e r a b l y lower than the average o f 3 4 .1 n . m . , b u t t h a t i s not too s u r p r i s i n g . The term l i e s above s o .one o f the two terms i s s t r o n g l y p e r t u r b e d . 6s5f F o r the terms independent o f c o u p l i n g , a ' = .555 a", thus A ( 3 F J = .12 5a + .486a" = .30 4 s A ( 3 F 2 ) = - . 1 6 7 a + 1.167a" = - . 3 2 , a g = 2.22 c m - 1 , u = 2 . 2 2 / . 5 9 1 , or )i = 3.76 n . m . Even though the 6s6d and 6s5f c o n f i g u r a t i o n s are p e r t u r b e d , the terms independent of c o u p l i n g gave c o n s i s t e n t r e s u l t s f o r p. I f these two terms a r e u n p e r t u r b e d , "they s h o u l d g i v e 3 3 good v a l u e s o f u . A look a t ( •]_ - ^/-l* "*"n t^rie i s o e l e c t r o n i c sequence , Hg I , T l I I ," Pb I I I , and B i IV shows the d i f f e r e n c e s i n B i IV are i n l i n e w i t h the o t h e r members 40 i n the i s o e l e c t r o n i c sequence , t h e r e f o r e the terms p r o b a b l y a r e no t p e r t u r b e d . Quadrupole Moment  6s6d 3 3 The two terms independent o f c o u p l i n g , and D-^, a r e c o n s i d e r e d . F o r / c a l c u l a t i o n s o f B gave an 3 _1 i n c o n s i s t e n t s i g n . F o r D-^, B =. - . 002 cm . U s i n g cSw° = 2618 c m - 1 , and e q . 8, Q = 395 B b a r n s , or Q = - . 7 0 b a r n s . 3 ° 1 T h i s v a l u e o f Q s h o u l d be t r e a t e d a l i t t l e s u s p i c i o u s l y , because the v a l u e o f B came from on ly one p a i r o f energy d i f f e r e n c e s , w h i l e 11 p a i r s o f energy d i f f e r e n c e s were used to c a l c u l a t e B ( 3 D ^ ) . O b v i o u s l y more measurements 3 f o r D-^ a r e d e s i r a b l e . 6s7p SW° - 8000 c m - 1 , and f o r 3 P 2 , e q . 8 g i v e s Q = 50B b a r n s . B = - . 0 3 , so 3 Q = - 1 . 5 , b a r n s . P 2 o B was o b t a i n e d from two i n t e r v a l s of the 2842 A h f s , i n two o r d e r s . A g a i n , more measurements of B would be d e s i r a b l e . C o n s i d e r i n g the p e r t u r b a t i o n s i n v o l v e d i n t h i s i c o n f i g u r a t i o n , an i n c o n s i s t e n t v a l u e o f Q would not be s u r p r i s i n g . 6s. 5 f Sw° = 48 5 cm \ and a p p l i c a t i o n o f e q . 9 y i e l d s Q=67 0B. 3 F o r F 2 , B = - . 0 3 , so 3 Q = -20 b a r n s • F 2 41 T h i s i s more than 10 t imes as g r e a t as Q from any o t h e r c o n f i g u r a t i o n , and w i l l be i g n o r e d i n the f i n a l a v e r a g i n g B i IV In B i I V , t h e r e are 6 l e v e l s t h a t have l i n e s o n l y i n the vacuum u . v . The f o l l o w i n g t a b u l a t i o n e x c l u d e s o n l y those 6 l e v e l s . L e v e l A B r i x 5 X D (6s6d) - . 589 (1 ) 61 S (6s7s) 1.556(2) 7 2 D 2 (6s6d) .413(2) 8 3 ° 3 < 6 s 6 d ) .421(5) 1 1 2 (Sp^p-^) s m a l l 11 (siufi .150 r> * o 3 8 - 1 1 (6s7p) P Q x 12. o 9 1 3 x (5d 6p) O , 9 14 2 (5d^6p) .091(2) .178(1) .190(2) 1 5 ° L P )6s7p) - . 4 1 4 B L i n e - . 591(4) - . 002 2629*, 3683 1.5556(3) .011(2) 2842, 3012 .410(2) - . 0 4 ( 1 ) 2677, 2823 .422(1) 3239, 3868 1 0 o ( 6 p ^ 6 p n i ) - . 127 (1 ) - . 1 2 9 05 . 150 095(7) 178(1) 3171 5029* 3683 3868 3766 190( 1) .052(5) 3012, 3239 - . 4 1 3 2756 * These h f s are odd; a n a l y s i s o f the hfm i s somewhat u n c e r t a i n , 42 L e v e l B r i x B L i n e 16 2 P 2 (6s7p) .516(1) 5174(2) - . 0 3 ( 1 ) 2842 1 7 ° ( 5 d 9 6 p ) , or (6s5f) 063 ,060(1) .06(1) 2823 1 8 ° (5d 9 6p) o r (6s5f) o 9 2 1 3 (5d 6p) o r (6s5f) .053 044 ,049 ,041 3171 2933** 1 9 ° 3 F 2 (6s5f) - . 322 (2 ) o 3 20. FA (6s5f) .30 4 4 - . 319 (1 ) - . 0 3 ( 2 ) 2677 22J (5d 9 6p) - . 1 2 4 - . 1 2 5 004 2768 1 3 1 (6s8s) 1.429 & 1 4 x T) ^6s7d) - . 6 4 6 & 1 5 2 D 2 (6s7d) 50 1 7 3 D 3 (6s7d) 433 & 18- h)^ (6s7d) - . 3 2 5 2641 1 8 2 i s s t r o n g l y p e r t u r b e d ; see the f o l l o w i n g page. * * 2933 A i s a l s o c l a s s i f i e d as the 7 2 - 1 5 ° t r a n s i t i o n o f B i IV, However, the i n t e r v a l s o f n e i t h e r 7 2 nor 1 5 ° showed up i n t h i s h f s i n the p r e s e n t work. & These h f s have no t been r e s o l v e d by any o f the workers d e s c r i b i n g the s p e c t r a o f B i . B r i x (19 52) c la ims the v a l u e s l i s t e d above are from Richmond (1937), b u t a d e s c r i p t i o n o f these l e v e l s are absent from Richmond's work. On the next two pages are the measurements o f the 2641A h f s o f B i I V . The upper l e v e l o f the l i n e , *D 6s7d, i s v e r y s t r o n g l y p e r t u r b e d . T h i s l e v e l i s o f s p e c i a l i n t e r e s t because the 6s7d c o n f i g u r a t i o n i s u n p e r t u r b e d ; K e l l y e t a l (1950) used t h i s l e v e l t o c a l c u l a t e yx. The o n l y ment ion i n the l i t e r a t u r e o f t h i s hfm i s by McLay and C r a w f o r d (1931) . They l i s t the t o t a l h y p e r f i n e 1 _ i o i n t e r v a l o f D o n l y as - 6 . 5 cm , and d e s c r i b e the 2641A 2 h f s as one b r o a d l i n e . I n t h i s work, the 264 1 ° h f s was observed i n two o r d e r s , and the l e v e l was deduced to have the f o l l o w i n g appearance . F = 13/2 . 2.16 cm ^ 11/2 1.10 9/2 — : ' .45 7/2 1.35 5/2 D„ (6s7d) L e v e l o f B i IV FS W L = 2 6 4 2 , B I 4 , FROM P L A T E C 1 1 5 8 9 . 4 9 9 4 0 6 2 6 4 1 . 4 3 7 3 3 7 8 4 6 . 9 0 0 8 9 . 6 5 4 3 9 6 2 6 4 1 . 4 6 8 5 3 7 8 4 6 . 4 5 3 8 9 . 7 9 4 2 8 5 2 6 4 1 . 4 9 6 7 3 7 8 4 6 . 0 4 9 8 9 . 9 0 2 2 8 3 2 6 4 1 . 5 1 8 4 3 7 8 4 5 . 7 3 3 9 0 . 1 2 5 2 9 7 2 6 4 1 . 5 6 3 3 3 7 8 4 5 . 0 9 5 9 0 . 2 7 5 1 3 4 2 6 4 1 . 5 9 3 5 3 7 8 4 4 . 6 6 3 9 0 . 4 3 7 2 1 9 2 6 4 1 . 6 2 6 1 3 7 8 4 4 . 1 9 5 9 0 . 5 4 1 3 5 1 2 6 4 1 . 6 4 7 0 3 7 8 4 3 . 8 9 6 9 0 . 9 3 0 8 0 2 2 6 4 1 . 7 2 5 3 3 7 8 4 2 . 7 7 4 HFS W L = 2 6 4 2 , B I 4 , FROM P L A T E C 1 1 5 COMP 1 COMP 2 COMP 3 COMP 4 COMP 5 COMP 6 COMP 7 COMP 8 COMP 9 COMP 3 9 . 4 9 9 8 9 . 6 5 4 8 9 . 7 9 4 8 9 . 9 0 2 9 0 . 1 2 5 9 0 . 2 7 5 9 0 . 4 3 7 9 0 . 5 4 1 9 0 . 9 3 0 . 4 0 6 3 9 6 2 8 5 2 8 3 2 9 7 1 3 4 2 1 9 3 5 1 8 0 2 8 9 . 4 9 7 8 9 . 6 5 4 8 9 . 7 9 4 8 9 . 9 0 3 9 0 . 1 2 2 9 0 . 2 7 5 9 0 . 4 3 8 9 0 . 5 4 0 9 0 . 9 2 8 4 0 8 3 9 9 2 8 8 2 9 3 2 9 3 " 1 3 9 2 2 6 3 5 5 8 0 5 8 9 . 4 9 5 8 9 . 6 5 4 8 9 . 7 9 4 8 9 . 9 0 2 9 0 . 1 2 1 9 0 . 2 7 5 9 0 . 4 4 0 9 0 . 5 3 7 9 0 . 9 3 0 4 0 1 39 5 0 . 4 5 2 8 0 . 2 9 4 2 9 8 4 0 3 7 0 . 3 1 2 4 0 . 2 8 9 6 3 5 4 0 . 1 4 3 4 3 9 3 0 2 3 3 . 4 7 1 0 0 . 3 4 8 2 9 1 2 1 . 8 1 3 0 . 0 0 5 8 0 . 0 0 0 0 0 . 0 0 1 7 0 . 0 0 6 7 0 . 1 . 0 7 4 6 0 0 6 0 0 . 0 0 4 4 0 . 0 1 0 4 0 . 0 0 7 6 . 0 . 8 5 6 5 0 . 7 1 6 1 0 . 9 4 7 0 0 . 9 1 0 2 0 . 7 6 2 2 1 . 4 1 5 7 0 . 0 0 5 8 0 . 0 0 1 7 0 . 0 0 6 0 0 . 0 0 1 7 0 . 0 1 0 1 0 . 0 0 6 0 0 . 0 0 5 0 1 . 13/2 ^ 16 89 1 . 3 5 1 5 1 . 3 8 7 0 1 . 5 4 5 6 1 . 2 0 1 4 1 . \Ai 0 . 0 0 6 0 0 . 0 0 6 0 0 . 1 . 8 0 4 3 1 . 7 9 0 8 0 0 0 0 0 . 1 . 8 5 8 0 0 0 5 0 0 1 . 8 3 6 8 . 0 0 33 0 . 2 . 3 2 5 9 0 0 3 3 0 . 0 0 1 7 0 . 0 0 0 0 |\ A U 0 . 0 0 4 4 0 . 0 0 5 8 0 . 0 0 6 0 2 . 2 4 3 5 2 . % 1 4 9 2 2 . 9 6 1 3 0 . 0 0 5 8 0 . 0 0 4 4 0 . 0 0 6 0 0 . 0 0 50 "" 2 . 7 1 4 5 2 . 5 5 3 0 3 . 2 7 3 7 0 . 0 1 0 1 0 . 0 0 6 0 0 . 0 0 3 3 3 . 0 0 5 7 3 . 6 7 7 4 0 . 0 0 1 7 0 . 4 . 1 3 0 2 0 0 3 3 0 . 0 0 6 7 46 The numbers on the d e n s i t o m e t e r t r a c e a r e the c a l c u l a t e d i n t e n s i t i e s . The V o f t h i s p a r t i c u l a r p l a t e was assumed to be 1 .5 , i . e . x was s e t e q u a l t o 1.5 (see page 30 ) . T h e r e f o r e the i n t e n s i t i e s a r e o n l y a p p r o x i m a t e . M a g n e t i c Moment From B i V F o r comple tenes s , data f o r B i V are i n c l u d e d . A l l V l i n e s a r e i n the vacuum u . v . ; the v a l u e s K e l l y e t a l (1950) g i v e a r e : a s » 6s 2 .6 4.2 7s .773 4 .11 Summary o f R e s u l t s My r e s u l t s a r e summarized i n the f o l l o w i n g t a b l e . ju v r e f e r s to the v a l u e quoted by K e l l y e t a l (1950), Q K ss r e f e r s to v a l u e s from S c h u l e r and Schmidt (1936), u and Q r e f e r t o my r e s u l t s . L e v e l u^ u ss B i I I o 3 2, (6p7s P ) 3 .9 1 - . 4 3 - . 5 5 ° , 3 X 9 0 (6p7s p ) 3.9 2 x r 2' .36 - . 3 8 1 0 ° (6p7s X P ) . 3.9 1 c 1' - . 3 9 - . 3 6 47 L e v e l p k p ° - s s Q B i I I I B i IV 2 7s Z S , 4 .03 4.18 -2 2 3.81 4 .26 ? P 2 p i ^ 6 - . 4 4 6 .6 6 s 6 p 2 4.06 8s 4 .09 4.27 5 (6s6d 3 D 1 ) 3 .91 4.18 - . 7 9 61 (6s7s 3 S ) 4.12 8 3 (6s6d 3 D 3 ) 4 .09 4.18 0 , 1 , 1 5 1 (6s7p P 1 ) 3.12 1 6 ° (6s7p 3 P 2 ) 3,12 - 1 . 5 1 9 ° (6s5f 3 F 2 ) 3.76 -20 2 0 ° (6s6f 3 F J 4 4 3.76 13-l (6s8s) 4.09 14 (6s7d 3 D i ) 4 .24 -17 (6s7d 3 D 3 ) A.22 48 I n a d d i t i o n to the above v a l u e s , work by the f o l l o w i n g peop le s h o u l d be n o t e d . D i c k i e and K e l l y (1966) found Q = - . 3 7 ( 4 ) b a r n s . T h i s was from the spectrum o f B i I , produced by a h o l l o w cathode d i s c h a r g e tube and photographed w i t h a F a b r y - P e r o t • i n t e r f e r o m e t e r . T i t l e and Smi th (1960), u s i n g a tomic beam resonance t e c h n i q u e s , found Q = - . 3 5 b a r n s . P r o c t o r and Yu (1950) , w i t h n u c l e a r magnet ic resonance a p p a r a t u s , found y\ - 4.0820(5) n .m. The average n u c l e a r moments, c a l c u l a t e d from my data a r e p = 4 .1(1) n . m . and Q = - . 5 ( 1 ) barns 2 These averages do n o t i n c l u d e u from P of B i I I I or 1*5 6s7p o f B i I V ; nor do they i n c l u d e Q from the 6s7p and 6s5f c o n f i g u r a t i o n s o f B i I V . 49 CONCLUSION AND COMMENTS When c a l c u l a t i n g p. from two e l e c t r o n s p e c t r a , a s was always u s e d . E q . 1 r e q u i r e s s p e c t r o s c o p i c i n f o r m a t i o n about the s e l e c t r o n , i . e . n a > Z ^ , Z & , and d a / d n . T h e r e f o r e , i n f o r m a t i o n from the a p p r o p r i a t e o n e - e l e c t r o n spectrum must be u s e d . In p r i n c i p l e , the two e l e c t r o n spectrum c o n t a i n s enough i n f o r m a t i o n t o de termine p. E q . 2 r e q u i r e s o n l y the f i n e -s t r u c t u r e s p l i t t i n g o f an sA c o n f i g u r a t i o n , 5w°. In p r a c t i c e a j from e q . 2 g i v e s poor v a l u e s o f p. The f o l l o w i n g t a b l e i l l u s t r a t e s t h i s . (The data f o r the 6s6p c o n f i g u r a t i o n : were -taken from the paper by C r a w f o r d and McLay ( 1933).) C o n f i g u r a t i o n Ion §W° ay(-h P > 6p7s I I .15 1.4 6s7p IV 8000 .62 5.6 6s6p IV 2 5460 .43 .013 6s6d IV 2618 .024 .12 6s5f IV 485 .046 120 The poor agreement f o r the above v a l u e s of p ar i ses e i t h e from p e r t u r b a t i o n s or from the way i n which r - 3 i s c a l c u l a t e d E q . 4 s t a t e s t h a t r ^ i s p r o p o r t i o n a l to SW°. I f s i g n i f i c a n t p e r t u r b a t i o n s are a b s e n t , then t h i s i s o b v i o u s l y not a s a t i s -f a c t o r y way to e s t i m a t e r ~ 3 . V a l u e s o f ji' c a l c u l a t e d from B i I I I and V (one e l e c t r o n c o n f i g u r a t i o n s ) are more c o n s i s t e n t w i t h each o t h e r and w i t h the resonance va lue , o f p. In t h i s t h e s i s , )i was c a l c u l a t e d f o r 8 c o n f i g u r a t i o n s 50 and 14 l e v e l s . Q was c a l c u l a t e d f o r 4 c o n f i g u r a t i o n s and 6 l e v e l s , and a l l the c o n f i g u r a t i o n s were two e l e c t r o n c o n f i g -u r a t i o n s . F o r the l e v e l s o f the 6p7s c o n f i g u r a t i o n o f B i I I , Q showed good agreement b o t h amongst the l e v e l s and w i t h a tomic beam measurements . E x p e r i m e n t a l l y , the most r e l i a b l e Q from B i IV was -20 b a r n s . The l a r g e d i s c r e p a n c y between t h i s and the a c c e p t e d v a l u e o f - . 4 barns might be e x p l a i n e d by an " a n t i - s h i e l d i n g " of the o u t e r e l e c t 5 o n s by the i n n e r c o r e . S t e r n h e i m e r (1967) s t a t e s t h i s e f f e c t can be v e r y l a r g e i n ions . From the data i n t h i s t h e s i s , the most r e l i a b l e l e v e l s from which to c a l c u l a t e the quadrupo le moment b e l o n g to the 9 6s7s and 5d 6p c o n f i g u r a t i o n s of B i I V . These l e v e l s have the s m a l l e s t u n c e r t a i n t y i n B . However, these l e v e l s were n o t u s e d , as t h e r e i s no r e a d i l y a v a i l a b l e t h e o r y to i n d i c a t e how t o do the c a l c u l a t i o n s . A d d i t i o n a l e x p e r i m e n t a l work c o u l d be done. I t i s known t h a t a m e t a l l i c h a l i d e i s much more v o l a t i l e than the m e t a l . I t i s s u s p e c t e d t h a t i n the case o f B i , i n s t e a d o f an oven a t 8 0 0 ° C , b i smuth i o d i d e would g i v e a d i s c h a r g e i n the con-densed e l e c t r o d e l e s s d i s c h a r g e tube a t room temperature or l e s s . I f the l i n e widths are r e a l l y p r o p o r t i o n a l to T 2 , u s i n g b i smuth i o d i d e s h o u l d reduce the l i n e widths by a f a c t o r o f two. The i n s t r u m e n t w i d t h o f the Argonne s p e c t r o g r a p h was c o n s i d e r a b l y l e s s than the n a t u r a l l i n e w i d t h o f the s p e c t r a l l i n e s . So , i f the n a t u r a l l i n e w i d t h c o u l d be d e c r e a s e d , more h y p e r f i n e s t r u c t u r e s would be r e s o l v e d , and the measur ing a c c u r a c y would i n c r e a s e . 51 BIBLIOGRAPHY B r i x , B . and Kopfermann, H . i n L a n d o l d t - B o r n s t e i n , Zah lenwerte  und F u n k t i o n e n , V o l . 1, p a r t 5, 6th e d i t i o n , 1952, S p r i n g e r , B e r l i n . Condon, E . U . and S h o r t l e y , G . H . The Theory o f A t o m i c S t r u c t u r e . Cambridge U n i v e r s i t y P r e s s , 1963. C r a w f o r d , M . F . and McLay , A . B . P r o c . Roy. S o c . London A143, 540, (1934) . D i c k i e , L . O . and K e l l y , F . M . C a n . J o u r . P h y s i c s 45, 2249, (1967) . E d l e n , B . Handbuch der P h y s i k , XXVII (1964) , E d . S . F l u g g e , S p r i n g e r , B e r l i n . F i s c h e r , R . A . and Goudsmi t , S . P h y s . Rev. _3_Z' 1057, (1931) . G a r t l e i n , C . W . a n d G i b b s , R . C . P h y s . Rev . 38, 1907, (1931) . G i a p h e t t i , A . Averages o f I n t e r f e r o m e t r i c Measurements o f T h o r i u m L i n e s ; ANL-7209 , AEC Research and Development R e p o r t , May, 1966. A v a i l a b l e from the C l e a r i n g House f o r F e d e r a l S c i e n t i f i c and T e c h n i c a l I n f o r m a t i o n . N a t i o n a l Bureau o f S t a n d a r d s , S p r i n g f i e l d , V a . 22151. Goudsmi t , S . and B a c h e r , R . F . P h y s . Rev . 4_3, 894, (1933) . K a s t l e r , A . P h y s i c s Today , _20, 34, ( S e p t . , 1967). K e l l y , F . M . , Richmond, R. and C r a w f o r d , M . F . P h y s . Rev . 80, .295, (1950) . Kopfermann, Hans , N u c l e a r Moments. T r a n s . E . E . S c h n e i d e r . New Y o r k , Academic P r e s s , 1958. Kuhn , H . G . A t o m i c S p e c t r a , London, Longmans, Green and C o . , 1962. L u r i o , A . M a n d e l , M . and N o v i c k , R. P h y s . Rev . 126, 1758, (1962) . McLay , A . B . and C r a w f o r d , M . F . P h y s . Rev . 44, 986, (1933) . M e i s s n e r , K . W . J o u r . Op. S o c . Amer. 31, 405, (1941) . Minnhagen, L . J o u r . R e s . N a t . B u r . S t d s . 68C, 237, (1964) . Moore,- C . A t o m i c Energy L e v e l s , V o l I I I , N a t . B u r . S t d s . C i r c u l a r 467, U . S . Government P r i n t i n g House , Wash ington , D . C . , 1958. M r o z o w s k i , S . P h y s . Rev. _62, 526, (1942) . 52 P r o c t o r , W . G . and Y u , F . C . P h y s . Rev. _7j3, 471, (1950) . Richmond, R. P h . D . T h e s i s , U n i v e r s i t y o f T o r o n t o , 1937. S c h u l e r , H . and S c h m i d t , T . Z e i t f u r P h y s i k , 99.* I l l , (1936) . Schwarz , C h a r l e s . P h y s . Rev . 9J_, 380, (1955) . S t e r n h e i m e r , R . N . P h y s . Rev . 164, 164, (1967) . T i t l e , R . S . and S m i t h , K . F . P h i l . Mag. _5, 1281, (1960) . Tomkins , F .S . and F r e d , M . J o u r . Op. S o c . Amer. Al, 641, (1951) . Tomkins , F . S . and F r e d , M . A p p . O p t i c s , 2, 715, (1963) . 53 APPENDIX I LINE LIST I n the f o l l o w i n g l i n e l i s t , the wavelengths and wave numbers a r e as measured i n the h i g h e s t o r d e r i n which the l i n e was f o u n d . F o r s h a r p , w e l l - r e s o l v e d l i n e s , the wave length i n a n o t h e r o r d e r d i f f e r s by as much as -.001/5. T h e r e f o r e , the number o f s i g n i f i c a n t f i g u r e s i n d i c a t e s the sharpness o f the l i n e as i t appears on the p l a t e . B i I I I e x p I t h e o X ( s e e P ' 3 0 ) 2368 4 2 - 4 ° o 2501 1 -18. o o 2503 4 • - 25. 2 2368.195 44213.36 • .334 10.87 .443 08.93 .458 .67 .539 07.22 .551 .01 .620 05.78 2501.0045 39971.886 .0232 .586 .0462 .219 2502.5319 39947.491 .55 .3 .6259 45.990 .6366 .820 .6524 .567 .7538 43.949 .7678 .726 .7866 .426 .9023 41.579 .9265 . 192 .948 5 40.843 3.0899 38.586 . 1141 .200 .1387 c 37 .808 2530.2788 39509.458 46 44 .2976 . 164 68 69 .3907 7.711 66 69 .41 .4 .4347 .025 69 69 . 5486 5.245 69 69 .5725 4.873 100 100 o 2530 2 l - 18 2530.2788 39509.458 46 44 1.0 54 B i I I 2544 2 ° - 2 2 2 2746 5 Q - 6 ° 2803 4 2 - 2 ° 3408 6 ° - 1 9 2 . 3411 4 ° - -13 3430 4 ° - 1 2 3 exp theo 2544.2912 39291.878 18 22 .3207 .423 35 35 .3438 .067 43 43 .3691 90.67 5 60 51 .4047 .126 47 46 .4343 89.668 25 22 .4655 .188 100 100 .5082 88.527 36 35 .5457 87.950 1-6 51 2746.1235 36404.201 65 67 . 1808 3.442 88 83 .2538 2.47 3 100 100 2803.3401 35661.223 .47 59.5 .4848 .383 .4914 .300 .4961 .239 3408.4979 29330.021 .5240 29.797 .55 .6 .6382 28.814 .6608 .620 .68 .5 .76 27.8 .77 .6 .78 .5 ' 3411.282 29306.09 .3 5.9 .316 .79 .4129 4.960 .4423 .708 .4640 .521 .5867 3.468 .6226 . 159 .6523 2.904 .8002 1.634 .8430 .266 11.8792 300.955 12.0532 299.461 .0988 .07 0 . 1493 8.636 3430.0 29145.7 3430.23 4.2 .25 4 .1 .4 2.4 .4593 2.260 .4766 42.113 .7377 39.895 30.7586 9.717 31.07 7 .10 .0908 6.896 55 B i I I 3648 6 ° - 21 1 o 3654 5 ° - 1 5 1 3815 5 ° - 1 2 3 3845 5 ° - 102 3863 6 ° - 151 4301 7 ° - 1 2 3 o 4476 6± - 21 exp theo 3648.5437 27400.388 100 100 .6714 399.429 89 83 .7750 8.650 66 67 3653.9559 27359.803 54.0150 9.361 .0968 8.749 .1995 7.980 .3163 7.106 3815.66 26200.3 .74 199.8 .84 .1 .86 9 .0 .94 8 .4 .96 .3 15.98 8 .1 16.08 7 .5 .10 .3 .13 .1 3845.68 25995.8 .75 5.4 .83 4 .8 5.94 4 . 1 6.07 3.2 3863.9173 25873.134 3.9392 2.989 4.0409 .308 .0585 2.190 .1 1.7 4301. 23241. .53 40.99 .56 .8 .6320 .453 .6603 40.300 .7529 39.799 .7880 .610 .8970 39.021 .9387 38.796 4476.4722 22332.753 48. 44 .5431 , 2.399 71 69 . 7148 1.542 69 69 6.8743 0.746 70 69 7.0833 29.704 70 69 7.1714 .265 100 100 56 B i I I 4916 9 ° - 18 2 1 4993 1 0 ° - 1 9 2 5091 9 ° - 17 5124 9 ° - 16 3 o 5144 1 - 8 o o 5209 2 - 9 2 o 5270 2 1 - & 1 ex p the o 4916.1171 20335.579 42 43 .2106 5.192 37 35 .288 2 4 .871 23 17 .3282 .706 21 22 .4045 4 .390 54 46 .5 4 . 11 8 .5457 3.806 59 51 .6367 .430 38 35 .7972 2.766 100 100 4993.382 20020.92 .437 .70 .527 .34 .577 20.14 .626 19.94 .696 .66 5091.104 19636.63 .232 6.14 .346 5.70 .481 5.18 .638 4.57 .826 3.85 5124.087 19510.23 .172 9.91 .280 9.50 .413 8.99 .57 .40 5144.3562 19433.364 62 67 .4777 2.905 86 83 .6262 .344 100 100 5208.8455 19192.768 8.9968 2.210 9.1196 1.7 58 .1351 .701 .3209 1.016 .4755 0.447 .5043 .340 .7216 89.541 .9058 8.862 5269.7668 18970.892 40 44 69.8947 70.431 79 69 70.2552 69.134 70 69 .5388 8 . 113 70 69 70.9799 6.526 69 69 1.1371 5.960 100 100 57 B i I I 5719 2 ° - 7 5718.4318 ° 9.0058 .7092 5818 6 - 1 7 ° 5817.5991 1 8.0078 8.5104 exp theo 17482.461 80.707 78.557 17184.457 68 67 3.250 83 83 1.765 100 100 58 B i I I I 2499 32h - 8 P 2P°^ 2 2 o 2855 6d D - 5f F 2h 3h 2944 - 7 P 2 P ° 3451 6. , - 5f 2 F ° Ik 2% 2 o 2 3540 7p - 8s 2 2 o 3848 6d D - 7p P 2 o 3930 8, - 8p P , 2 2 4561 7s S, - 7p P ° 2498.498 40011". 98 .568 10.85 .661 9.37 .776 7.53 .913 5.33 .057 3.03 .725 2.78 2855.403 35011.04 .437 10.61 .484 10.04 .543 9.32 .613 8 .46 .696 7 .45 2943.8206 .9560 .0016 .1802 .2262 .4465 3450.830 .886 .932 .965 3540.6308 .6976 .7457 .8130 3848.82 .899 .918 .971 8.994 9 .0 33959.532 7.970 7.444 5.384 4.854 2.314 28970.24 69.76 .38 . 10 28235.486 4.953 .569 .032 25974. 4. 3. 6 09 96 60 45 2 Energy d i f f e r e n c e between the two components = 10.150 cm - 1 . 4561.0640 .17 54 .5533 .6644 21918.565 8.029 6.213 5.680 B i I I I 47 52 3 59 2 o „. - 5f F 2 2 ° 5079 6d D - 6p P 2h m 4749.9 21047.0 50.17 5 5.9 .515 4 .4 0.937 2 .6 1.440 40.4 2.022 37 .8 5078.760 19684.36 8.866 3.9.5 9.007 ' 3 .40 .185 2 .71 .403 1.86 .650 80 .91 60 B i IV 2627 14" - 17. 2629 5. " " J 2641 18, 2677 - 195 2756 1 5 1 " 16 I I x exp theo 2626.714 38059.03 .853 7.02 .941 5.7 3 .974 .25 7 .048 4 .20 .080 4 .00 .139 2.86 .214 1.78 .273 50.92 .3 .6 .316 .58 .348 .15 2629.15 38023.8 .27 22.0 .37 20. 5 .41 20.0 .45 19.3 .49 8.8 .55 7 .9 2641.437 37846.90 19 8 .468 .45 21 35 .496 6.05 32 43 .518 5.74 32 22 .563 5.09 33 100 .594 4 .66 100 46 .626 4 .19 47 51 .647 3.90 25 35 .725 2.77 7 17 2676.5580 37350.317 28 27 .6389 49.188 31 29 .6626 8.858 33 29 .8463 6.294 44 43 .8772 5.864 48 43 6.9815 4.409 . 7 . 1 0 5 8 2.674 44 48 .1424 2.164 46 44 .2686 40.404 40 38 .4145 38.369 30 30 .4577 7.768 32 30 .6057 5.703 100 100 2755.502 36280.30 .67 5 78.03 .816 6.17 Assuming x = 1.5 1.1 61 B i IV 2768 7 2 - 1 8 ° 2823 7 2 - 1 7 ° 2842 61 - 1 6 ° 2933 1 0 2 - 2 1 ° 3012 6 - 1 4 ° exp theo 2766.918 36130.62 7.011 29.41 .122 7.96 .140 7.72 .268 6.05 .293 5.73 .440 3.80 .469 3.43 .495 3.10 2822.98 35413.1 23.00 2 .9 .08 1.9 .10 1.6 .1987 10.392 .2236 10.080 .24 9.8 . 347 0 8. 532 .3779 8.146 .40 7 .9 .5196 6.368 .5564 5.907 .589 5.49 2840.9406 35189.262 41.1300 6.917 .27 5 .1 .5051 82.272 .69 79.9 1.9673 6.550 2.1970 3.708 2932.8585 34086.456 .88 6.2 .9569 5.313 2.98 5.1 3.042 4.32 .059 4.12 .07 3 .9 .11 .5 .13 3.3 .2 3. 3011.4473 33196.951 16 17 .5231 6.115 36 35 .5815 5.47 1 48 43 11.9843 91.031 56 51 12.0787 89.993 52 46 .1546 9.156 21 22 .6441 3.764 100 100 .7 579 2.510 36 35 .8522 1.47 2 8 8 62 B i IV 3171 10., - 18-exp theo 3239 8. - 14, 3171.3071 31523.618 100 100 .345 3.24 27B 23 .4281 2.415 66 67 .460 2.09 34B 37 .5326 1.377 41 41 .559 1.11 39B 46 .624 0.47 38 22 .64 20.3 39B 49 .71 19.6 4 IB 53 3238.3187 30871.312 21 25 .3616 70.903 15 18 . .429 70.26 30 32 .5171 69.421 36 30 .5836 8.787 8 8 .6275 8 . 3 £ 9 37 34 .7150 7.534 19 2 2 .7610 7.096 31 31 .8703 6.055 44 41 8.9161 5.618 19 20 9.0484 4.357 ' 70 67 .2471 2.465 100 100 3643 - ( 8 ° - l l U ) 1 3640.1137 27463.842 .5423 60.608 0.7604 58.963 1.1895 5.723 1.5390 53.093 2.0703 49.088 2.4220 6.437 3.7100 6.736 4.1390 3.506 4.4908 0.858 3681 e , -^ 0 - ! ! 0 ) 3679.7754 27167.836 80.0624 5.717 .6758 61.190 1.2221 57.159 .6235- 4.198 .8819 2.293 2.776 45.69 3.79 38.2 4.8996 "30.057 X 1.1 1.6 T h i s h f s o v e r l a p the f o l l o w i n g h f s . • "B" i n the i n t e n s i t y column means t h a t the l i n e was a B lend o f more than one component. The p r i n t e d i n t e n s i t y i s the sum o f the i n t e n s i t i e s o f the i n d i v i d u a l components . 63 B i IV I I . . exp theo 3683 5, - 7 ° 3682.776 27145.69 .8881 4.875 2.9966 4 .075 3.3258 1.649 .4348 0.846 .5225 40.200 .79 38.2 .8812 7.558 .9465 7.076 3766 9 - 13? 3765.8734 26546.722 o 1 o 6.0125 5.741 .1268 4.936 3868 8 - 12 3866.23 25857.6 J 4 .4409 6.249 .8929 3.226 .9414 2.902 6.9742 2.683 7.0160 2.403 .0517 2.164 .1136 1.750 .1614 .431 .2228 1.021 .2617 0.760 .3368 50.259 .3968 49.858 .5203 9.032 .6106 8.428 .6830 7.945 .8289 6.970 .9316 6.283 8.1868 4.579 .303 3.80 64 APPENDIX I I UNCLASSIFIED LINES A number of u n c l a s s i f i e d h y p e r f i n e s t r u c t u r e s were p h o t o g r a p h e d , b u t the o n l y one t h a t was d e f i n i t e l y r e s o l v e d was the 3 2 5 5 ° . h f s . T h i s l i n e appeared i n one o r d e r on the Argonne p l a t e s , w i t h wave length e i t h e r 32555 or 488 2 ° . . A subsequent s p a r k - i n - H e l i u m exposure on our p r i s m s p e c t r o g r a p h showed i t was a I I l i n e , and wave length o f 32 5 58. The i n t e n s i t i e s and measurements i n d i c a t e d the t r a n s i t i o n was e i t h e r J A J A Upper l e v e l 2 .058 1 - . 2 6 7 or Lower l e v e l 1 .267 2 - . 0 5 8 A d e s c r i p t i o n o f the hf s f o l l o w s . Wavelength Wavenumber ''"exp * theo 3254.9503 30713.576 13 17 .978 .31 35 35 4.997 3.14 46 43 5.0431 2.701 51 51 .0775 .377 53 46 .1042 2.124 23 22 .1581 1.616 100 100 . 1987 1.233 38 35 5.2331 0.909 8 8 APPENDIX I I I ENERGY DIFFERENCES The energy d i f f e r e n c e s t h a t were observed f o r each hfm a r e l i s t e d under the upper F v a l u e . F o r example , measurements f o r the 2 ° l e v e l were made from the 5209A5 h f s t h a t appeared on p l a t e a l l 5 . The energy d i f f e r e n c e between the F = 5h and the F = Ah l e v e l s was 2.1528 c m - 1 , and i s l i s t e d under F = 5%. B i I I L e v e l X P l a t e 7^ eh 5h ^h 3h A 2368 c l 3 1 ( 5^+4i_)A=. 256cm" 1 , (43_+3i_)A=. 209cm" 1  2 2803 a95 .1379 A=.025 1 2 ° 5209 a l l 5 ' 2.1528 1.7527 5270 a l l 5 2.1504 1.7551 5270 b l l 5 2.1510 1.7556 5719 b l27 2.1498 1.7562 2530 c l l l 2.1517 1.7476 A=.3905(3 ) , B=.003(2) 4_ 2503 c l l l 2.6471 2.2326 1.8540 3411 c l l l 2.2015 1.8003 1.3675 A=.404(3) "2, 5 ° 3845 c l27 20A=2.81 -A=. 14 '1 6? 2746 c91 .969 .759 3408 c l l l .98 .83 3648 c83 .962 .779 A = - . 174(1) 72 4301 a95 .5914 .4993 A=.091 83 4259 b95 .6362 .5521 .4615 These v a l u e s a r e averages b l 4 3 from the two o r d e r s . A = . 0845(4) 6, 4476 b99 1.4816 1.2101 5818 b l27 1.480 1.212 A=.268(1) 66 B i I I L e v e l \ P l a t e 7% 6h 5% 4% 3% 2J_ 8 5144 b i l l .5590 .4578 1 5270 a l l 5 .565'4 .4583 . 5270 b l l 5 .5629 .4588 A=- .1021(3) 9 ° 4916 c l 0 7 .6640 .5827 .4848 .3881 A=.1057(3) , B = - . 0 4 ( l ) 9 2 5209 a l l 5 .7990 .6781 .5580 A = . 1234(1) , B=-.007 (3) 12 3430 a79 .2070 .1799 .1471 J 3815 c l 2 7 .18 .134 A = - . 028(1) 13-. 3411 c l l l .368 .309 .252 .18 .093 J A=.056(1) 2 lJ 4476 b99 .4385 .3534 A = - . 0 7 9 3 , B=.003 22 2544 c l 4 3 .657 .57 .457 .354 • A = . 102(1) 18, .3290 .2750 2501 c l l l .300 .367 2501 c l 3 9 .3100 .3740 2530 c l l l .3699 .2956 4916 c l07 .3175 .3776 A = - . 068(1) ? 3408 e l l "A=.035l , B=-.0064 1 9 2 c l l l .2245 .1929 67 B i I I I L e v e l 1 \ P l a t e 7 6 5 4 2944 c l 3 1 3.0725 2.5874 2.0906 A=.5160(2 ) , B=-.038(3) •2h 3039 c99 3.5488 3039 c l 3 5 3.5381 A=.503 9^ 4561 b99 A=.4704(2) 11 j 2855 b l27 1.009 2 ^ 5079 b i l l .957 A=.140(2) 6]> 3450 b l l '5 2 A=.076 3.0311 3.0327 2.5140 2.5132 .861 ,844 .47 6 ( 2.3514 2.3529 .718 .693 381 2.0092 2.0026 .574 .545 279 1.4968 The 4 1.5021. i s lh l e v e l n o t r e s o l v e d . .424 .409 2 y 2499 c l l l 2.551 4752 c l 0 3 2.575 A=.370(2) 3? 2944 c99 2944 c l 3 1 3540 b l l 5 4561 b99 A=.106(1) 2.193 2.224 1.845 1.873 .521 .5303 .5340 .5335 1.484 1.497 1.123 1.141 lh ~2 3848 b l27 A=.017 3930 c l 3 1 A=2.030 .153 10.150 12 3540 b l l 5 A= . 107 535 68 B i IV L e v e l \ P l a t e 8k Ik 6h 3683 c83 A = - . 5 9 1 ( 4 ) , B=-.002 6 2842 c95 1 2842 c l 2 3 3012 c99 3012 c l 3 1 A=l .5556(3) , B=.011(2) 72 2677 c91 2823 c l23 A=.410(2), B= - . 0 4 ( l ) 8 ? 3239 c l07 3.1650 3239 c l 4 3 3.1545 3868 c l 2 7 3.1661 A=.422(1) 2.650 2.6391 2.7417 2.7376 2.7479 5H 3.2281 8.57 02 8.5664 8.5645 8.5603 2.270 2 .2532 2.3236 2.3129 2.3305 10- 3171 c l 0 3 A=- .129 1 1 2 5029 c l l l A=.05 7 ° 3683 c83 2 A=.141(8) , 124 3868 c l27 A=.095(7) 1 3 ° 3766 c l 2 3 1 A=. 178(1) 1 4 ° 3012 c99 3012 c l 3 1 3239 c l 0 7 3239 c l 4 3 A=.190(1) , B= 15" 2756 c91 A=- .413 (5l_+6J_)A = 1.547 cm -1 -1 20A - 1.0 cm B=-.16(9) .7746 .6861 .8183 ,6018 052(5) 1.2623 1.2593 1.2577 1.2583 16o 2842 c95 2842 c l 2 3 A=.5174(2) , B= - . 0 3(l) ( : 7998 8013 5021 .9805 1.0427 1.0439 1.0450 1.0428 2.8469 2.8450 4*5 2.6643 6.9856 6.9889 6.9806 6.9890 1.9000 1.8899 1.9040 6457 .4133 .4113 .7985 .8397 ,8412 .8449 .8354 2.268 1.860 2.3358 2.3420 3*5 1.459 1.4754 1.47 59 2k .4833 3219 .2220 These v a l u e s are averages .6355 .6455 .6457 .6375 69 Bi IV Level 18 3 o 3 o 3 \ Plate lh eh 5 V 4h 2823 cl23 A=.06(l) .4749 ,3974 .3223 3171 cl03 A=.049 .3783 .321 .719 2933 cl27 A=.041 .267 2677 c91 A=-.319(l) , B=-.03(2) 2.050 1.7 60 1.129 2768 c91 A=-.12 5, B= -.004 .6815 .5650 Levels 8 ° - l l ° 3643 c83 3681 c83 11° 10° 9 ° 8 ° 15.582 6.647 4,.883 15.571 6.645 4.865 

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