MANY BODY THEORY FOR SPECTROSCOPIES OF Ce MIXED VALENCE COMPOUNDS

I. I n t r o d u c t i o n The 4 f o r b i t a l i n t h e l a n t h a n i d e s e r i e s has a s m a l l s p a t i a l e x t e n t and i s l o c a t e d i n s i d e t h e 5s5p c o r e . As a r e s u l t t h e 4 f 4 f Coulomb i n t e r a c t i o n U i s l a r g e and t h e h y b r i d i z a t i o n A b e t w e e n t h e 4 f s t a v e and t h e c o n d u c t i o n s t a t e s i s sma 1. I n some l a n t h a n i d e compounds t w o f c o n f i g u r a t i o n 4 f n and 4 f n + ' a r e , however , s u f f i c i e n t l y c l o s e i n e n e r g y so t h a t t h e m i x i n g o f t h e s e c o n f i g u r a t i o n s mus t be t a k e n i n t o a c c o u n t , i n s p i t e o f t h e weak c o u p l i n g A . Such compounds have u n u s u a l and i n t e r e s t i n g p r o p e r t i e s . At l o w t e m p e r a t u r e s t h e s p i n s u s c e p t i b i l i t y and t h e l i n e a r t e m p e r a t u r e c o e f f i c i e n t i n t h e s p e c i f i c h e a t a r e v e r y l a r g e , s u g g e s t i n g a l a r g e d e n s i t y o f l o w l y i n g e x c i t e d s t a t e s [I]. F o r Ce compounds t h e s e and o t h e r t h e r m o d y n a m i c p r o p e r t i e s w e r e o f t e n i n t e r p r e t e d i n t e r m s o f a v e r y s m a l l A (-0.01 eV) and an a l m o s t p e r f e c t ( w i t h i n -0.1 eV) d e g e n e r a c y o f t h e f O and f1 c o n f i g u r a t i o n s [ 2 , 3 ] . T h i s c o u l d g i v e a n a r r o w r e s o n a n c e a t t h e F e r m i e n e r g y and a l a r g e d e n s i t y o f s t a t e s . I n t h e l a s t 5 10 y e a r s t h e r e has been much i n t e r e s t i n e l e c t r o n s p e c t r o s c o p i e s , s i n c e t h e y s u g g e s t v e r y d i f f e r e n t v a l u e s o f t h e p a r a m e t e r s . V a l e n c e p h o t o e m i s s i o n s p e c t r o s c o p y (PES) shows a r a t h e r Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868178 C8-924 JOURNAL D E PHYSIQUE -b road f r e l a t e d peak a t 2 eV b i n d i n g e n e r g y , s u g g e s t i n g t h a t t h e f 0 f1 e n e r g y s e p a r a t i o n i s o f t h e o r d e r 2 eV and t h a t A i s o f t h e o r d e r 1 eV [ 4 ] . L a t e r i s was r e a l i z e d t h a t t h e P E S s p e c t r u m a l s o has f w e i g h t a t t h e F e r m i e n e r g y [5], c r e a t i n g a l i v e l y d e b a t e a b o u t t h e i n t e r p r e t a t i o n o f t h e s p e c t r a . S i n c e b o t h t h e t h e r m o d y n a m i c and s p e c t r o s c o p i c d a t a p r o v i d e r a t h e r i n d i r e c t i n f o r m a t i o n a b o u t t h e p a r a m e t e r s o f t h e sys tem, i t i s d e s i r a b l e t o s t u d y a m i c r o s c o p i c model t o d e t e r m i n e what i n f o r m a t i o n t h e d i f f e r e n t e x p e r i m e n t s can p r o v i d e . T h e o r e t i c a l s t u d i e s o f Ce compounds a r e o f t e n based on t h e A n d e r s o n i m p u r i t y mode l . A g r e a t p r o g r e s s i n t h e t r e a t m e n t o f t h i s model was t h e i d e a o f And e r s o n [ 6 ] and R a m a k r i s h n a n [ 7 , 8 ] t o t r e a t l / N f as a s m a l l paramet e r , where N f i s t h e d e g e n e r a c y o f t h e f l e v e l . We have d e v e l o p e d a method f o r c a l c u l a t i n g s p e c t r a i n a l / N f e x p a n s i o n [9, 1 0 1 w h i c h g i v e s e x a c t T = 0 s p e c t r a f o r Nf = m . L a t e r , a l t e r n a t i v e m e t h o d s were d e v e l o p e d f o r a f i n i t e T b u t an i n f i n i t e U [ll].