Download e-book for iPad: Atomic and Molecular Scattering by Berni Alder

By Berni Alder

ISBN-10: 0124608108

ISBN-13: 9780124608108

Atomic And Molecular Scattering: tools In Computational Physics, by way of Alder, Berni, Et Al., Eds

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Example text

N e x t w e r e q u i r e t h a t N c yk+N+ NE j = - 2 £ N oo f ( A TJ% VuinZijir') I 1=1 i = l dr', 0 k = 1, Nc; j = 1, J V A , (264) w h i c h f o l l o w s f r o m t h e r e q u i r e m e n t t h a t t h e coefficient m u l t i p l y i n g Uk m u s t b e g i v e n b y E q s . (213) a n d (215). F i n a l l y w e h a v e NL e q u a t i o n s (Zy|P«) = 0 , j=l,NA (265) for e a c h Pa o c c u r r i n g i n E q . (213) w h e r e / c o r r e s p o n d s t o t h e a p p r o p r i a t e r o w i n E q .

N + NA + NEJ ' ^ = 1, Nc + NL '9 j = l 9N A9 (263) w h i c h follows f r o m t h e requirement t h a t t h e solution in t h e inner a n d in t h e o u t e r r e g i o n m u s t satisfy t h e s a m e e q u a t i o n . N e x t w e r e q u i r e t h a t N c yk+N+ NE j = - 2 £ N oo f ( A TJ% VuinZijir') I 1=1 i = l dr', 0 k = 1, Nc; j = 1, J V A , (264) w h i c h f o l l o w s f r o m t h e r e q u i r e m e n t t h a t t h e coefficient m u l t i p l y i n g Uk m u s t b e g i v e n b y E q s .

T h e e q u a t i o n s (87) c a n b e w r i t t e n a s = 2 £ (V + W + K )Fj(r) u tJ u j=l Here V u + £ A P (r), i = 1, N. iaa (213) a is t h e d i r e c t p o t e n t i a l defined explicitly b y E q . (107). I t is a f u n c t i o n o n l y o f t h e r a d i a l c o o r d i n a t e r. W tj is t h e e x c h a n g e p o t e n t i a l i n t e r a c t i o n w h i c h c a n b e w r i t t e n q u i t e g e n e r a l l y in t h e f o r m 2W tJ Fj(r) w h e r e Pi (r) a n d P (r) k 2k = £ a y (P F \ r)P (r), kXklk k } are atomic orbitals, a k i n t e g e r o r z e r o , a n d w h e r e y (AB\r) (214) 2k is a c o n s t a n t , X is a p o s i t i v e k is defined b y E q .

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Atomic and Molecular Scattering by Berni Alder


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