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Exact and asymptotic X‐ray intensity values from 20‐parameter hylleraas‐type wave functions. He and He‐like ions
Author(s) -
Benesch Robert,
Smith Vedene H.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560050806
Subject(s) - wave function , cusp (singularity) , electron , ion , intensity (physics) , type (biology) , atomic physics , physics , chemistry , quantum mechanics , mathematical physics , mathematics , geometry , ecology , biology
X‐ray form factors and total scattered X‐ray intensity values, computed analytically from radial electron‐nuclear and electron‐electron distribution functions, D 0 ( r )'s and P 0 ( r 12 )'s, are presented for the 1 S ground states of H − , He, Li + , B 3+ , O 6+ , Ne 8+ , and Mg 10+ . The distribution functions are those obtained algebraically from the 20‐parameter Hylleraas‐type wave functions of Hart and Herzberg. Asymptotic total intensity values, which have been shown to depend on the derivatives of even order of g ( r 12 ) = P 0 ( r 12 )/ r 12 , are in excellent agreement with those computed directly from P 0 ( r 12 ). The asymptotic values are listed only for He; numerical values of the derivatives g (2) (0), g (4) (0), g (6) (0) and g (8) (0) are given for He and the 2‐electron ions. None of the wave functions studied here satisfy the Kato electron‐nucleus cusp condition.