Exact and asymptotic X-ray intensity values from 20-parameter hylleraas-type wave functions. He and He-like ions

Abstract

X-ray form factors and total scattered X-ray intensity values, computed analytically from radial electron-nuclear and electron-electron distribution functions, D0(r)'s and P0(r12)'s, are presented for the 1S ground states of H−, He, Li+, B3+, O6+, Ne8+, and Mg10+. 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(r12) = P0(r12)/r12, are in excellent agreement with those computed directly from P0(r12). 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.