Form factors and total scattering intensities for the helium-like ions from explicitly correlated wavefunctions

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Abstract
Integral formulae necessary to compute X-ray form factors F( mu ) and total scattered X-ray intensities It( mu ) from explicitly correlated wavefunctions of the form psi (r1,r2,r12)=(4 pi )-1 Sigma k=1LCk(1+or-P12)exp(- alpha kr1- beta kr2- gamma kr12) are derived. They are then applied to such wavefunctions recently constructed by the authors for the ground states of the helium-like ions from H- through Mg10+. The results are presented in the form of convenient theoretically-based interpolation functions for F( mu ) and It( mu ). Numerous tests indicate that these interpolation functions are very accurate. Parameters that appear in the small and large mu expansions of F( mu ) and It( mu ) are tabulated along with some parameters that appear in the Bethe-Born asymptotic cross section for total inelastic scattering of fast charged particles. New internal consistency conditions for the exact and experimental F( mu ) and It( mu ) functions are derived.