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

Integral formulae necessary to compute X-ray form factors F( mu ) and total scattered X-ray intensities I t ( mu ) from explicitly correlated wavefunctions of the form psi (r 1 ,r 2 ,r 12 )=(4 pi ) -1 Sigma k=1 L C k (1+or-P 12 )exp(- alpha k r 1 - beta k r 2 - gamma k r 12 ) 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 Mg 10+ . The results are presented in the form of convenient theoretically-based interpolation functions for F( mu ) and I t ( 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 I t ( 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 I t ( mu ) functions are derived.