Accurate charge densities and two-electron intracule functions for the heliumlike ions

Integral formulas necessary to compute charge densities and intracule functions from explicitly correlated wavefunctions of the form ψ (r1, r2, r12) = (4π)−1ΣNk=1ck(1 ±P12) exp(−αkr1−βkr2−γkr12) are derived. They are applied to such wavefunctions recently computed by us for the ground states of the heliumlike ions from H− through Mg10+. An analysis of the resulting distribution functions is given. A simple method for obtaining reasonable approximations to an intracule function from its moments is developed.