Wigner intracule for the Kellner helium-like ions

The Kellner wavefunction for a helium-like ion is the Hartree-Fock solution wherein the orbital is a Slater-type function with the variationally optimal exponent zeta = Z - 5/16. The Wigner intracule W(u, v) of a system gives the joint quasiprobability of finding two electrons whose position space and momentum space separations are \r(1) - r(2)\ = u and \p(1) - p(2)\ = v, respectively. In this article, we extend Wigner intracule theory beyond Gaussian-type functions by deriving W(u, v) for the Kellner helium-like ions. Although we have not been able to express W(u, v) in closed form, our formulation reduces it to a two-dimensional integral that can be treated by quadrature. (C) 2004 Wiley Periodicals, Inc.