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 ζ = 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. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004