Inner and outer radial density functions in correlated two-electron systems

A method is presented for determining inner- and outer-electron radial density functions for two-electron systems by partitioning the fully correlated, two-electron, radial density function. This is applied to the helium isoelectronic series (Z = 1 to 10 and 100) and the critical nuclear charge system, which has the minimum charge for which the atomic system has at least one bound state, to separate out the motions of the two electrons in both weakly and strongly bound systems. It is found that the inner electron experiences a negative screening effect due to the perturbation by the other electron. This is quantified and shown to increase with increasing Z. For the weakly bound systems the inner radial density distribution closely resembles that of a hydrogenic atom with the outer radial density distribution becoming very diffuse.