Adiabatic coordinate separation and large N‐dimensional limit in two‐electron ions

The 1/N expansion is used to generate semiclassical effective potentials for two‐electron ions. These potentials can be considered an improvement over the conventional ones computed by Lin and Fano for the full two‐electron coulomb potential insofar as they incorporate some of the quantum mechanical effects. No falling into the nucleus is allowed. Furthermore, the minima of these effective potentials are in surprising agreement with those computed by Fano, Macek, and Lin. This would indicate that the collective variable R, associated with N = 6, leads to a much smaller expansion parameter N, making the adiabatic separation more justified. The role and significance of these broken symmetry solutions with geometric localization are discussed as well as generalizations. The procedure is semiclassical in the sense that the kinetic energy becomes negligible by having a large effective mass.