Large-dimension limit of higher-angular-momentum states of two-electron atoms

To apply the methods of dimensional scaling to higher-angular-momentum states, a formalism needs to be developed which factors the D-dimensional rotational degrees of freedom from the internal degrees of freedom. The rotational degrees of freedom multiply with increasing dimensionality, while the internal degrees of freedom remain finite in number. A suitable expansion which achieves this has been presented by the authors recently and is an N-electron D-dimensional generalization of the Schwartz expansion. A derivation of the coupled differential equations in the internal variables that result from the application of the Hamiltonian to this wave-function expansion for the atomic two-electron system has been presented by the authors in another recent paper. The coupled differential equations admit continuation in D and clearly show the complete spectrum of exact interdimensional degeneracies of the two-electron system. However, to apply the methods of dimensional scaling to the two-electron system, the system of coupled differential equations have to be solved for large D. This paper concerns itself with this issue.