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

To apply the methods of dimensional scaling to higher-angular-momentum stat es, a formalism needs to be developed which factors the D-dimensional rotat ional degrees of freedom from the internal degrees of freedom. The rotation al degrees of freedom multiply with increasing dimensionality, while the in ternal degrees of freedom remain finite in number. A suitable expansion whi ch achieves this has been presented by the authors recently and is an N-ele ctron 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 fo r the atomic two-electron system has been presented by the authors in anoth er recent paper. The coupled differential equations admit continuation in D and clearly show the complete spectrum of exact interdimensional degenerac ies of the two-electron system. However, to apply the methods of dimensiona l scaling to the two-electron system, the system of coupled differential eq uations have to be solved for large D. This paper concerns itself with this issue. [S1050-2947(97)07608-7].