Two-electron wave functions in hyperspherical coordinates

Abstract

In order to investigate the potential precision of quantitative calculations using hyperspherical coordinates, we have reexamined this method in detail. By developing an analytic solution of the angular equation in the form of a series expansion in the variable x = tan(..cap alpha../2), we are able to isolate the numerical errors in the solution from those caused by the truncation of the angular momentum expansion and by the exclusion of radial coupling terms, which we then examine separately. This new method enables us to extend the calculation of the potential curves and channel functions to the large-R region and to obtain asymptotic expansions for the potential curves and radial couplings. From these we determine general expressions for the boundary conditions of the radial equation. Finally, we present the first nonadiabatic result for the ground-state energy of helium.