General computational method for two-electron systems

Abstract

We develop the hyperspherical coordinate method into a numerically reliable method competitive with other accurate ones. To this end, we present an efficient and accurate numerical scheme for setting up the hyperspherical channel functions which dictate the accuracy of the whole method. The diabatic-by-sector method is employed to integrate numerically the hyperspherical close-coupling equations. The two-dimensional matching procedure is implemented to impose the asymptotic boundary conditions in the independent-particle coordinates. The proposed scheme leads to accurate bound-state energies and resonance positions as well as accurate phase shifts and widths. The efficiency and accuracy of the method are tested on the He atom. For singly excited states, our results agree with experimental results to within five significant digits. For elastic phase shifts, ours agree with other accurate theoretical results to within a few milliradians. For doubly excited states of the N=2 and 3 manifolds, our level positions agree with recent theoretical results to within four to five significant digits, and with experiments to a similar degree of accuracy. Detailed comparisons of our resonance widths with other data are presented.