A general method to obtain sturmian functions for continuum and bound state problems with coulomb interactions

Abstract

In this article, we investigate discretization schemes to represent Sturmian functions for both positive and negative energies in the presence of a long range Coulomb potential.We explore two methods to obtain Sturmian functions for positive energy. The first one involves the expansion of the radial wave function in a L2 finite basis set, whereas the second one introduces the discretization of the radial coordinate domain of the Hamiltonian or, alternatively, the Green function. We apply them to find the bound states and scattering phase shift for N-electron atoms close to the critical charge. Both methods are able to describe bound states near threshold, as well as continuum states with very good convergence properties.