J.M.: Computational methods for generalized Sturmians basis

The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds

Double photoionization of helium: a generalized Sturmian approach

In this work we study the double photoionization of helium induced by low intensities laser fields in the regime where only one photon absorption occurs. The method proposed here is based on a Generalized Sturmian Functions (GSF) spectral approach which allows the imposition of outgoing boundary conditions for both ejected electrons. These, in turn, construct an hyperspherical flux characteristic of double continuum wave functions. We compare our calculated cross sections at 20 and 40 eV above threshold with absolute and relative measurements, and with other calculations. Our results definitively demonstrate the applicability of the GSF approach for dealing with break-up Coulomb problems