New approach for approximating the continuum wave function by Gaussian basis set

A new approach for approximating the continuum wave functions for hydrogenic atoms with Gaussians basis sets is developed and tested. In this the plane wave is left unchanged and the distorting factor, represented by the Confluent Hypergeometric function, is expanded as a sum of Spherical Harmonics multiplied by a series of Gaussians. In this way the number of spherical waves and Gaussians will be significantly reduced and the plane wave will be responsible for the momentum conservation. As compared with previous methods that expand the full continuum, including the plane wave, our strategy does not require a great quantity of partial waves for convergence. Dense oscillations which are characteristic of the plane wave, are avoided. To test the performance of this approximation to describe a free-bound atomic form factor, the ionization cross section of hydrogen by impact of protons in first Born approximation is calculated. Compared with the exact results, a good agreement with just 4 spherical waves and ten Gaussians each is obtained. The method looks very interesting, especially to speed up atomic and molecular collision calculations involving the continuum.