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In this work we present a new method of approximating the continuumwavefunctions with a discrete basis set. This method aims to be at leastcompatible with other well known methods of the electronic structure theory todescribe processes in the electronic continuum. As an example of theapplication we present the results of the calculations of the photoionizationcross sections for the hydrogen atom and hydrogen molecule and for the heliumatom. We also obtained the photoelectron angular distribution for the hydrogenmolecule. The agreement of our results with the experimental data is very goodin the energy range from the ionization threshold up to photon energies ofabout 60 eV.

Theoretical description of the ionization processes with a discrete basis set representation of the electronic continuum