Extrapolation method for the evaluation of above threshold ionization cross sections for one- and two-electron systems

We present a new method for the calculation of above-threshold ionization (ATI) cross sections based on a description of the atomic structure through a discretized basis. This new approach handles the divergent terms within the discretized continuum by assigning a width epsilon to the nearest discretized continuum level and then extrapolating to the value of the amplitude as epsilon goes to zero. The method is in principle applicable to any discretized basis and to atoms with more than one electron. We demonstrate its usefulness through the calculation of up to four photons absorbed above threshold in hydrogen and up to two photons above threshold in helium.