EXTRAPOLATION METHOD FOR THE EVALUATION OF ABOVE-THRESHOLD IONIZATIONCROSS-SECTIONS FOR ONE-ELECTRON AND 2-ELECTRON SYSTEMS

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