Direct versus sequential double ionization in atomic systems

In view of recent papers on two-photon double ionization of helium, pertaining to a perceived anomaly in the behavior of the sequential process and its influence on the direct process, as well as the dependence of both on the laser pulse duration, we show that upon the proper formulation, the sequential is well defined and free of divergence, and that the dependence on pulse duration is considerably more intricate. We also argue that the apparent sharp rise of the cross section for the direct process, around 54.4 eV, is due to the unintended inclusion of the sequential process, which in any case is not properly describable in terms of a single cross section.