Abstract
Through an exact solution of the time-dependent Schr\"odinger equation for an electron in a static electric field plus the time-dependent electric field of the detaching radiation, the photodetachment cross section of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ is calculated. Careful attention is paid to ensuring proper limiting behavior as the frequency of the time-dependent field goes to zero. We do not find observable effects of a cross term between the two fields on the detachment cross section. Our results point to possible gauge dependence and other difficulties of S-matrix formulations of multiphoton detachment and ionization.
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