Through an exact solution of the time-dependent Schrodinger equation for an
electron in a static electric field plus the time-dependent electric field
of the detaching radiation, the photodetachment cross section of H- is cal
culated. Careful attention is paid to ensuring proper limiting behavior as
the frequency of the time-dependent field goes to zero. We do not find obse
rvable effects of a cross term between the two fields on the detachment cro
ss section. Our results point to possible gauge dependence and other diffic
ulties of S-matrix formulations of multiphoton detachment and ionization.