Energy shifts due to the ponderomotive potential

We show, by simple classical arguments, that the explicit time dependence of the ponderomotive potential causes both a shift and a broadening of the photoelectron lines in high-intensity multiphoton experiments. If the laser pulse is short enough, some of the energy from the absorbed photons will be lost by an electron when it separates from the pulse. Since different atoms are ionized at different intensities, the shifts of the energies of the individual electrons will differ. This will be detected as an inhomogeneous broadening of the electron lines. Both the shift and the broadening will be of the same order of magnitude as the ponderomotive potential. Fast electrons experience a lower shift than slow electrons. The important parameter is the ratio between the transverse pulse diameter and the pulse duration. If the electron velocity is much higher than this ratio, there will be no shift. If the velocity is much lower than this ratio, there will be a maximum shift. These predictions have just recently been confirmed, at least qualitatively, by experiments.