The use of relativistic action in strong-field nonlinear photoionization

Nonlinear relativistic ionization phenomena induced by a strong linearly polarized laser field are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. This action has been used to calculate semiclassical transition rates. Simple analytical expressions for the ionization rate, the photoelectron emission velocity and for the drift momentum distribution of the photoelectron have been found. The analytical formulas apply to nonrelativistic bound systems as well as to initial states with an energy corresponding to the upper boundary of the lower continuum and to the tunnel as well as the multiphoton regime. In the case of a nonrelativistic bound system we recover the Keldysh formula for the ionization rate. Relativistic effects in the initial state lead to a weak enhancement of the rate of sub-barrier ionization and to the appearance of a nonzero photoelectron leaving velocity.