On the relativistic generalization of Keldysh ionization theory

Relativistic generalization of the semiclassical theory of tunnel and multiphoton ionization of atoms and ions in the field of a high-intensity electromagnetic wave (Keldysh theory) with linear and elliptic polarizations is developed. The exponential factor in the ionization rate of relativistic bound state is calculated for arbitrary values of the adiabaticity parameter γ. In the case of low-frequency laser radiation, $\gamma \ll 1$, the asymptotically exact formula is derived for the ionization rate of atomic s-level, including the Coulomb, spin and adiabatic corrections and the pre-exponential factor. The ionization rate of the ground state of a hydrogen-like atoms (ions) with $Z\lesssim 100$ is calculated, depending on laser intensity and ellipticity of radiation.