Generalized momentum of tunnelling ionization of hydrogenic atom in linearly polarized laser

We extend the Keldysh theory to study the characteristics of ionization rate of a hydrogenic atom subjected to intense lasers field. We obtain an exact semianalytical result of the ionization rate for the linearly polarized laser field. The Keldysh´s theory is generalized for arbitrary momentum of the photoelectron. We study the contribution of an additional term, associated with the second pole neglected in Keldysh´s theory, to the photoionization spectra of the exact rates as functions of frequency and electric field strength.