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.