Transition rate dependence on the non-zero initial momentum in the ADK-theory

Tunneling regime, introduced by Keldysh, in the interaction of strong lasers with atoms has been now accepted as the reliable method for describing processes when low frequency lasers are involved. Yet it was always assumed that the ionized electrons are leaving the atom with zero initial momentum. Because we are interested in how non-zero momentum influences the transition probability of tunnel ionization, we obtained the exact expression for the momentum. Here the estimation of the transition probability with nonzero momentum included was conducted. Potassium atoms in the laser field whose intensity varied from 10(13) W/cm(2) to 10(14) W/cm(2) were studied. It seems that all energy of laser field is used for tunneling ionization process at the beginning of laser pulse - ionization probability is large. After that, with further action of laser pulse, ionization probability decreases, probably because part of laser pulse energy is used for increasing momentum of ejected electrons, leaving smaller amounts of light quanta, available for ionization of remaining electrons. If laser pulse lasts long enough, then the amounts of light quanta available for ionization become larger, resulting in increase in ionization probability, now with greater starting energy of ejected electrons.