  A model describing the electronic transitions in an atom subject to a strong
high frequency laser pulse is proposed in the velocity gauge. The model
accounts for the initial state coupling with the the remaining discrete and
continuum spectra. Continuum-continuum transitions are also taken into account
following well known strong-field approximation. A single integro-differential
equation for the initial state amplitude has been obtained. Exact numerical
solutions of this equation are computed and compared with the full time
dependent Schr{\"o}dinger equation solution for Hydrogen atoms. The initial
state amplitude is well described by two versions of the model: with and
without the continuum-continuum coupling model. However the electron energy
spectrum is only well described when the model accounts for the coupling
between continuum states. Improvement on SFA arise from using Coulomb final
wave function as well as regarding the initial state probability depletion.
