Joint probability calculation of the lateral velocity distribution in strong field ionization process

We describe an approach to the description of the time-development of the process of strong field ionization of atoms based on the calculation of the joint probability of occurrence of two events, event B being finding atom in the ionized state after the end of the laser pulse, event A being finding a particular value of a given physical observable at a moment of time inside the laser pulse duration. As an example of such an physical observable we consider lateral velocity component of the electron's velocity. Our approach allows us to study time-evolution of the lateral velocity distribution for the ionized electron during the interval of the laser pulse duration. We present results of such a study for the cases of target atomic systems with short range Yukawa and Coulomb interactions.