Analytical solutions for strong field-driven atomic and molecular one- and two-electron continua and applications to strong-field problems

Abstract

We develop the eikonal-Volkov approximation (EVA) to describe atomic and molecular strong-field dynamics. The main component of this approach is the approximate solution for the continuum states of one and two electrons in the presence of a long-range ionic potential and a strong laser field. These solutions include the laser field fully, the ionic potential, and the electron-electron interaction in the eikonal approximation, and describe the nonperturbative coupling between these interactions. Comparison with numerically evaluated continuum electron wave functions demonstrates quantitative accuracy of the approximate solutions. Their long-time limit yields the quasienergy (Floquet) states of the continuum electron. We also show how to extend the applicability of these solutions to deal with the singularities of the ionic potential, where straightforward eikonal approximation breaks down. The large-angle scattering (hard collision) is incorporated in the EVA formalism using an expansion in the number of hard collisions. Finally, we describe how the EVA formalism can be used to obtain simple analytical expressions for various strong-field problems.