Abstract
We develop a flexible analytical approach to describe strong-field dynamics in atoms and molecules. The approach is based on the ideas of the $R$-matrix method. Here, we illustrate and validate our approach by applying it to systems with one active electron bound by the Coulomb potential and benchmark our results against the standard theory of Perelomov, Popov, and Terent'ev [Sov. Phys. JETP 23, 924 (1966)]. We discuss corrections to the ionization amplitude associated with the interplay of the Coulomb potential and the laser field on the sub-laser cycle time scale and the shape of the tunneling wave packets associated with different instants of ionization.
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