**Figure 1.** Electron spectra for ionization of H(1s) as a function of the ejected electron energy for a laser pulse with *N* = 1 (up), *N* = 7 (middle) and *N* = 27 (bottom) cycles. Laser frequency ω = 0.855 au, *F*_{0} = 0.05 au (Γ = 17.1). Full line: CVA; dotted line: DipA; full line with circles: TDSE results.

**Abstract**

We present a detailed study of the ionization probability of H and H_{2}^{+} induced by a short intense laser pulse. Starting from a Coulomb–Volkov description of the process we derive a multipole-like expansion where each term is factored into two contributions: one that accounts for the effect of the electromagnetic field on the free-electron final state and a second factor that depends only on the target structure. Such a separation may be valuable to solve complex atomic or molecular systems as well as to interpret the dynamics of the process in simpler terms. We show that the series expansion converges rapidly, and thus the inclusion of the first few terms is sufficient to produce accurate results.