Multiphoton ionization of atoms by an ultrashort laser pulse

Closed analytical expressions for the probability of multiphoton ionization of atoms and ions by a time-varying electric field $\mathcal{E}(t)$ are obtained by the imaginary time method. These expressions apply for arbitrary values of the Keldysh parameter $\gamma$. The dependence of the ionization probability and the photoelectron momentum spectrum on the shape of an ultrashort laser pulse is considered.