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Resonant 3--photon ionization of hydrogenic atoms by non-monochromatic laser field

We present ionization probability and line shape calculations for the two-step 3-photon ionization process, $1S \stackrel{2\hbar ω}{\longrightarrow}2S \stackrel{\hbar ω}{\longrightarrow}εP $, of the ground state of hydrogenic atoms in a non-monochromatic laser field with a time--dependent amplitude. Within the framework of a three--level model, the {\it AC Stark} shifts and non-zero ionization rates of all states involved were taken into account together with spatial and temporal inhomogeneities of the laser signal. In contrast with the usual perturbative technique, the time evolution of the atomic states was simulated by direct numerically solving the system of coupled time--dependent inhomogeneous differential equations, being equivalent to the appropriate non-stationary Schrödinger equation. Particular numerical results were obtained for typical parameters of the pulsed laser field that are employed in a new experiment to measure the $1S-2S$ energy separation in muonium at the Rutherford Appleton Laboratory. The shifts and asymmetries of the photoionization line shapes revealed may be of relevance for ultra-high precision experiments in hydrogen in CW laser fields.