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Calculation of the light-shifts in the ns-states of hydrogenic systems

We present the results of the light-shift calculations in the ns-states of hydrogenicsystems in the presence of a weak laser field. This is done by means of analytical calculations of the scalar dynamic polarizabilities (DP) of the corresponding levels. In contrast to the usual technique, 1.e. by solving certain inhomogeneous differential equation. As a result, we obtained for the DP a closed analytical expression valid for all principal quantum numbers, n. Within a framework of such an approach we succeeded both in retrieving the well known results and finding several new ones, as well.Our interest is focused mainly on the states with low n, n=1,2, since they are of particular importance.Various analytical properties of the DP of such levels are discussed in full details. Numerical values of light-shifts are computed for those energies and intensities of the laser field that are used in the 1S-2S experimental investigation of the muonium atom.