Inelastic scattering of gamma-quanta by hydrogen-like atoms

The differential and total cross sections for inelastic scattering of γ-quanta by hydrogen-like atoms involving electron transitions from the 1s state to the 2s or 2p states are calculated analytically taking into account terms of the order of α2Z2 inclusively. The differential cross section formulas derived with such an accuracy are valid for small angle scattering. The results are applicable in the photon energy region in which ω>>mαZ (m is the electron mass). They are consistent with the results of Gorshkov, Mikhailov and Sherman for energies mαZ<<ω<<m