Low-energy K-shell Compton scattering

We calculate the photon energy distribution and the total cross section for the Compton scattering on the K electrons for the case when the photon wave length is much smaller than the size of the K shell. We show that at the energies of the order of the binding energy I of the K electron most part of the spectrum is governed by the low-energy behavior. The total cross section has a local maximum at the energies (1.5-2)I, reaching the values of the order 1 barn. At higher photon energies the spectrum curves have two maxima, corresponding to low-energy ejected photons or electrons. The cross sections in the whole region are calculated. The actual calculations are carried out employing the nonrelativistic Coulomb functions, thus being valid for the single-electron atoms. However, the main features of the analysis are expected to be true for many-electron ions and neutral atoms. The results of the present analysis may be useful in calculations of the laser-induced and laser-assisted processes.