The Compton effect in a strongly magnetized plasma

The process of Compton scattering $\gamma e^{\pm} \to \gamma e^{\pm}$ in a strongly magnetized medium of arbitrary temperature and zeroth chemical potential was considered. The analytical expressions for the partial cross section in the small concentration limit of the electron-positron plasma are obtained. The numerical estimations for the partial probabilities of this process are presented by taking into account the photon dispersion in a strong magnetic field and charge-symmetric plasma of arbitrary temperature. The comparision of the scattering probability with photon splitting in a plasma was investigated. The astrophysical applications of the obtaining results are considered.