Resonance mechanism of the production of electron-positron pairs in a strong magnetic field

The Compton-like process γe ^± → e ^± e ⁺ e ^? involving the production of an electron-positron pair in the interaction of an ultrarelativistic electron with a soft x-ray photon in the vicinity of the polar cap of a magnetar is considered. It is shown that the amplitude for this reaction has a resonance character. A simple analytic expression is obtained for the electron-absorption coefficient. Possible astrophysical implications of the resonance process γe ^± → e ^± e ⁺ e ^? are discussed.