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We investigated the effects that occur during the circulation of ultrarelativistic electrons and positrons in the field of an X-ray pulsar. A resonant process in annihilation and the subsequent production of the electron–positron pairs were studied theoretically. Under the resonance, the second-order process in an original fine-structure constant process effectively decays to two first order processes of the fine-structure constant: single-photon annihilation of the electron–positron pair stimulated by the external field, and the Breit–Wheeler process (single-photon birth of the electron–positron pair) stimulated by the external field. We show that resonance has a threshold energy for a certain combinational energy of the initial electron and positron. Furthermore, there is a definite small angle between initial ultrarelativistic particles’ momenta, in which resonance takes place. Initial and final electron–positron pairs fly in a narrow cone. We noticed that electron (positron) emission angle defines the energy of the final pair. We show that the resonant cross-section in the field of the X-ray pulsar may significantly exceed the corresponding cross-section without the field (Bhabha cross-section).

The Resonant Effect of an Annihilation Channel in the Interaction of the Ultrarelativistic Electron and Positron in the Field of an X-ray Pulsar