One-photon pair production in pulsars: non-relativistic and relativistic regimes

The process in which photons, emitted by primary particles, decay into pairs is usually assumed to be responsible for populating a pulsar magnetosphere with highly relativistic secondary pairs. Synchrotron emission from these secondary pairs is then assumed to contribute to the high-energy emission from some pulsars. We show that the perpendicular motion of the secondary pairs is highly relativistic only if the magnetic field is sufficiently weak. We consider pair production as a function of the energy of the curvature photons emitted by the primary electron (or positron). The secondary electrons and positrons are in their lowest Landau levels for strong magnetic fields, B greater than or similar to 0.5B(cr), and all have non-relativistic perpendicular momenta for B greater than or similar to 0.1B(cr). The conventional treatment of one-photon pair creation in terms of the asymptotic limit, where the electron and positron have highly relativistic perpendicular momenta, is invalid for such fields. For weaker fields, the asymptotic theory applies for the higher energy portion of the photon spectrum, and it is valid for the entire spectrum only for B less than or similar to 0.02B(cr). Synchrotron emission by secondary pairs cannot be relevant to high-energy emission from pulsars for B greater than or similar to 0.1B(cr).