Production of a pair by a polarized photon in a uniform constant electromagnetic field

The total probability of production of an electron-positron pair by a polarized photon in a constant uniform electromagnetic field of an arbitrary configuration is determined using the imaginary part of the diagonalized polarization operator. Approximate expressions are derived for this probability in four ranges of photon energy. In the high-energy range, the corrections to the standard semiclassical approximation are calculated. In the range of intermediate energies, in which this approximation is inapplicable, the probability of the process is calculated using the steepest descent method. It is shown that in the range of photon energies higher than the pair production threshold in a magnetic field, a weak electric field removes root divergences in the probability of production of the particles at the Landau levels. For relatively low photon energies, a low-energy approximation is developed. At such energies, the effect of the electric field on the process is decisive, while the effect of the magnetic field is associated with its interaction with the magnetic moment of the particles being produced. Such an interaction is manifested, in particular, in the difference in the probabilities of production of a pair by an external field for scalar and spinor particles.