Resonant Threshold Two-Photon e–e+ Pair Production Onto the Lowest Landau Levels in a Strong Magnetic Field

Abstract

The process of electron-positron pair production by two photons in a strong magnetic field has been studied. The process kinematics is considered, and the probability amplitude for arbitrary polarizations of particles is found. The resonance conditions are established, and the resonant cross-section is estimated in the case where the electron and the positron occupy the lowest levels (le = 1, lp = 0) that satisfy these resonance conditions. K e y w o r d s: electron-positron pair, photon-induced production, magnetic field, quantum electrodynamics, resonance.

Electron-Positron Pair Photoproduction in a Strong Magnetic Field Through the Polarization Cascade

“…( 13) depend on ′ . Note that this propagator is widely used, when calculating the amplitudes of the second-order processes in which the electron plays the role of an intermediate particle (see, e.g., works [38][39][40]49]).…”

“…In works [12,18,37], the optical theorem was used to derive general expressions for the probabilities of the electron-positron pair production by a photon. Note also that, in the works [38,39], the resonant case of the process of electron-positron pair generation in a magnetic field by two photons was considered. In work [40], the 1 and resonant 2 pair creation processes were compared at the parameter values that are typical of the neutron star magnetosphere, and the limiting concentration of cyclotron photons at which the second-order process dominates over the first-order one was determined.…”

Vacuum Birefringence in a Supercritical Magnetic Field

“…Later, it was found in works [25,26] using a slightly different method and in work [27] using precise solutions of the Dirac equation. It should be noted that this propagator was used in works [28][29][30][31] to calculate the amplitudes of second-order processes with the electron as an intermediate particle. The propagator has the form…”

“…In other words, the resonance condition is obeyed. In this case, the process width, which is usually associated with the total probability of the intermediate state decay [29][30][31], has to be taken into account. From expression (22), it is evident that the parameter˜plays the role of the resonance process width.…”

A cascade ofe−e+pair production by a photon with subsequent annihilation to a single photon in a strong magnetic field

“…where κ belongs to the interval (0, 1). Taking into account the general amplitude and the condition (34) the nonresonant amplitude in LLLapproximation (25) takes on the form…”