Remarks on the one-photon-pair annihilation in strong magnetic fields

Abstract

We report specifically on a quantum electrodynamic feature of the one-photon-pair annihilation. Most of the calculation related with this process (not excluding other ones) have been carried out usually utilizing the wave functions obtained from the Dirac equation in the Landau gauge Aα = (0,Bx, 0), where B is oriented along the z-axis (Johnson and Lippman, 1949). Although, the eigenstates of the Dirac Hamiltonian as it was introduced by Johnson and Lippman, do not consider the coupling to the radiation field and consequently they reflect only forp z = 0 the same linear combination of the two degenerate polarization states. We report the transition rate function for the one-photon-pair annihilation in a strong magnetic field by using the Sokolov and Ternov eigenstate |±〉 as far asp z = 0 andN > 0 is concerned. The difference between the expression for the transition rate by using the Sokolov and Ternov eigenstates and the one calculated by (Wunneret al., 1986), is just the functionI s,s′ which corresponds to the degeneracy of the orbit center of the electrons characterized by the quantum numberss ands′.