Photon Damping Caused by Electron-Positron Pair Production in a Strong Magnetic Field

Damping of an electromagnetic wave in a strong magnetic field is analyzed in the kinematic region near the threshold of electron-positron pair production. Damping of the electromagnetic field is shown to be noticeably nonexponential in this region. The resulting width of the photon γ → e+e− decay is considerably smaller than previously known results. PACS numbers: 13.40.Hq; 95.30.Cq E-mail address: [email protected] E-mail address: [email protected] 1 The problem of propagation of electromagnetic fields through an active medium is inherent in a variety of physical phenomena. The birth and evolution of supernova and neutron stars, where the matter density can be on the order of nuclear density ρ ≃ 10 − 10g/cm and the temperature can achieve several tens of MeVs, are the largest scale and the most interesting such phenomena. In addition to dense and hot matter, a strong magnetic field, which can be several orders of magnitude as high as so-called critical, or Schwinger, value Be = m 2 e/e ≃ 4.41 · 10G , can be generated in the above-mentioned objects [1, 2]. This strong magnetic field can induce new phenomena which can considerably affect the evolution of these astrophysical objects. Electromagnetic-field damping caused by electron-positron pair production in an external magnetic field is one of these phenomena. Recall that the γ → ee process is kinematically forbidden in vacuum. The magnetic field changes the kinematics of charged particles, electrons and positrons, allowing the production of an electron-positron pair in the kinematic region q ‖ = q 0 − q 3 ≥ 4me, where q0 is the photon energy and q3 is the momentum component along the magnetic field 2 In 1954, Klepikov [3] examined the production of an electron-positron pair by a photon in a magnetic field and obtained the amplitude and width of the γ → ee decay in the semiclassical approximation. Later, the authors of [4]–[9] considered this process in the context of its astrophysical applications. It was pointed out in [7, 8] that the use of the expression derived in [3] for the width considerably overestimates the result in the strong magnetic field limit. In this case, one should use an exact expression for the width of one-photon production of a pair when electrons and positrons occupy only the ground Landau level. However, it was found that the expression for the decay width in the limit of strong magnetic field has a root singularity at the point q ‖ = 4 me. Shabad [9] emphasized that this behavior indicates that the decay width calculated in the perturbation theory cannot be treated as a damping coefficient. In this case, the damping coefficient is primarily determined from the time evolution of the photon wave function in the presence of a magnetic field. Shabad [9] suggested that this dependence be obtained by solving the dispersion equation with account taken of the vacuum polarization in a magnetic field with complex values of photon energy. In our opinion, this method has several disadvantages. First, it is well known but rarely mentioned that the dispersion equations with complex energies have no solutions in the physical sheet. Solutions are in the nonphysical Riemannian sheets (analyticity region of We use the system of units where h̄ = c = 1. Hereafter, we consider the magnetic field directed along the third axis.