Electromagnetic radiation from positive-energy bound electrons in the Coulomb field of a nucleus at rest in a strong uniform magnetic field

Abstract

A classical analysis is presented of the electromagnetic radiation emitted by positive-energy electrons performing bound motion in the Coulomb field of a nucleus at rest in a strong uniform magnetic field. Bounded trajectories exist and span a wide range of velocity directions near the nucleus (compared to free trajectories with similar energies) when the electron Larmor radius is smaller than the distance at which the electron-nucleus Coulomb interaction energy is equal to the mechanical energy of an electron. The required conditions occur in magnetic white dwarf photospheres and have been achieved in experiments on production of antihydrogen. Under these conditions, the radiant power per unit volume emitted by positive-energy bound electrons is much higher than the analogous characteristic of bremsstrahlung (in particular, in thermal equilibrium) at frequencies that are below the electron cyclotron frequency but higher than the inverse transit time through the interaction region in a close collision in the absence of a magnetic field. The quantum energy discreteness of positive-energy bound states restricts the radiation from an ensemble of bound electrons (e.g., in thermal equilibrium) to nonoverlapping spectral lines, while continuum radiative transfer is dominated by linearly polarized bremsstrahlung.