Abstract We revisit the problem of radiative transitions of electrons in the presence of a strong magnetic field. We derive fully relativistic cyclotron transition rates for an arbitrary magnetic field, for any orientation of electron spin and for any polarization of the emitted radiation. Also, we obtain the transition rates for any value of the initial electron's parallel momentum. For very strong magnetic fields, transitions to the ground state predominate. Transition rates summed over the electron's spin orientation and for unpolarized radiation are also obtained, which confirm previous results by Latal. Transition widths are calculated for different electron spin orientations and different polarizations of radiation. We obtain general expressions for transition rates that reduce to the results for the non-relativistic case and for unpolarized radiation. Additionally we get, for the non-relativistic approximation, the transition rates for any polarization of radiation. As an application, the first five emission lines are evaluated and compared to the X-ray emitting neutron star V0332+53, which has multiple observable cyclotron lines, taking into account gravitational redshift. The most probable polarization is (2).

Keywords stars: neutron — radiation mechanisms: non-thermal — stars: magnetic fields — polarization

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