Abstract. We derive the probability and attenuation coefficients for pair creation in first order of polarized electrons and positrons. The positron and electron can occupy arbitrary Landau levels and the attenuation coefficient is evaluated for any direction and polarization of the photon. When we take θ = 90• and sum over polarization of the spins of the e + − e − pair, we obtain results which differ from the expressions for the attenuation coefficient obtained by Daugherty & Harding (1983), by the factor (1 + δN,0)(1 + δ N ,0 )/4, in agreement with Frangodimitraki-Georgiadou (1991).

Abstract. We derive the cross-section for one-quantum annihilation of polarized electrons and positrons. The electron and positron can occupy arbitrary Landau levels and have non-zero momentum parallel to the field, and the cross-section is calculated for any polarization of the radiation. When we take zero parallel momentum for the electron and sum over photon polarization we obtain results which agree with the existing calculation of Wunner et al. (1986).

We perform the second-order calculation for an electron in a strong magnetic field which emits two photons during its transition between any Landau level and any lower Landau level. The calculation is valid for any value of magnetic field, and is of particular interest for processes in magnetars, which are pulsars in which the magnetic field is near, or exceeds, the critical value B cr ϭ4.414ϫ10 13 G. The dependence of the transition rate on the spin polarization of the electron along the external magnetic field and the linear or circular polarization of the emitted radiation is given explicitly. ͓S0556-2821͑99͒00419-1͔

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 isε (2) .

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