Polarizability tensor of a strongly magnetized plasma and the polarization vectors and opacities of normal electromagnetic waves are studied for the conditions typical for the atmospheres of radio and X-ray pulsars, taking into account vacuum polarization and partial ionization effects. Vacuum polarization at arbitrary magnetic field is described by simple fitting formulae. Detailed calculations are performed for a model of a partially ionized nonideal hydrogen plasma. In this case, the full account of the coupling of the quantum mechanical structure of the atoms to their center-of-mass motion across the magnetic field is shown to be crucial for the correct evaluation of the polarization properties and opacities of the plasma. The self-consistent treatment of the polarizability and absorption coefficients proves to be necessary if the ionization degree of the plasma is low, which can occur in the atmospheres of unusually cold or ultramagnetized neutron stars. For high degree of ionization, which is more typical, the polarizability of a fully ionized plasma remains a good approximation even in the photon frequency range where the absorption of radiation is mainly due to the bound-bound and bound-free atomic transitions.

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