Quantum effects in cyclotron plasma absorption

It is shown that X-ray radiation of neutron stars with magnetic fields B=10¹¹-10¹³ G near cyclotron resonances ω=sω_B(s=1,2,...) is deeply affected by such quantum effects as electron-positron vacuum polarization (significant at V=3×10²⁸n_e^-1(B/B_C⁴)≳1, where B_C=4.4×10¹³G), the quantizing character of the magnetic field (significant at V=3 x 10²⁸n_e^-1(B/B_c)⁴≳1 where B_c=4.4 x 10¹³G), the non-harmonic character of the Landau levels, and the quantum recoil of electrons. The latter two factors shift the resonances by the frequency -s²ω_B(B/2 B_c)sin²θ{symbol}, θ{symbol} being the angle between the direction of radiation propagation and the magnetic field. If V≪V₀ (for θ{symbol}∼1, V₀∼β^-1=(mc²/2 T)^1/2), the normal mode (NM) polarizations, as well as the absorption coefficient k₁ of the extraordinary NM in the Doppler core of the first resonance (|ω-ω| ≲ω_Bβ cos θ{symbol}), is only slightly affected by varying b and/or V, whereas for the ordinary NM (at θ{symbol}∼1)k₂∼k₁β²[b + (3 + tan²θ{symbol}-2 V)²]≪k₁. For sufficiently large b and/or V the quantum effects amplify resonant absorption of the ordinary NM at ω∼ω_B, with spin-flip transitions playing a major role at b≳1+V². If V∼V₀, the coefficients k₁ and k₂ in the Doppler core of the resonance are of the same order and acquire some peculiar features (shifts, intersections, etc.), with the NM polarizations depending sharply on ω and being strongly non-orthogonal. At V≫V₀, k₂=k₁(cos² θ{symbol}+B/2 B_C) and the polarizations are almost linear. Near high resonances (s≥2), as a rule, k_1,2α(1 + b)^s-1β^{2 s-3} i.e., absorption increases with b due to replacement of the thermal energy of the transverse motion of electron, T, by the magnetic energy h{combining short stroke overlay}ω_B. The above effects should be taken into account for an interpretation of observational data on X-ray pulsars (e.g., Her X-1) and other X-ray sources associated with neutron stars.