Abstract 
1.Context. Radiative transfer calculations in strong (few x10^{12} G) magnetic fields, observed in Xray pulsars, require accurate resonant differential scattering cross sections. Such cross sections exist, but they are quite cumbersome. Aims. Here we compare the classical (nonrelativistic) with the quantummechanical (relativistic) resonant differential scattering cross sections and offer a prescription for the use of the much simpler classical expressions with impressively accurate results.
Methods. We have expanded the quantummechanical differential cross sections and kept terms up to first order in ∊ ≡ E/m_{e}c^{2} and B ≡ B/B_{cr}, where E is the photon energy and B_{cr} is the critical magnetic field, and recovered the classical differential cross sections plus terms that are due to spin flip, which is a pure quantummechanical phenomenon. Results. Adding by hand the spinflip terms to the polarizationdependent classical differential cross sections, we find that they are in excellent agreement with the quantum mechanical ones for all energies near resonance and all angles. We have plotted both of them and the agreement is impressive.
Conclusions. We give a prescription for the use of the classical differential cross sections that guarrantees very accurate results.
2. Context. Accretion onto magnetic neutron stars results in Xray spectra that often exhibit a cyclotron resonance scattering feature (CRSF) and, sometimes, higher harmonics of it. Two places are suspect for the formation of a CRSF: the surface of the neutron star and the radiative shock in the accretion column.
Aims. Here we explore the first possibility: reflection at the neutronstar surface of the continuum produced at the radiative shock. It has been proposed that, for highluminosity sources, as the luminosity increases, the height of the radiative shock increases, thus a larger polar area is illuminated, and as a consequence the energy of the CRSF decreases, because the dipole magnetic field decreases by a factor of two from the pole to the equator. This model has been proposed specifically to explain the observed anticorrelation of the cyclotron line energy and luminosity of the highluminosity source V 0332+53.
Methods. We use a Monte Carlo code to compute the reflected spectrum from the atmosphere of a magnetic neutron star, when the incident spectrum is a powerlaw one. We restrict ourselves to cyclotron energies ≪ m_{e}c^{2} and use polarizationdependent scattering cross sections, allowing for polarization mode change.
Results. As expected, a prominent CRSF is produced in the reflected spectra, if the incident photons are in a pencil beam, which hits the neutronstar surface at a point with a welldefined magnetic field strength. However, the incident beam from the radiative shock has a finite width and thus various magnetic field strengths are sampled. As a result of overlap, the reflected spectra have a CRSF, which is close to that produced at the magnetic pole, independent of the height of the radiative shock.
Conclusions. Reflection at the surface of a magnetic neutron star cannot explain the observed decrease of the CRSF energy with luminosity in the highluminosity Xray pulsar V 0332+53. In addition, it produces absorption lines much shallower than the observed ones.
