2021/08/12 by Nick Loudas, N. A. Loudas, N. D. Kylafis +2
Earth and Planetary Sciences · Physics and Astronomy · #Astrophysical Phenomena and Observations #Atomic physics #High-pressure geophysics and materials #Magnetic field #Photon #Physics #Pulsars and Gravitational Waves Research #Quantum #Quantum electrodynamics #Quantum mechanics #Radiative transfer #Scattering #astro-ph.HE
paper · pdf · doi:10.1051/0004-6361/202039268
published as A&A 655, A38 (2021)
openalex publication_date 2021/08/12 · arxiv created 2021/08/17 · openalex created_date 2021/08/30 · arxiv updated 2021/11/10 · openalex updated_date 2026/08/05
Context. Radiative transfer calculations in strong (few ×10 12 G) magnetic fields, which are observed in X-ray pulsars, require accurate differential cross-sections of resonant scattering. While such cross-sections exist, their application is cumbersome. Aims. Here, we compare the classical (non-relativistic) with the quantum-mechanical (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 expanded the quantum-mechanical differential cross-sections and kept the terms up to the first order in ϵ ≡ E / m e c 2 and B ≡ ℬ/ℬ cr , where E is the photon energy and ℬ cr is the critical magnetic field. We recovered the classical differential cross-sections along with the terms that are due to spin flip, which is a pure quantum-mechanical phenomenon. Results. When adding the spin-flip terms to the polarization-dependent classical differential cross-sections by hand, we find that they are in excellent agreement with the quantum mechanical ones for all energies near resonance and all angles. We plotted both of them and the agreement is impressive. Conclusions. We give a prescription for the use of the classical differential cross-sections for radiative transfer calculations that guarantees accurate results.