Derivation of the master equation for the atomic density matrix for line polarization studies in the presence of magnetic field and depolarizing collisions in astrophysics
Résumé
The authors derive in a coherent manner the master equation for the density matrix of an atom interacting with a bath of perturbers and photons, in the presence of a weak magnetic field. This paper has been inspired by astrophysical purposes: the interpretation of line polarization induced by anisotropic excitation of the levels, eventually modified by the local magnetic field (the Hanle effect); the polarization can be due to scattering of the incident anisotropic radiation, as in solar prominences, or to impact polarization, as in solar flares. The physical conditions are then those of numerous astrophysical media: any directions of polarization and magnetic field, two-level atom approximation not valid, weak radiation field, weak density of perturbers. The master equation for the atomic density matrix has been derived in the framework of the impact approximation.