Master equation theory applied to the redistribution of polarized radiation, in the weak radiation field limit - II. Arbitrary magnetic field case

This paper addresses the problem of partial redistribution of polarized radiation in the presence of a magnetic field of arbitrary strength. It is the continuation of a previous paper (Paper I) devoted to the same problem, treated in the simpler case of vanishing magnetic field. In the present paper, we give the results of the derivation of the master equation for the atomic density matrix, and of the coefficients of the radiative transfer equation, following the method described in Paper I (which makes use of the summation of the perturbation series development for the atom-radiation interaction), now applied to the case of a non-zero magnetic field of arbitrary strength. The other hypotheses underlying the derivation of Paper I are maintained in the present paper, namely: (a) weak radiation field (stimulated emission is neglected with respect to spontaneous emission); (b) 2-level atom; (c) unpolarized lower level. The redistribution matrix, that relates the frequency, polarization and direction of the incident photon to those of the scattered photon, is derived in the presence of a magnetic field of arbitrary strength. 3 successive levels of approximation are proposed, in the case of a weak magnetic field, in order to derive simpler expressions for the redistribution matrix that might conveniently be used in radiative transfer calculations.