The partial redistribution in the atomic density matrix formalism

The basic equations describing the atom-radiation interaction, statistical equilibrium and transfer equations, have been derived from the Schroedinger equation, in the density matrix formalism, by Bommier (1997a, 1997b). The partial redistribution effect has been taken into account by summing the development in series of perturbations of the interaction. Magnetic field and polarization effects have been taken into account. As a result, the partial redistribution appears as, only, an additional term in the emissivity coefficient. In these papers, these equations are expressed in the atomic reference frame. Transition to the laboratory reference frame has been performed in Bommier (1999), in the very general case. In the present paper, it is shown that, besides the very general equations that exist and/or can be written, for the multilevel approach, a few simplifying assumptions, as infinitely sharp unpolarized lower level, lead to more tractable expressions that are provided. These equations are compared to the ones used by Hubeny and Lites (1995) for studying the hydrogen lines formation with PRD. Finally, 2-level atom is considered, which permits to solve the two coupled systems of equations into an integral equation taking into account polarization, magnetic field and partial redistribution.