The Density Matrix Theory for Polarized Radiation Redistribution

Abstract

The density matrix theory is a powerful tool to investigate non-equilibrium phenomena connected with atomic and radiation polarization, particularly in the presence of a magnetic field. In this formalism, the atom-radiation interaction is described through the two basic sets of coupled equations: the statistical equilibrium equations for the density matrix elements, and the radiative transfer equations for the Stokes parameters. These are the basic equations of the NLTE problem. In Bommier (1997a, 1997b), radiation redistribution has been introduced in the formalism through a new formulation of this problem: Rayleigh scattering is taken into account by an additional term in the emissivity coefficient of the transfer equation, which could be applied to new iterative numerical schemes for PRD codes. Alternatively, Landi Degl’Innocenti et al. (1997) take advantage of the metalevels concept to introduce coherent scattering in the formalism, leading thus to possible multilevel applications. The present work has been devoted to investigate the extension of the work of Bommier (1997a, 1997b) on PRD to multilevel atoms: this requires considering Raman scattering, which can be done in the same way as for Rayleigh scattering, i. e., by introducing additional terms in the emissivity coefficient of the transfer equation. Transition from the atomic rest frame to the laboratory frame has also been investigated, and atomic velocity effects have been introduced, leading thus to velocitydependent density matrix elements in the laboratory frame. With these last extensions, the two basic sets of equations of the NLTE problem can now handle complicated problems involving PRD effects, multilevel atoms, polarization and magnetic field.