Multipole rates for atomic polarization studies: the case of complex atoms in non-spherically symmetric states colliding with atomic hydrogen

¹ Laboratoire d'Étude du Rayonnement et de la Matière en Astrophysique (LERMA), UMR CNRS 8112, Observatoire de Paris-Meudon, 92195 Meudon, France e-mail: sylvie.sahal-brechot@obspm.fr
² Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain
³ Department of Astronomy and Space Physics, Uppsala University, Box 515, 75120 Uppsala, Sweden

Received: 27 October 2006
Accepted: 22 December 2006

Abstract

Context.Interpretation of linearly polarized parameters of the lines of complex atoms for the second solar spectrum needs a lot of collisional coefficients which are often poorly known.

Aims.We provide general and simple formulae giving the coefficients of the atomic master equation (depolarization, polarization transfer, population transfer, and relaxation coefficients) for the case of any atomic level (but not a spherically symmetric) that is perturbed by collisions with hydrogen atoms.

Methods.We use the theory of the density matrix and the theory of atomic collisions with a few assumptions (frozen core and spin neglected during the collision). We only study collisional transitions between levels of the same configuration with no equivalent electrons in the external shell, and with the rest of the configuration (the core) frozen. We use the basis of the  irreducible spherical tensor operators.

Results.The formulae giving the depolarization and polarization transfer coefficients due to collisions with neutral hydrogen for  levels of complex atoms can be expressed as a linear combination of the k-pole depolarization and elastic collisional rate coefficients obtained for simple atoms.

Conclusions.It should be possible to apply this method for fast calculation of multipole rates for any level having an external shell .