Polarization properties of resonance scattering in molecular bands

The intermediate (a-b) coupling regime

¹ Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy
² Universität-Sternwarte Göttingen, Geismarlandstr. 11, 37083 Göttingen, Germany e-mail: landie@arcetri.astro.it

Received: 22 October 2004
Accepted: 25 August 2006

Abstract

The polarimetric properties of the phenomenon of resonance scattering in molecular bands are analyzed in detail for the general case where both the lower and upper electronic states of the molecule are described in the coupling scheme intermediate between Hund's cases (a) and (b). A semi-analytical expression is derived for the line polarizability factor in the special case where atomic polarization is neglected in the lower electronic state, and particular attention is devoted to clarifying the role played by the phenomenon of Λ-doubling, which turns out to be particularly relevant in the case of  transitions. The expression for the line polarizability factor is derived for both cases where the energy eigenvectors are expressed as a linear combination of the eigenvectors relative to Hund's case (a) and of those relative to Hund's case (b). Such expressions are then combined with the corresponding expressions of the Einstein coefficient and of the Landé factors to obtain an estimate of the linear polarization signals to be expected in molecular bands observed at the solar limb either in the quiet atmosphere or in magnetic regions. Illustrative results are shown for the bands of MgH and of C₂ around 5100 Å.