## 1. IntroductionOne can describe spicules as cylindrical structures appearing at
the boundaries of the supergranules of the solar atmosphere. Their
diameters are about 700 km, and the spicules mount in the corona
conducted by the magnetic field. One can observe matter up to a height
of km with a mean inclination of
relative to the normal to the solar surface.
This paper deals with the theory of the density matrix of photons
resonantly scattered by atoms having an ensemble velocity. The theory
of the multilevel atom scattering the incident photospheric radiation
is outlined by a quantum formalism (Bommier 1977 ; Bommier &
Sahal-Bréchot 1978 ). We apply the theory to neutral H atoms
in spicules. We illustrate our method by calculating the Stokes
parameters The method of calculation described hereafter is derived from the theoretical method that has been developed for a two-level atom by Sahal-Bréchot et al. (1998 ), as outlined in Sahal-Bréchot et al. (1992 ) and in Sahal-Bréchot & Choucq-Bruston (1994 ). The present paper is concerned by the adaptation of the method to the particular multi-level case of the H line of hydrogen. In Sects. 2and 2.1we define the photospheric profile of the H
line used for our theoretical model, and also
the density matrices of the incident and scattered radiation allowing
for correlations due to the Doppler effect. In Sect. 2.1and 7, we give
the equations of statistical equilibrium in tensorial notation. We
solve these equations and find an analytical approximation for the
tensors (Sects. 3, 3.1and 3.2). This enables us to calculate the
density matrix of the scattered photons opening the way to the
expression of the Stokes parameters © European Southern Observatory (ESO) 1998 Online publication: April 28, 1998 |