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Astron. Astrophys. 334, 1136-1144 (1998)

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1. Introduction

Particles are accelerated in solar flares in a wide range of energies. Electrons are detected through the radio, X-ray and [FORMULA] -ray emission, or through the enhancement of the visible and UV emission continua produced by their interaction with the solar atmosphere (Vogt & Hénoux 1996). High energy protons produce detectable [FORMULA] -ray emission by bombarding the solar atmosphere. They are also detected in the interplanetary space. But low energy protons are more difficult to detect.

One possible diagnostic is the interpretation of the line profiles. The observed lines are very large and show an enhancement of the red wing (Fang et al. 1995), interpreted as due to the Doppler shifted emission of the neutral H atoms formed by charge exchange. In the line centre, the profile may be broadened by a macroscopic Doppler effect due to the H atom recoil motion after excitation. As shown in the following, this recoil motion may be of the same order of magnitude or larger than the thermal isotropic velocity distribution. The velocity direction of such excited atoms is perpendicular to the velocity of the outgoing protons, the Doppler broadening is thus directly related to the differential excitation cross section.

Another method is the observation of impact linear polarization of atomic lines (Henoux et al. 1990). Excitation of a set of atoms (or ions) by non isotropic collisions leaves it in an anisotropic state. Light emitted in the subsequent decay manifests this anisotropy through its polarization (Percival & Seaton 1958, Dyakonov 1965, Fano & Macek 1973, Blum 1981). Much attention has been paid to this mechanism, both for excitation by electron beams (Percival & Seaton 1958, Fano & Macek 1973, Blum 1981) or by ionic beams (Carré et al. 1977, Petrashen et al. 1984) in relation with laboratory measurements. Recent observations of solar chromospheric flares (Henoux et al. 1990, Henoux 1991) show linearly polarized H [FORMULA] emission. The observed polarization degree can be as high as [FORMULA] for a flare located near the limb and one minute integration time. This polarization can be interpreted as anisotropic collisional excitation of the [FORMULA] level of the H atom by vertical protons beams with initial energies at the coronal level of a few hundred keV, and thus energies of a few keV in the chromosphere.

For a quantitative interpretation of the observed polarization, one needs accurate values of all the collisional and radiative processes for populating and depopulating the Zeeman sublevels of the H atom (Vogt et al. 1997). The radiative contribution due to absorption of the local Ly [FORMULA], Ly [FORMULA] and H [FORMULA] radiation may be easily calculated when the radiation field is known, and thus depends on the model of atmosphere. Two collisional processes are present: firstly excitation from the [FORMULA] level by the beam particles, and secondly collisional transfer of populations and alignment between Zeeman sublevels of the same n level due to local electrons and protons. The latter process has been correctly evaluated in the semiclassical perturbation approximation (Sahal-Brechot et al. 1996), but this approximation is no longer valid for excitation by the beam protons, since strong molecular short range interactions are dominant. Furthermore, charge exchange significantly contributes to the excitation for the considered collisional energies and thus must be taken into account. It should be emphasized that excitation by the directive proton beam is the only process giving rise to polarization of the emitted line whereas the other processes all contribute to its depolarization.

To date, only crude values of the excitation cross sections have been used (Vogt et al. 1997). Calculated in a perturbative approach, these cross sections cannot accurately take into account the really important molecular processes occuring in the 0 to 50 keV energy range. Therefore, better cross sections are actually needed. Recently much experimental or theoretical work has been devoted to this problem and new accurate data have become available. However, the partial cross sections for excitation of each magnetic sublevel as well as the differential cross sections, still unknown, are needed to solve the rate equations and to determinate the macroscopic Doppler broadening. In the present work, we have used the most accurate methods, valid in the considered energy range (1-100 keV), to calculate all the relevant integrated and differential cross sections for direct excitation and capture as well as the polarization of the subsequently emitted lines. Sect. 2 briefly outlines the theoretical methods. The results are presented in Sect. 3 and compared to the measurements when available. Astrophysical consequences are discussed in Sect. 4.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998