Multi-order TODCOR: Application to observations taken with the CORALIE echelle spectrograph - I. The system HD 41004

The present paper extends the method of Anstee, Barklem and OʹMara (Anstee 1992; Anstee & OʹMara 1991, 1995; Anstee et al. 1997; Barklem 1998; Barklem & OʹMara 1997; Barklem et al. 1998), developed during the 1990s for collisional line broadening by atomic hydrogen, to the depolarization of spectral lines of neutral atoms by collisions with atomic hydrogen. In the present paper, we will limit the calculations to p ( l=1) atomic levels. The depolarization cross sections and depolarization rates are computed. In Table [see full text] cross sections as functions of the relative velocity and effective quantum number are given, allowing for the computation for any p atomic level. Our results are compared to quantum chemistry calculations where possible. The sensitivity of depolarization cross sections to regions of the potential is examined. We conclude that the accuracy obtained with our method ( <20% for the depolarization rates) is promising for its extension to higher l-values for the interpretation of the "second solar spectrum". This will be the object of further papers.