On inelastic hydrogen atom collisions in stellar atmospheres
  The influence of inelastic hydrogen atom collisions on non-LTE spectral line formation has been, and remains to be, a significant source of uncertainty for stellar abundance analyses, due to the difficulty in obtaining accurate data for low-energy atomic collisions either experimentally or theoretically. For lack of a better alternative, the classical "Drawin formula" is often used. Over recent decades, our understanding of these collisions has improved markedly, predominantly through a number of detailed quantum mechanical calculations. In this paper, the Drawin formula is compared with the quantum mechanical calculations both in terms of the underlying physics and the resulting rate coefficients. It is shown that the Drawin formula does not contain the essential physics behind direct excitation by H atom collisions, the important physical mechanism being quantum mechanical in character. Quantitatively, the Drawin formula compares poorly with the results of the available quantum mechanical calculations, usually significantly overestimating the collision rates by amounts that vary markedly between transitions. 
P. S. Barklem, A. K. Belyaev, M. Guitou, N. Feautrier, F. X. Gadea, A.   Spielfiedel
astro-ph.SR