Some fundamental questions concerning the kinetic theory of electrons in molecular gases and the e-H₂ vibrational cross section controversy

We commence a fundamental re-examination of the kinetic theory of charged particle swarms in molecular gases, focusing on collisional excitation of molecular rotational and ro-vibrational states by electrons. Modern day analysis of electron swarms has been based upon the kinetic equation of Wang-Chang et al, which simply treats all processes as scalar energy excitations, and ignores angular momentum conservation and the vector dynamics associated with rotational excitation. It is pointed out that there is no alternative, more exact kinetic equation readily available for electrons which enables one to directly ascertain the degree of error introduced by this approximation. Thus in this preliminary study, we approach the problem indirectly, from the standpoint of the neutral molecules, using the Waldmann-Snider quantum kinetic equation, and insist that an electron-molecule collision must look the same from the perspective of both electron and molecule. We give a formula for quantitatively assessing the importance of scalar versus vectorial treatments of rotational excitation by looking at the post-collisional 'echo' produced by an electron swarm as it passes through the gas. It is then pointed out that in order to remedy any deficiency, it will be necessary to introduce a kinetic collisional operator non-local in space to properly account for angular momentum conservation, as has long been established in the literature. This is a major exercise and given the preliminary nature of this study, we consider the inclusion of such effects from a formal point of view only. In particular we show how non-local effects lead to a spatially dependent 'source' term in the equation of continuity, and hence to corrections for both drift velocity and diffusion coefficients. The magnitude of these corrections has yet to be established.