The v = 0 → 1 vibrational cross-section for e-H₂scattering: An unresolved problem with wide implications

Controversy has surrounded the determination of the v≤ 0 1 vibrational cross-section for e-H₂ scattering for some thirty years: differences exist between values measured in crossed-beam experiments, which agree well with ab-initio quantum mechanical values, and cross sections derived from swarm experiments. These differences are far larger than the estimated errors associated with all three determinations, which will all remain under something of a cloud until the discrepancy is resolved. Following the suggestion of Buckman et al. [1], research on this problem has recently refocused on the transport theory used to determine cross sections from swarm data. This paper will review the results and implications of this recent research and will present new results on the validity of conventional semi-classical transport theory. We consider approximations used in contemporary solutions of the semi-classical Boltzmann equation including steady-state hydrodynamic assumptions. In addition, we address the validity of the semi-classical Boltzmann equation itself with particular reference to conservation of angular momentum and to the importance of taking into account the essentially fermionic nature of electrons in transport theory.