Analytic Elastic Cross Sections for Electron-Atom Scattering from Generalized Fano Profiles of Overlapping Low-Energy Shape Resonances

Abstract

The variation with energy of the total cross section for elastic electron scattering from atoms of several elements is caused primarily by shape resonances corresponding to the formation of temporary negative ions. It is shown that such cross sections are expressible analytically in terms of a constant background added to a "generalized Fano profile" [Durand Ph, et al (2001) J. Phys. B: At. Mol. Opt. Phys. 34, 1953, ibid (2002) 35, 469]. In three cases (sodium, magnesium and mercury), a detailed consideration proves that this representation is accurate in a fairly wide energy range. Moreover, the related momentum transfer cross sections are tailor-made for studying "elastic" electron transport in terms of the two-term solution of the Boltzmann equation: Not only are the resulting swarm transport coefficients adjustable to the experimental values, but above all they are calculable very easily because the unnormalized energy distribution is obtainable analytically. The ample saving in computational effort is exploited in order to test the Wannier-Robson "momentum-transfer approximation"; it is found that, in these cases of resonance-dominated cross sections, the latter method can be so accurate that it can be used to recover the momentum transfer cross section from experimental data algebraically. In the margin, a model profile is presented that gives rise to negative differential conductivity.