Electron distribution and mobility in a dense gas of repulsive scatterers

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Abstract
This work attempts to put the theory of the dependence of electron mobility mu upon density N on a firmer mathematical basis for the relatively complex case of repulsive scatterers (negative energy shift). Starting from a model by the author (1980), the two characteristic energies in the electron distribution are derived in a reasonably mathematical way, replacing former physical arguments. On the way it is necessary to derive an Ioffe-Regel-like criterion for nonpropagating electron states, namely lambda > pi L (L is the mean free path). The derived energies in turn lead to a modified exponential formula. The result, in addition to being based on derived quantities, still predicts the mobility experiments well at both low and high N.