Short-time behavior of electron thermalization in gases

A simple power series expansion in time is shown to complement nicely the eigenfunction expansion in electron thermalization problems. With the hot-electron zero-field mobility as an example, a recursion relation is derived to facilitate the calculation of higher-order short-time expansion coefficients. The electron–atom momentum transfer cross section is modeled by a velocity polynomial. Numerical results for the mobility in helium are discussed to see the usefulness of the present expansion.