Calculation of the mobility of electrons injected in liquid argon

A model calculation is carried out in which we evaluate the mobility of electrons injected in liquid argon. Scattering by both phonons and static density fluctuations is taken into account. The calculation for the mobility limited by phonon scattering differs from the usual calculation in crystals by considering both the local changes in the deformation potential and the changes of the amplitude of the phonons that are caused by the existence of density fluctuations. The calculation of the mobility limited by scattering from density fluctuations is carried out with the assumption that they give rise to a square-well (or barrier) potential that will scatter the electrons. The above perturbation Δ$V_0$ is related to a density fluctuation Δn by Δ$V_0$=$V_0$(n¯+Δn)-$V_0$(n¯). The scattering volumes Ω, where the density fluctuation Δn is located, are weighted by exp(-r/ξ) where ξ is the correlation length and r is the radius of Ω. The magnitude of the different density fluctuations is weighted by exp[-(Δn${)}^2$Ω/2nS(0)], where S(0)=${\mathrm{nk}}_B$ ${\mathrm{TK}}_T$, $K_T$ is the isothermal compressibility. The calculation of the mean free path is carried out using partial waves. Both scattering mechanisms, scattering by phonons and static density fluctuations, give comparable contributions to the mobility.