A MEAN-FIELD THEORY OF A LOCALIZED EXCESS ELECTRON IN A CLASSICAL FLUID

A mean-field, density-functional theory for a ground-state, localized excess electron in a classical solvent is presented. We obtain a Schro dinger equation for the electron's wave function, with a mean-field po tential dependent on the local density of the solvent, and an integral equation for the electron-solvent correlation function, with an effec tive (averaged over the electron density) electron-solvent interaction potential. We show that this effective interaction is weak and use th is feature to suggest closures of the integral equation characterizing the electron-solvent correlations. The coupled system of the Schrodin ger and integral equations are solved self-consistently, using an iter ative method. The results are in good agreement with path-integral and time-dependent self-consistent-field simulations of an excess electro n in supercritical helium. We show that these two simulation methods s hould agree when the electron is essentially always in its ground elec tronic state, as is the case for an electron in sufficiently dense hel ium.