HYDRODYNAMIC MODEL OF AN INHOMOGENEOUS ELECTRON-GAS

We present a simple hydrodynamic model for the ground state of an inho mogeneous electron gas. The profile relation and response are obtained explicitly. In the case of a uniform reference system the profile rel ation reduces to that of the Sjolander-Stott theory. We confirm their results using the most recent numerical data. We compare numerical res ults for a heavy impurity problem in two dimensions with the correspon ding results in three dimensions. A density modulation is conjectured to develop in the region just around a negative impurity at sufficient ly low electron densities, as a signature of the Wigner transition.