Behavior of the electron density near an impurity

The behavior of the electron density n(r) and potential energy V(r) near the origin, where an impurity of charge Z is located, is studied using the Lindhard dielectric theory of the free-electron gas. The leading odd terms in the power-series expansion of n(r) and V(r) are obtained. It is shown that the derivative n′(0) = ?2Zn₀/a₀, where n₀ is the free-electron gas density and a₀ is the Bohr radius.