Short-Range Correlations and Electron-Gas Response Functions

The behavior of interacting electrons is dominated by the Coulomb repulsion in the limit of zero interparticle separation. Hence, in this limit the derivative of the two-particle correlation function is equal to the two-particle correlation function itself divided by the Bohr radius. Because correlation functions can be obtained from linear-response functions, the relation between the correlation function and its derivative can be used as a criterion for the validity of approximate linear-response functions. Some of the more familiar dielectric functions and spin susceptibilities are discussed in this context. For these response functions it is shown that the electric and magnetic response should approach the same ($q\to \infty$) asymptotic limit.