The three-dimensional electron gas at the weak-correlation limit: how peculiarities of the momentum distribution and the static structure factor give rise to logarithmic non-analyticities in the kinetic and potential correlation energies

Abstract

Partial summations of the ring diagrams for the momentum distribution n ( k ) and the static structure factor S ( q ) of the uniform three-dimensional electron gas at the weak-correlation limit are revisited. New light is shed on the thus-far overlooked properties of n ( k ) and S ( q ) . In particular, it is elucidated how the peculiar behavior of n ( k ) near the Fermi surface and of S ( q ) near its q-space origin give rise to the logarithmic divergences in the kinetic and potential energies, respectively. Moreover, the trajectory of the inflexion point of S ( q ) and the jump discontinuity of S ″ ( q ) at q = 2 are analyzed.