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

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. (c) 2005 Elsevier B.V. All rights reserved.