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.