Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k,r(s)), with the momenta k measured in units of the Fermi wave number k(F) and with the density parameter r(s), is constructed with the help of the convex Kulik function G(x). It is assumed that n(0,r(s)),n(1(+/-),r(s)), the on-top pair density g(0,r(s)), and the kinetic energy t(r(s)) are known (respectively, from accurate calculations for r(s)=1,...,5, from the solution of the Overhauser model, and from quantum Monte Carlo calculations via the virial theorem). Information from the high- and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k,r(s)), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculations of Takada and Yasuhara [Phys. Rev. B 44, 7879 (1991)], is compatible with quantum Monte Carlo data, and is valid in the density range r(s)less than or similar to12. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.