Static properties of a uniform electron gas: A phenomenological approach

The model formula of Rajagopal, Kimball, and Banerjee [Phys. Rev. B 18, 2339 (1978)] for the pair correlation function has been combined with the known properties of the static structure factor at low momentum in order to perform an analytic parametrization of the static properties of uniform electron gas. One-parameter analytic formulas for the pair correlation function and the static structure factor which satisfy all known constraints in the short- and long-wavelength limits are thus obtained. The value of the free parameter having been fixed by comparison with the Ceperley-Alder Monte Carlo data for the correlation energy, numerical results are presented for $r_s$≤10. By comparing our results with the original formula of Rajagopal et al., it is seen that the unphysical behavior of S(q) at low momentum is effectively corrected; in addition the present g(r) compares quite well with the values obtained from hypernetted-chain theory. Extension of the present formulation to a polarized phase and its applicability to band-structure calculations in the local-density approximation are also examined.