  We study, through the diffusion Monte Carlo method, a spin one-half fermion
fluid, in the three dimensional Euclidean space, at zero temperature. The point
particles, immersed in a uniform "neutralizing" background, interact with a
pair-potential which can be continuously changed from zero to the Coulomb
potential depending on a parameter $\mu$. We determine the radial distribution
functions of the system for various values of density, $\mu$, and polarization.
We discuss about the importance, in a computer experiment, of the choice of
suitable estimators to measure a physical quantity. The radial distribution
function is determined through the usual histrogram estimator and through an
estimator determined via the use of the Hellmann and Feynman theorem. In a
diffusion Monte Carlo simulation the latter route introduces a new bias to the
measure of the radial distribution function due to the choice of the auxiliary
function. This bias is independent from the usual one due to the choice of the
trial wave function. A brief account of the results from this study were
presented in a recent communication [R. Fantoni, Solid State Communications,
{\bf 159}, 106 (2013)].
