  Based on its known exact properties and a new set of extensive fixed-node
reptation quantum Monte Carlo simulations (both with and without backflow
correlations, which in this case turn out to yield negligible improvements), we
propose a new analytical representation of (i) the spin-summed
pair-distribution function and (ii) the spin-resolved potential energy of the
ideal two-dimensional interacting electron gas for a wide range of electron
densities and spin polarization, plus (iii) the spin-resolved pair-distribution
function of the unpolarized gas. These formulae provide an accurate reference
for quantities previously not available in analytic form, and may be relevant
to semiconductor heterostructures, metal-insulator transitions and quantum dots
both directly, in terms of phase diagram and spin susceptibility, and
indirectly, as key ingredients for the construction of new two-dimensional spin
density functionals, beyond the local approximation.
