  We investigate the effects of many-body correlations on the ground-state
properties of a single component ultra-cold Rydberg-dressed Fermi liquid with
purely repulsive inter-particle interactions, in both three and two spatial
dimensions. We have employed the Fermi-hypernetted-chain Euler-Lagrange
approximation and observed that the contribution of the correlation energy on
the ground-state energy becomes significant at intermediate values of the
soft-core radius and large coupling strengths. For small and large soft-core
radii, the correlation energy is negligible and the ground-state energy
approaches the Hartree-Fock value. The positions of the main peaks in static
structure factor and pair distribution function in the homogeneous fluid phase
signal the formation of quantum droplet crystals with several particles
confined inside each droplet.
