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.
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