  Background: Idealised systems are commonly used in nuclear physics and
condensed matter. For instance, the construction of nuclear energy density
functionals involves properties of infinite matter, while neutron drops are
used to test nuclear interactions and approximations to the nuclear many-body
problem. In condensed matter, quantum rings are also used to study properties
of electron systems. Purpose: To investigate the possibility to use quantum
rings with systems of nucleons including many-body correlations. Methods: A
quantum ring model of a finite number of same spin fermions is developed.
Several attractive and repulsive interactions with finite and infinite ranges
are considered. Quantum Monte Carlo calculations are used to provide exact
ground-state energies. Comparisons with analytical Hartree-Fock solutions are
used to get an insight into the role of correlations. Results: Hartree-Fock
results with no breaking of space translational symmetry are able to describe
many systems. However, additional spatial correlations are required in the case
of dense systems with a strong short-range repulsion, or with attractive
interactions in large rings. Conclusions: Self-bound systems of fermions with
spatial correlations produced by basic features of the nuclear interactions can
be described on a quantum ring, encouraging applications with realistic
interactions, as well as investigations with higher dimensional geometries such
as spherium.
