Correlations in a Confined gas of Harmonically Interacting   Spin-Polarized Fermions
  For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220 and filling the Fermi level completely. 
F. Brosens, J. T. Devreese, L. F. Lemmens