Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

TL;DR

This paper derives explicit expressions for the density and pair correlation function of a confined fermion gas with harmonic interactions, using path integral methods, for systems with 1 to 220 particles at zero temperature.

Contribution

It provides a novel analytical approach to compute density and correlation functions in a confined fermion system with harmonic interactions, covering a range of particle numbers.

Findings

Explicit formulas for density and pair correlation functions.

Results valid for systems with 1 to 220 particles.

Ground state properties of confined fermions analyzed.

Abstract

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.