  The physics of a two-component cold fermi gas is now frequently addressed in
laboratories. Usually this is done for large samples of tens to hundreds of
thousands of particles. However, it is now possible to produce few-body systems
(1-100 particles) in very tight traps where the shell structure of the external
potential becomes important. A system of two-species fermionic cold atoms with
an attractive zero-range interaction is analogous to a simple model of nucleus
in which neutrons and protons interact only through a residual pairing
interaction. In this article, we discuss how the problem of a two-component
atomic fermi gas in a tight external trap can be mapped to the nuclear shell
model so that readily available many-body techniques in nuclear physics, such
as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the
study of these systems. We demonstrate an application of the SMMC method by
estimating the pairing correlations in a small two-component Fermi system with
moderate-to-strong short-range two-body interactions in a three-dimensional
harmonic external trapping potential.
