No-Core Shell Model Approach for Fermions in Harmonic Traps

The physics of strongly interacting Fermi gases has been the object of great interest in recent years. Systems with large two-body scattering length are of particular interest (when the particle momenta are small compared to the inverse of the range of the two-body interaction) because these systems exhibit universal behavior. While large two-body scattering length systems have become popular in atomic physics only in the last decade, in nuclear physics they have been investigated since its beginning. Hence, it is not surprising that techniques developed for solving the nuclear few-body problem are immediately applicable to such systems in atomic physics. In this talk, I will present an effective-field theory approach to constructing the two-body interaction in finite model spaces for identical fermions in harmonic traps, which can be realized experimentally in three-dimensional optical latices. This will allow an extensive study in the no-core shell model framework of the properties of three- and four-body system in the unitary limit and away from it. Finally, I will argue that such systems are relevant for the ab initio description of nuclei.