Effective theory approach to few-fermion systems in a trap

The properties of strongly interacting Fermi gases have been the object of great interest in recent years. When the scattering length $a_2$ is much larger than the effective range of the interaction $r_0$, few-atom systems serve as a testing ground for techniques developed for the ab-initio solution of few-nucleon systems. We have applied the principles of Effective Field Theory to describe few-fermions systems in a harmonic trap. The interaction is written as a controllable expansion of contact interactions with derivatives. The no-core shell model is used to solve the many-body Schr\"odinger equation at leading order and corrections beyond LO are treated in perturbation theory. We have also adressed the relationship between the two-body and many-body cutoffs needed for a consistent model space. Results for the energies of the 3-fermions system at unitarity will be presented and shown to agree with known results. Results for systems with 3, 4 fermions for different values of $a_{2}/b$ (b being the trap length) and $r_{0}/b$ will also be presented.