Effective theory for two fermions in a trap

Systems with large scattering length $a_2$ are of particular interest since they exhibit universal properties when particle momenta are small compared to $1/r_0$ with r0 being the range of the interaction. This situation occurs for instance, in nuclear physics where the two-nucleon system has two S-wave channels where $a_2 >>r_0$. We have applied the general principles of Effective Field Theory for the description of two fermions in a harmonic oscillator trap. Our formalism is based on a controlled expansion of the interaction between the two fermions as a series of contact interactions with an increasing number of derivatives. Corrections to the interaction beyond leading order are treated in perturbation theory. Results for the energies of the two-fermion system for different values of $a_2/b$ ($b$ being the trap length) and $r_0/b$ will presented.