Effective Field Theory for Few Particles in a Trap

In this contribution we show applications of effective field theory (EFT) to few-particle systems trapped in a harmonic oscillator potential. The principles of EFT allows to construct interactions among the particles in a systematic and improvable manner. We first consider systems of two-component fermions and show excellent agreements with the exact solution at unitarity (for the two- and three-body problem) and results obtained by other methods (in the four-body case). We then consider trapped systems of three nucleons and extract neutron–deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data. We also show the collapse of the system in the J ^π  = 1/2⁺, T = 1/2 (triton) channel at Leading-Order when no three-nucleon force is included.