1302.4301 (J. Rotureau)

Effective interaction for the trapped fermi gas with a unitary
transformation of the exact two-body spectrum    [PDF]

J. Rotureau

We study systems of few two-component fermions interacting in a Harmonic Oscillator trap. The fermion-fermion interaction is generated in a finite basis with a unitary transformation of the exact two-body spectrum given by the Busch formula. The few-body Schr\"odinger equation is solved with the formalism of the No-Core Shell Model. We present results for a system of three fermions interacting at unitarity as well as for finite values of the S-wave scattering length $a_2$ and effective range $r_2$. We also present results for the four- and five-fermion systems at unitarity. In all cases, we observe a fast convergence of the many-body energies with respect to the size of the basis in which the effective two-fermion interaction is defined. The many-body energies are in excellent agreement with exact solutions for the three-body problem, and results obtained by other methods in the other cases.

View original: http://arxiv.org/abs/1302.4301