Eur. Phys. J. D (2013) 67: 153
https://doi.org/10.1140/epjd/e2013-40156-8

Regular Article

Interaction for the trapped fermi gas from a unitary transformation of the exact two-body spectrum

Fundamental Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden

^a e-mail: rotureau@chalmers.se

Received: 20 March 2013
Received in final form: 2 May 2013
Published online: 24 July 2013

Abstract

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 Schrödinger 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 a₂ and effective range r₂. Unitary systems with four and five fermions are also considered. We show that the many-body energies obtained in this approach are in excellent agreement with exact solutions for the three-body problem, and results obtained by other methods in the other cases.