Trapping effects on short-range two-body interactions

Abstract

In contrast to conventional ideal Bose and Fermi degenerate gases, atoms in experimental ultracold gases interact among themselves and are trapped by an external potential. In this work, we consider two particles of mass $m$ trapped by a $3D$ harmonic potential of frequency $\omega$, and interacting through an isotropic short range potential of intensity $V_0$ and range $b/2 $, with $b/2 \ll \sqrt{\hbar/m\omega}$. Eigenfunctions and eigenenergies are obtained and compared with those resulting (a) from an effective contact interaction and (b) in the absence of the trapping potential. Concepts like zero-resonance and binding energy, usually introduced for problems that allow a continuum spectra, are discussed for trapped particles.