Fermi pseudopotential approximation: Two particles under external confinement

In this paper we calculate the energy levels of two trapped atoms interacting through a spherical two-body potential $V(r)$ under external confinement quantum mechanically. We then replace $V(r)$ by either a regularized energy-independent or an energy-dependent {δ}-function potential. A comparison shows that the use of an energy-dependent pseudopotential improves significantly upon the use of an energy-independent pseudopotential. The accuracy of the pseudopotential approximation is approximately determined by the ratio β₆/aₕₒ, where β₆ and aₕₒ denote the characteristic length scale of the two-body interaction potential $V(r)$ and of the trapping potential, respectively.