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/a_ho, where β₆ and a_ho denote the characteristic length scale of the two-body interaction potential V(r) and of the trapping potential, respectively.