Asymptotic-bound-state model for Feshbach resonances

Abstract

We present an asymptotic-bound-state model which can be used to accurately describe all Feshbach resonance positions and widths in a two-body system. With this model we determine the coupled bound states of a particular two-body system. The model is based on analytic properties of the two-body Hamiltonian and on asymptotic properties of uncoupled bound states in the interaction potentials. In its most simple version, the only necessary parameters are the least bound state energies and actual potentials are not used. The complexity of the model can be stepwise increased by introducing threshold effects, multiple vibrational levels, and additional potential parameters. The model is extensively tested on the $^{6}\mathrm{Li}$-$^{40}\mathrm{K}$ system and additional calculations on the $^{40}\mathrm{K}$-$^{87}\mathrm{Rb}$ system are presented.