The presence of shape resonances due to tunneling through the centrifugal barrier modifies strongly the dynamics of cold atom scattering. As shown on the example of the ground and lowest triplet electronic states of the ${}^{85}\mathrm{Rb}$${}^{133}\mathrm{Cs}$ molecule, the crucial parameter is, as usual for cold collisions, the scattering length. A general description of shape resonances of diatomic molecules is given from three simple single channel asymptotic models, whose respective performances are discussed. The first model, which consists of a $R^{-6}$ potential limited at short range by a repulsive wall, positioned to reproduce the $s$-wave scattering length, accounts satisfactorily for the main system-independent properties of shape resonances. Introduction in the model of energy- and angular-momentum-dependent nodal lines specific to the inner part of the potential greatly improves its efficiency. When the energy and angular momentum dependence of the nodal lines cannot be deduced from full potential calculations or from experiment, a rough, but universal, estimate of these properties is obtained by extending the $R^{-6}$ behavior of the potential up to the origin.

• Received 28 April 2010

DOI:https://doi.org/10.1103/PhysRevA.82.012510