Quantum suppression of cold atom collisions

Very-low-energy collisions between two atoms are usually suppressed, in that the probability of close approach of the atoms becomes greatly reduced as the collision energy vanishes, even if the potential is completely attractive (with the exception of the Coulomb interaction). The suppression is a quantum effect, related to the Wigner threshold law. It is gauged by comparing the ratio of the probability of being inside the well to the probability of being outside for both the classical and quantum regimes. As the asymptotic kinetic energy vanishes, the approaching atoms reach a minimum distance of typically 20 or 30 a.u. Here we study attractive interaction potentials of the form -α/${\mathit{r}}^{\mathit{n}}$, and give some numerical results for accurate X${\mathrm{}}^1$ ${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ and a${\mathrm{}}^3$ ${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ states of ${\mathrm{Li}}_2$ and ${\mathrm{Na}}_2$ molecules. We show that in some circumstances it is possible to use Wentzel-Kramers-Brillouin theory in the suppression regime (where it fails) and to correct for its failure with a simple factor. © 1996 The American Physical Society.