Quenching of curve crossing probabilities by quantum reflection

When potential energy curves for the relative motion of two atoms in different electronic states cross, the probability for diabatic or adiabatic passage can be described by the Landau-Zener formula. For near-threshold energies, close to the asymptotic value of one of the curves, the corresponding velocity is very small at large separations. Then quantum reflection, which can prevent the atoms from coming close to the avoided crossing, becomes a dominating effect. The probabilities for transmission to smaller separations - in either electronic state - thus vanish towards threshold, a feature not contained in conventional Landau-Zener theory. We propose a correction which takes the effect of quantum reflection into account so that the correspondingly modified Landau-Zener formula remains accurate at low energies, all the way down to threshold.