Excited-state survival probabilities for cold collisions in a weak laser field

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Abstract
We show that in the cold collisions between laser-cooled and trapped atoms the probability to survive in the excited state during the collision can be obtained, in the weak-field limit, from a simple Landau-Zener approach. This is shown by comparing the method with a fully quantum and time-dependent wave-packet treatment. We also show that the optical Bloch equation method is not the proper semiclassical tool to use at low energies, at least in its present form. The unexpectedly low quantum survival probability reported by Boesten et al. [Phys. Rev. A 48, 1428 (1993)] is in fact predicted by the semiclassical Landau-Zener approach. This in turn shows that off-resonant excitation is not important in the low-energy regime.