We show that in the cold collisions between laser-cooled and trapped a
toms the probability to survive in the excited state during the collis
ion can be obtained, in the weak-field limit, from a simple Landau-Zen
er approach. This is shown by comparing the method with a fully quantu
m and time-dependent wave-packet treatment. We also show that the opti
cal Bloch equation method is not the proper semiclassical tool to use
at low energies, at least in its present form. The unexpectedly low qu
antum 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 impor
tant in the low-energy regime.