Accurate quantum calculations have been carried out at ultralow energies (from 10(-2) to 10(-6) cm(-1)) for the vibrational deexcitation of Li-2((1)Sigma(+)(g)) by collisions with He, starting from a broad range of initial highly excited vibrational levels. The results indicate the clear dominance of a few transitions with the smallest Delta nu changes and show the overall deexcitation cross sections to markedly depend on the initial vibrational state of the molecule, in line with earlier results on H-2+He [Balakrishan Phys. Rev. Lett. 80, 3224 (1998)] vibrational quenching. A connection is made with very recent measurements on the vibrational quenching of ultracold Cs-2 molecules in optical traps that were instead found to behave in a very different manner. Numerical experiments on the present system as well as on the H-3 reaction strongly suggest a possible explanation for such differences.
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