  This paper is a continuation of a previous work about the study of the
survival probability modelizing the molecular predissociation in the
Born-Oppenheimer framework. Here we consider the critical case where the
reference energy corresponds to the value of a crossing of two electronic
levels, one of these two levels being confining while the second dissociates.
We show that the survival probability associated to a certain initial state is
a sum of the usual time-dependent exponential contribution, and a reminder term
that is jointly polynomially small with respect to the time and the
semiclassical parameter. We also compute explicitly the main contribution of
the remainder.
