  We study non--adiabatic transitions in scattering theory for the time
dependent molecular Schroedinger equation in the Born--Oppenheimer limit. We
assume the electron Hamiltonian has finitely many levels and consider the
propagation of coherent states with high enough total energy. When two of the
electronic levels are isolated from the rest of the electron Hamiltonian's
spectrum and display an avoided crossing, we compute the component of the
nuclear wave function associated with the non--adiabatic transition that is
generated by propagation through the avoided crossing. This component is shown
to be exponentially small in the square of the Born--Oppenheimer parameter, due
to the Landau-Zener mechanism. It propagates asymptotically as a free Gaussian
in the nuclear variables, and its momentum is shifted. The total transition
probability for this transition and the momentum shift are both larger than
what one would expect from a naive approximation and energy conservation.
