Does the Berry's phase [geometric phase] associated with the conical intersection [CI] have important observable consequences?There is a nice 2005 Perspective in Science by David Clary which discusses this for the specific case of the simplest possible chemical reaction H2 + H to H + H2. It seems that [contrary to what was claimed in the 90's] molecular scattering experiments associated with the ground state surface below are not sensitive to the geometric phase due to cancellations of terms associated with different angular momentum channels. However, showing this cancellation is rather subtle!
Aside 2: For more background see the nice Physics Today article by Berry, Anticipations of the Geometric Phase.
I thank Seth Olsen and Ben Powell for discussions stimulating this post.