Rotation of a generalized Eckart frame in atom-diatomic molecule scattering*

A cyclic change in the shape of an atom-diatomic molecule complex can lead to net rotation of not only the complex, but also the rotating axes of a generalized Eckart frame of the complex. Large-amplitude, ``internal'' motions of an atom-diatomic molecule van der Waals complex can lead to overall rotation of the complex in the center-of-mass frame. When the total angular momentum is conserved, the net angle of overall rotation is the sum of a dynamic phase plus a geometric phase. The classical geometric phase is describable in terms of molecular rotational constants. The scattering angle of the atom in a nonreactive ``slightly sticky collision'' between an atom and a diatomic molecule in molecular beams depends on an analogous ``internal'' motion. Thus, the scattering angle of the atom is also given by the sum of a dynamic phase plus a geometric phase.