Semiclassical theory of rotationally induced nonadiabatic transitions

A general procedure is proposed to treat a many-state atomic-collision problem involving both nonadiabatic radial and rotational couplings. The procedure is based on the classical $S$-matrix theory in a new "dynamical-state" representation. The dynamical states are defined as the eigenstates of a new Hamiltonian operator which is composed of an ordinary electronic Hamiltonian and a Coriolis coupling term. The dynamical potential energies thus obtained avoid crossings even for the rotationally coupled states. At these avoided crossing points the rotationally induced transitions predominantly occur, which are delocalized in the ordinary adiabatic-state representation. The theory is applied to certain two-state- and three-state-model problems, and is shown to work well. An interesting catalytic phenomenon is found in a three-state problem. A certain transition is enhanced by a rotational coupling not directly associated with that transition; besides, a transition directly induced by that rotational coupling is not affected by the coupling responsible for the first transition. This phenomenon can be successfully explained and reproduced by the theory. A condition is discussed for this kind of phenomenon to occur in a general many-state collision problem involving rotational couplings.