Numerical test of the semiclassical approximation to the multicurve-crossing problem: Three-state model for He+ + Ne collisons
Transitions between adiabatic surfaces are described semiclassically via trajectories propagating about their complex intersection point. This intersection point is a branch point of the potential function and a simple pole of the nonadiabatic coupling. Thus transitions may be described without explicit introduction of the nonadiabatic coupling. This structure is independent of the total number of states, but is most easily shown for two-state systems. A thrėe-state model of the He+ + Ne collision system is solved by treating the three-state interaction as a sequence of two-state interactions. The results are in excellent agreement with accurate quantum calculations.