Usefulness of the newly completed semiclassical theory of curve crossing: multi-channel resonant scattering

A resonant multi-channel curve crossing problem is investigated by using the two-state semiclassical theory recently completed by the authors. The complex phase integral in the non-adiabatic tunneling type curve crossing is accurately replaced by the phase integral on the real axis. Thanks to this, the transition matrix propagation method based on the two-state theory can be applied to multi-state curve crossing problems without any restriction on the number of crossings and states. The present theory can handle even the case that the collision energy is lower than the highest avoided crossing. Numerical comparisons with the exact quantum results for a three-state problem demonstrate the excellence of the theory. Even the detailed feature of dense resonances is accurately reproduced. The theory does not require any complex calculus, any diabatization procedure nor any information on the couplings.