Semiclassical treatment of nonadiabatic transitions: Multilevel curve crossing and nonadiabatic tunneling problems

Abstract

Nonadiabatic transition in a multilevel curve crossing system and the one accompanying quantum mechanical tunneling are investigated theoretically and numerically for the one-dimensional case. The first problem is analyzed using the semiclassical formulation based on the sophisticated two-state theory for nonadiabatic transition. This formulation is applied to three- and four-level model systems and is found to work surprisingly well even when the avoided crossings (or the transition zones) cannot be regarded to be well separated. The significance of the Stokes phase is noticed. As for the second problem, analysis is made not only for the simple tunneling but also for the elastic scattering accompanied by the nonadiabatic tunneling. A combination of the following two formulas is recommended for practical use: (1) the formula essentially based on the one proposed by Coveney et al., and (2) the formula of Ovchinnikova with additional Stokes phase and tunneling corrections. © 1987 American Institute of Physics.