UNIFIED SEMICLASSICAL THEORY FOR THE 2-STATE SYSTEM - ANALYTICAL SOLUTIONS FOR SCATTERING MATRICES

Unified semiclassical theory is established for general two-state syst em by employing an exactly analytical quantum solution [C. Zhu, J. Phy s. A29, 1293 (1996)] for the Nikitin exponential-potential model which contains the two-state curve crossing and noncrossing cases as a whol e. Analytical solutions for scattering matrices are found for both thr ee- and two-channel cases within the time-independent treatment. This is made possible by introducing a very important parameter d(Ro) = roo t 1 + 4V(12)(2)(R(0))/[V-22(R(0))-V-11(R(0))](2) (V-11(R), V-22(R) and V-12(R) are diabatic potentials and coupling, R(0) is real part of co mplex crossing point between two adiabatic potentials) which represent s a type of nonadiabatic transition for the two-state system. For inst ance, d=infinity represents the Landau-Zener type and d=root 2 represe nts Rosen-Zener type. Since d(R(0)) runs from unity to infinity, this parameter provides a quantitative description of nonadiabatic transiti on. The idea used here is the parameter comparison method which makes a unique link between the model and general potential system at the co mplex crossing point. This method is testified not only by numerical e xamples, but also by agreement of the present semiclassical formulas w ith all existing semiclassical formulas. (C) 1996 American Institute o f Physics.