Theory of nonadiabatic transition for general two-state curve crossing problems. I. Nonadiabatic tunneling case

Based on the achievements for the linear potential model, new accurate and compact formulas are established for general two-state nonadiabatic tunneling type curve crossing problems. These can cover practically the whole range of energy and coupling strength and can be directly applied not only to nonadiabatic tunneling itself, but also to the various problems such as inelastic scattering, elastic scattering with resonance, and perturbed bound state problem. All the basic potential parameters can be estimated directly from the adiabatic potentials and the nonunique diabatization procedure is not required. Complex contour integrals are not necessary to evaluate the nonadiabatic transition probability and thus the whole theory is very convenient for various applications. The previously proposed simple and compact formula, better than the famous Landau–Zener formula, is shown to be applicable also to general curved potentials. The explicit expressions are derived also for the nonadiabatic tunneling (transmission) probability. Now, the present theory can present a complete picture of the two-state curve crossing problems.