The two-state linear curve crossing problems revisited. II. Analytical approximations for the Stokes constant and scattering matrix: The Landau–Zener case

Publisher Website
Google Scholar
Abstract
Based on the exact solution of the linear curve crossing problems reported in the previous paper of this series, approximate analytical solution is discussed here for the same sign of slopes of the diabatic potentials (the Landau–Zener case). A new general method is proposed for connecting wave functions along Stokes lines in the complex plane. Two new compact analytical formulas for reduced scattering matrix are derived and compared with others. The whole range of the two parameters which effectively represent the coupling strength and the collision energy is divided into five regions, in each one of which the best recommended formulas are proposed. The new formulas proposed here are simple and explicit functions of the two parameters and thus useful for practical application. Especially, a simple and compact formula which works better than the conventional Landau–Zener formula is obtained for nonadiabatic transition probability for one passage of crossing point. Furthermore, in a region near the crossing point at intermediate coupling strength where no analytical approximation works well, certain fitting formulas are provided for the Stokes constant.