Non-adiabatic transitions in a tilted conical intersection

We consider the following Schrodinger equation: (h) over bar /i d psi(t,z)/dt = [GRAPHICS] psi(t,z), where the parameters z and chi are assumed to be positive real constants. This equation is widely known as the Landau-Zener problem, and it serves as a paradigmatic model for non-adiabatic transitions that occur in conical intersections. Indeed, the role of the off-diagonal term a in the Hamiltonian is to couple the potentiahenergy surfaces in the neighborhood of the intersection. For the special value chi = 1, an explicit solution can be expressed in the form of the Weber function, and in its ivake, the scattering matrix S(z) is entirely determined. The aim of this paper is to extend the classic transition probability a(Weber)(z) = exp(-pi z(2)/2 (h) over bar) for any arbitrary chi. Thus, in the strong coupling (large z), intermediate z = root(1 + x)(h) over bar, and weak coupling (small z) regimes, we shall successively compute both components a(chi)(z) and b(chi)(z) of the S-matrix governing the transitions behveen the 2 eigenstates Psi(+/-). Published under license by AIP Publishing.