30a-L-6 New Formulae for Nonadiabatic Transition in Two-State Curve Crossing with General Potentials

博幸 中山

Yōsuke Kayanuma

N. A. Chigir

Chaoyuan Zhu, Hiroki Nakamura

Based on the achievements of the previous three papers of this series, the best working formulas for scattering matrix are obtained for both the Landau–Zener (LZ) and the nonadiabatic tunneling (NT) case: two formulas valid at b2≥0 and b2≤0 in the LZ case, and three formulas valid atb2≤−1, −1≤b2≤1 and b2≥1 in the NT case, where b2 represents the effective energy. Simple and compact formulas which work far better than the LZ formula are proposed for nonadiabatic transition probability by one passage of crossing point for both the LZ and NT cases. Furthermore, compact expressions are derived, for the first time, for the nonadiabatic tunneling probability at b2≤1, i.e., at energies lower than the bottom of the upper adiabatic potential. All the formulas proposed here can be usefully utilized at any coupling strength, namely the validity range has been very much expanded compared to the previous formulas by employing certain empirical corrections. Besides, these formulas have convenience to enable an extension to general curved potentials.

Jon P. Davis, Philip Pechukas

We show rigorously, within the two-state approximation, that in the semiclassical limit h/→0 a nonadiabatic transition induced by an analytic time-dependent Hamiltonian is localized to the vicinity of a complex crossing of the two adiabatic potential curves, with transition amplitude independent of the nonadiabatic coupling and given by a simple formula of A. M.Dykhne.

Hiroki Nakamura

The compact analytical complete solutions recently obtained for the two-state Landau-Zener-Stueckelberg problems are reviewed and explained. The theory covers both Landau-Zener (LZ) type in which the two diabatic potential curves cross with the same sign of slopes and the nonadiabatic tunneling (NT) type in which the potentials cross with different signs of slopes. The theory is applicable virtually in the whole range of energy and coupling strength and is convenient for practical use. The new theory for time-dependent nonadiabatic transition can be formulated from the time-independent theory of the LZ-type. The utilizability of the theory to various multi-channel problems and also to multi-dimensional problems is demonstrated and explained. The intriguing phenomenon of complete reflection which appears in the NT-case is explicitly utilized to propose a new type of molecular switching and to control molecular processes such as molecular photodissociation. Also proposed is a new way of controlling molecular processes by using time-dependent external fields. Finally, a trial to formulate a unified analytical theory to cover both Landau-Zener-Stueckelberg and Rosen-Zener-Demkov types of nonadiabatic transitions is briefly touched upon.