Nonadiabatic decay of metastable states on coupled linear potentials

Abstract

Avoided crossings of level pairs with opposite slopes can form potential-energy minima for the external degree of freedom of quantum particles, giving rise to metastable states on the avoided crossings (MSACs). Nonadiabatic decay of MSACs is studied by solving the two-component Schrödinger equation in diabatic and adiabatic representations. Non-perturbative lifetime values are found by evaluating wave function flux and scattering phases of time-independent solutions, as well as wave-function decay of time-dependent solutions. The values from these methods generally agree well, validating the utilized approaches. As the adiabaticity parameter, V, of the system is increased by about a factor of ten across the mixed diabatic/adiabatic regime, the MSAC character transitions from marginally to highly stable, with the lifetimes increasing by about ten orders of magnitude. The dependence of MSAC lifetime on the vibrational quantum number, ν, is discussed for several regimes of V. Time-dependent perturbation theory yields lifetimes that deviate by ≲30% from non-perturbative results, over the range of V and ν studied, while a semi-classical model based on Landau–Zener tunneling is up to a factor of twenty off. The results are relevant to numerous atomic and molecular systems with metastable states on intersecting, coupled potential energy curves.