Radiative and radiationless decay of multichannel resonances resulting from electronically non-adiabatic interactions: a computational approach valid for both narrow and broad line-widths and large energy shifts

Abstract

A non-perturbative computational approach is developed to treat resonances attributable to non-adiabatic radiationless decay into several electronically distinct channels. Expressions for both the radiative and radiationless decay rates are developed. An alternative derivation of the classic multichannel line shape formula of U. Fano and J. W. Cooper (1965, Phys. Rev. A, 137, 1364) is obtained. Although the approach is non-perturbative, the line-width is expressed in a golden rule type formula. The resonance energy is obtained from the iterative solution of an eigenvalue problem in the bound state space, avoiding the tedious characterization of the S matrix as a function of scattering energy. These attributes enable the efficient determination of both narrow line widths and large resonance energy shifts.