Identification of the Beutler-Fano formula in eigenphase shifts and eigentime delays near a resonance

Abstract

Eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are shown to be functionals of the Beutler- Fano formulas using appropriate dimensionless energy units and line profile indices. Parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays are identified. Similarly, parameters responsible for the eigentime delays due to a frame change are identified. With the help of new parameters, an analogy with the spin model is pursued for the S matrix and time delay matrix. The time delay matrix is shown to comprise three terms, one due to resonance, one due to a avoided crossing interaction, and one due to a frame change. It is found that the squared sum of time delays due to the avoided crossing interaction and frame change is unity.