## Research Papers in Physics and Astronomy

#### Date of this Version

July 1977

#### Abstract

Starting from the treatment of Fano for the behavior of the total cross section in a photoionization (or electron-ion scattering) experiment in the vicinity of a resonance, we present a theoretical formula for the behavior of an individual final-state channel in the neighborhood of a resonance. This result is then used to derive another theoretical formula for the behavior of the ratio of two partial cross sections (i.e., the branching ratio) in the vicinity of a resonance. This branching-ratio formula depends on the profile parameters *q*, Γ, and ρ2 for the resonance, on the branching ratio outside the resonance, and on two new parameters which are explicitly related to scattering-matrix elements and phase shifts.

## Comments

Published by American Physical Society.

Phys. Rev. A16, 231 (1977). http://pra.aps.org. Copyright © 1977 American Physical Society. Permission to use.