Research Papers in Physics and Astronomy


Date of this Version

July 1977


Published by American Physical Society. Phys. Rev. A 16, 231 (1977). Copyright © 1977 American Physical Society. Permission to use.


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.

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