Explanation
The Fano resonance line-shape is due to interference between two scattering amplitudes, one due to scattering within a continuum of states (the background process) and the second due to an excitation of a discrete state (the resonant process). The energy of the resonant state must lie in the energy range of the continuum (background) states for the effect to occur. Near the resonant energy, the background scattering amplitude typical varies slowly with energy while the resonant scattering amplitude changes both in magnitude and phase quickly. It is this variation that creates the asymmetric profile.
For energies far from the resonant energy the background scattering process dominates. Within of the resonant energy, the phase of the resonant scattering amplitude changes by . It is this rapid variation in phase that creates the asymmetric line-shape.
Fano showed that the total scattering cross-section assumes the following form,
where describes the line width of the resonant energy and q, the Fano parameter, measures the ratio of resonant scattering to the direct (background) scattering amplitude. (This is consistent with the interpretation within the Feshbach–Fano partitioning theory.) In the case the direct scattering amplitude vanishes, the q parameter becomes infinite and the Fano formula boils down to the usual Breit–Wigner (Lorentzian) formula:
Read more about this topic: Fano Resonance
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