Fano response

Line shape for different Fano parameters q

In physics , a certain characteristic change in an effective cross-section is called Fano resonance (after the Italian physicist Ugo Fano , who for the first time mathematically derived this resonance curve ).

Reason for the generally asymmetrical line shapes that z. B. occur in the inelastic electron scattering in gases or in photoelectron spectroscopy , are resonance effects. They arise from the interaction of two or more end states, more precisely from the interaction between continuum states and discrete energy levels .

The course of the cross-section is proportional to in the Fano resonance

${\displaystyle {(q+\epsilon )^{2} \over (1+\epsilon ^{2})}={1+{q^{2}+2q\epsilon -1 \over (1+\epsilon ^{2})}}}$,

with the reduced energy

${\displaystyle \epsilon ={{E-E_{0}} \over \Gamma /2}}$.

Here is

• q the Fano parameter
• ${\displaystyle \Gamma }$the line width and
• ${\displaystyle E_{0}}$ the energetic position of the Fano resonance.

For the special case q = 0 , there is a Lorentz profile (pointing downwards from 1) with the width centered around ; in the borderline case of a large one , the curve approaches an upward-pointing Lorentz profile. ${\displaystyle \Gamma }$ ${\displaystyle E_{0}}$ ${\displaystyle q}$

References

1. ↑ Ugo Fano, Effects of Configuration Interaction on Intensities and Phase Shifts Phys. Rev. 124 , 1866 (1961) doi : 10.1103 / PhysRev.124.1866