The isolated autoionising resonance

We use the K-matrix formalism, described above, in a form derived for nuclear scattering by Lane and Thomas [371] and Lane [379, 393]. In the present context, it provides a convenient and simple description of atomic 

As noted above (equation (8.2)), one can separate out resonant and non-resonant parts of the phase shift. For a single open channel, the K-matrix reduces to just one element  

We also begin in the elastic scattering approximation, which has the advantage of being very simple in this approximation, radiative channels are neglected, and all the observed spectral fluctuations are due to particle widths, i.e. to the decay of the excited state via autoionising channels. Radiative widths are included at a later stage, once the basic effects have been illustrated. 

The variation of the phase shift near an isolated resonance has the standard form (see, e.g., [259]) given by  

One thus obtains the standard form for the Fano formula for an autoionising line, which was obtained by a different route in section 6.4  

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