Applicability of the Fano formula

It is important to recognise the limitations of formula (6.20), which are as follows (i) the formula applies to a single, isolated resonance (ii) the background continuum must be flat, or vary very little over the width of the resonance (iii) the radiative width must be much smaller than the particle width and (iv) there must be no other channel for particle broadening than the one considered. 

In the presence of several continua, the Fano formula still describes the general lineshape of autoionising resonances rather well, but the cross section does not fall to zero near the resonance, i.e. the transmission window is filled in by the presence of several continua. If the cross section falls to zero near the resonance, one can in fact deduce that only one continuum is involved. 

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