Rydberg series in a modulated continuum

In the cases treated so far, the continuum was assumed to be flat as in the original Fano problem. However, experiments tell us that this is usually not the case, and the question arises how will the series be modified if the continuum itself varies appreciably within its range To answer this question, we clearly need to know the form of the variation. As an example, consider a series on the continuum background of a shape or giant resonance, which is generally a much broader feature than an autoionising line, but for which the continuum phase shift can be expected 

We use Fano s notation within our K-matrix and, for consistency with the literature [380] emphasise the fact by an additional subscript F let rBF and Ebf be, respectively, the particle width and resonance energy of the giant resonance. 

We follow the treatment of [375, 377]. As in most cases in this chapter so far, the analysis considers only particle widths strictly, it applies only to elastic scattering and may or may not extend to photoionisation, depending on the case considered. It does, however, even in this simple form, exhibit all the main features of the problem. 

The Rydberg series of narrower autoionising lines is denoted as TnF and Enp. The resonant part of the phase shift Ao as defined in previous cases is then given by (see [375] and also section 8.27)  

We now follow the connection to MQDT as in section 8.23 and find that Ao can be written 

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