Two series of resonances and one continuum

For the limiting case of two autoionising series in the presence of one continuum, the meromorphic form again results from adding phase shifts 

When the resonances are not symmetric, the maxima are shifted, so that they no longer occur at positions defined only by Ml and M2 and equation (8.103) should be used it contains an additional term involving Ej + E2, and thus, in general, describes two-dimensional plots with a structure slightly different from the usual MQDT pattern described by equation (8.105). 

In general, the full range of variation of has the effect shown in fig. 8.25 for a case in which X = X2. changes in the combined asymmetry parameter alter the appearance of the avoided crossing in a manner which can fill the whole of the available area in the graph, while preserving positive slope. 

We may further consider the case in which the fine structure due to series 1 overlaps with a broad resonance Fb/2(Eb — E) = e 1 which dominates T,2 in the energy range of interest. From equation (8.103) we 

So that the two-dimensional graph of v against E, plotted modulo 1, contains a single discontinuity shifted from the pole at E — Eb to an energy near E = Eb — b/2, which is clearly related to the profile of the 

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