Beutler-Fano lineshape

The intensity interference pattern illustrated by Fig. 6.8 for bound-bound transitions is very similar to the Beutler-Fano lineshape for bound-free transitions discussed in Sections 7.9 and 8.9. The 101,000-106,000 cm-1 region of Fig. 6.8 is a band-by-band rather than a continuous representation of a Fano profile with q < 0 [see Fig. 7.26 and compare Eq. (7.9.6) to Eq. (6.3.17)]. 

The photoionisation continuum of H is clean and featureless. Its intensity declines monotonically with increasing energy. Many-electron systems, in general, always exhibit structure embedded in the continuum. Such features are neither purely discrete nor purely continuous, but of mixed character, and are referred to as autoionising resonances. They were discovered experimentally by Beutler [254], and the asymmetric lineshape which they can give rise to follows a simple analytic formula derived by Fano [256]. For this reason, they are often referred to as Beutler-Fano resonances. A typical autoionising resonance is shown in fig. 6.1... 

Another way of considering the problem which is perhaps physically more meaningful is that in fact the two bound states 0 > and 1 > are coupled to each other by the two lasers, in one case via a bound virtual state (the Raman path) and in the other via the continuum (the autoionising path) as marked in fig. 8.4. It turns out that, if the Raman channel dominates, the resulting lineshapes tend to become symmetric, while if the autoionisation channel dominates, the characteristic interference asymmetries of Beutler-Fano resonances emerge. ... 

For an isolated or Beutler-Fano resonance, q = 0 implies a symmetric window. In the present situation, the presence of other resonances arranged as a Rydberg series, with energy intervals which are not the same on both sides of any given resonance means that the lineshapes are not symmetrical even for q = 0. However, when q = 0 and B = tan7r/x, from the first equation (8.44), the transmission maxima coincide with the resonance energies as they do for isolated resonances. 

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