Beutler-Fano profile

Fig. 8.14 (a) Photoionization spectrum of the ground state of Rb in the presence of a 158 V/cm static field for an excitation energy in the vicinity of 33,614 cm-1 and a light polarization parallel to the field, (b) Example of a charcteristically asymmetric profile. Dots represent the best fit to a Beutler-Fano profile. This fit has been obtained by assuming a linear variation of the ionziation background vs the excitation energy (dotted line). 

If we again consider Fig. 21.4, we can see that the cross section vanishes at v2 = 0.32 and that the profile does not match the spectral density, A2, of the autoionizing state. The Beutler-Fano profile of Fig. 21.4 is periodic in v2 with period 1, so the spectrum from the ground state consists of a series of Beutler-Fano profiles. At higher values of v2 the profiles become compressed in energy since dW/dv2 = l/vf. Fig. 19.2 shows two regular series of Beutler-Fano profiles between the Ba+ 6p1/2 and 6p3/2 limits. In this case the absorption never vanishes because there is more than one continuum. 

Here, we return to the radiative contribution, and consider how the notion of / value can be extended to a Beutler-Fano profile, by taking account only of the discrete part, and we show that this yields the relevant quantity for studies of the refractive index of an autoionising resonance by MOR. 

This generalised definition of the / value for autoionising resonances turns out to be useful in describing the Zeeman and Faraday rotation effects for a Beutler-Fano profile. It also yields a more symmetric form... 

For MOR between bound states, it is in principle possible to determine absolute / values, because the number density N can be eliminated if both a(v) and n(v) are known, as first pointed out by Weingeroff [293]. For a Beutler-Fano profile, this is not possible, essentially because rfano... 

Fig. 6.5. A plot of the rotation angles in a Beutler-Fano profile as a function of detuning, for several values of the shape index in the special case defined in the text. For negative values of q, reverse the abscissa (after J.-P. Connerade [294]).

But, from equation (6.16), the avoided crossing occurs when AE = 0 or Ei = E2, in which case, by equation (6.35), cf = 4- Since it was assumed at the outset that hq2 — fj,01, the case of zero intensity will generally lie to one side of the avoided crossing. This can be compared with the minimum intensity which generally lies to one side of the Fano profile. The analogy with autoionisation is that, in a Beutler-Fano profile, all the possible values of AE are present simultaneously. 

The excited state is hollow, because the Is2 shell is completely empty. It turns out that the observed photoabsorption spectrum of the ls22s 2S — 2s22p2P transition exhibits a broad and asymmetric Beutler-Fano profile... 

If the probing conditions are appropriate (for further discussion, see section 9.12), the induced structure is expected to possess a Beutler-Fano profile, with the specific attraction that both the resonance energy and the width are controllable, which gives some experimental meaning to the otherwise somewhat elusive concept of prediagonalisation in Fano s theory (see chapter 6). 

Fig. 8.7. The form of a single resonance in the Rydberg series defined by the Dubau-Seaton formula (a) plotted with different combinations of parameters so that the maximum and minimum in the absorption cross section remain at fixed energies and (b) comparing a Dubau-Seaton profile (curve A) with a Beutler-Fano profile of the same shape near the resonance energy (curve B) (after J.-P. Connerade [413, 414]).

In order to extract information on the parameters of a resonance one must fit a parameter function that describes the interaction of a doubly excited state with continua to the experimental data. The most commonly used form is the Beutler-Fano profile [10]... 

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