Window resonance

The distinction between shape resonance and autoionization processes, on a theoretical level, is one of single-channel versus multi-channel characteristics15. On an experimental level, the situation is less clear. However, shape resonances tend to be very broad and to exhibit delayed onset whereas autoionization leads to highly asymmetric profiles which often exhibit window resonance behaviour. We will discuss some of these distinctions in Section IV.A.l, in which photoelectron spectroscopy of the halomethanes is described. 

Lorentzian shape) such features are called pure window resonances or antiresonances (ii) if q — oo, then we have a pure, symmetric absorption maximum, again of Lorentzian shape. 

The term window resonance is useful for the q = 0 case, because it avoids confusion with other kinds of localised minima in the continuum cross section, such as the Seaton-Cooper minimum (see section 4.6.2), whose origin is quite different. 

Regarding window resonances, the following picture, though oversimplified, is useful. If the transition to Ev is unlikely (for example, because double excitations are improbable in the independent electron model), whereas the transition to e > is allowed (for example, it is a singly-excited continuum state), then the mixture of the two depresses the intensity in the vicinity of Eq. Conversely, allowed transitions in the predi-agonalised scheme tend to yield strong, nearly symmetric maxima in the absorption cross section. 

The opposite case to a giant resonance, which exhausts the oscillator strength within its width, is an antiresonance, or a Fano resonance with q = 0. In principle, nothing prevents such a resonance from acting as the intruder. Double excitations appear above the first ionisation potentials of many-electron atoms, and are frequently observed as window resonances. An example where an antiresonance acts as the intruder [418] occurs in the spectrum Ar shown in of fig. 8.12. 

Fig. 8.18. Case of a q reversal straddling one intervening, almost symmetrical window resonance as obtained in (a) a calculation using identical parameters to those of the first q-reversal calculation above, except that the coupling strength was increased and (b) an experimental situation which also occurs in the Tf spectrum (after J.-P. Connerade and A.M. Lane [381]).

Fig. 8.23. Vanishing fluctuations in a doubly-excited series of Ba. Note the existence of a point (marked X in the figure) at which spectral structure disappears, and which is not a series limit. Note also the q reversal about a window resonance (after J.-P. Connerade and S.M. Farooqi [442]).

Several instances where a q reversal straddles a q = 0 window resonance were described above. The form of the variation of q is then ... 

A pure or perfect q = 0 window resonance would of course be missed in a search for maxima in the cross section. Very few resonances can satisfy this condition exactly for interacting series. In practice, one misses at most one resonance, and this does not change the shapes of the graphs. 

In Fig. 7, we show the cross section for photodetachment of Li via the S Skp channel over photon energies of approximately 5.04-5.16 and 5.29-5.46 eV. These ranges cover the regions below, and including, the Li(42p) and Li(52p) thresholds, respectively. Several Feshbach window resonances are observed to lie below these thresholds. In the figure the present measurements are compared with the result of a recent eigenchannel R-matrix calculation by Pan et al. [28]. The experimental resolution, which is estimated to be about 25 p,eV, is sufficiently high compared to the typical resonance widths that a direct comparison with theory can... 

The window resonances shown in Fig. 7 partially overlap each other, and it is therefore not possible to fit a single Fano profile to each resonance. We have instead fitted a form representing the sum of two Fano profiles to the data in order to extract the energy and width of each resonance pair ... 

The radiationless decay of a quasidiscrete excited state of an atom or molecule into an ion and electron of the same total energy is called autoionization. The quasidiscrete state must, of course, lie above the first ionization potential of the atom or molecule. The occurrence of autoionization may be inferred from the appearance of absorption spectra or ionization cross-section curves which exhibit line or band structure similar to that expected for transitions between discrete states. However, in the case of autoionization the lines or bands are broadened in inverse proportion to the lifetime of the autoionizing state, as required by the uncertainty principle. In the simple case of one quasidiscrete state embedded in one continuum, the line profile has a characteristic asymmetry which has been shown to be due to wave-mechanical interference between the two channels, i.e., between autoionization and direct ionization. In an extreme case the line profile may appear as a window resonance, i.e., as a minimum in the absorption cross section. 

The Photoassociation Process Time Window, Resonance Window, Concept of a Photoassociation Window... 

The time window, resonance window, and PA window have been indicated in Figure 7.1. The sensitivity of the results to the choice of the pulse parameters (detuning, intensity, spectral width, linear chirp rate) is discussed in detail in Refs. [18] and [19], where many different pulses have been considered. In the present work, we concentrate on two typical pulses, hereafter referred to as and with a central frequency chosen to be resonant with the vibrational levels v = 98 and 122, described above in Table 7.1 and in Figure 7.2. Two other pulses will also be considered in the discussion of Section 7.6. We give in Table 7.2 the parameters for the various pulses, as well as the associated PA windows. Another characteristic timescale associated with the radiation is the Rabi period, discussed in detail in Ref. [18], which is larger than 20 psec for the chirped pulses considered here. 

Volume 37 Invariant Sets for Windows — Resonance Structures, Attractors, Fractals and Patterns... 

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