Q reversal

Type I. Figure 1 illustrates reversible refrigeration machines of Type I. This machine receives an amount of heat q reversibly at temperature Tc and discharges it reversibly at a higher temperature, Ta. By the first principle of thermodynamics the necessary energy input, w, must also be discharged reversibly at Ta. The coefficient of performance of this machine is the same as that of a Carnot refrigeration machine. Thus we have... 

A new class of conjugated hydrocarbons is the fullerenes [9b], which represent an allotropic modification of graphite. Their electrochemistry has been studied in great detail during the last decade (see Chapter 7). The basic entity within the series is the Cgo molecule. Due to its high electron affinity, it can be reduced up to its hexaanion [10,116]. Solid-state measurements indicate that the radical anion of C q reversibly dimerizes. NMR measurements confirm a a-bond formation between two radical anion moieties [117]. 

Arylpiperidines with an Oxygen Substituent at Q Reversal of the ester in meperidine gives MPPP (iV-methyl-4-phenyl-4-... 

Fig. 6.2. Family of curves generated from the Fano lineshape formula for different values of the shape index q. For negative values of q, reverse the abscissa, (after U. Fano [256]).

Fig. 6.6. Rotation per unit depth in a Beutler-Fano profile as a function of the detuning, for several values of the shape index q, in the special case described in the text. For negative q, reverse the abscissa (after J.-P. Connerade [294]).

In addition to this important effect, the inner-shell excitations from the 6s and 5d subshells also overlap in energy with each other, giving rise to prominent interchannel coupling and examples of the q reversal effect which will be discussed in chapter 8. The 5d spectrum of Tl is thus unexpectedly rich and interesting. 

Fig. 8.1. Examples of the -reversal effect (a) experimental, as observed in the photoabsorption spectrum of T (note that the q reversal, in this case, does not coincide in energy with the maximum in the cross section of the broad perturber) (b) computed, in a rough simulation of the skewed q reversal effect based on the simplified equation given in the text (note that this is not a parameter fit, but simply an example - after J.-P. Connerade [382] and J.-P. Connerade and A.M. Lane [381]).

However, we pick out one specific aspect here, because its appreciation does not require a detailed preliminary discussion of the underlying high field interactions the use of a laser to create or embed autoionising structure in an existing continuum is of great significance to the study of how the symmetries of autoionising resonances can be reversed (the so-called q-reversal effect, first discovered in the spectrum of an unperturbed neutral atom [382]). 

The change in symmetry or -reversal effect is accounted for in section 8.28 we note here that it occurs in a Rydberg series of autoionising lines when a broad intruder is present, but that it also occurs when a relatively sharp autoionising line is tuned through a broad resonance. Early theories of strong field laser effects [411] provided this picture, used by Connerade to discuss q reversals [382] when they were first observed,... 

Fig. 8.16. Experimental spectrum of doubly-excited resonances in the barium spectrum obtained by three-photon spectroscopy. The horizontal arrows in the figure indicate lines which are not spectral features but frequency markers. Because of the mode of excitation, the lines tend to be more symmetrical than in some of the other spectra, but nevertheless exhibit a clear q reversal as the main feature is traversed. A theoretical fit by MQDT is also shown (after F. Gounand et al. [421]).

From the simplified formula (8.69), one can represent a number of situations in which radiative widths do not appear to be important. Thus, fig. 8.1(b) shows a skewed -reversal effect similar to the observed one in fig. 8.1(a). Similarly, fig. 8.17 shows enhancements of upper series members in observed and calculated spectra, and fig. 8.18 shows a q reversal straddling one resonance of q —> 0 in both experimental and calculated spectra. 

Finally, in fig. 8.19 we show an example in which the perturber has more pronounced asymmetry, but nevertheless induces a q reversal. 

An important conclusion from such numerical studies [380] is that q reversals are the hallmark of weak coupling, i.e. they tend to disappear... 

We now consider how many q reversals are expected in a Rydberg series and the conditions under which they occur. Experimental data (such as those in fig. 8.18) demonstrate that there can be more than just one q reversal in a Rydberg series perturbed by an intruder level. One might ask is this a sign of perturbations due to more than one interloper, or can one interpret the two reversals as having a common origin ... 

Some insight is gained by asking how many q reversals can be expected... 

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]).

General K-matrix expressions have been derived for the variation of q as a function of detuning, both in elastic scattering and in photoionisation [375, 377]. It turns out that as many as six q reversals can occur in the general case in photoionisation but that, in elastic scattering, there are at most two. 

With just one particle channel open, one can also show that the q reversals occur at two poles, one of which corresponds to a zero in the particle widths, while the other does not. Thus, one of the poles only is associated with a vanishing width (cf section 8.29 and the spectra in fig. 8.18). 

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 ... 

We infer that a vanishing width in the case of a single open channel becomes a vanishing fluctuation in the presence of several open channels The data also demonstrate that the influence of a single perturber is enough for a disappearance of fluctuations to occur, as witnessed by the simultaneous occurrence of a single q reversal. 

Other remarkable points in the spectra are the q reversal energies. Since these have been discussed at length in the present chapter, we merely note that they are due to sign changes which do not affect the energies of the poles in the K-matrix, and therefore do not induce new structure in two-dimensional graphs. 

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