Autoionising resonances

The study of resonances in chapter 8 involved cross sections for elastic and inelastic scattering that are affected by resonances in the electron—target compound system. A new dimension in the study of resonances and the ionisation mechanism is provided by kinematically-complete experiments that can be considered as the excitation of autoionising resonances of the... 

The main theme of this chapter has been the distribution of oscillator strengths amongst transitions between bound states in a Rydberg spectrum. This subject is closely related to the properties of autoionising resonances, which will be discussed in chapters 6 and 8. As regards measuring / values, the MOV technique is used to determine the refractive index of an autoionising resonance (section 6.15). 

A distinction has already been made in section 5.19 between giant and autoionising resonances. In the present section, we point out further differences between them, and establish a simple connection to quantum scattering theory. 

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... 

Fig. 6.1. A typical autoionising resonance, as observed in the spectrum of Ba by laser spectroscopy. Note the broadening and asymmetry of the observed line profile. The inset shows the 5d5/ resonance on an expanded scale, together with a theoretical fit (smooth curve) based on the Fano formula (see text). Note that the discrepancies between theory and experiment occur mainly in the wings of the line (after J.-P. Connerade [257]).

Autoionisation is one of the most fundamental correlation phenomena. There are different ways of arriving at the Fano lineshape formula for an autoionising resonance. Since these are also alternative approaches to... 

For a pure autoionising resonance embedded in a single continuum, absorption by the underlying continuum is cancelled out at one energy close to the resonance energy, and the resulting transparency is referred to as a transmission window. 

In the presence of several continua, the Fano formula still describes the general lineshape of autoionising resonances rather well, but the cross section does not fall to zero near the resonance, i.e. the transmission window is filled in by the presence of several continua. If the cross section falls to zero near the resonance, one can in fact deduce that only one continuum is involved. 

In photoabsorption spectroscopy, the distinction can also be made in a different way the probability that an electron on a Rydberg orbit is ejected depends on its penetration of the core, which scales as 1/n 3. On the other hand, the Auger electron has a constant probability Tauger of being ejected. Thus, if we observe a Rydberg series of autoionising resonances in photoabsorption, then the total width rn of the nth member is given by... 

Thus we see immediately that the magnitude d of the avoided crossing in the spectrum of the bound states determines the widths of the autoionising resonances directly. 

It was implicit in the last section and indeed in all the discussion so far that the decay of an autoionising resonance should be exponential in time. This may seem to be obvious, and is indeed verified with good accuracy in experiments, but there are also fundamental reasons for believing that it is not strictly correct [280] according to quantum mechanics, the exponential decay law is violated for very long times, where the probability of nonexponential decay eventually prevails, a fact which has been recognised in nuclear and particle theory [282], but has not so far been verified experimentally. 

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... 

In the present chapter, we have described many aspects of the simplest problem which can arise when an isolated resonance is formed in a single continuum we have shown that autoionisation is an interference phenomenon and compared it with the behaviour of a discrete three-level system. Two different derivations of the Fano formula have been given, and its connection with MQDT has been described. A third approach will be provided in chapter 8. Beutler-Fano autoionising resonances occur in all many-electron atoms, and a number of examples will be provided in the next two chapters. In chapter 8, the interactions between autoionising resonances will be considered, and two further questions will be discussed, namely the influence of coherent light fields on autoionising lines, and the use of lasers to embed autoionising structure in an otherwise featureless continuum. 

Many-electron atoms differ from H in an essential respect when they are excited up to and above the first ionisation potential, they exhibit structure which is not simply due to the excitation of one valence electron. The clearest manifestation of this behaviour occurs in the ionisation continuum. For H, the continuum is clean, i.e. exempt from quasidiscrete features. In any many-electron atom, there will be autoionising resonances of the type discussed in chapter 6. Autoionisation is therefore a clear manifestation of the many-electron character of nonhydrogenic atoms. 

Fig. 7.2. A typical inner-shell excitation spectrum the 3p spectrum of Ca. Note the wide doublet splitting between the two series limits due to the large spin-orbit interaction of the nearly-closed core, the prominent Rydberg series and the broad, asymmetric autoionising resonances (after J.-P. Connerade et aL [302]).

Even more recently, the experimental resolution has been still further enhanced, and both partial cross sections and photoelectron angular distributions have been determined [332]. The data shown provide fine examples of interfering autoionising resonances (see chapter 8) and have been analysed in remarkable detail using the hyperspherical close-coupling method they represent a critical test of the dynamics of double excitation in He. 

Fig. 8.2. Diagram of a typical thermionic diode arrangement to observe interacting autoionising resonances (after W.G. Kaenders et al. [389]).

A fundamental issue in the description of even the simplest, isolated autoionising resonance in the parametric approach followed by Fano [391] - and further pursued in K-matrix theory - is that the atom cannot be deperturbed, that is one cannot access the so-called prediagonalised states which are imagined to exist prior to autoionisation being included as a perturbative interaction, since the effect is anyway internal to the atom and cannot truly be turned off. This has the disadvantage that the parameters, once they have been obtained, must still be calculated from an ab initio model of the atom for a full comparison with theory. It might seem that the parametric theory cannot really be checked independently of ab initio calculations whose accuracy is hard to ascertain. 

Fig. 8.3. Autoionising resonances coupled to a power-broadened continuum. The pure profile of the power-broadened line was also determined experimentally, and is shown by the broken curve (after A. Safinya and T.F. Gallagher [401]).

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 formula for unperturbed Rydberg series of autoionising resonances in terms of only three shape parameters B, C and D, which are constant for the whole series. 

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