Seaton-Cooper minima

Fig. 4.4. Seaton-Cooper minima for a selection of alkali spectra (schematic), showing their evolution as a function of the atomic species. Theoretical curves are shown on the left and corresponding plots of the experimental photoionisation cross sections on the right. The figure demonstrates the large difference between the alkalis (after M. Nawaz et al [166]).

The possibility of such minima in the observed cross section, and the explanation of how they arise were first discussed by Rudkjpbing [138], in a pioneering paper which is unfortunately hard to find and has therefore been rarefy quoted. Accurate calculations of cross sections near such minima in the alkalis were first reported by Seaton [139]. Similar calculations were also performed by Cooper [140]. In line with current usage, we shall refer to such features as Seaton-Cooper minima. They are not to be confused with another type of minimum of the photoionisation cross section (the Combet-Farnoux minimum), which occurs in the presence of a centrifugal barrier (see section 5.4). 

For a more recent example of how Seaton-Cooper minima arise in laser spectroscopy and a more up-to-date comparison between theory and experiment, see [141]. 

The Seaton-Cooper minima of alkali spectra are the best known. Because of the continuity between discrete and continuous spectra noted in the previous subsection, if a Seaton-Cooper minimum drops below the threshold, it will turn into a minimum in the course of intensities of the corresponding Rydberg series, in such a manner that continuity of the df/dE plot is preserved (see above). In the discrete part of the spectrum, one may find a minimum rather than a zero, because it is not necessary that a transition should exist at precisely the energy where cancellation occurs, i.e. the Seaton-Cooper minimum may very well fall between two members of a Rydberg series. However, the anomaly in the course of intensities in the series will be apparent. 

The delayed onset effect was discovered experimentally by Ederer [180] in 1964 in the photoionisation spectrum of Xe gas. A more recent compilation of results for the same spectrum is presented in fig. 5.1. If one considers the ionisation continuum of H, then just above the ionisation threshold, there is a maximum in the cross section, which is followed by a monotonic decline with increasing energy. Such situations are illustrated in fig. 4.1 until the observations of Ederer, it had been believed that this would be the most general behaviour of continuum cross sections and that, apart from the Seaton-Cooper minima discussed in section 4.4, or the local influence of interchannel perturbations, revealed in spectra such as that of fig. 4.3, unperturbed continuum cross sections would usually follow a monotonic course of declining intensity comparable to that of H. 

Continuum effects Seaton-Cooper minima in solids 407... 

In an interesting theoretical study, Msezane and Manson [142] have considered the opposite situation where, instead of becoming more compact, as when the Seaton-Cooper minimum drops into the bound states, the wavefunctions become more diffuse, and the minima tend outwards. They have taken as their initial state an excited rather than a ground state. For photoexcitation from ground state wavefunctions, at most a single Cooper minimum is found, but this is not necessarily true for photoexcitation from excited states. In this case, even if the initial state wavefunction has no nodes, a Cooper minimum may occur. When the initial state wavefunction has nodes, then in addition to the usual Cooper minimum, further minima also appear. Some of these may also drop into the bound state spectrum, and an example of this kind is discussed in section 5.18. 

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. 

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