The special case of He

Before giving examples of the behaviour of many-electron atoms in general, it is worth describing the case of He, which is exceptional in that it contains no inner-shell spectrum, but only a doubly-excited spectrum in addition to the usual valence-shell excitations. 

The history of observations of the doubly-excited spectrum of He is comparatively recent, because of the rather high excitation energies required. The first observation of double excitations in He is due to Silverman and Lassettre [321]. The earliest high resolution spectrum was 

Such observations led Macek [324], Fano [327], Herrick [328] and others 

Until recently, another problem with the so-called correlation quantum numbers was that they did not enable the most accurate calculations of doubly-excited spectra to be performed. With the work of Tang and Shi-mamura [330] on the hyperspherical close-coupling method, this situation has changed, and there is renewed interest in this approach since the situation is still evolving, we merely summarise developments in this area in section 7.11. 

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. 

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The first ionisation limit of a many-electron atom corresponds to the ground state of the corresponding or parent ion. Higher thresholds correspond to excited states of the parent ion. Apart from the special case of He, which has a hydrogenic parent ion, they are not simply related to fundamental constants. The many-electron Schrodinger equation must also be solved for the parent ion in order to determine the energies of the thresholds. 

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