Inner-shell and double-excitation spectra

In chapter 7, spectra due to inner-shell and double excitations will be discussed. Here, we concentrate on the lineshapes which occur when resonances are embedded in the continuum. 

For all atoms with inner shells (i.e. all atoms heavier than He) the extraction of an inner-shell electron requires sufficient energy for double excitations to lie fairly close to the inner-shell spectrum. Double excitations need not involve two valence electrons, as in the spectra of rare earths mentioned above they can also involve one deep inner-shell excitation, and the excitation of a valence electron, in which case the doubly-excited spectrum lies a little above the associated inner-shell spectrum [340]. 

In short, we can say that these atoms exhibit fairly regular subvalence shell spectra, with properties which are well accounted for within the independent particle basis as a first approximation, and double excitations which do not intrude too heavily in the main inner-shell spectrum. 

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

The systematics of the double-ionisation thresholds turn out to be very important in determining the properties of doubly-excited spectra. These are most prominent for elements lying close to local minima, which is why alkaline-earth elements play a special role (see chapter 7). Another important issue is the existence of crossing points between the curves for double ionisation and for ionisation from an inner shell. This is further discussed in section 7.14. 

An instance of this type is found in the spectrum of Li I, as shown in fig. 4.4 note in particular how the df/dE curve for Li is distorted from the expected shape by the minimum below threshold, so that the curve rises rather than falls towards the threshold. The effect is not a perturbation alkali spectra have double excitations and inner-shell spectra very far in energy from the optical spectrum, so there are no intruders in this range. 

These spectra have already been used in section 2.12 as examples of the extended alkali model. They correspond to the excitation scheme d10 2 1So — d9 2np,nf(J = 1), where 2 are the valence electrons. Double excitations have also been investigated, especially in Zn [344] and are very significantly enhanced as they approach an inner-shell excited transition. This shows that final state mixing is the dominant mechanism for double excitation. 

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