Double ionisation

The appearance potential for this ion should thus be equal to, or larger than, the sum of the potentials for double ionisation of phosphorus, /(P ) + /(P ), and the dissociation energy of phosphine should be given by... 

Helms, S., Brinkmann, U., Deiwiks, J., Schneider, H. and Hippier, R. (1994a). Double ionisation of rare gas atoms by positron impact. Hyperfine Interactions 89 395 400. 

The cross section Oai represents a useful cross section for the production of free electrons, and it can be obtained quite accurately (e.g. Tate and Smith, 1932, and Rapp and Englander-Golden, 1965) since nondiscriminating detectors with essentially 100% efficiency are used. At energies below the double ionisation threshold the apparent cross sections will yield the true integrated cross section cr/. 

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. 

Fig. 1.3. Double-ionisation potentials as a function of atomic number. Some inner-shell thresholds are shown as dashed lines. Note the degeneracies or crossing points between inner-shell and double ionisation, which give rise to a variety of effects discussed in chapter 7.

After the ejection of an electron from an inner shell, relaxation generally occurs by the emission of a secondary electron. This is known as the Auger effect. It can be reasonably well described as a two-step process, leading to double ionisation, because the primary and Auger electron are usually separate. However, if the initial photoelectron is emitted with a very low kinetic energy, then the Auger electron can catch up and interact with it. This process is described as post-collision interaction or PCI. 

There exists, in addition, another possibility. It will not have escaped the reader that the two electrons, in the description just given, are not treated completely symmetrically. Were one to do so, it would be necessary to increase both nj and 2, so as to form a sequence of levels with n = 2 spaced differently from the normal Rydberg series, converging on the double-ionisation potential. At the limit of this series, both electrons would escape in a completely symmetric way, and so this possibility is often referred to as the double-escape problem . 

Double Rydberg states (double because both electrons are running electrons in this case) and the symmetrical double-ionisation problem were considered first by Wannier [320], and so the completely symmetric excited states with i = I2 and nj = ri2 as the double-ionisation threshold is approached are called Wannier states. These states have very interesting... 

Fig. 7.5. The double-excitation spectrum of He as the double-ionisation threshold is approached, showing a whole family of Rydberg series each one associated with a different parent state of the ion (after M. Domke et al. [331]).

The outermost d subshell spectra of Ga [348], In [349] and Pb[350] all have the characteristic that they straddle the double ionisation thresholds. As a result, many of the inner-shell transitions are quenched, while the probability of photo double-ionisation is enhanced. This situation has been discussed [351] in terms of diagrams such as those of fig. 7.8 in which the ionisation potentials for double-ionisation and single-ionisation from an inner-shell threshold are plotted as a function of atomic number. One looks for crossing points, where mixing between the two becomes particularly strong. 

Two-step autoionisation may be regarded as the lowest energy Auger effect it sets in as one crosses the double-ionisation threshold towards higher energies. 

The series limit on which the autoionising resonances converge may or may not be stable. If the corresponding parent ion state can decay ra-diatively, then because radiative widths are (for low excitation energies) usually much smaller than autoionisation widths, the series observed is not much affected until high values of n. On the other hand, if the parent ion state itself lies above the double-ionisation threshold, it becomes susceptible to particle decay and acquires its own intrinsic width through autoionisation. 

J. H. D. Eland. A theoretical and experimental study of the double photoionisation of molecular bromine and a new double ionisation mechanism. Chem. Phys., 343 (2008) 270-280. 

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