Electron distribution, double photoionization

After these preliminaries, one can introduce the intensity distribution function /s( kjni, kin2) for electron pairs created in the source volume (subscript s ) with kinetic energies kinl and kin2. For direct double photoionization one obtains... 

Its chief characteristic is that the excess energy of the photon above the double ionization threshold is shared as a continuous monotonic distribution between the two outgoing electrons. This direct double photoionization is contrasted with several indirect processes, of which by far the most important can be written... 

Figure 11. Electron distributions from double photoionization producing the ground states of Ar2+ and Kr2+ at 48.37 eV and of Hg2+ at 40.81 eV. The whole distribution is shown for Ar, and it illustrates the lower resolution of TOF-PEPECO for higher-energy electrons.

For some molecules the quantum yield of double photoionization is low and the electron energy distributions are both flat and relatively smooth. This... 

Figure 21. The inner valence Auger effect in formaldehyde (methanal). The broad peak in the regular photoelectron spectrum near 34 eV is an inner valence (IV) band based on C2s ] ionization. It recurs as a peak in the electron distribution for double photoionization and in the quantum yield. The uppermost curve shows the spectrum of HCH02+, where the ground state is strongly populated by this effect. 

Direct Double Photoionization. This is the sole mechanism for He, and it is present (though sometimes only weakly) for other species. At high energies it occurs mainly by shake-off, which gives deeply concave electron distributions. Nearer threshold, direct knockout is the main mechanism and gives flatter distributions. The very low intensity of direct ionization to molecular dication states with separated charges on distant atoms accords with the knockout model. 

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