Correlation energy, double photoionization

The direct knockout mechanism had earlier been evoked by Samson [36, 37], who pointed out that the variation of some double photoionization cross sections as a function of energy closely resembles the form of electron impact ionization cross sections of ions. This is, of course, the expected behavior if direct knockout dominates, which is expected in the energy range relatively near threshold. Further consideration of these model mechanisms is left for a later section where the role of initial state electron correlation is discussed. 

If pairwise electron correlation is really an important progenitor of direct two-electron photoionization, as the usual introductory statements imply [3-9], it should be interesting to discover experimentally which particular pairs of electrons are removed most effectively in direct double photoionization transitions. Is removal of electrons from the same shell or the same orbital favored relative to removal of electrons from different shell or orbitals How about electrons of the same spin relative to pairs of different spin The TOF-PEPECO method, with its lack of bias on the basis of energy or emission angle, is ideally suited to make such comparisons and thus in principle to contribute direct measurements of electron correlation. Other known factors thought to affect transition strengths such as photon energy or electron pair symmetry should be allowed for, and direct photoionization must be isolated. So far, there are very few examples where this can be done, so the jury is still out. One possibly indicative observation is that in double photoionization of small molecules with a full 71-orbital, the lA term is always the most intense (e.g., HBr, Fig. 18, OCS, Fig. 26). To form 1 A, two electrons must be removed from exactly the same spatial orbital. The same intensity pattern is found in every full n 2 ionization, and it may be remembered that for small molecules, the process is mainly direct. 

The process of double photoionization in which one photon is absorbed and two electrons ejected is very interesting since it cannot occur in an independent particle model using orthogonal states. As a result, it is difficult to calculate this process, and there has been only a small number of calculations thus far. Early calculations by Brown and by Byron and Joachain used a correlated initial state wave function but neglected correlations in the final state. However, a recent MBPT calculation for He found that at low energies the final state correlations are larger but that there is much cancellation between terms representing correlations in the initial and final states. Calculations have also been carried out for Ne m, Be, and... 

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