4. Conclusions

We have analyzed the correlation effects in two electron atoms and ions which can be probed in double ionization with high energy photons. The analysis is made for the two dominant photoionization processes (photoabsorption and Compton scattering) in which, due to the correlation effects, simultaneous ejection of two electrons may occur. In the case of high energy photoabsorption two correlation effects in the initial state are responsible for the mechanisms, shake-off and the quasi-equal-energy sharing, which determine the total cross section. The correlation effects in the initial state which lead to these mechanisms are: (1) monopole interaction (correlation between the electrons when one electron is close to the nucleus) for the shake-off mechanism (one electron takes all photon energy and the nucleus recoils with nearly equal but opposite momentum) and (2) correlation between the electrons when they are close to each other (nonrelativistic electrons share the photon energy nearly equally and they are ejected with nearly equal and opposite momenta while the nucleus recoils with relatively small momentum). In the case of Compton scattering the total cross section is dominated by the shake-off mechanism. However, unlike in photoeffect, this shake-off mechanism is a result of an averaged correlation between the two electrons at all positions in the initial state.

Analyzing differential observables (cross sections) we are able to distinguish the shake from the non-shake contributions in photoabsorption, or the variation of the shake-off result with distance probed in Compton scattering. In the case of double photoabsorption (for differential cross sections) the shake-off mechanism probes the same correlation effects as in the case of total cross section (one electron must approach close to the nucleus in order to accept almost all photon energy). Therefore, it provides no further information on correlation in the initial state. Due to the non-shake mechanisms (both quasi-equal-energy sharing and final state interaction), additional information on correlation effects can be obtained from the differential cross sections for high energy photoabsorption. In the case of high energy Compton scattering, unlike in photoabsorption, the study of differential cross sections, even in the shake region, can provide further information on correlation effects in the initial state. Particularly, as discussed, the double ionization Compton profile can be used for studying two-electron wave functions of helium-like atoms or ions in momentum space in a similar way as the ordinary Compton profile is used in studying momentum distribution of bound electrons within independent particle approximation. Varying the energy transfer varies the regions of the initial state electron (to be ejected fast) in which correlations with the subsequent shake-off electron are probed.