1. Introduction

Double ionization of two electron atoms and ions by one photon is attracting significant attention both experimentally and theoretically. The motivation is the investigation of electron-electron correlation effects. The interest in the use of photons in ionizing two electron systems (particularly helium) is based on the observation that the interaction between electrons and the radiation field is described by a one-body operator. This means that, in the lowest order for a given ionization process, a photon interacts with only one electron. Hence the simultaneous ejection of two electrons is due to the electron-electron interaction between the two electrons, and therefore double ionization by a photon provides a clear probe of electron-electron correlation. In a two electron system no other correlations are present. For this simplest many-body system we may be able to develop more exact theoretical approaches and more detailed experimental methods. We wish to understand eventually all possible correlation effects in this relatively simple system, with the purpose of better understanding of these effects in more complex systems.

The photoionization processes are photoeffect (incident photon absorbed) and Compton scattering (incident photon scattered). Photoeffect dominates the total cross section at lower photon energies and its relative contribution in photon atom interaction decreases as photon energy increases. For a He-like system, at energies for which the incoming photon momentum k is comparable to the average momentum of the bound electrons p_av (of a two electron atom or ion in its ground state), photoeffect and Compton scattering are comparable. For higher energies Compton scattering dominates. In the case of helium Compton scattering dominates above, roughly, 6.5 keV.

The simplest observable, for both experimental and theoretical treatment of the correlation effects, has been the ratio between probabilities for double and single photoionization. This ratio is nonzero because of electron-electron correlation; its value depends on incident photon energy. Also, the value depends on the process under consideration. Therefore we talk about the Compton double to single ionization ratio R_C and the photoeffect ionization ratio R_P. The energy dependence of these observables, and particularly their high energy limits, are subjects of extensive studies. In the last several years significant progress has been achieved [1]. However, the relatively large disagreements in theoretical predictions as well as in experimental data indicate that we still do not understand all relevant aspects of the processes which are involved in determining the ratio for the double to single ionization for both Compton scattering and photoeffect.

As we will see, much understanding of these processes can be obtained within the shake-off approximation, i.e. a sudden approximation. By shake-off approximation we mean the assumption that the final state electron-electron interaction can be neglected, and that one electron scatters the high energy photon and accepts almost all momentum transfer [2].