We have studied the dependency and sensitivity of the triple differential cross section (TDCS) for (γ, 2e) on He with respect to the gauge formulation that one employs to represent the TDCS. This analysis has been performed using a variety of analytic initial-and final-state wavefunctions. It was found that the TDCS is very sensitive to the representation of the finalstate wavefunction in all geometries and all formulations of the TDCS. When the detected electrons are of unequal energy the TDCS is also sensitive to the initial-state wavefunction. The predictions using all combinations of initial-and final-channel wavefunctions are gauge dependent and vary enormously in absolute size.

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We present a critical analysis of the analytic ansatz wave functions that have been proposed for use in the calculation of triple-differential cross-sections for the electronimpact ionization of atoms. We will first discuss, in detail, the mathematical background to these approximations, and we will give, for the first time, cross-sections for the electron-impact ionization of hydrogen using the most elaborate of these. We will show that they give generally unsatisfactory agreement with experiment. We will argue that this failure comes from an inability to model the crucial region where the three particles are close together. The analysis presented should be of value not only in the case of electron-impact ionization but also for a wide range of Coulombic three-body problems in atomic physics.

For the first time theoretical predictions for (e, 2e) on a hydrogen minus, , target are presented. This study shows that the size and shape of the TDCS for this process is extremely sensitive to the form of the approximation used for the wavefunction. In particular, the TDCS is enormously model sensitive in the Bethe ridge region (when the recoil ion momentum is zero).