The triple differential cross-sections for ionization of hydrogen at incident energies in the range 17.6 eV to 13.7 eV are calculated in the distorted-wave Born approximation in the equal energy sharing andϑ_ab = 180° kinematics. It is found that a maximum in the cross-section, as was observed in the case of helium under similar conditions is also found here at excess energyE_ex ≤ 1.0 eV. This ‘maximum’ becomes more pronounced asE_ex decreases indicating dominance of short rangee-e correlations at these low energies. The angular distribution of the singlet and triplet partial waves and the asymmetry parameter have been analysed.

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.

A simple scaling law is obtained for asymmetric (e, 2e) process on helium isoelectronic ions by fast electrons. It is based on treating the targets as having one active electron moving in the effective Coulomb field of the atomic core with an effective chargeZ′ = Z- 5/8. This effective charge is also used in the description of the scattered and ejected electrons. The model has been tested against other available (e, 2e) results on helium in asymmetric geometry. The scaling law is found to work reasonably well for fast incident electrons and becomes increasingly accurate as targetZ increases.