Doubly differential cross sections ͑DDCSs͒ for single ionization of molecular hydrogen by 75-keV proton impact have been measured and calculated as a function of the projectile scattering angle and energy loss. Interference structures are observed in the scattering angular dependence of the DDCSs, which disappear, however, at electron speeds near the projectile speed. The comparison to our calculations shows that the projectile-target nucleus interaction plays a central role. Furthermore, our data suggest that for a given scattering angle, ionization favors well-defined molecular orientations.

Using a wavefunction with the radial correlation only for the bound electrons and a correlated double-continuum wavefunction for the ejected electrons, an analytical expression is obtained in the Born approximation for the fully differential cross section of double ionization of helium-like ions by electrons. The result is found within the framework of the shake-off model considering only the radial correlation of electrons in the target.An analytical expression is obtained for the fourfold differential cross section following integration of the fully differential cross section over the solid angles of the ejected electrons. For the first time the total cross sections (TCS) are calculated for direct double ionization of twoelectron atomic systems from H − (Z = 1) to N 5+ (Z = 7). The calculations are carried out for energies extending up to a maximum 200 times the double-ionization threshold. The calculated values of TCS are found to be in fair agreement with the available experimental data for He and Li + . Disagreement between theory and experiment is discussed. TCS are found to be very sensitive to the inclusion of repulsion between the ejected electrons in the final state.

The one-Coulomb-centre problem is considered in the prolate spheroidal coordinate system. The asymptotic expansions for the separation constant and the Coulomb spheroidal quasiradial and quasiangular wavefunctions are derived when the distances between the foci of the spheroidal system R are large. The constructed wavefunctions are in excellent agreement with the exact wavefunctions in intra-atomic space, when the condition is fulfilled. The formulae obtained in the present paper can easily be generalized for the case of the two-Coulomb-centre problem.

Using a Chandrasekhar-type wavefunction for the initial state and a correlated double-continuum wavefunction for the final state, an analytical expression is obtained in the first Born approximation for the fully differential cross section (8DCS) of double ionization of H- by fast electrons. The main attention is paid to the investigation of the influence of kinematical conditions on angular distributions of the ejected electrons. In particular, kinematical conditions leading to extrema of 8DCS are defined. In the framework of shake-off mechanism, a relation between double ionization of H- and ionization of the hydrogen atom is found.

Applying the animated beam method the total cross sections (TCS) for double ionization (DI) of helium by electrons are measured in the collision energy region from threshold to 3 keV. The TCS for the same process are calculated at intermediate and high incident energies in the first Born approximation (FBA). The radial and angular correlations between the bound electrons and repulsion between the ejected electrons are accounted. In order to go beyond the FBA the scattered electron is considered as a particle being in the Coulomb field of the nucleus, the charge of which is screened by the ejected electrons. On the basis of the obtained results some conclusions concerning the behaviour of the TCS in the intermediate and high-energy regions are drawn.