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.
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.
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.
The recombination of an electron and a proton is assumed to occur in the presence of another proton, which participates in the process. The system of colliding particles is considered as a quasi-molecule temporarily formed during a collision. This model is employed to treat the formation of atomic hydrogen in the pre-recombination period of evolution of the early universe. According to a quasi-molecular mechanism of recombination, two processes are responsible for the formation of hydrogen in the early universe – a radiative transition of an electron to an excited repulsive state of $\mathrm{ H}_2^ + $ with a subsequent dissociation into a hydrogen atom and a proton, and a radiative transition of an electron to an excited attractive state of $\mathrm{ H}_2^ + $ with a subsequent cascade downward to a low-lying repulsive state. The participation of the nearest neighbouring proton in the process is shown to decrease the probability of recombination on an isolated proton.
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