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.

Context. Quasi-molecular line satellites in the red wings of Lyman series of atomic hydrogen have been identified in the spectra of hydrogen-rich white dwarfs. These features are produced by radiative collisions. Aims. Structures observed about 995 Å in the Lyman-γ wing of hot white dwarfs have been shown to be caused by quasi-molecular absorption of H + 2 molecules. Methods. Improvements to previous theoretical calculations of the Lyman-γ line profiles can be achieved by using a unified theory that takes into account the dependence of the dipole moments on internuclear distance during the collision. Results. For the first time, we have computed the transition dipole moments. We measure a significant increase in the region of the formation of the satellites, which alters the general shape of the profile. Conclusions. A large increase in the strength of the two main satellites at 992 and 996 Å leads to a deeper broad absorption in the synthetic spectra, which should improve the comparison with observation as previous predicted Lyman-γ satellites were too weak.

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.

Changes in the metal properties, caused by periodic indents in the metal surface, have been studied within the limit of quantum theory of free electrons. It was shown that due to destructive interference of de Broglie waves, some quantum states inside the lowdimensional metal become quantum mechanically forbidden for free electrons. Wave vector density in k space, reduce dramatically. At the same time, number of free electrons does not change, as metal remains electrically neutral. Because of Pauli exclusion principle some free electrons have to occupy quantum states with higher wave numbers. Fermi vector and Fermi energy of low-dimensional metal increase and consequently its work function decrease. In experiment, magnitude of the effect is limited by the roughness of metal surface. Rough surface causes scattering of the de Broglie waves and compromise their interference. Recent experiments demonstrated reduction of work function in thin metal films, having periodic indents in the surface. Experimental results are in good qualitative agreement with the theory. This effect could exist in any quantum system comprising fermions inside a potential energy box of special geometry.8530 St *

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.

The total cross sections (TCS) for double ionization of helium-like ions by electrons are obtained at high incident energy. For the first time, the leading term and the following term of the asymptotic expression of the TCS are calculated for two-electron atomic systems from He(Z = 2) to N5+(Z = 7). The obtained values of TCS are in perfect agreement with the numerically calculated ones in the asymptotic region. For helium the discrepancy between the theory and some of existing experimental data is revealed at high energies.

The problem of dipole transition-matrix element calculation for optical transitions in multiply charged one-electron diatomic quasimolecules with unequal nuclear charges Z 1 and Z 2 has been stated and solved. The quasimolecule Z 1 eZ 2 is a unique example of a two-center system for which the energy terms and dipole transition moments have been calculated precisely in the frame of a nonrelativistic approach. Particular examples for the optical transitions with Z 1 = 1.5, 2 , 2.5, 3 and Z 2 = 1 and with the principal quantum number of the united ion n u =1,2,3,4 have been tabulated. The scaling rules make it possible to determine the matrix elements for quasimolecules having nuclear charge ratios such as 2:1, 3:1, 3:2, and 5:2. Zeros at intermediate R and zero limiting values at large R are the highlighted features of the matrix elements. The heteronucleus case generates a large number of asymptotically forbidden transitions corresponding to transitions of an electron from one ion to another.

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.