Owing to the degeneracy of the energy levels, the wavefunction of the electron in the excited states of the hydrogen atom and hydrogen-like ions perturbed by a neutral atom B is significantly different from the wavefunction of the unperturbed state. The perturbed function has a wide high maximum in the region of atom B, which is explained by multiple collisions of the electron with atom B, because the classical trajectories in the Coulomb field are closed and the size of atom B is much smaller than the size of the excited-state orbit. The radiative lifetimes of the excited states are much larger than those of unperturbed states. The orbital angular momentum L of the excited electron is strongly changed in collisions with atom B owing to the quantum interference or mixing of the temporal phases of adiabatic wavefunctions. The cross sections for such a change in the orbital angular momentum are several orders of magnitude larger than the cross sections found in early investigations in the approximation of the single collision of the electron with atom B.

The cross sections of the Rydberg electron L -mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*( n , L ) + A + = H*( n , L ′) + A + without variation of the principal quantum number n . The probability of the L -mixing L → L ′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(− i ∫ E k ( t ) dt ). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.

Two-Coulomb-centre quasiradial and quasiangular wavefunctions asymptotic for large distances between the fixed positive charges (nuclei) are derived for the entire space of the negative particle (electron). Explicit expressions of the wavefunctions are presented for some low-lying states. Excellent agreement is found between the expressions presented here and numerically calculated wavefunctions when the internuclear distance is greater than the size of the shell on either centre.

Sums of products of the Coulomb wavefunctions over degenerate manifolds have been obtained in a closed form. These sums appear in many atomic and molecular problems, The sums have been obtained making use of the properties of the Coulomb Green function G ((r) over right arrow, (r) over right arrow', E) in the limit E --> E-n where E-n is the eigenenergy of the hydrogen-like atomic ion. This paper develops the method described in our previous paper.

Collisions between negative and positive atomic ions are investigated. The ionic wave function is expressed in terms of the Coulomb Green’s function. Normalizing this function allows the system of two ions to be described completely. The exchange matrix elements turn out to be the sums of products of the Coulomb wave functions over degenerate states. These sums are expressed in terms of the quadratic form of the wave function for a state with zero angular quantum numbers, l=m=0. The nonadiabatic coupling of quasi-crossing terms with other terms of the system is analyzed; this effect significantly increases the cross section for single-electron capture.

The cross sections of the detachment of one and two electrons during the collision of two negative ions H − + H − , H − + Cs − , and Cs − + Cs − are calculated in a wide range of collision energies: from the energy threshold to approximately 100 keV. In adiabatically slow collisions, the detachment of electrons occurs as a result of one-or two-electron Auger decays whose rates are calculated in the approximation of asymptotically large separations between ions. For high collision energies, the cross sections of the electron detachment are calculated by the method of close coupling of states. The calculated cross sections are in good agreement with the results of experimental measurements made for the H − + H − collision.

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green’s function G ( r , r ′, E ), where the energy parameter E approaches an atomic energy level: E → E n , E n = − Z 2 /2 n 2 . The Green’s function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem.

We formulate the semiclassical close-coupling method for a theoretical description of ion-pair formation in Rydberg-atom-ground-state-atom collisions at thermal energies and apply it to the process Ca(4s(2)) + Ne*(n) --> Ca- (4s(2)4p) + Ne+. Our results for the formation of an isolated negative-ion state are very close to those obtained previously using the decay model, although the results for S states are somewhat higher, since the decay model underestimates the survival probability for the ion pair. After the inclusion in our close-coupling calculations of the two fine-structure components of Ca-, we find that the cross section increases substantially (by about a factor of 2) because of correlation between probabilities for population of two hue-structure sublevels.

The energy level shifts of one-electron atomic particles H, He + , Li ++ , etc. which interact with a metal surface have been investigated. In the approximation of image charges, an operator describing perturbations of atomic levels has been obtained. By numerically solving the Schro dinger equation, we have calculated energy levels of H(1 s ), H*( n =2), and C 5+ ( n ) as functions of the distance between an atom and surface. Asymptotic behavior of atomic levels at large distances from the surface has been studied. The linear Stark effect for excited states, which was earlier mentioned by A. V. Chaplik, has been found and investigated in detail.

The cross section of single-electron capture in slow H- + A(3+) --> H + A(2+)(n) collisions is calculated in the one-electron approximation by using the close coupling approach. It is found that the change of the electronic configuration, that takes place at every avoided crossing of the ionic and covalent energy terms, is a source of nonadiabatic transitions in the system. This effect leads to a substantial increase of the total cross section and produces an effective repopulation of individual covalent states.

The cross section for one-electron transfer is calculated in this paper. The collisional system is treated as a three-electron one and matrix elements for the formation of excited helium in both singlet and triplet states (1S, , P and , P, D) are obtained. Close-coupling calculations were done for the 27 (1S, , P and , P, D) final states covering the range 1 - of the relative collision velocity. An approximation is used for the effective potential of and Coulomb Green's functions are used to describe the weakly bound electron of . A satisfactory agreement is obtained with the experimental cross section.

The dissociative recombination (DR) of vibrationally excited H-2(+) ions to form products in high Rydberg states has been investigated experimentally and theoretically for small (0.01 - 0.1 eV) center-of-mass energies of the projectile electron. The merged beam method was used in the experiment and very large cross sections were found for DR from highly vibrationally excited states. The Rydberg states population was analyzed by the application of an electric field ionizer with an axial electric field in excess of 70 kV/cm, which is sufficient to ionize Rydberg states with n greater than or equal to 10. Experiments with and without the ionizer were performed acid cross sections sigma(0 < n less than or equal to 21), sigma(n < 10), and sigma(10 less than or equal to n less than or equal to 21) were measured. The dipole approximation was used for the interpretation of the experimental results. Molecular rovibrational transitions were considered quantum mechanically. At low collision energy (0.01 eV), DR cross sections with high n = 10-21 Rydberg products arise from initial vibrational states v greater than or equal to 15. Absolute values of these cross sections are found to be of the order of magnitude of 10(-12)-10(-13) cm(2). Comparison of theoretical and experimental results has shown that the modified back autoionization (involving transitions to the continuum and to very high n; that is the ''indirect'' mechanism of DR) plays a significant role for all cross sections.

The dissociative recombination of vibrationally excited H2+ ions to form products in high Rydberg states has been measured. Surprisingly large cross-sections are found for this channel. This seems to be an example of super-dissociative recombination.