A variational method based on results for self-adjoint operators due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)] is developed to calculate upper and lower bounds on the energy eigenvalues for the one-electron Dirac Hamiltonian. The method avoids relativistic variational collapse for any one-electron potential. This result is confirmed analytically in the case of the Coulomb potential and numerically in the case of hydrogenic atoms in very strong magnetic fields for which standard variational techniques cannot preserve bounds. The upper bound thus obtained converges rapidly to the best available numerical results, and provides a very efficient technique for the search of the optimal variational energy by means of a minimization procedure.

The retardation (or Casimir) potential for Rydberg ${\mathrm{H}}_2$—a hydrogen molecule with one electron in a highly excited, hydrogen-atom-like electronic state and an ${\mathrm{H}}_2^{+}$ core—is determined using time-dependent quantum electrodynamics in the Coulomb gauge. The potential obtained is valid over a range of r, the Rydberg electron-core separation, from several ${\mathit{a}}_0$ to infinity, and accurate numerical results for the magnitude of the corresponding energy shift are calculated using a discrete representation of the electric dipole oscillator-strength spectrum. The prospects for measurement are analyzed.

The collision-induced dissociation of ${\mathrm{H}}_3^{+}$ on He at a relative energy of 4.8 keV was performed. The laboratory energy distributions of ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{H}}^{+}$ were measured. The energy-analyzed spectrum of ${\mathrm{H}}^{\mathrm{-}}$ was measured in coincidence with ${\mathrm{H}}^{+}$, and the energy-analyzed spectrum of ${\mathrm{H}}^{+}$ was measured in coincidence with ${\mathrm{H}}^{\mathrm{-}}$. From these results, the energy absorbed by the ${\mathrm{H}}_3^{+}$ molecule in the excitation process induced by the collision with He previous to its breakup, was evaluated. The center-of-mass energy distributions of both fragments (${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{H}}^{+}$) were obtained, and from these the average angle between the positive fragments was determined, as well as the mean total kinetic energy gained by the fragments, and the most probable energy for both charged products. Comparisons with previous measurements are given.

The cross section for single-photon detachment of an electron from the metastable ${\mathrm{Be}}^{\mathrm{-}}$ ion has been measured at a photon energy of 2.076 eV to be 31±3 Mb. The method of laser photodetached electron spectroscopy was used in the measurement and the asymmetry parameter that characterizes the angular distribution of the detached photoelectrons was also measured to be β=0.49±0.02 at the same energy.

The theory and numerical methods required for extending the distorted-wave Born approximation to the description of relativistic (e,2e) processes are developed. We compare the results of our theoretical approach with the absolute experimental data available in coplanar asymmetric geometry. A significant improvement over earlier calculations is achieved. It is shown that both the shape and the absolute magnitude of the triple differential cross section are strongly influenced by elastic electron-nucleus collisions in the incident and final channels. We predict an important increase of the magnitude relative to the binary peak and changes in shape of the secondary maximum of the triple differential cross section as a function of the nuclear charge.

High-resolution (e,2e) energy spectra are presented which enable the isolation of interference effects between J=0,1,2 multipoles in electron-impact ionization of cadmium. It is found that both resonant and nonresonant processes are important. Relative magnitudes and phases of ionization amplitudes are obtained which disagree with plane-wave Born approximation calculations.

Single- and double-photoionization processes of carbon dioxide (${\mathrm{CO}}_2$) have been studied in the photon-energy region of 30–100 eV by use of time-of-flight mass spectrometry and the photoion-photoion coincidence method together with synchrotron radiation. The single- and double-photoionization cross sections of ${\mathrm{CO}}_2$ are determined. Ion branching ratios and the partial cross sections for the individual ions, respectively produced from the precursors ${\mathrm{CO}}_2^{+}$ and ${\mathrm{CO}}_2^{2+}$, are determined separately at excitation energies where the molecular and dissociative single- and double-photoionization processes occur simultaneously. The threshold for the molecular double photoionization was found to be 37.6±0.3 eV. The thresholds for the ${\mathrm{CO}}^{+}$+${\mathrm{O}}^{+}$ and ${\mathrm{C}}^{+}$+${\mathrm{O}}^{+}$ channels of ${\mathrm{CO}}_2^{2+}$ are at 39.2±0.3 and 47.2±0.5 eV, respectively. Furthermore, in single photoionization, the production of ${\mathrm{CO}}_2^{+}$ is dominant, whereas with double photoionization, dissociation becomes dominant.

Screening effects for transition probabilities in collisions of charged particles with an atom or stripped ion are investigated using the modified hyperbolic-orbit path in the semiclassical approximation. Effective nuclear charges for bound electrons in many-electron atoms are determined by new screening constants [Y.-D. Jung and R. J. Gould, Phys. Rev. A 44, 111 (1991)]. Applications were made to O, ${\mathrm{O}}^{4+}$, and ${\mathrm{O}}^{7+}$. For these targets, the transition probabilities are calculated for 1s→2p transitions. The results show that the maximum point of the transition probability is shifted to the nucleus with an increase of the screening effect. Moreover, the maximum amplitude of the transition probability is appreciably reduced as the screening effect increases.

We analyze the convergence of the Legendre polynomials expansion of the doubly differential cross section (DDCS) for soft electron emission (SEE) in ion-atom collisions. This expansion has been recently employed in the analysis of the angular shape of theoretical as well as experimental data on SEE. Numerical calculations using the continuum-distorted-wave–eikonal-initial-state (CDW-EIS) approximation show that for sufficient low electron velocity, the DDCS for ionization is well described with a few terms of the expansion. Besides, we show analytically that the expansion reduces to the first three terms in the zero-emission-velocity limit, within CDW or CDW-EIS approaches.

Experimental small-angle electron differential cross sections (DCS’s) for the resonance transition in Na at 10, 20, and 54.4 eV are contrasted through the generalized oscillator strength (GOS) and with the GOS from a recent universal extrapolation function [A. Z. Msezane and I. A. Sakmar, Phys. Rev. A 49, 2405 (1994)]. We conclude that almost all of the measurements reported suffer from an incorrect determination of the DCS near-zero scattering angles and/or from an improper normalization. Dynamic effects are unimportant at 20 and 54.4 eV at small scattering angles.

Many-body perturbation theory has been used to calculate photoionization cross sections with excitations (3${\mathit{d}}^{10}$4s→3${\mathit{d}}^9$5skl, ${3\mathrm{d}}^9$4pkl, 3${\mathit{d}}^8$4${\mathit{s}}^2$kl, ${3\mathrm{d}}^8$4s5skl, and 3${\mathit{d}}^8$4s4dkl) of atomic copper from the single-ionization threshold 7.7–120.0 eV. Resonance structures due to both one-electron excitations (3p→nl and 3d→nl) and two-electron excitations (3${\mathit{d}}^{10}$4s→3${\mathit{d}}^9$5snl and 3${\mathit{d}}^9$4pnl) are included. The large nonresonant photoionizations (satellites) leaving the ion in 3${\mathit{d}}^9$5s and 3${\mathit{d}}^9$4p final states are found. The resonant satellites in the region of the 3p threshold are the enhanced resonances in the ${\mathrm{Cu}}^{+}$ 3${\mathit{d}}^8$4${\mathit{s}}^2$ via a super-Coster-Kronig (SCK) transition, and the resonant satellites between 80 and 90 eV in the experiment are the enhanced resonances in the ${\mathrm{Cu}}^{+}$ 3${\mathit{d}}^8$4s5s and 3${\mathit{d}}^8$4s4d due to SCK decay. The total cross section is in good agreement with the experimental value.

A fully quantal calculation of the excitation cross sections for the fine-structure levels of ground-state atomic oxygen, in collisions with oxygen atoms at low energies, is presented. The results are compared with the cross sections obtained in a previous calculation.

The fully retarded dispersion interaction potentials, including many-body interactions, among neutral molecules are found in a systematic way. The method used relates the total zero-point energy of all the electromagnetic modes with the spectral sum of a linear operator. The difference between the zero-point energies with and without the molecules present is given as a contour integral. From the value of this integral it is possible to extract the N-body dispersion energy by locating those terms which depend on the product of the polarizabilities of those N molecules. The Casimir-Polder pairwise energy is the two-body result. General formulas are found, and the special cases for N=3 and 4 are discussed in detail. The nonretarded interaction potentials are found as the asymptotic limits for small intermolecular separations, and the London and the Axilrod-Teller results are the N=2 and N=3 special cases. The N=4 near-zone limit is presented in its explicit form. It is of interest to note that, for the one-body case, the energy shift given by this method is the nonrelativistic Lamb shift.

Ionization and charge-transfer cross sections of atomic hydrogen in collision with multiply charged ions are calculated for various projectile charges (Z=2–8) in the energy range from 1 to 400 keV/amu by the atomic-orbital close-coupling method. Many pseudostates constructed from Gaussian-type orbitals are used on the projectile and the target for the representation of continuum states. The present ionization cross sections show systematic agreement with measurements for ${\mathrm{He}}^{2+}$, ${\mathrm{Li}}^{3+}$, and ${\mathrm{C}}^{6+}$ impact over the entire energy range where experimental data are available. The present calculations also produce reliable consistent cross sections for excitation and electron capture simultaneously.

Some heuristic aspects of one-channel transparency are revealed and explained. Particularly, the prediction of peculiarities of the transparency for waves moving in the space of discrete variables (numbering, e.g., channels or mixing configurations) is presented. The phenomenon of complete multichannel penetrability, which requires the potential barriers in interaction matrices, is investigated using exactly solvable models with different number of bound states, channels, and variation of thresholds. These models can help to deepen our understanding of properties of real quantum (nuclear, atomic) multichannel systems.

A theoretical model, which is free of adjustable or fitted parameters, for calculating electron-impact ionization cross sections for atoms and molecules is presented. This model combines the binary-encounter theory with the dipole interaction of the Bethe theory for fast incident electrons. The ratios of the contributions from distant and close collisions and interference between the direct and exchange terms are determined by using the asymptotic behaviors predicted by the Bethe theory for ionization and for stopping cross sections. Our model prescribes procedures to calculate the singly differential cross section (energy distribution) for each subshell using the binding energy, average kinetic energy, and the differential dipole oscillator strengths for that subshell. Then the singly differential cross section is integrated over the ejected electron energy to obtain the total ionization cross section. The resulting total ionization cross section near the threshold is proportional to the excess energy of the projectile electron. We found that this model yields total ionization cross sections for a variety of atoms and molecules from threshold to several keV which are in good agreement (∼10% or better on average) with known experimental results. The energy distributions also exhibit the expected shapes and magnitudes. We offer a simpler version of the model that can be used when differential oscillator strengths are not known. For the ionization of ions with an open-shell configuration, we found that a minor modification of our theory greatly improves agreement with experiment.

Photoabsorption cross sections of the ground state of four oxygen-group atoms are calculated using the eigenchannel R-matrix method. The calculation is performed in the energy range from the first to the third ionization threshold of the residual ions. The present calculations are in good agreement with experimental results except for Te. We investigate the origin for some of the generic features of the cross section. A systematic study of the convergence as a function of type of basis demonstrates the importance of the polarizability of the valence shell. The lessons learned from these atoms should be generally applicable to other columns of the periodic table.

Calculations of the electron-positron pair production by a single photon in the Coulomb field of a nucleus with simultaneous capture of the electron into the K shell are presented. Numerical results are given for some nuclear charges up to 92 and energies from threshold to 15 MeV. Using the equivalent-photon method of Weizsäcker and Williams, reliable estimates of the cross sections for the production of ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$ (K orbit) pairs by very-high-energy fully stripped heavy ions can be made for arbitrary nuclear charges.

Cross sections for double ionization and ionization plus excitation of ${\mathrm{H}}_2$ by the high-energy charged particles are calculated as a function of the orientation of the ${\mathrm{H}}_2$ internuclear axis. The contributions of the double collision, the shake-off or shake-up, and ground-state correlation mechanisms have been considered. The calculated cross sections have been compared with the data of Edwards et al. [Phys. Rev. A 42, 1367 (1990); 44, 797 (1991); 46, 6970 (1992)]. Our results for double ionizations are acceptable, while the ionization-excitation cross sections have a strong dependence on the bound-state and continuum-state wave functions.

Equilibrium charge-state distributions for singly and doubly ionized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ ions of energy E${(}^3$He)=200 MeV (β=0.36) have been measured for atomic targets ranging from carbon to bismuth (Z=6,14,28,40,50,67,73,83). A magnetic spectrometer was used to simultaneously measure the rate of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions and the current of the incident beam of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions. The ratio of the fraction of ions Y${(}^3$${\mathrm{He}}^{+}$/Y${(}^3$${\mathrm{He}}^{2+}$) was found to increase from 3×${10}^{\mathrm{-}9}$ for Z=6 to 2×${10}^{\mathrm{-}7}$ for Z=83. Very good agreement with the experimental ratios was obtained for calculated ratios based on theoretical stripping (ionization) and capture cross sections. The cross sections are dominated by capture from K orbits only for atoms up to about Z=25. For target atoms with high Z, contributions up to principal quantum numbers n=4 (N orbits) must be included.