We describe a class of periodic tiling that corresponds to toroidal arrangements of trivalent atoms with pentagonal, hexagonal, and heptagonal rings. The relaxation of model carbon atoms in molecules represented by these tilings is used to yield estimates of the energy per bond, the energy of the least bound atoms, and the highest occupied and lowest unoccupied molecular-orbit energies. The results support the point of view that stable toroidal carbon molecules can exist.

We calculate the energy-level shifts of an atom near a dielectric microsphere. With the quantum electrodynamic linear-response formalism and the exact field susceptibility satisfying the boundary conditions, the energy shifts of a ground-state atom are calculated numerically. From the numerical results, in particular, we are able to identify the short-range instantaneous van der Waals interaction energy and the long-range Casimir-Polder retarded interaction energy between two polarizable objects (atom and cavity).

The photoionization (PI) cross section of hydrogen in external electric and magnetic fields was studied by a direct version of the recursive residue generation method, combined with complex dilation and discretization. The PI cross section was computed for three different combinations of fields: an electric field only, perpendicular electric and magnetic fields, and, finally, an electric field with an angle of 80° to the magnetic field. The field-induced resonances were shown to have Fano-type profiles, with a shape depending on the field combination. The fluctuations of the base line were studied using an autocorrelation function C(ε). For the field combinations studied here, C(ε) has for small ε an initial Lorentzian shape. With increasing ε different oscillatory structures in C(ε) were observed. The correlation functions were studied for several energy ranges, achieving a common Lorentzian shape for the highest range, independent of the field combinations. A simple interpretation of the behavior for all cases in terms of chaotic ionization is possible.

The linear-response contribution to the exchange-correlation energy functional ${\mathit{E}}_{\mathrm{xc}}$[n] of density-functional theory is reconsidered. An alternative form for this functional is suggested that resolves the convergence problems for finite systems inherent in the original form introduced by Hohenberg and Kohn [Phys. Rev. 136B, 864 (1964)]. Within the exchange-only approximation in which the linear response kernel is known exactly and the optimized-potential model serves as a rigorous comparative standard, the present functional is applied to spherical atoms and jellium spheres. Self-consistent results for these systems indicate that this functional might be worth a more detailed examination.

A complete, numerical calculation of the effect of the exchange of two virtual photons between the electrons in the ground states of heliumlike systems is presented. Feynman diagrams with uncrossed and crossed photons are evaluated, using the Furry interaction picture [Phys. Rev. 81, 115 (1951)], neglecting nuclear recoil. The calculations are carried out in the Feynman gauge as well as in the Coulomb gauge, and the gauge invariance of this set of diagrams is verified with high numerical accuracy. The numerical technique employed is similar to that recently developed for our self-energy calculations. [H. Persson, I. Lindgren, and S. Salomonson, Phys. Scrip. T 46, 125 (1993); I. Lindgren, H. Persson, S. Salomonson, and A. Ynnerman, Phys. Rev. A 47, R4555 (1993)]. An explicit summation is performed over a complete set of intermediate states with positive and negative energy, generated with the technique of discretization. The photon propagators are expanded in spherical waves, and the radial integrations are performed numerically using analytical Bessel functions. Moreover, the integration over the photon energy is performed numerically. The calculations are performed for different values of the nuclear charge in the range Z=2–92. Corresponding calculations are also performed without retardation and neglecting the effect of negative-energy states (virtual electron-positron pairs), thus simulating relativsitic many-body calculations in the no-virtual-pair approximation. The difference, which in this way is obtained with high numerical accuracy, represents the ‘‘quantum electrodynamics (QED) correction,’’ which should be added to the many-body result in a combined QED–many-body procedure. The various contributions to the two-photon exchange have been analyzed in detail and compared with the analytical results to order (Zα${)}^3$ of Sucher [Phys. Rev. 109, 1010 (1958)]. From our analysis, general conclusions can also be drawn concerning the accuracy of various relativistic many-body approaches.

Relativistic many-body perturbation theory is applied to determine energies of [2${\mathit{p}}^5$3s] excited states of neonlike ions with nuclear charges in the range Z=10–92. These calculations start with a ${\mathit{V}}^{\left(\mathit{N}\mathrm{-}1\right)}$ Hartree-Fock potential and include correlation corrections. Core-hole corrections are treated to all orders in perturbation theory while the core-core, valence-core, and valence-hole corrections are treated to second order only. The Breit interaction is also included to second order, but the dominant correlation corrections to the Breit interaction are identified and iterated to all orders. Frequency-dependent corrections to the Breit interaction and mass-polarization corrections are treated to first order only. Lowest-order radiative corrections are included by evaluatng the electron self-energy and vacuum polarization in a local potential that approximates the Hartree-Fock potential. Detailed comparisons are made with measurements and with other calculations.

Measurements of collision-induced absorption spectra in the ${\mathrm{H}}_2$ fundamental band are reported for gaseous mixtures of hydrogen and helium at temperatures of 78 and 298 K and frequencies from about 3900 to 5200 ${\mathrm{cm}}^{\mathrm{-}1}$. Spectral line shapes are calculated from the fundamental theory with the isotropic interaction approximation, which has been successful in all previous comparisons of the kind for pure hydrogen and hydrogen–rare-gas mixtures. In the present case, however, the comparison of measured and calculated absorption profiles suggests that small differences between theory and measurement may exist for ${\mathrm{H}}_{2\mathrm{-}}$He in the ${\mathrm{H}}_2$ fundamental band, which are marginaly greater than the combined uncertainties of theory and measurement. Presumably, these are due to the neglect of the anisotropy of the interaction; the ${\mathrm{H}}_2$-He system in the ${\mathrm{H}}_2$ fundamental band is more sensitive to the anisotropy of the interaction than the systems and bands studied previously.

The cross sections for electron-impact excitation of the heliumlike forbidden line z, intercombination lines y and x, and the resonance line w, together with the associated lithiumlike collisional satellite lines q, r, t, u, and v have been measured for Ti, V, Cr, Mn, and Fe (Z=22–26) on the Livermore electron beam ion trap. The measurements were made near the threshold for excitation of the heliumlike transitions, where no other processes can contribute to the excitation of the lines, and are normalized to the cross sections for radiative electron capture. The uncertainties in the measurements are less than 8% for the heliumlike Fe transitions and between 11% and 15% for the lithiumlike Fe transitions together with a 3% systematic uncertainty from the normalization to theoretical radiative recombination cross sections. We find good agreement with results from a distorted-wave calculation.

The absorption coefficients for the free-free transitions in collisions between slow electrons and neutral oxygen atoms have been calculated for wavelengths in the range of 1 to 30 μm and temperatures between 5000 and 50 000 K. The wave functions of the unbound electron are the solutions of a one-electron Schrödinger-like continuum equation that includes the Coulomb, exchange, and polarization interactions with the oxygen atom. The polarization potential is determined by a first-principles calculation based on the method of polarized orbitals. Our absorption coefficients are in good agreement with those of John and Williams [J. Quant. Spectrosc. Radiat. Transfer 17, 169 (1977)], but are much smaller than the experimental data of Taylor and Caledonia [J. Quant. Spectrosc. Radiat. Transfer 9, 681 (1969)] and of Kung and Chang [J. Quant. Spectrosc. Radiat. Transfer 16, 579 (1976)].

Two schemes for solving the time-dependent Schrödinger equation are presented. One is based on path-integral techniques, i.e., an explicit expression for the matrix element of the propagator exp (-${\mathit{iH}}_{0,}$lt) in coordinate representation is given, and another is based on a complex Chebychev polynomial expansion of the propagator. The calculating results show that the two schemes presented here are not only accurate but also are efficient.

In calculating the infrared (IR) band shape for bending modes, the angular-momentum coupling between vibration, rotation, and radiation must be taken into account. The accuracy of the energy-corrected-sudden (ECS) model has been proved through many recent applications in isotropic Raman Q-branch profiles. Furthermore, this model is based on the physical infinite-order-sudden (IOS) approximation, which allows inclusion of the other relaxation mechanisms required when considering other spectroscopic branches, such as IR Q-bending bands. To include, in a consistent way, the role of the vibrational angular momentum in the rovibrational relaxation matrix, the relaxation of the rotational angular momentum J and of its associated higher-order tensors [J${]}^{\mathrm{}\left(2\right)\mathrm{}}$,. . . (basically absent in the IOS approximation) is enforced in the present ECS model. Application to the 2076.86 ${\mathrm{cm}}^{\mathrm{-}1}$ infrared rovibrational band of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{16}{}_{}{}^{}$${\mathrm{O}}_2$ leads to the determination of the [J${]}^{\mathrm{}\left(2\right)\mathrm{}}$ relaxation time in agreement with previous values obtained from different measurements. The present theory may be applied to other spectroscopic bands, such as the anisotropic Raman ones.

In the experimental observation of radiationless resonant Raman scattering, features that differ from the idealized case can arise when the spectral width of the incident photon distribution is comparable to the width of pertinent atomic energy levels. These features include nonlinear dispersion of the peak maxima and changes in the symmetry and width of the ejected-electron lines with changes in the average incident photon energy. Under certain conditions, the electron line shapes can become highly asymmetric or even double peaked. The origin of these features in actual experiments is explored through a model calculation for large spectral widths. Some possible applications of these effects are pointed out.

We show that diffraction oscillations in elastic electron-atom scattering can be quantitatively accounted for semiclassically in terms of path interferences. The quantum scattering amplitude is expressed as a topological sum over classical and pseudoclassical paths, containing only information on the classical dynamics. The sum is shown to converge rapidly. The validity of the semiclassical theory of potential scattering is analyzed in terms of the angular-momentum dependence of the classical action for the radial motion.

Measurements of direct Coulomb electron-positron pair production have been made on the tracks of relativistic heavy ions in nuclear track emulsion. Tracks of ${\mathrm{O}}^{16}$ and ${\mathrm{S}}^{32}$ at 200 GeV/nucleon were studied. The measured total cross sections and energy and emission angle distributions for the pair members are compared to theoretical predictions. The data are consistent with some recent calculations when knock-on electron contamination is accounted for.

Theoretical calculations of quantum interference effects occurring in photodetachement of ${\mathrm{H}}^{\mathrm{-}}$ with short-pulse lasers in the presence of a uniform static electric field [Q. Wang and A. F. Starace, Phys. Rev. A 48, R1741 (1993)] are examined in more detail and extended to the case of parallel static electric and magnetic fields. We show that modulation factors characterizing near-threshold cross sections resulting from detachment by relatively long laser pulses may be employed to set the parameters that are most effective for control of detachment cross-section magnitudes with short coherent laser pulses. Use of a static magnetic field to control detached electron wave-packet motion perpendicular to the static field axis is shown to increase greatly the magnitude of quantum interference effects on the cross sections (from 10% of the field-free cross section in an optimized static electric-field case to 50% in a parallel static electric and magnetic-field case). Theoretical dependence of calculated cross sections on laser pulse lengths, time delays, relative phases, frequencies, and classical electron orbit times are presented and discussed in detail.

An improved version of the Siegert method to calculate resonance state parameters directly is presented. A prediagonalization of the Hamiltonian in a real ${\mathit{L}}^2$ basis and an equation partitioning technique are utilized along with an inverse iteration method (combined with a rational fraction root search) to find accurate positions and widths of narrow resonances. Model calculations suggest that the present method is efficient and accurate especially for narrow resonances regardless of the potential range.

Photoionization cross sections of the Be atom are calculated using the hyperspherical close-coupling method where a model potential is employed to approximate the screening of the 1${\mathit{s}}^2$ closed-shell core electrons. The cross sections obtained below the ${\mathrm{Be}}^{+}$(2p) threshold agree well with the results of other calculations and with experiment. Total and partial photoionization cross sections for photon energies between the ${\mathrm{Be}}^{+}$(2p) and ${\mathrm{Be}}^{+}$(3s) thresholds are also calculated.

The deexcitation spectra of the resonantly excited Xe 4${\mathit{d}}_{3/2,5/2}^{\mathrm{-}1}$6p states have been recorded with very high photon and electron energy resolution using the new Finnish beam line at Max-lab, Lund, Sweden. The high resolution enables us to resolve the fine structures of the spectra by utilizing the Auger resonant Raman effect. By comparing the detailed intensity distribution of the 4${\mathit{d}}_{3/2,5/2}^{\mathrm{-}1}$6p→5${\mathit{p}}^{\mathrm{-}2}$6p transitions with the results of the single-channel multiconfiguration Dirac-Fock calculations, the strength of the configuration interaction in both the initial and final states of the resonant Auger decay is clarified. The probabilities of shake transitions are determined by both experiment and theory and the differences in the intensity distribution of spectator, shake, and normal Auger transitions are also discussed.

Electron capture by ${\mathrm{Xe}}^{30+}$ from Ar has been studied for projectile velocities between 0.3 and 1.0 a.u. Coincidence measurements were used to identify experimentally the final states of both target and projectile. The capture of up to eight electrons from the target was observed, while retention of more than three electrons by the projectile was found to be rare. Longitudinal recoil momentum spectroscopy was used to determine average Q values for the capture process as a function of recoil charge state. The Q values were found to have no measurable dependence on projectile velocity and were found to be in good agreement with those values predicted by the extended overbarrier model. Relative cross sections for the different final channels were measured and found to be in adequate agreement with the model prediction. A slight increase with increasing projectile velocity in the radiative-stabilization probability for the two-electron states finally formed on the projectile was observed.

Fully stripped and hydrogenlike Si and Cl ions, in the energy range 2–5 MeV/amu and channeled through a 0.17 μm thick Si single crystal, were used to study the radiative electron capture (REC) into the K shell of the ions. The associated effects due to the solid medium of the target were also investigated from the energy and the derived cross section of the REC photons. The K-shell REC cross sections were found to fall on a universal curve when plotted against the adiabaticity parameter of the collision system. The measured energy shifts in the REC photon energy and the higher yield of REC photons using crystalline targets, as compared to the available gas-target data, are indicative of an ‘‘ion–solid-state effect’’ caused by the electron-wake potential. The magnitude of these effects is shown to increase with Z/v of an ion with charge Z and velocity v, and are in qualitative agreement with recent calculations. The REC cross sections are, however, observed to be slightly smaller than the theoretical estimates after taking into account the effects associated with the solid medium. The widths of the REC peaks are compared with the theoretical models. The results of the present investigation using Si and Cl ions are presented coherently along with our earlier data using lighter ions.