We describe a phenomenon of nonlinear optics that occurs in the framework of transverse effects and optical vortices in lasers. We find that in a class-B laser vortices can never be at rest, but move, starting from an initial symmetry breaking of the direction of motion, continuously. In a cylindrically symmetric laser this motion will normally be about the laser axis, while in a constant background the motion is toruslike.

A symmetric eikonal model is developed to study the electron excitation of dielectronic atomic targets by impact of bare nuclei. An independent-electron approximation is used, where one of the electrons, the passive one, is assumed to remain frozen during the reaction. The influence of the passive electron on the trajectory followed by the projectile is determined in calculating the differential cross sections. Total cross sections are also computed and compared with available experimental data for the impact of different projectiles with He, ${\mathrm{Fe}}^{24+}$, and ${\mathrm{Kr}}^{34+}$ targets.

We have measured the differential excitation cross sections of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Delta }_{\mathrm{g}}^{}{}_{}{}^{}$ and b ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$ states of molecular oxygen by electron impact. The energy range was from 5.0 to 20 eV. The angular range was from 12° to 156°. We found maximum cross sections near 7 eV for the electronic excitations. Our results are compared with theory and other experimental results. Our results agree very well with theoretical prediction at 5 eV, but other experimental results have noteworthy differences.

The generalized Breit interaction is included in the scattering matrix elements when determining collision strengths for electron-impact excitation of highly charged ions. We use a relativistic distorted-wave approach that employs a Dirac-Fock-Slater potential to calculate the free-electron wave functions. This same potential is used to calculate the atomic-structure data. Collision strengths are presented for H-like, He-like, and Li-like ions for a range of Z values and impact-electron energies. Good agreement is obtained when comparing to the few existing calculations for hydrogenic ions. The effect of including the interaction is found to be small for ions with Z≊26, but increases steadily with Z. Changes of nearly 70% are observed for Z=92. Effects for the more complex He-like and Li-like ions are greater than for the hydrogenic analogs for the entire range of Z values considered. The accuracy of some simpler forms of the Breit interaction is also discussed.

We have measured positron-ionization time-of-flight mass spectra of butylbenzene, decane, tetraethylsilane, and other organic molecules as a function of the positron kinetic energy. Our data show that fragment ions are produced at onset energies above the positronium- (Ps) formation threshold, while the molecular ions are formed starting at the Ps threshold. The onset energies have been found to depend strongly on the nature of the fragment and to be equal to the dissociation energy of the fragmentation reaction. Decreases in the molecular-ion populations in the mass spectra were observed to be accompanied by increases in fragment-ion populations. A two-step process, stripping followed by unimolecular dissociation, is proposed to be responsible for the production of the fragment ions. The degree of dissociation can be controlled by selecting the positron incident energy.

A time-dependent description of the dissociative-attachment process is formulated within the framework of the projection-operator formalism of scattering theory. A generally applicable computational scheme for the solution of the resulting integro-differential equation of motion is developed. The concepts and computational techniques are illustrated for a model of a d-wave shape resonance as well as for the p-wave ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ shape resonance in electron-${\mathrm{H}}_2$ collisions. It is shown that the time-dependent wave-packet picture yields qualitative insight into the dynamics of the dissociative-attachment reaction. The origin of the complete failure of the local-complex-potential approximation for the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ resonance in e+${\mathrm{H}}_2$ becomes apparent in the time-dependent picture.

We have measured the scattering-angle dependence of electron loss in 1.1-MeV/u ${\mathrm{Li}}^{2+}$+(${\mathrm{H}}_2$,He) and 0.88-, 2.0-, and 3.1-MeV/u ${\mathrm{C}}^{5+}$+(${\mathrm{H}}_2$,He) collisions and have attempted to extract the impact-parameter dependence of electron loss, as well as to separate the elastic (screening) and inelastic (antiscreening) target-electron contributions to this process. By dividing the experimental electron-loss probability by the (resolution folded) theoretical probability for screening only, we show that a separation can be effected. For ${\mathrm{Li}}^{2+}$+${\mathrm{H}}_2$ and ${\mathrm{C}}^{5+}$+${\mathrm{H}}_2$ the experimental loss probability is in good agreement with expressions derived from the straight-line and Coulomb trajectory approximation, but with the He target deviations can be seen, especially at lower bombarding energies. This contrasts with integrated cross sections which fit equally well in all cases.

Electron excitation from monoelectronic targets by impact of bare ions from low intermediate to high collision energies is theoretically studied by using the symmetric eikonal approximation. In addition, multichannel semiclassical impact-parameter calculations are also carried out. Distortion effects introduced by the projectile charge are shown to appear in the theoretical models at low intermediate collision energies.

The laboratory energy distribution of protons in coincidence with an ${\mathrm{H}}^{\mathrm{-}}$ ion, resulting from the dissociation of excited ${\mathrm{H}}_3^{+}$, has been measured for ${\mathrm{H}}^{+}$-${\mathrm{H}}^{\mathrm{-}}$ pairs emitted along the beam for 4.0-keV ${\mathrm{H}}_3^{+}$-He collisions. An approximate energy distribution of ${\mathrm{H}}^{+}$-${\mathrm{H}}^{\mathrm{-}}$ pairs for the collinear configuration of the dissociation products is obtained by transforming the measured laboratory spectrum to the ${\mathrm{H}}_3^{+}$ center-of-mass (c.m.) frame. Coincidence data suggest that the reaction producing ${\mathrm{H}}^{+}$-${\mathrm{H}}^{\mathrm{-}}$ pairs where the ${\mathrm{H}}^{+}$ ion has near-zero energies (<0.5 eV) in the c.m. frame is a low-probability process. We have also computed the adiabatic Born-Oppenheimer energies of ${\mathrm{H}}_3^{+}$ ions using a full configuration-interaction calculation with a basis set of atomic orbitals consisting of 1s, 1s’, 1p’, 2s, and 2p centered on the protons forming an isosceles (${\mathit{C}}_{2\mathit{v}}$ symmetry) or an equilateral (${\mathit{D}}_{3\mathit{h}}$ symmetry) triangle. The states leading to asymptotic ${\mathrm{H}}^{+}$+${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$ limits have been identified by calculating 〈1/${\mathit{r}}_{12}$${\mathrm{〉}}^{\mathrm{-}1}$, the inverse of the expectation value of the electron-electron repulsion term. The states identified by this procedure have adiabatic Born-Oppenheimer energies of 40–45 eV above the ${\mathrm{H}}_3^{+}$ ground state at the ${\mathrm{H}}_3^{+}$ equilibrium separation. The limits on the total available internal energy to be shared by the three dissociation products that one obtains from the experimentally determined ${\mathrm{H}}^{+}$-${\mathrm{H}}^{\mathrm{-}}$ coincidence spectrum are consistent with the identified ${\mathrm{H}}_3^{+}$ excited states.

Partial and differential cross sections are calculated for Cl and Br near the ${\mathit{nsnp}}^5$ thresholds. We compare our calculations with experiment, obtaining good agreement over part of the energy range. The autoionizing structure is well reproduced, but the slowly evolving direct contribution to the photoionization cross section does not have the correct shape. Most of the discrepancies with experiment in the autoionizing part of the spectrum appear to derive from our neglect of doubly excited resonances in the calculations. This possibility points to the importance of an accurate theoretical description of doubly excited states of open-shell atoms. The similarity of the Cl and Br spectra in this energy range is not as pronounced as their similarity near the ${\mathit{ns}}^2$${\mathit{np}}^4$ thresholds.

A reliable knowledge of the short-range behavior of the generalized response function in low-energy electron scattering from atoms (or molecules) is a very important tool for the quantitative study of low-energy resonances, elastic- and inelastic-scattering cross sections, and the corresponding angular distributions. In the present study, a description of the required function is used by starting from a short-range representation of the correlation forces via local density-functional theory. Results are reported for elastic scattering from rare gases at various collision energies and rather good agreement is found in all cases both with experiments and with more sophisticated calculations. The physical correctness of the present approach and its capability of describing angular distributions and elastic collision processes over a broad range of energies through fairly simple calculations make it an attractive proposition for further extensions to molecular targets and to electronic excitation processes.

Ll, Lα, Lβ, and Lγ x-ray fluorescence cross sections have been measured for the elements Pr, Ho, Yb, Au, and Pb using photon energies of 23.62 and 24.68 keV. Measurements have been performed using an x-ray tube with a secondary-exciter system as the excitation source. The secondary exciters of Cd and In were pure metals (>99.9%). The x-ray tube with a secondary-target arrangement was used to obtain high intensity with a high degree of monochromatization. By using an x-ray tube, it is possible to measure x-ray fluorescence cross sections and ratios even for low-intensity x rays (Ll). Experimental results have been compared with the theoretically calculated values of L x-ray fluoresence cross sections. A fairly good correspondence is observed between experimental and calculated values. The intensity ratios for the intense transitions ${\mathit{I}}_{\mathit{L}\mathrm{\beta }}$/${\mathit{I}}_{\mathit{L}\mathrm{\alpha }}$ are in good agreement with the calculated values.

Within the framework of scattering integral equations in momentum space, we present numerical results of scattering of three identical bosons at low energies in two dimensions for short-range separable potentials. An analysis of the present numerical results reveals the three-particle scattering observables to be independent of potential shape provided the low-energy two-particle binding energy and scattering length are held fixed throughout the investigation. We think that the present conclusion of model independence will be valid for any potential, local or nonlocal, whose range is much smaller than the size of the two-particle bound state.

We present calculations of spin asymmetries for the elastic and 2 ${}_{}{}^2{}_{}{}^{}$P channels, differential and integrated cross sections for the elastic through to 4 ${}_{}{}^2{}_{}{}^{}$F channels, and total cross sections of electrons scattering on lithium at a range of energies from 1 to 200 eV. Very good agreement is found with available measurements at all energies, which for the spin asymmetries may only be achieved by the inclusion of coupling of the low-lying target states to the target continuum.

We present an application of pseudopotentials to ab initio calculations of elastic and electronically inelastic electron-molecule-collison cross sections. We use the Schwinger multichannel method (SMC) implemented with the local-density norm-conserving pseudopotentials of Bachelet, Hammann, and Schlüter [Phys. Rev. B 26, 4199 (1982)]. In our procedure, the core electrons and protons are replaced by the nonlocal but single-particle pseudopotential and the valence electrons are treated in a many-body framework, as in the SMC method. Our calculated integral and differential cross sections are in very good agreement with previous all-electron calculations.

The electronic stopping power of hydrogen beams penetrating He gas has been calculated by solving the time-dependent Schrödinger equation. Special attention has been given to low incident energies where capture and loss of the projectile electron are the most important energy-loss mechanisms. These mechanisms are included in a consistent theoretical treatment and good agreement with experimental data has been obtained for high- as well as for low-energy projectiles in a gas target.

We report polarization propagator calculations within the random-phase approximation of several isotropic moments and their directional components of the dipole-oscillator-strength distribution of ${\mathrm{H}}_2$ and of ${\mathrm{H}}_2$O. The calculations show that there is strong dependence on the polarization direction of the incoming beam. The dependence of the moments on the molecular geometry is also discussed. In particular, the mean excitation energy for stopping is found to be very directionally sensitive, leading to the necessity of using directionally specific mean excitation energies when discussing oriented targets. It is possible that the sample phase dependence of the stopping power of water may be in part due to directional effects in ${\mathit{I}}_0$. A transferable bond mean excitation energy for the O-H bond is calculated, and is found to be constant within ±1% for ?H-O-H from 95° to 120° at constant bond length ${\mathit{R}}_{\mathrm{OH}}$. It agrees well with previous results.

We have measured the vacuum-ultraviolet 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$–1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,0}$ transition wavelengths in heliumlike neon by photographic spectroscopy of a recoil-ion source. The results are 1248.10±0.01 and 1277.74±0.04 Å, respectively, and are a sensitive test of present relativistic and quantum-electrodynamic calculations. Earlier photographic data have been reanalyzed for comparison with these results.

The K-shell excitation spectra of the hydrides water, ammonia, and methane have been measured in photoabsorption experiments using synchrotron radiation in combination with a high-resolution monochromator. For the case of methane, in particular, a wealth of spectral detail is observed which was not accessible in previous studies. The measured excitation energies and relative intensities compare well with values calculated using a complete second-order approximation for the polarization propagator. In order to determine the extent of admixing of valence excitations (i.e., transitions into virtual ${\mathrm{\sigma }}^{\mathrm{*}}$ orbitals) to the Rydberg manifolds, the X-H bond lengths have been varied in the calculations. In the case of ${\mathrm{H}}_2$O, the two lowest-energy bands are due to the O 1s-4${\mathit{a}}_1$/3s and O 1s-2${\mathit{b}}_2$/3p transitions and have strong valence character; their width indicates that both excitations are dissociative. The ${\mathrm{NH}}_3$ and ${\mathrm{ND}}_3$ spectra are also broad which is not only due to possible dissociation but also to unresolved vibrational fine structure (${\nu }_2$ mode) and a Jahn-Teller instability. Valence character is concentrated in the lowest excited state in the Rydberg ns manifold, but is distributed more uniformly over the np(e) manifold. The weak dipole-forbidden C 1s-3s(${\mathit{a}}_1$) transition in ${\mathrm{CH}}_4$ and ${\mathrm{CD}}_4$ is accompanied by vibrational structure due to the ${\nu }_4$ mode, indicating that it derives its intensity from vibronic coupling with the C 1s-3p(${\mathit{t}}_2$) transition. The structure on the latter band is extremely complicated due to Jahn-Teller coupling and cannot be assigned at present, as is the case for the Rydberg transitions at higher energies. The higher np Rydberg excitations contain considerable valence character.

Isotope shifts and hyperfine constants are reported for the radioactive isotopes ${\mathrm{Kr}}^{81}$ and ${\mathrm{Kr}}^{85}$ and the stable isotope ${\mathrm{Kr}}^{83}$. The previously unreported nuclear moments of ${\mathrm{Kr}}^{81}$ were determined to be ${\mathrm{\mu }}_{\mathrm{I}}$=-0.909(4) nuclear magneton and Q=+0.630(13) b from the hyperfine constants. This work increases the number of transitions for which ${\mathrm{Kr}}^{85}$ hyperfine constants and isotope shifts have been measured from 1 to 4. The hyperfine anomaly for krypton reported in the previous measurement of ${\mathrm{Kr}}^{85}$ hyperfine constants [H. Gerhardt et al., Hyperfine Interact. 9, 175 (1981)] is not supported by this work. The isotope shifts and hyperfine constants of ${\mathrm{Kr}}^{83}$ measured in this work are in excellent agreement with previous work. Saturation spectroscopy was used to study transitions from krypton's metastable ${1\mathrm{s}}_5$ state to the ${2\mathrm{p}}_9$, ${2\mathrm{p}}_7$, and ${2\mathrm{p}}_6$ states. In saturation spectra, different line shapes were observed for the even- and odd-mass krypton isotopes. This even- versus odd-line-mass shape difference can be explained using the large cross section that has been reported for collisional transfer of the ${1\mathrm{s}}_5$ state excitation between krypton atoms. Two-color two-photon laser-induced fluorescence was used to measure the hyperfine spectra of the ${1\mathrm{s}}_5$-${4\mathrm{d}}_4^{\prime }$ transition using the ${2\mathrm{p}}_9$ state as the intermediate state. This technique proved to be more sensitive than saturation spectroscopy.