We have computed direct and charge-exchange cross sections for ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ collisions, for projectile energies 1-7 keV, using the close-coupling method with $\mathrm{H}_2^{}{}_{}{}^{+}$ molecular states modified by electron translation factors (ETF's); switching functions recently derived analytically for exact $\mathrm{H}_2^{}{}_{}{}^{+}$ states were used to construct ETF corrections. Basis sets with up to 10 molecular states were used in systematic calculations, and good convergence is found for all atomic cross sections with $n\le 2$. Results have been compared with other theoretical calculations [especially that of Crothers and Hughes (1978-1979)] and with recent experiments. Where differences between our results and those of Crothers and Hughes are found, our results agree more closely with experiment. The most notable case is the $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ charge-exchange (and direct) cross sections, where our results show no minimum whatever near $E=2-4\mathrm{}$ keV, in agreement with experiments of Morgan et al. (1980) and Hill et al. (1979), but in strong disagreement with the calculations of Crothers and Hughes and 1969 experiments of Bayfield. In one case discrepancies between our results and those of Crothers and Hughes can be shown to arise from their treatment of ETF effects (using a different switching function for the $2p{\sigma }_u$ state)—i.e., they obtain a much larger population of the $4f{\sigma }_u$ state than is found here. We have also carried out selected studies with larger basis sets (up to $16u$ states) to examine the behavior of cross sections for excitation to atomic levels with $n\ge 3$. These studies strongly suggest that a "ladder-climbing" sequence of excitations via upper levels is the dominant process by which ionization occurs in ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions at these energies.

Velocity distributions of electrons ejected into the forward direction have been measured with proton beams of energies comprised of between 40 and 240 keV interacting with a helium-gas target. An electron spectrometer was used, which permitted us to study the shape of the resulting peaks as a function of the instrumental angular acceptance. These data are analyzed by introducing a general parametric expression for the scattering amplitude of the ionization process. Strong skewness of the electron cusps towards lower electron velocities are observed, which appear to be independent of the large variation of peak widths as determined by different angular acceptances. It is found that this skewness is important up to the closest neighborhood of the peak top and that it leads to the inclusion of an asymmetric singular behavior of the cross section. Partial peak widths at half maximum, measured towards each side of the peak top, and also the total peak width depend linearly on the transverse experimental acceptance, as given by the product of the ion velocity times the half-angle of the electron acceptance cone. The cusp skewness, defined by the ratio of the partial widths, tends to decrease at the higher ion velocities.

The effect of post-collision interaction (PCI) in inner-shell ionization processes has been investigated observing the xenon $N_{4,5}-O_{2,3}{O}_{2,3}$ Auger spectrum following ionization or excitation by photons with energies above (42 eV), close to (5.05, 0.85, 0.55, and 0.20 eV), and even below (- 0.05 eV) the $4d_{\frac{5}{2}}$ ionization threshold. A detailed quantitative analysis of the experimental spectra is given which takes into account the PCI energy shift and energy distribution as calculated in the semiclassical model of Niehaus. Good agreement between the experimental data and the theoretical predictions is achieved.

We establish the correct mathematical relationship between the Schwinger and Kohn variational principles for scattering theory and show that the Schwinger principle is one rank higher than the Kohn principle. If the same trial scattering wave function is used in these two principles, the Schwinger method should hence give superior results. Application of the Schwinger and Kohn variational principles to scattering by a simple model potential gives results which clearly illustrate this relationship.

The differential cross sections for the elastic scattering of electrons and positrons by lithium are calculated for energies ≥ 10 eV in the corrected static approximation and in an approximation which combines the contribution of the nonstatic parts of the higher-order (n ≥ 3) terms in the Glauber sense with the corrected static contribution. The latter approach yields results which are better when compared to those in the eikonal-Born—series approximation in the entire angular range for the energies where data are available. Results for the total elastic-scattering cross sections in the energy ranges of 10 -200 eV, have also been reported. The present results are in reasonably good agreement with the absolute measurements of Williams et al. and other theoretical results.

Cross sections for the elastic low-energy electron scattering on the singlet-state metastable helium atom have been calculated in 0.01-10-eV energy range, by making use of an extended Hartree-Fock theory in the frozen-core approximation. Both the polarization and exchange effects have been accounted for, within the single-channel scattering approximation model. Computed results are compared with calculations by other authors and with the available experimental data.

An extension of the Jeffreys-Wentzel-Kramers-Brillouin approximation to inelastic processes is used to obtain the scattering amplitude which describes the collisionally induced depolarization of magnetic substate coherences. It is found that the scattering amplitudes contain contributions from two overlapping regions. For large interatomic separations, the different Zeeman sublevels are shifted and mixed by collisions, but follow a common collision trajectory. For small interatomic separations, it is possible to find adiabatic eigenstates which follow distinct collision trajectories. The theory is used to investigate the nature of the depolarizing collision kernels and rates which enter into the analysis of laser spectroscopy experiments.

Radiative and radiationless transition probabilities have been computed relativistically for Li-, N-, F-, K-, and Co-like ions with atomic numbers up to $Z=92\mathrm{}$ and with initial configurations consisting of a few closed inner shells with one deep-lying vacancy. Relativity is found to have a pronounced effect on the Auger rates of these highly ionized systems. Radiationless-transition rates are seen to increase with degree of ionization; the stripping of outer shells has a much smaller effect than creation of an empty inner shell of spectator holes. Fluorescence yields are found to increase with the degree of ionization. In the radiative decay of $1s2s^2$ Li-like ions, initial-state correlation and configuration interaction boost the fluorescence yield by six orders of magnitude at low and medium $Z$.

Multiplet Auger and x-ray emission rates for the $1s2s2p$ configuration of Li-like ions ($13\le Z\le 92$) have been calculated relativistically in the intermediate-coupling scheme, using Dirac-Hartree-Slater wave functions and the Møller two-electron operator. The effects of relativity on the Auger rates of the ${}_{}{}^4{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states are found to be as large as two orders of magnitude. Relativity also very substantially affects the multiplet fluorescence yields of the ${}_{}{}^4{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{\mathrm{}(+)\mathrm{}}{}_{}{}^{}$ states. Inclusion of the Breit interaction, in addition to the Coulomb interaction, in the energy matrices for the intermediate-coupling calculations is found to have a pronounced effect on some multiplet Auger rates. The Breit interaction strongly influences the fine-structure splitting of some states, and, e.g., reverses the ${}_{}{}^4{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level order above $Z\simeq 75$.

The photoabsorption and photoemission of Cu in the region of the $3p$ threshold have been calculated. The resonance in the ${\mathrm{Cu}}^{+}$ $3d^{8}4s^2$ emission due to super-Coster-Kronig decay is found to occur primarily in the ${}_{}{}^1{}_{}{}^{}G$ multiplet (62%) with lesser amounts in ${}_{}{}^3{}_{}{}^{}F$ and ${}_{}{}^1{}_{}{}^{}D$ (29% and 8%). We find a comparatively large nonresonant emission due to inelastic scattering into $3d^{9}4p$ final states which occurs at approximately the same binding energy as $3d^{8}4s^{23}F$. Shake-up processes, in particular those leading to $3d^{9}5s$, are shown to be important. It is concluded that interference in the $3p\to nd,\epsilon d$ channel leads to the dip in absorption found above the $3p\to 4s$ peaks.

Precision wavelength measurements are presented for the $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1s2p{}_{}{}^3{}_{}{}^{}P_{0,2}^{}{}_{}{}^{}$ transitions of silicon, sulfur, and chlorine. Calculations have been made for these transitions using a double expansion in $Z^{-1\mathrm{}}$ and ${\alpha }^2{Z}^2$. These calculations include the nonrelativistic energy, one-electron Dirac energy, plus relativistic corrections and the Breit interaction calculated in first-order perturbation theory in both high-$Z$ and low-$Z$ approximations. After considering the one-electron Lamb-shift corrections to high order, comparison with our measurements and with other experiments for $Z=4-26\mathrm{}$ reveals a discrepancy which is approximately $0.015Z^3$ ${\mathrm{cm}}^{-1\mathrm{}}$. We show that this can arise from two-electron quantum electrodynamic corrections to the one-electron Lamb shift and we derive an ab initio estimate of this correction in good agreement with the observations.

Deviations of subshell photoionization branching ratios from the statistical ratio are examined, using full numerical calculations in screened central potentials and high-energy-limit results, focusing on the intermediate- and high-energy regimes of photoelectron energies greater than 1 keV. For intermediate- and high-$Z$ elements there are no regions characterized by statistical branching ratios. At intermediate energies ratios for fixed photoelectron energy fall below the statistical value since at the smaller distances which have then become important the $J=L-\frac{1}{2}$ bound state is pulled in and becomes larger in comparison to the $J=L+\frac{1}{2}$ state. However, at high energies, once retardation and higher multipole effects become important, ratios rise again for low-$Z$ elements and also for higher-angular-momentum states.

Nuclear spin relaxation of ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ produced by collisions of the xenon atoms with the walls of the experimental cell has been studied. The xenon nuclear ensemble is polarized through spin-exchange collisions with an optically oriented rubidium vapor. Depolarization of the ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ ensemble in the wall collisions is assumed to be due to the quadrupole coupling between the ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ nucleus and the electric field gradients which appear at the nucleus during collisions of the atoms with the cell walls. Model equations describing the nuclear relaxation are derived and estimates of the electric field gradients are given.

Model calculations were made of the effective extended x-ray-absorption-fine-structure (EXAFS) phase factor for excitation of the $1s$ level in the bromine molecule. A comparison is made for non-self-consistent potentials constructed from atomic Br and ionic ${\mathrm{Br}}^{1+}$ ($1s \mathrm{hole}$) charge densities and for fully self-consistent potentials determined in the context of the self-consistent-field-$X\alpha$-scattered-wave method. One-electron energy levels are tabulated and the effect of the screening charge transfer described. Calculations were also made for the lowest-lying $\sigma \to {\sigma }^{*} \mathrm{and} \pi \to {\pi }^{*}$ excited states for $\mathrm{Br}_2^{}{}_{}{}^{1+}$ ($1s \mathrm{hole}$). The effective phase factor was calculated as a function of the momentum of the excited-final-state electron for $k\lesssim 16.2$ ${\mathrm{\AA }}^{-1\mathrm{}}$ corresponding to energies to ∼ 1000 eV above the absorption edge. All of the calculated curves have similar slopes for $k\gtrsim 6$ ${\mathrm{\AA }}^{-1\mathrm{}}$ but their behavior differs significantly for lower momentum values. The implications of this for surface EXAFS are discussed. A comparison is made with experimental measurements and with other theoretical calculations.

Time-delayed measurement of naturally broadened transitions can lead to a narrowing of the linewidth. Moreover, under appropriate conditions, it may result in the appearance of a dip at the line center. An analysis of time-delayed measurement thus provides a theoretical basis for useful optical techniques yielding high spectral resolution. Such an analysis is presented in this work.

The "perturbation theory" for the imaginary part of the resonance energies of the hydrogen atom in the Stark effect and of the two-dimensional anharmonic oscillator with negative anharmonicity, which is a separation constant in the Stark problem, is solved to high order. The solution is based on the Langer-Cherry generalization of the JWKB method, which can be carried out in closed form, order by order. The numerical results should be useful both in interpreting experimental measurements of excited-state lifetimes and in understanding the analytic properties of the Stark and anharmonic-oscillator resonances.

Discontinuities resulting from the simultaneous creation of two electronic vacancies in the inner atomic shells of zinc were observed in the x-ray absorption spectra of the element. Their observed energies and the results obtained from relativistic Hartree-Fock-Slater calculation are in good agreement. Based on the magnitude of the observed discontinuities, the cross section for the one-photon — two-electron transition in zinc was calculated and found to be (126.0±20.7) barn/atom. This represents a change of about 0.5% in the mass absorption cross section.

Multiple-scattering artifacts are a not uncommon difficulty in applications of quasielastic-light-scattering spectroscopy (QELSS). An earlier proposal [G. Phillies, J. Chem. Phys. 74,260 (1981)] for a two-beam, two-detector light-scattering spectrometer, which is only sensitive to singly scattered photons, is subject here to an experimental test. The device is found to work essentially as predicted. The diffusion coefficient of $0.091-\mu$m polystyrene spheres in water is concentration independent for solute volume fraction ≲0.01. Multiple scattering does not have a significant effect on the QELSS spectrum of bovine serum albumin at a protein concentration of 20 wt.%.

We have detected the electric quadrupole $S\left(5\right)\mathrm{}$ and $S\left(7\right)\mathrm{}$ transitions in the 1-0 band of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$ using a tunable diode laser and a 40-m path of ${\mathrm{O}}_2$ at pressures of 10 to 80 Torr. This is the first observation of quadrupole vibrational transitions in a molecule other than hydrogen. Each transition is observed to be a triple due to the spin splitting of the ${\mathrm{O}}_2$ rotational levels, and the measured separations of the lines, in the 0.02 to 0.04-${\mathrm{cm}}^{-1\mathrm{}}$ range, agree with values derived from microwave spectroscopy of ${\mathrm{O}}_2$. The total integrated intensity of the ${\mathrm{O}}_2$ 1-0 quadrupole band was determined to be (1.77 ± 0.63) × ${10}^{-5\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$/(m amagat). We were not able to detect magnetic-dipole transitions in the band, and thus determined a conservative upper limit of 0.86×${10}^{-5\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$/(m amagat) for the strength of a magnetic-dipole 1-0 band in ${\mathrm{O}}_2$.

Motivated by recent experiments on second-harmonic generation in three-level systems [K. S. Yngvesson and E. L. Kollberg, Appl. Phys. Lett. 36, 104 (1980)], a semiclassical description of resonant three-wave parametric interactions in three nondegenerate levels is considered. Within the limitations of the rotating-wave approximation, analytical nonperturbative solutions for the nonlinear polarization are derived, which are then coupled to Maxwell's equations and integrated numerically. The results of sample calculations for second-harmonic generation show (a) a maximum harmonic conversion occurs on full resonance, (b) the conversion efficiency can be > 50% but requires a strongly saturating pump, (c) the conversion distance increases with pumping intensity, and (d) the inclusion of ac Stark splittings is crucial for the achievement of high conversion efficiency. The role of level splittings is further explored for the case of a resonant parametric oscillator.