The now classic optimized-effective-potential (OEP) approach of Sharp and Horton [Phys Rev. 90, 317 (1953)] and Talman and Shadwick [Phys. Rev. A 14, 36 (1976)] seeks the local potential that is variationally optimized to best approximate the Hartree-Fock exchange operator. The resulting OEP can be identified as the exchange potential of Kohn-Sham density-functional theory. The present work generalizes this OEP approach to treat the correlated case, and shows that the Kohn-Sham exchange-correlation potential is the variationally best local approximation to the exchange-correlation self-energy. This provides a variational derivation of the equation for the exact exchange-correlation potential that was derived by Sham and Schlüter using a density condition. Implications for an approximate physical interpretation of the Kohn-Sham orbitals are discussesd. A correlated generalization of the Sharp-Horton–Krieger-Li-Iafrate [Phys Lett. A 146, 256 (1990)] approximation of the exchange potential is introduced in the quasiparticle limit.

We have constructed a beam-laser lifetime-measuring apparatus and tested it by measuring the well known lifetime of the v=0 level of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_2^{+}{}_{}{}^{}$. Our result of 61.8(5) ns is in excellent agreement with previous high-precision measurements. Employing this technique we performed measurements of the lifetimes of the four lowest vibrational levels of the B ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ state of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}_{}^{16}{}_{}{}^{}$${\mathrm{O}}^{+}$. The results are (in ns) 69.5(6), 72.4(5), 75.2(5), and 78.0(8) for v=0, 1, 2, and 2, respectively.

Accurate ab initio multiconfigurational-Dirac-Fock (MCDF) calculations of the lifetimes of the spin-forbidden 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$–2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ transition and the allowed 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$–2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ transition in Be-like ions have been performed. The importance of the inclusion of the Breit interaction to obtain accurate fine-structure splittings and mixing coefficients is discussed and the noted discrepancy between the length and velocity gauges for the intercombination line in the lighter ions is addressed. Different optimization procedures are evaluated. For C iii the experimental intercombination transition rate has been measured to be 121.9 ${\mathrm{s}}^{\mathrm{-}1}$ with an accuracy of 6%. The current calculation gives 100.3±4 ${\mathrm{s}}^{\mathrm{-}1}$, in agreement with other recent calculations.

We are investigating the hyperfine quenching of 1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0^{\mathit{o}}$ for the three heliumlike ions ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{7+}{}_{}{}^{}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}_{}^{9+}{}_{}{}^{}$, and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}_{}^{11+}{}_{}{}^{}$ in the multiconfigurational Hartree-Fock-Breit-Pauli scheme. The configuration expansions are generated with the active-space method and are increased in a systematic way, allowing the convergence of the calculated parameters to be studied. A careful comparison is done with the pioneering work of Mohr using a perturbation approach [Beam-Foil Spectroscopy, Atomic Structure and Lifetimes, edited by I. Sellin and D. Pegg (Plenum, New York, 1976), Vol. 1, pp. 97–103]. In the present calculations the orbital and spin-dipole magnetic contributions, which were previously neglected, are added to the dominant Fermi contact interaction term and a detailed analysis of the hyperfine induced transition rate is done in order to learn how to get an accurate description of the property in the multiconfiguration Hartree-Fock-Breit-Pauli approximation.

An exact expression in terms of density matrices (DM) is derived for δF[n]/δn(r), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohn-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchange-correlation potential ${\mathit{v}}_{\mathrm{xc}}$(r) is obtained which is analogous in character to that for δF[n]/δn(r), but involving, besides the interacting-system DMs, also the noninteracitng DMs. Equating the former DMs to the latter ones, we reduce the result for the exact ${\mathit{v}}_{\mathrm{xc}}$(r) to that for an approximate exchange-only potential ${\mathit{v}}_{\mathit{x}}$(r). This leads naturally to the Harbola-Sahni exchange-only potential.

We employ a quantum Monte Carlo method for the oscillator strength to the computation of the controversial 2 ${}_{}{}^2{}_{}{}^{}$S→2 ${}_{}{}^2{}_{}{}^{}$P transition of the Li atom. We use simple trial functions that are optimized for accuracy in coordinate expectation values as well as the energy. We obtain an oscillator strength of 0.7431(6), in very good agreement with the experimental value of 0.7416(12) [A. Gaupp, P. Kuske, and H. J. Andrä, Phys. Rev. A 26, 3351 (1982)]. The precision obtained here, an order of magnitude greater than that of our previous value [R. N. Barnett, P. J. Reynolds, and W. A. Lester, Jr., Int. J. Quantum Chem. 42, 837 (1992)] shows that the quantum Monte Carlo oscillator strength unambiguously supports the experimental value over recent theoretical values.

The extreme ultraviolet photoabsorption spectra of neutral to three-times-ionized strontium have been recorded in a comprehensive series of experiments with the dual laser-produced plasma technique. Striking differences were found in the spectra, which can be attributed to the transfer of oscillator strength from 3d→np to 3d→nf transitions at ${\mathrm{Sr}}^{2+}$ due to nf wave-function contraction. In Sr and ${\mathrm{Sr}}^{+}$, 3d→5p transitions dominate; in ${\mathrm{Sr}}^{2+}$, 3d→nf transitions are most intense, while in ${\mathrm{Sr}}^{3+}$ the 4p subshell opens and 3d→4p transitions are the strongest features. Partial cross sections for 3d→ɛf and 3d→ɛp photoionization were calculated and compared with experiment.

Electron capture in collisions of ${\mathrm{N}}^{+}$ ions with He atoms is studied by using a molecular representation. Because excitation channels to ${\mathit{N}}^{+\mathrm{*}}$${(}^3$D) lie very close to the electron-capture channels, electron capture by the ground ${\mathrm{N}}^{+}$${(}^3$P) state, which strongly couples with ${\mathrm{N}}^{+\mathrm{*}}$${(}^3$D) excitation channels, is dominant below 6 keV. As the energy increases, electron capture by metastable ${\mathrm{N}}^{+\mathrm{*}}$${(}^5$S) ions becomes dominant due to a smaller energy defect. The excitation cross section to the ${\mathrm{N}}^{+\mathrm{*}}$${(}^3$D) states and the cross section of electron capture interfere with each other, showing complex patterns of in-phase and out-of-phase oscillations that depend on the energies.

We report medium-resolution [0.025 nm full width at half maximum (FWHM)] electron-impact-induced emission spectra of CO for 20-, 100-, and 200-eV impact energies. The emission spectra correspond to the extreme-ultraviolet transitions from the B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0), ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0), and E ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$(0) vibronic states to the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0) ground state. The present measurements are carried out at 20 times higher spectral resolution (to separate the many blended components) compared to our previous measurements, which were at a spectral resolution of 0.5 nm FWHM. The emission cross sections corresponding to the B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0) →X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0), C ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0)→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0), and E ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$(0)→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0) resonance transitions were measured. In addition, excitation functions (0–1 keV) extending well into the Born region have been measured for the strong transitions [B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0)→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0) and ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0)→X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$(0)] and oscillator strengths have been determined, using a modified-Born-approximation analytic fit to the measured excitation function.

Explorations of the classical phase space for ion collisions with circular Rydberg atoms are presented. Intermediate-energy capture and ionization processes are studied through the numerical integration of Newton’s equations of motion and through the graphical depiction of the outcomes of large numbers of trajectories. Maps which correlate initial conditions with final outcomes are used to identify zones of parameter space leading to Thomas capture, direct capture, binary-encounter ionization, saddle-point ionization, and ionization by S superpromotion (E. A. Solov’ev, Zh. Eksp. Teor. Fiz. 81, 1681 (1981) [Sov. Phys. JETP 54, 893 (1981)]). Charge-transfer channels in which the electron passes once or three times through the midplane between the nuclei are shown to occur in separate zones of parameter space over the entire range of projectile speeds above the mean velocity of the target electron.

Absolute cross sections for photoionization of isotropically populated Ba(6s6p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$) to each accessible final J state (0, 1, and 2) have been determined from threshold to 370 nm using spectra obtained with four different combinations of linear and circular polarizations of the exciting and ionizing radiation. The effects of dealignment due to hyperfine interaction of the nuclear spin I=3/2 isotopes of barium have been taken into account. The results are generally in good agreement with R-matrix predictions of shapes and positions of autoionizing resonances as well as the magnitudes of the background (nonresonance) cross sections, but there are some discrepancies with oscillator strengths of the autoionizing states. It is shown that, to obtain the correct magnitude of the background cross section theoretically, the inclusion of electron correlation effects in the wave functions of both initial and final states is required. Data are also presented that verify the equivalence of obtaining the total photoionization cross section by properly combining two sets of data, each acquired with a different angle between linear polarization vectors, e.g., parallel and perpendicular, or by making a single measurement with the angle set at the ‘‘magic’’ angle, 54.7°.

Optical emissions in single-collision, beam-beam reactions of fast (3–22-eV translational energy) O${(}^3$P) atoms with ${\mathrm{C}}_2$${\mathrm{H}}_2$ have been measured in the wavelength range 300–850 nm. Two features were observed, one with a peak wavelength at 431 nm, corresponding to the CH A ${}_{}{}^2{}_{}{}^{}\mathrm{X}$ ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{r}}^{}{}_{}{}^{}$ transition, and a second weaker emission in the range 380–400 nm corresponding to the B ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{-}}{}_{}{}^{}$→X ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{r}}^{}{}_{}{}^{}$ transition. Both the A→X and B→X emissions were fit to a synthetic spectrum of CH(A) at a vibrational temperature ${\mathit{T}}_{\mathit{v}}$ of 10 000 K (0.86 eV) and a rotational temperature ${\mathit{T}}_{\mathit{r}}$ of approximately 5000 K (0.43 eV); and CH(B) to ${\mathit{T}}_{\mathit{v}}$=2500 K (0.22 eV) and ${\mathit{T}}_{\mathit{r}}$=1000 K (0.09 eV). The energy threshold for the A→X emission was measured to be 7.3±0.4 eV (lab) or 4.5±0.2 eV (c.m.). This agrees with the energy threshold of 7.36 eV (lab) for the reaction O${(}^3$P)+${\mathrm{C}}_2$${\mathrm{H}}_2$→CH(A)+HCO.

The process of radiative electron capture (REC) in relativistic collisions of high-Z ions with low-Z gaseous and solid targets is studied experimentally and theoretically. The observed x-ray spectra are analyzed with respect to photon angular distributions as well as to total K-REC cross sections. The experimental results for angle-differential cross sections are well reproduced by exact relativistic calculations which yield significant deviations from standard ${\sin }^2$θ distributions. Total cross sections for K-REC are shown to follow a simple scaling rule obtained from exact relativistic calculations as well as from a nonrelativistic dipole approximation. The agreement between these different theoretical approaches must be regarded as fortuitous, but it lends support to the use of the nonrelativistic approach for practical purposes.

We present results for the photoionization of ground and excited S states of two-electron systems by x-ray photons. The method uses the asymptotic formulation of Dalgarno and Stewart [Proc. Phys. Soc. London 76, 49 (1960)] with highly correlated Frankowski-Pekeris–type wave functions for N ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ and N ${}_{}{}^3{}_{}{}^{}\mathrm{S}$ initial states. The calculations show a smaller ratio of double-to-single photoionization R for triplet states due to the spatial antisymmetry of the wave function near the nucleus. We find an asymmetric population of photoion satellite states and provide expressions for the asymptotic single and total photoionization, and R as a function of nuclear charge. We also make predictions for the differential double photoionization cross sections in the extreme energy sharing case when one electron is ejected with zero energy.

Angular distributions from 45° to 135° in 15° intervals of LMM Auger electrons produced by 1.2-MeV and 1.8-MeV ${\mathrm{He}}^{+}$-ion bombardment of argon, methyl chloride (${\mathrm{CH}}_3$Cl), and hydrogen sulfide (${\mathrm{H}}_2$S) have been measured. The LMM total Auger yields were measured at 1.8-eV resolution with an experimental probable error not exceeding 9%. The results revealed that the angular distributions of the LMM total Auger yields of Ar, Cl, and S were isotropic at these bombarding energies.

We report an experimental study of the single-quantum annihilation of positrons in a number of elements having atomic numbers between 49 and 90, utilizing a monoenergetic positron beam. Measurements were made of the differential cross sections for the forward direction for the K, L, and M atomic shells in targets of Th, Pb, Au, Hf, Gd, and In, having thicknesses that vary between 2.7 and 4.4 mg/${\mathrm{cm}}^2$. A shielded HPGe detector of high relative photopeak efficiency was used for recording the photon spectrum. Values for the individual atomic shells were obtained in the positron kinetic-energy range 1.02–2.24 MeV. It was observed that the differential cross sections measured for the forward direction varied with energy for each major shell almost alike so that the shell ratios appeared to remain constant while the positron energy varied. The dependence of the cross section on the atomic number Z of the target element was tested for each of the major shells at various energies of measurement. It was seen that the cross sections follow a ${\mathit{Z}}^{\nu }$ relation with ν≊5.1 as the exponent for the K shell. For the higher shells, the exponent is approximately 6.4, which is significantly larger. It was also noted that this pattern is fairly independent of the positron energy. The results on the Z dependence are seen to be clearly at variance with the most updated theoretical predictions.

The electron capture by multicharged ions colliding with H and He at intermediate and high impact energies is studied using the eikonal impulse approximation. Based on this theoretical method, we derive scaling rules for the partial capture cross sections to different shells and subshells. A large number of results are plotted in a comprehensible way using the proposed scaling. We also show that this scaling is verified by a large variety of theoretical methods. Total capture cross sections are also calculated and they compare quite well with the available experiments.

We have measured projectile-energy-loss spectra for 50-, 100-, and 150-keV p+He collisions. From the data we obtained differential double-excitation cross sections as a function of projectile scattering angle. At 150 keV a pronounced peak structure was observed at about 0.7 mrad for double excitation to the (2${\mathit{p}}^2$) ${}_{}{}^1{}_{}{}^{}$D and (2s2p) ${}_{}{}^1{}_{}{}^{}$P states. Our data provide indications for the dominance of a first-order mechanism involving the electron-electron interaction in double excitation for 150 keV at small scattering angles. At lower projectile energies and larger scattering angles a second-order mechanism appears to be of the same order of magnitude as the first-order mechanism. In these regimes, interference effects between the first- and second-order mechanisms could be important.

In this work, single-differential and total ionization cross sections of a hydrogen atom by electron impact are calculated. The final-state wave function used here considers all three two-body interactions on an equal footing and satisfies the exact Coulomb boundary conditions. The calculated values of the single-differential cross sections for the energy distribution of secondary electrons and the total cross sections are compared with the available theoretical and experimental data. The spin asymmetries are also found and the values are compared with other existing results.

A small electric field is shown to increase the dielectronic recombination, via autoionizing Rydberg states, of an electron from a continuum of finite bandwidth. The continuum of finite bandwidth is a broad autoionizing state which is part of a series converging to a higher limit, and the field enhancement of the rate occurs because the field converts the nl Rydberg states to nk Stark states, increasing the number of contributing recombination paths. The experimental results are in excellent agreement with the predictions of an isolated resonance approximation treatment and show clearly both the positive effect of Stark mixing and the negative effect of field ionization on dielectronic recombination.