Witten’s generalization to arbitrary dimension has afforded new insight into the correlated motion of quantum particles [Phys. Today 33, (7), 38 (1980)]. We have used a classically based method to understand the resultant dimensionality dependence of the ground-state energy of the helium atom in the approximation which regards the quantum fluctuations of the system as being harmonic oscillations about a classical, correlated state of minimum effective potential energy. Making an analogy with thermal systems, this provides a ‘‘phase diagram’’ of a single helium atom that features a first-order melting transition, with inverse dimensionality playing the role of temperature. Our approximation gives an understanding of the high-dimensionality behavior of the quantum solution found with a perturbation theory expansion in inverse dimensionality by Goodson and Herschbach [Phys. Rev. Lett. 58, 1628 (1987)]. From comparison with variational quantum ground-state solutions by Loeser and Herschbach [J. Chem. Phys. 84, 3882 (1986)] for atomic numbers 2, 3, and 6 we find that the harmonic description improves with decreasing nuclear charge.

Radiative lifetimes of eight states in Ba are measured in a metal vapor oven via pulsed laser excitation with time- and wavelength-resolved fluorescence detection. The lifetimes found for these states are τ(6s8p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$)=136±2 ns, τ(6${\mathit{p}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$)=12±1 ns, τ(6${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$)=7.3±0.4 ns, τ(6s7d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_3$)=30±1 ns, τ(6s7d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_2$)=39±1.8 ns, τ(6s7d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_1$)=39±1.2 ns, τ(5d6d ${}_{}{}^3{}_{}{}^{}$${\mathit{G}}_3$)=22±1.2 ns, and τ(5d6d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_1$)=23±1.8 ns. The 6s8p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ state is excited by a pulsed, frequency-doubled dye laser at 278.5 nm, and its lifetime is determined from the exponential decay of 408.2-nm emission on the 6s8p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$→6s5d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ transition. With He buffer gas in the cell at densities of around 6×${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$, population is transferred to the other seven states lying within 550 ${\mathrm{cm}}^{\mathrm{-}1}$ of the 6s8p state. Radiative lifetimes of these collisionally populated states are determined from the exponential rise times of their wavelength-resolved emissions.

The mean lifetime τ of the 4p’ ${}_{}{}^2{}_{}{}^{}$F${\mathrm{°}}_{7/2}$ level of Ar ii has been measured using a variant of the collinear laser-beam–fast-ion-beam spectroscopy technique. Our variant requires no mechanical motion or laser frequency tuning. The result is τ=8.414±0.025 ns in agreement with an earlier, comparably precise, measurement based on a crossed laser–ion-beam technique. The result lies above all theoretical calculations.

Ground- and excited-state energies are calculated by the relativistic coupled-cluster open-shell Fock-space method for Li, C, O, F, and Na and their ions. The coupled-cluster approximation including single and double excitations in a self-consistent manner, is implemented. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. Mean-length basis sets of balanced Gaussian spinors are used to span the atomic orbitals.

A universal Gaussian basis set is developed for accurate ab initio relativistic Dirac-Fock calculations on atoms and molecules. The Dirac-Fock energies computed by using this single set of the universal Gaussian basis for the atoms, He (Z=2) through No (Z=102), are in excellent agreement with the corresponding numerical finite-difference Dirac-Fock method. The total Dirac-Fock energies for lighter atoms agree with the corresponding numerical limit to a part in ${10}^9$ and for heavier systems to a part in ${10}^8$. The total energy for the heaviest system, No (Z=102), calculated with our universal Gaussian basis set differs from the corresponding numerical limit by only 4 mhartrees.

Three states in Kr i were studied in a pure Kr discharge at pressures ≤15 mTorr. Two-photon excitation from the metastable 4${\mathit{p}}^5$5s[3/2] J=2 state produced the 4${\mathit{p}}^5$5d[7/2] J=4 state whose photoionization cross section and lifetime were measured. The photoionization cross section at λ=1064 nm is 32±5 Mb, and the radiative lifetime is 142±12 ns. One-photon excitation produced the 4${\mathit{p}}^5$5p[5/2] J=2 and J=3 states of Kr i, whose radiative lifetimes were measured. In contrast to previous lifetime measurements of these two 5p states, this work used both state-specific excitation and low pressures. The pressures were low enough that collisional transfer between these two states was negligible. In a very clean 8-mm-diam cell, the 5p[5/2] J=3 lifetime increased with Kr pressure. This increase is attributed to radiation trapping on the 5s[3/2] J=2 to 5p[5/2] J=3 transition. This radiation trapping by the metastable first excited state of Kr i was observed in a pure Kr discharge at pressures below 4 mTorr.

A particle-density distribution is said to be v-representable if it is the ground-state density for some potential v(r). By developing the idea of proper order, proposed earlier [J. Chen and M. J. Stott, Phys. Rev. A 44, 2816 (1991)], to any number of energy levels which are involved in possible ground-state configurations, we show that any reasonable density with an arbitrary number of spinless fermions is either pure-state or ensemble v-representable. This result supports the general applicability of the Kohn-Sham method [Phys. Rev. 140, A1133 (1965)] in density-functional theory.

Oscillator strengths have been calculated for the ultraviolet transition array 2${\mathit{p}}^{2\mathrm{-}}$2p3s in the N ii spectrum. Recent astrophysical, experimental, and theoretical works have called attention to two interesting features of these lines. First, the intercombination line at 748 Å is exceptionally strong; second, the branching ratio between the ${}_{}{}^1{}_{}{}^{}$D and ${}_{}{}^1{}_{}{}^{}$S decay modes of the ${}_{}{}^1{}_{}{}^{}$P° level is unusually large. Both these effects reflect the strong interaction of 2${\mathit{s}}^2$2p3s with the ‘‘plunging’’ configuration 2s2${\mathit{p}}^3$; unlike other ions in the carbon isoelectronic sequence, these configurations are overlapping for N ii. In the present work multiconfiguration Hartree-Fock (MCHF) wave functions have been used to compute oscillator strengths for all the lines in the 2${\mathit{p}}^{2\mathrm{-}}$2p3s transition array. The MCHF results give wavelengths which are within 1% of the observed wavelengths; the length and velocity forms of the oscillator strengths agree with each other to within 7%; and the predicted mean lifetime of the 2p3s ${}_{}{}^1{}_{}{}^{}$P° level agrees with a recent beam-foil–laser result to 4% [Y. Baudinet-Robinet et al., Phys. Rev. A 42, 1080 (1990)].

The spin-unrestricted optimized-effective-potential (OEP) method and an approximation to it due to the authors (KLI) have been applied to atoms from Li (Z=3) to Ba (Z=56) plus Au (Z=79) and Hg (Z=80) within the exchange-only scheme. Calculations were performed for the term with the lowest energy in the ground-state configuration. For a few transition elements, terms in the low-lying excited-energy-state configuration are also self-consistently calculated. We have compared our OEP and KLI results with each other and with those obtained from the spin-unrestricted Hartree-Fock (SUHF) method and the local-spin-density exchange-only (LSDX) approximation. As the spin-restricted OEP, the spin-unrestricted OEP yields nearly identical results as the corresponding SUHF. The relative difference of the total energy from that of the SUHF is only 40 ppm for ${}_{}{}^3{}_{}{}^{}\mathrm{Li}$ and monotonically decreases as Z increases to less than 2 ppm for ${}_{}{}^{80}{}_{}{}^{}\mathrm{Hg}$. The highest occupied energy eigenvalues of each spin projection, ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$, and the various expectation values for the operators ${\mathit{r}}^2$, ${\mathit{r}}^{\mathrm{-}1}$, and δ(r) are all very similar to the SUHF theory.

For most of the atoms, even the spin density mimics the SUHF value quite well. Differences appear to be larger for some transition- and noble-metal atoms. Nevertheless, even in these cases, the total energy and the total electron density of the OEP calculations are still very similar to the corresponding SUHF values. For atoms with the highest occupied energy eigenvalues having the same spatial quantum numbers for both spin projections, the spin splitting, ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\downarrow }}$-${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\uparrow }}$, corresponding to the difference between the highest occupied eigenvalues of the minority (↓) and majority (↑) spin states, is also studied. It is found that the OEP and SUHF spin splittings are nearly identical for atoms with the highest occupied eigenstate being a p state. Noticeable differences (of the OEP and HF spin splitting) occur for a few transition elements having an empty (n-1)d↓ subshell. However, such larger differences are steadily diminished as the (n-1)d↓ subshell is progressively filled. As an approximate Kohn-Sham (KS) potential, the KLI method shows itself to be a much improved one compared to the LSDX. The exchange potential constructed from this method retains many of the essential properties of the exact OEP that the LSDX approximation lacks and thus always yields better densities, lower total energies, and more accurate eigenvalues for the highest occupied energy state of each spin projection than the LSDX approximation. In particular, the total energies overestimate the OEP results by only 9 ppm for Li, with the overestimate decreasing for increasing atomic number Z to less than 1 ppm for Z>50. In addition, for atoms other than transition elements or noble metals, the ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$ are within 0.4% of the corresponding OEP results with slightly larger differences for the other atoms. In all cases, the KLI results for the expectation values ${\mathit{r}}^2$,${\mathit{r}}^{\mathrm{-}1}$ and the density at the origin are very close to the exact KS results and are a significant improvement over those provided by the LSDX approximation.

Photoionization cross sections for the 3p and 3s subshells of 3${\mathit{s}}^2$3${\mathit{p}}^5$ ${}_{}{}^2{}_{}{}^{}$P° ground state of atomic chlorine are calculated in the photon energy range from the ${\mathrm{Cl}}^{+}$ 3${\mathit{p}}^4$ ${}_{}{}^3{}_{}{}^{}$P ionization threshold to 65 eV using the R-matrix method. The initial Cl (3${\mathit{s}}^2$3${\mathit{p}}^5$ ${}_{}{}^2{}_{}{}^{}$P°) bound state, the final ${\mathrm{Cl}}^{+}$ plus photoelectron ${(}^2$S${,}^2$P${,}^2$D) states, and the residual ${\mathrm{Cl}}^{+}$ (3${\mathit{p}}^4$ ${}_{}{}^3{}_{}{}^{}$P${,}^1$D${,}^1$S, 3s3${\mathit{p}}^5$ ${}_{}{}^3{}_{}{}^{}$P°${,}^1$P°) states are represented by extensive configuration-interaction wave functions. The photoionization cross sections are dominated by Rydberg series of resonances in the threshold region. The present results are compared with the available experimental measurements and other calculations.

Double charge exchange in fast collisions between completely stripped projectiles and heliumlike atomic systems is investigated by means of the correct first Born approximation. The theory is devised beyond the usual independent-particle model. For the reason of consistency, the usual proper boundary conditions must be reformulated when dealing with atoms or ions containing more than one electron. Consequently an appropriate correction ought to be introduced in the perturbation potential, which conveniently deals with the difficulty related to the unavailability of exact two-electron bound-state wave functions. For the purpose of illustration, numerical computations are performed for electron capture by α particles from helium. Total cross sections are found to be in satisfactory agreement with the available experimental data from 100 to 2000 keV.

Electron capture from diatomic molecular targets by the impact of bare ions is studied at high collision velocities. Different distorted-wave models, which take account of the long-range Coulombic behavior of perturbative potentials, are introduced here. Impact-parameter probabilities and single-differential cross sections, depending on the alignment of the intermolecular axis, are studied for ${\mathrm{H}}^{+}$+${\mathrm{H}}_2^{+}$ collisions. Interference patterns characteristic of scattering from the two molecular centers associated with each one of the nuclei of the target are obtained. Total cross sections, summed over all possible alignments of the intermolecular axis, are also calculated for the ${\mathrm{H}}^{+}$+${\mathrm{H}}_2$ system for which experimental data exist.

A simple way to obtain a completely general distorted-wave excitation program in the convenient factorized form of Bar-Shalom, Klapisch, and Oreg [Phys. Rev. A 38, 1773 (1988)] is described. Procedures for improving numerical accuracy are also discussed, and results obtained by these procedures are compared with other work.

Ionization, pair creation, and electron excitations in relativistic heavy-ion collisions are investigated in the framework of the coupled-channel formalism. Collisions between heavy projectiles and ${\mathrm{Pb}}^{82+}$ are considered for various bombarding energies in the region E=500 up to 2000 MeV/u. Useful symmetry relations for the matrix elements are derived and the influence of gauge transformations onto the coupled-channel equations is explored.

Recent experimental studies of the photoionization cross section of excited barium are compared with detailed R-matrix calculations, carried out in the energy range between the ${\mathrm{Ba}}^{+}$ 6s and 5${\mathit{d}}_{3/2}$ thresholds. The study sheds light on existing discrepancies between theory and experiment, showing in particular that many of them derive from hyperfine-induced mixing of magnetic substates ${\mathit{M}}_{\mathit{J}}$. Experimental measurements shown here confirm this effect. Except for discrepancies in the shape of a few resonance features, generally good agreement is now obtained between experiment and theory.

The target dependence of equilibrium charge-state distributions was studied for medium-energy (50–500-keV/u) hydrogen and boron emerging from solids. Using a backscattering method, charge fractions were measured for various elemental solid substances with atomically clean surfaces in a pressure range of ${10}^{\mathrm{-}8}$ Pa. The respective charge fractions of hydrogen and boron are found to oscillate with target atomic number ${\mathit{Z}}_{\mathit{t}}$, reflecting the periodic electron shell structures of the target atoms. Comparison between the ${\mathit{Z}}_{\mathit{t}}$ oscillations of hydrogen and boron revealed that the oscillatory behavior depends on the final bound state of the captured electrons. This oscillatory behavior can reasonably be explained by the Oppenheimer-Brinkman-Kramers approximation.

Zeeman cross sections ${\mathrm{\sigma }}_{\mathrm{j},{\mathrm{m}}_{\mathrm{j}}\to \mathrm{j}\prime ,{\mathrm{m}}_{\mathrm{j}}^{\prime }}$ for the spin-changing 6s6p ${\mathrm{P}}_1^1$–6s6p ${\mathrm{P}}_2^3$ transition of barium induced by single collisions with ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{H}}_2$ have been measured using a crossed-beam apparatus. State-selective preparation of 6s6p ${\mathrm{P}}_{1,{\mathrm{m}}_{\mathrm{j}}}^1$ and detection of 6s6p ${\mathrm{P}}_{2,{\mathrm{m}}_{\mathrm{j}}^{\prime }}^3$ was achieved using the laser excitation technique in the presence of a magnetic field that breaks the degeneracy of the magnetic sublevels. The results showed that the Zeeman cross sections σ(${\mathrm{P}}_{1,{\mathrm{m}}_{\mathrm{j}}}^1$→${\mathrm{P}}_{2,{\mathrm{m}}_{\mathrm{j}}^{\prime }}^3$) are fairly dependent upon ${\mathrm{m}}_{\mathrm{j}}$ and ${\mathrm{m}}_{\mathrm{j}}^{\prime }$ for ${\mathrm{N}}_2$ and ${\mathrm{H}}_2$, whereas the Zeeman cross sections all have the same value with ${\mathrm{O}}_2$. Additionally the flux-velocity contour map of Ba(6s6p ${\mathrm{P}}_2^3$) for scattering with ${\mathrm{H}}_2$ depends significantly upon the magnetic sublevel of barium in the exit channel. The results for Ba-(${\mathrm{N}}_2$,${\mathrm{H}}_2$) scattering were accounted for semiquantitatively by a very simple model. The model was then used to stress which physical phenomena are at the origin of the preservation of the orbital alignment and orientation during collisions. The present work also compared the kind of information obtained by the direct measurement of Zeeman cross sections to that found in other experiments that deal with the effect of polarizing the collision partners.

The complex Kohn method is used to calculate elastic electron-${\mathrm{Li}}_2$ scattering cross sections. The effect of including target correlation and polarization is systematically investigated. Various levels of ab initio treatment of the target ground and excited states are shown to have a major influence on the resulting scattering cross section for energies below 1 eV. Comparisions are made with previous calculations and experiment.

Total cross sections are reported for electron transfer and ionization from the K shell of carbon atoms by proton impact at energies from 75 to 600 keV. The coupled-Sturmian-pseudostate approach applied previously by Winter [in Phys. Rev. A 35, 3799 (1987)] to collisions between protons and hydrogenic ions has been generalized to quasi-one-electron systems using an analytic Hartree-Fock potential. The calculated cross sections for ionization agree closely with the experimental values of Ro/dbro et al. [Phys. Rev. A 19, 1936 (1979)]. For electron transfer, there is still a small discrepancy of 15% at 200 and 300 keV after a binding-energy correction is made to the potential.

The scattering length for electron-argon scattering is calculated very accurately by an ab initio method with wave functions computed exactly at zero energy. The multiconfiguration Hartree-Fock method, which takes into account the effects of target polarization and electron correlation through the configuration-interaction procedure, is used for the calculation. The differential, total, and momentum-transfer cross sections are also calculated for very low energies ranging from 0–1 eV. The present result for the scattering length is found to be in excellent agreement with the experimental results of Buckman and Lohmann [J. Phys. B 19, 2547 (1986)] and Haddad and O’Malley [Aust. J. Phys. 35, 35 (1982)].