The correlated wave functions of the 2s state, (1s${)}_{\mathit{e}}$(2s${)}_{\mathrm{\mu }}$ of muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms are calculated by the variational approach, employing an improved set of the Hylleraas-type basis functions to study the 2s state of muonic He atoms. The energy and radial expectation values are calculated. Our proposed wave functions for the muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms are good enough to describe the electron and muon at small, intermediate, and large values of radial coordinates. The hyperfine splittings of the (1s${)}_{\mathit{e}}$(2s${)}_{\mathrm{\mu }}$ muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms are also presented. Including relativistic, QED, and other corrections up to O(${\mathrm{\alpha }}^2$), we arrive at the values Δν=(4287.01±0.10 and 4052.64±0.10 MHz for the total hyperfine splittings of the 2s state of muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms, respectively.

A relativistic coupled-cluster calculation including single and double excitations has been performed for the ground-state energy of beryllium. Comparison with corresponding nonrelativistic calculations shows the effect of relativity on the pair correlation which, together with the relativistic corrections to the Hartree-Fock energy, can be combined with the most accurate nonrelativistic ground-state energy available. Many-body radiative corrections were estimated by multiplying accurate results for hydrogenlike Be with the ratio between the Dirac-Hartree-Fock and hydrogenic electron densities at the nucleus. The energy associated with the motion of the nucleus with its finite mass can be deduced with sufficient accuracy from experiment. Subtraction of all these corrections from the experimental result leads to an ‘‘experimental nonrelativistic energy’’ of -14.667 353(2) hartrees.

We have calculated the total energy and s-d promotion energies of 3d-transition-metal atoms using a common set of orbitals but various expressions for the energy. These include Hartree-Fock (HF), local-spin-density-approximation (LSDA), and self-interaction-corrected (SIC) LSDA expressions. The orbitals were generated from a self-consistent, spherically averaged, local-density calculation. The results using the HF expression are in remarkably good agreement with self-consistent Hartree-Fock calculations both for the total energy and for the HF eigenvalues. Further, the LSDA underestimates the total correlation energy by roughly 30 eV, while the SIC calculation overestimates the correlation energy in calcium by ∼15 eV.

A Hanle experiment has been used to determine the following radiative lifetimes (in nsec) of rubidium: ${\mathrm{\tau }}_{6\mathit{D}3/2}$=298±8, ${\mathrm{\tau }}_{7\mathit{D}3/2}$=345±9, ${\mathrm{\tau }}_{8\mathit{D}3/2}$=586±15, and ${\mathrm{\tau }}_{9\mathit{D}3/2}$=638±17. These data were taken at a temperature of 293 K and are not corrected for effects due to blackbody radiation. The effect of the hyperfine interaction on the Hanle signal is discussed in detail for an excited state of arbitrary angular momentum.

The behavior of the density-functional correlation energy under general linear coordinate transformations is considered. It is demonstrated that it is uniform and nonuniform scaling that yield new conditions which are fulfilled by the exact correlation energy functional, besides the well-known requirements of rotational, reflectional, and translational invariance. By considering various types of nonuniform scaling in the limit of the scale factor λ going to zero and infinity, a set of relations for the correlation energy is derived. These relations, which are easy to test on approximate functionals, are of the type ${\lim }_{\lambda \to 0}$(1/λ)${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\lambda \lambda }^{\mathit{x}\mathit{y}}$]=0 and ${\lim }_{\lambda \to \mathrm{\infty }}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]=0. In addition, a previous proof is simplified for ${\lim }_{\lambda \to \mathrm{\infty }}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\lambda }$]=const, which is bounded from below, and we identify the constant as a second-order energy. Here ${\mathit{n}}_{\lambda }$(r)=${\lambda }^3$n(λx,λy,λz), ${\mathit{n}}_{\lambda }^{\mathit{x}}$(r)=λn(λx,y,z), and ${\mathit{n}}_{\lambda \lambda }^{\mathit{x}\mathit{y}}$(r)=${\lambda }^2$n(λx,λy,z) where n is the electron density. The limiting relations are not all met by any known approximate correlation energy functional. These relations apply to a correlation energy for addition to a Hartree-Fock calculation as well as to a correlation energy for use as part of a full density-functional calculation.

In this paper we present a useful analysis for higher-order static properties involving three different response approaches based on coupled-cluster methods, namely, the nonvariational, the variational and the more recent bivariational methods.

The shifted large-N technique (SLNT) has been applied to study the relativistic motion of a particle in the presence of vector and scalar interactions with special emphasis on the construction of both large- and small-component Dirac radial wave functions. Numerical results for the binding energy for a particle in the presence of the Coulomb plus linear confining potential compare very well with those obtained by the elaborate analytic approximation method using the Padé-approximation technique. We illustrate that one recovers not only the exact analytic results for binding energies for vector and scalar Coulomb potentials, but also exact wave functions from the leading-order SLNT calculation. This motivates future applications of the same method to more realistic atomic systems governed by screened Coulomb potentials where the knowledge of the large and small components of the radial wave function is essential.

Wavelengths of xenon L-series x-ray lines were measured with high accuracy using a double flat-crystal vacuum spectrometer. Wavelengths of the more prominent xenon K-series lines which had been obtained previously are fully reported and corrected for recent scale changes. Energies of forbidden transitions, such as 1s-2s, have been determined from redundant combinations of K- and L-series measurements. Transition energies have been calculated relativistically including relaxation to all orders, correlation to second order, and QED effects. Agreement between experiment and theory is of the order of 0.1 eV, except for transitions involving 3s holes where it is 1 eV.

The method of threshold-photodetachment spectroscopy has been used to measure the electron affinity of Li. Changes in the partial cross sections for the resolved hν+${\mathrm{Li}}^{\mathrm{-}}$(2 ${}_{}{}^1{}_{}{}^{}$S)→Li(2 ${}_{}{}^2{}_{}{}^{}$S)+${\mathit{e}}^{\mathrm{-}}$(εp) ${(}^2$Sεp) and hν+${\mathrm{Li}}^{\mathrm{-}}$(2 ${}_{}{}^1{}_{}{}^{}$S)→Li(2 ${}_{}{}^2{}_{}{}^{}$P)+${\mathit{e}}^{\mathrm{-}}$(εs) ${(}^2$Pεs) channels were separately investigated in the vicinity of the 2 ${}_{}{}^2{}_{}{}^{}$P threshold. The near-threshold data in the ${}_{}{}^2{}_{}{}^{}$Pεs channel were fitted to a Wigner law to determine a threshold photon energy of 19 884.8±1.6 ${\mathrm{cm}}^{\mathrm{-}1}$. An electron affinity of 4980.9±1.6 ${\mathrm{cm}}^{\mathrm{-}1}$ (617.6±0.2 meV) is obtained upon subtraction of the well-known 2 ${}_{}{}^2{}_{}{}^{}$P excitation energy. The position of the Wigner cusp in the ${}_{}{}^2{}_{}{}^{}$Sεp channel was measured to be 19 882.4±4.0 ${\mathrm{cm}}^{\mathrm{-}1}$, in agreement with the more precise ${}_{}{}^2{}_{}{}^{}$Pεs-channel threshold energy.

A semiclassical quantization of the hydrogen atom in a generalized van der Waals potential is carried out using the Kustaanheimo-Stiefel transformation and Birkhoff-Gustavson normal-form procedure, employed by Kuwata, Harada, and Hasegawa [J. Phys. A 23, 3227 (1990)] for the diamagnetic Kepler problem. We derive here the generalized approximate Solov’ev constant of motion. By using appropriate action-angle variables in the normal Hamiltonian, we derive four canonically equivalent action integrals that take an especially simple form for the three classically integrable cases and provide exact quantum numbers. For near-integrable cases the semiclassical spectrum can be generated by integrating the appropriate action integrals numerically.

The accuracy of the widely used Van Regemorter formula [Astrophys. J. 136, 906 (1962)] for calculating the collision strengths needed in applications to high-temperature plasmas is tested by comparison with numerous more accurate calculations. It is found to be frequently a very poor approximation, especially for Δn≥1 excitation transitions from levels with l<n-1, and the recommendation is made that with the recent advances in calculational procedures and available accurate atomic data use of the Van Regemorter formula should be discontinued.

Cross sections have been determined for electron transfer and ionization in collisions between protons and ${\mathrm{He}}^{+}$ ions at proton energies from several hundred kilo-electron-volts to 2 MeV. A coupled-Sturmian approach is taken, extending the work of Winter [Phys. Rev. A 35, 3799 (1987)] and Stodden et al. [Phys. Rev. A 41, 1281 (1990)] to high energies where perturbative approaches are expected to be valid. An explicit connection is made with the first-order Born approximation for ionization and the impulse version of the distorted, strong-potential Born approximation for electron transfer. The capture cross section is shown to be affected by the presence of target basis functions of positive energy near ${\mathit{v}}^2$/2, corresponding to the Thomas mechanism.

An experimental verification of the theoretically predicted density enhancement of the dielectronic satellite spectra emitted by multiply charged lithiumlike ions in high-density plasmas is reported. These plasmas were created by the interaction of solid ${\mathrm{MgF}}_2$ and ${\mathrm{SiO}}_2$ targets with high-intensity, subpicosecond, ultraviolet laser radiation. Comparisons between the observed and theoretically predicted values for the intensity ratios between two different pairs of dielectronic satellite lines have enabled determinations of electron densities of the order of ${10}^{23}$ ${\mathrm{cm}}^{\mathrm{-}3}$ to be made in these high-density laser-produced plasmas.

Electron-capture and -loss cross sections in ${\mathrm{C}}^{3+}$ and ${\mathrm{O}}^{5+}$ collisions with ${\mathrm{H}}_2$ and He are measured in the 1.5- to 4.0-MeV energy range. The results for projectile electron loss are compared with the plane-wave Born approximation including the interaction between target and projectile electrons. It is shown that such single-channel analysis is not sufficient to explain the results, but that projectile electron loss, electron capture by the projectile, and target ionization must be considered together to interpret the data. This interpretation allows one to extract the electron-capture probability at small impact parameters. A theoretical estimate based on the independent-particle model and the decay model to unitarize the electron-capture and target-ionization probabilities is described. This analysis explains the main features of the cross sections involved as well as the electron-capture probability at small impact parameters.

We present a proof that there are no zeros in nonrelativistic Coulomb continuum-continuum transition dipole matrix elements. There is a positive singularity in these matrix elements as the case of equal energies is approached. Considering one energy as fixed, matrix elements are monotonically increasing (decreasing) functions of the other energy below (above) the singular case. This is an extension of our earlier demonstration that the Coulomb dipole matrix elements, connecting a bound state to a state of greater energy, never vanish and are monotonic. For the present proof, we utilize asymptotic expansions of the matrix elements for large angular momentum, together with fixed energy recursion relations between pairs of successive angular momentum states (l,l+1) and (l-1,l).

We combine an eigenchannel R-matrix calculation with an analytic description of electron motion in a dipole field to predict photodetachment cross sections of the hydrogen negative ion, including resonant structures up to the n=4 hydrogenic threshold. Partial cross sections for the production of hydrogen-atom fragments in states with specific principal quantum numbers n are also presented for comparison with a recent experiment. An analysis of the delay-time matrix indicates that the autodetaching Feshbach resonances decay primarily into the nearest energetically accessible continuum channel, an observation which is not at all apparent from the calculated and observed partial cross sections, but has been anticipated in previous theoretical work. We find, for instance, that the ${}_{\mathit{n}=4\mathrm{}}{}^{}{}_{}{}^{}\mathit{v}$=0${\mathrm{\}}}_{\mathit{m}=4\mathrm{}}^{\mathit{A}=+}$ resonant state below the H(n=4) threshold decays 73% of the time to the ${}_3{}^{}{}_{}{}^{}\mathrm{\}}_{}^{+}{}_{}{}^{}$ photodetachment channel.

In this paper we give an arbitrary-order phase-intergral formula for the S matrix in Regge-pole theory. This formula is valid for a particular situation when there are three relevant transition points, two of which may lie at an aribtrary distance from each other, possibly close together, but far away from all other transition points, the pole at the origin inclusive. When the formula is particularized to the first order of the phase-integral approximation, it agrees with formulas given by Connor, Jakubetz, and Sukumar [J. Phys. B 9, 1783 (1976)] and by Brink and Takigawa [Nucl. Phys. A 279, 159 (1977)], after these formulas have been rewritten conveniently.

New experimental electron-energy-loss data have been used to extract differential and integral cross sections for excitation of the 2 ${}_{}{}^1{}_{}{}^{}$P level, and for the overlapping (3 ${}_{}{}^1{}_{}{}^{}$P,3 ${}_{}{}^1{}_{}{}^{}$D,3 ${}_{}{}^3{}_{}{}^{}$D) levels of helium, at 30-, 50-, and 100-eV incident electron energies. First-order many-body theory (FOMBT) has been used to calculate the differential and integral cross sections for excitation of the ${\mathit{n}}^1$P (n=2,...,6) levels of helium by electron impact, for incident electron energies from threshold to 500 eV. Detailed comparisons between these two new sets of data are made as well as comparisons with appropriate published experimental and theoretical results. A simple scaling relationship is derived from the FOMBT results for n=2,...,6 that provides differential and integral cross sections for all symmetry final levels of helium with n≥6.

First-order many-body theory has been used to calculate collision-frame magnetic-sublevel differential cross sections for electron-impact excitation of the ${\mathit{n}}^1$P (n=2,3,4,5,6) levels of helium for electrons with incident energy in the 25–500-eV range. By combining results from electron-impact differential-cross-section measurements and electron-photon coincidence measurements, experimental magnetic-sublevel cross sections have also been derived for the excitation of the 2 ${}_{}{}^1{}_{}{}^{}$P and 3 ${}_{}{}^1{}_{}{}^{}$P levels. The theory predicts a pronounced minimum for the M=0 magnetic-sublevel differential cross section for incident electron energies around 30 eV. Our theoretical results are compared to the experimental data and some other theoretical results.

We report low-energy (0.001–10-eV) electron-CO scattering cross sections obtained using an exact-exchange (via a separable-exchange formulation) plus a parameter-free correlation-polarization model in the fixed-nuclei approximation (FNA). The differential, total, and momentum-transfer cross sections are reported for rotationally elastic, inelastic, and summed processes. To remove the limitations of the FNA with respect to the convergence of total and differential cross sections, the multipole-extracted-adiabatic-nuclei approximation is used. The position and width of the well-known ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ shape-resonance structure in the cross section around 2 eV are reproduced quite well; however, some discrepancy between theory and experiment in the magnitude of the total cross section in the resonance region exists. We also present results for ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ shape-resonance parameters as a function of internuclear separation. Differential-cross-section results agree well with the measurements of Tanaka, Srivastava, and Chutjian [J. Chem. Phys. 69, 5329 (1978)] but are about a factor of 2 larger than the results obtained by Jung et al. [J. Phys. B 15, 3535 (1982)] in the vicinity of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ resonance.