Four fine-structure intervals separating the n=10, L=2 and 3 Rydberg states of helium have been measured using a fast-beam microwave-optical technique. These are found to agree both with previous measurements of these intervals and with high-precision calculations. The experimental results for the four intervals are 10 ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$–10 ${}_{}{}^{+}{}_{}{}^{}$${\mathit{F}}_3$, 10 918.826(37) MHz; 10 ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_1$–10 ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}_2$, 15 760.667(17) MHz; 10 ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_2$–10 ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$${\mathit{F}}_3$, 15 770.704(15) MHz; and 10 ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_3$–10 ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}_4$, 15 781.991(11) MHz. The ${}_{}{}^{+}{}_{}{}^{}$F ${(}^{\mathrm{-}}$F) state is the mixed singlet-triplet state of higher (lower) energy. The result for the spin-averaged 10D-10F interval in helium is 14 560.650(13) MHz, which has an experimental uncertainty of better than one part per million. The good agreement with theory breaks the pattern of discrepancies between theory and experiment observed in measurements of the higher-L n=10 helium fine structure. Possible explanations for those discrepancies are discussed.

Ab initio calculations of the static longitudinal polarizability of molecular hydrogen model chains have been performed at different levels of approximation to investigate the effects of including electron correlation. Unlike uncoupled and coupled Hartree-Fock calculations for which a split-valence atomic basis set already provides suitable longitudinal polarizability estimates, the techniques of the Mo/ller-Plesset partitioning leading to successive electron corrections, namely, MP2, MP3, and MP4, and the coupled-cluster ansatz including all double excitations, all single and double excitations, and all single and double excitations as well as a perturbational estimate of the connected triple excitations require at least additional polarization functions and a triple-ζ-type basis set in order to give suitable polarizability values. It has also been shown that including electron correlation decreases the longitudinal polarizability values and that the electron correlation effects are overemphasized when using a too small basis set. Within the Mo/ller-Plesset treatment of electron correlation, the relative importance of the different orders and the different classes of substitutions used in the intermediate states has been investigated. The double substitutions present the largest electron correlation correction to the coupled Hartree-Fock longitudinal polarizabilities per unit cell. If the atomic basis set is sufficiently extended, the third-order contribution is dominant.

Population and alignment relaxation for the Doppler broadening case in the infinite plane parallel geometry has been studied in the range of the optical thickness at the line center between ${10}^{\mathrm{-}3}$ and ${10}^2$. The obtained population and alignment relaxation rates are compared with analytical estimates. The validity of two approximations used in the estimates, i.e., the complete frequency redistribution of absorbed and successively emitted photons and the pure-parabolic distribution of excited atoms, is discussed. Also studied is the mixing of the population and the alignment, which is due to the spatial anisotropy of the geometry. This mixing leads to the self-alignment effect, which develops at a sufficiently late time after excitation. A separate simulation with the alignment effect omitted has revealed that, at a large optical thickness, the population relaxation rate agrees with the result with the alignment effect included. It is therefore concluded that the previous estimate on the influence of the self-alignment to the population relaxation rate is too large. The velocity distribution of the excited atoms in the direction perpendicular to the planes shows an effectively lower (higher) temperature at the center (boundary) than the base temperature (≊5%) under the self-alignment condition.

The hyperfine interactions in the alkaline-earth-metal ions, ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$, have been investigated using the relativistic linked-cluster many-body perturbation theory (RLCMBPT). The calculated theoretical hyperfine fields are found to be 135.3 and 266.3 T for ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$, respectively, in good agreement with the experimentally obtained values of 139.0 T for ${\mathrm{Ca}}^{+}$ and 267.2 T for ${\mathrm{Sr}}^{+}$. The contributions from the various mechanisms, direct, exchange core polarization, and many-body correlation effects, are analyzed and combined with results obtained from earlier first-principles RLCMBPT investigations to study the trends in the relative importance of these mechanisms over the entire alkaline-earth-metal series. These trends are compared to the corresponding ones found for other single s-valence electron series, namely, the alkali-metal-atom, noble-metal-atom, and group-IIB-ion series. A number of similar features involving the behaviors of the exchange core polarization and correlation effects within and among these series are observed. Several factors, such as the deformabilities of the valence electron shells, the relative separations between core and valence electrons, and the effective charges of the systems, are analyzed to achieve a satisfactory general understanding of the physical underlining of the observed features in these trends.

Accurate measurements of the autoionization widths of 5d5g levels of barium coupled to theoretical calculations, based on the eigenchannel R-matrix method and the multichannel quantum-defect theory, permit an investigation of the quadrupolar autoionization mechanism. The direct polarization of the inner electron by the outer one is an important correction to the Coulomb repulsion that causes autoionization. Also, the dielectronic polarization interaction significantly influences the autoionization widths. The occurrence of these polarization effects in the 5d5g doubly excited states with nonoverlapping valence electrons results in a significant narrowing of their widths and explains the failure of the ‘‘single-configuration model’’ for high-l Rydberg levels.

The pair-function formalism has been extended to the calculation of atomic and ionic properties in plasma environments that are modeled in terms of analytic screening potentials of the usual Debye form and the more general Debye-Laughton type. The theory has been applied to two-electron systems. As particular applications, the stability of ${\mathrm{H}}^{\mathrm{-}}$ and the energy splitting of several 1sns and 1snp states of the He atom have been studied in model plasma environments as well as the energies of allowed and forbidden transitions.

The sticking probability for the μdt molecular ion is estimated with the help of directly calculated nonvariational wave functions obtained by the correlation function hyperspherical harmonic method. The method generates an accurate, locally correct μdt wave function which leads to precise estimates of the partial-wave sticking coefficients and the fusion rate. Our calculations are compared with other precision computations.

Very extensive multiconfiguration-Dirac-Fock calculations in the modified special average-level version with the inclusion of the transverse (Breit) interaction and quantum electrodynamics corrections have been carried out on molybdenum, palladium, and lanthanum to elucidate the structure of the K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$${\mathit{M}}^{\mathit{r}}$ lines in their x-ray spectra and to explain reliably the influence of additional holes in the M shell on the shapes and positions of K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$ bands. For each type of line, two theoretical spectra have been synthesized, one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. It has been shown that the structures of the appropriate groups of K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$${\mathit{M}}^{\mathit{r}}$ lines of molybdenum, palladium, and lanthanum are similar, while the relevant bands being the sum of the Lorentzian natural line shapes are much smoother for lanthanum (large natural line width) than for molybdenum and palladium. For atoms having sufficiently large atomic mumbers (such as lanthanum), the convolution of a sum of the Lorentzian line shapes with the Gaussian instrumental response can be well represented as two Voigt functions in all cases (large distances between the K${\mathrm{\beta }}_1$${\mathit{L}}^0$${\mathit{M}}^{\mathit{r}}$ and K${\mathrm{\beta }}_3$${\mathit{L}}^0$${\mathit{M}}^{\mathit{r}}$ lines).

For mid-Z atoms (such as molybdenum and palladium), only in some cases do the resultant bands keep a structure of the reference K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$${\mathit{M}}^0$ lines. It has been found that the most significant effect in producing K${\mathrm{\beta }}_{1,3}$${\mathit{L}}^0$ energy shifts is the effect of removing a 3s electron and, next, a 3p electron, while this occurs far less with 3d electrons. The shift effects are nonadditive and increase remarkably with increasing atomic number. The results of this and previous papers of this series can be used to determine the M-shell ionization probability in near-central collision processes via the theoretical analysis of various experimental Kα and Kβ spectra of molybdenum, palldium, and lanthanum induced by different energetic light ions (such as electron, proton, and He ions) and heavy ions (such as N, O, Ne, Ar, and other ions).

A method is presented for the generation of valence-only local Hamiltonians, or pseudo-Hamiltonians, within the framework of the local-density-functional theory. Extensive transferability tests for atoms and crystals show that the performance of pseudo-Hamiltonians in density-functional-theory calculations matches the standards of other state-of-the-art methods. These pseudo-Hamiltonians represent a useful tool for quantum Monte Carlo simulations of many sp-bonded valence-only systems.

Angular correlation of annihilation radiation (ACAR) from silica-powder pellets and silica aerogel has been measured in order to investigate the slowing down of free positronium (Ps) atoms by collisions with silica grains and gas molecules. The data for the pellets and the aerogel in vacuum show that the slowing down of parapositronium (p-Ps) in the free space between the silica grains depends on the number of collisions and hence on the mean distance between the grains. The momentum distribution of orthopositronium (o-Ps) shows further slowing down because of its long lifetime. From the ACAR data obtained from specimens of aerogel filled with gases (He, Ne, Ar, Kr, Xe, ${\mathrm{H}}_2$, ${\mathrm{CH}}_4$, ${\mathrm{CO}}_2$, and iso-${\mathrm{C}}_4$${\mathrm{H}}_{10}$), the momentum-transfer cross sections between Ps and the gas molecules are estimated. It is concluded that the Ps kinetic energy is transferred only to the translational motion of the gas molecules, i.e., the excitations of vibration and rotation of the molecules are negligible.

Term energies are determined for the n=2 states of lithiumlike ions with nuclear charges in the range 10≤Z≤92. These calculations are based on the relativistic no-pair Hamiltonian, which includes both the Coulomb and the retarded Breit interactions. Single-particle wave functions are expanded in a B-spline basis constructed from Dirac-Slater orbitals restricted to a finite cavity. The Hamiltonian matrix is evaluated and Davidson’s method is used to determine the lowest few eigenenergies and eigenfunctions for each angular symmetry. Quantum electrodynamic and mass polarization corrections are also calculated. Precise agreement between theory and experiment for the 2s-2p transition energies is found throughout the Periodic Table.

We give the expressions for the zeroth and first spectral moments of collision-induced absorption (CIA) in the infrared by atom-diatom pairs. The perturbation treatment takes into account both the anisotropy of the interaction potential and its dependence on the vibrational coordinate. With the help of reliable ab initio induced dipole and potential surfaces of the ${\mathrm{H}}_2$-He collisional complex, we compute these expressions numerically. Under conditions for which laboratory measurements of CIA exist, accounting for the anisotropy lowers absorption, the more so the greater the anisotropy (especially of the repulsive core) is. Moreover, systems that possess relatively strong overlap-induced dipole components show more substantial anisotropy corrections. Specifically, while for ${\mathrm{H}}_2$ pairs in the rototranslational CIA band we see only small anisotropy corrections, in the vibrational bands the corrections are more significant, especially at the higher temperatures. ${\mathrm{H}}_{2\mathrm{-}}$He complexes show even more substantial corrections. In a comparison of a recent measurement of the absorption profile in hydrogen-helium mixtures in the ${\mathrm{H}}_2$ fundamental band with quantum line shape calculations, the effects of the anisotropic interaction are actually discernible.

We present a relativistic self-interaction-free density-functional formalism based on the local-density approximation with additional correction terms, and propose an algorithm for its numerical solution. The rigorous foundations of the scheme in density-functional threory and the resulting effective one-electron picture are discussed. Calculations for several atoms are shown as a practical example.

The relativistic Fock-space coupled-cluster method was applied to the Yb, Lu, and Lr atoms, and to several of their ions. A large number of transition energies was calculated for these systems. Starting from an all-electron Dirac-Fock or Dirac-Fock-Breit function, many electrons (30–40) were correlated to account for core-valence polarization. High-l virtual orbitals were included (up to l=5) to describe dynamic correlation. Comparison with experiment (when available) shows agreement within a few hundred wave numbers in most cases. Fine-structure splittings are even more accurate, within 30 ${\mathrm{cm}}^{\mathrm{-}1}$ of experiment. Average errors are at least three times smaller than for previous calculations. Two bound states of ${\mathrm{Lu}}^{\mathrm{-}}$ are predicted, 6p5d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ and 6${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$, with binding energies of about 2100 and 750 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. The ground state of lawrencium is ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$, relativistically stabilized relative to ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{3/2}$, the ground state of Lu. Two states of the ${\mathrm{Lr}}^{\mathrm{-}}$ anion are bound, 7${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ (by 2500 ${\mathrm{cm}}^{\mathrm{-}1}$) and 7p6d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ (by 1300 ${\mathrm{cm}}^{\mathrm{-}1}$).

We use the quantized surface mode technique to evaluate the interaction V of a ‘‘particle’’ (an electron or atom) with two sets of plane parallel walls of arbitrary thicknesses and arbitrary permittivities; one set is on one side of the particle and the other set is on the other side. It is shown that a set of walls on either side of the particle can be treated as a single wall with an effective reflection coefficient scrR, a function of the frequency and angle of incidence of an incoming plane wave. The two sets of walls have thereby been effectively reduced to one wall on each side. Using a modified version of the standard image technique—the locations of the images are the usual ones, but the strengths are modified—one finds that the closed form for V can be reexpressed as a sum of interactions of the set of images on a given side with the wall on the other side. Taking various limits (thin walls, thick walls, metallic walls, dilute media) reproduces many known interactions and also provides a number of results not previously obtained. The latter results enable us to give quantitative estimates of the error incurred in approximating a wall of finite thickness by a wall of semi-infinite thickness, or approximating a wall with large permittivity by a wall of infinite permittivity. In an attempt to make the paper user friendly, we provide a tabulation of many of the short-range (van der Waals-like) and long-range (retardation) interactions now known, with equation references.

A formalism of degenerate perturbation theory is presented, in which the initial basis set of functions is fully adapted to the perturbation. This full adaptation is obtained by imposing a simple condition which leads to an iteration procedure free of singularities. The formalism includes as a special case nondegenerate perturbation theory. By using it we calculate the dispersion coefficients of alkali-metal dimers for molecular states which dissociate into one atom in the ground state and the other in one of the first two S, P, or D excited states. The dispersion forces are extracted from the first- and second-order energy corrections. Model potentials are used in order to describe the motion of the valence electron in the field of the alkali-metal positive-ion core. Using the first-order wave-function correction, we investigate the leading terms of the long-range expansion of the electronic transition dipole moments. An extension of the Dalgarno-Lewis method is developed in order to handle the radial matrix elements which involves a reduced Green’s function for real and complex energies. The results are compared with previous computations.

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes’s theorem and standard quantum theory. These probabilities are equivalent to the ‘‘weak measurement’’ predictions due to Aharonov, Albert, and Vaidman [Phys. Rev. Lett. 60, 1351 (1988)] and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle that has tunneled across a barrier. A gedanken experiment is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a band-gap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse delay time are related to the imaginary value of the momentum of a tunneling particle and it is suggested that this might help explain a small discrepancy in an earlier experiment.

The results of close-coupling calculations are reported for low-energy electron collision processes involving ${\mathrm{NF}}_3$. We have used the complex Kohn variational method to calculate the elastic differential and momentum-transfer cross sections, as well as cross sections for (dissociative) excitation of the lowest singlet and triplet electronically excited states. Comparison is made between the results of this study and the limited body of experimental results available for this system.

A beam of molecular ions (${\mathrm{ArH}}^{+}$, ${\mathrm{ArD}}^{+}$, or ${\mathrm{D}}_3^{+}$) was neutralized by passage through an excited cesium vapor; two single-mode diode lasers were used to populate the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ state of the cesium atoms. The charge-transfer cross section could be increased by laser excitation of the Cs target, in some cases by orders of magnitude. This was established by observing the intensity of the luminescence from the neutralized molecules, which was enhanced by a factor of up to 10. The enhancement factors are in qualitative agreement with results of computations that follow the theoretical treatment for atoms introduced by Rapp and Francis [J. Chem. Phys. 37, 2631 (1962)]. This experimental technique is a generally applicable method for any molecular-beam technique that relies on charge transfer.

Rotational rainbows in the collision Xe+${\mathrm{CO}}_2$ are analyzed using quantum and classical two-dimensional models. We discuss the effect of the single- and the multiple-collision rotational rainbows on the differential cross sections, both for the fixed transitions and varying scattering angle and for the fixed scattering angle and varying transitions. A comparision is made with the existing centrifugal sudden calculations for this system.