Explicit formal formulas for exact density-functional correlation energies are derived and expressed in terms of correlating first-order density matrices (one-matrices) that are functionals of the density. The correlation energy for a full calculation is considered, as well as one intended as an addition to a completed calculation that excludes correlation. Several constraints for the one-matrices are shown.

The l-changing transitions in collisions of Rydberg atoms with ions, A(${\mathit{nl}}_0$)+${\mathit{B}}^{+}$→A(nl)+${\mathit{B}}^{+}$, are considered within the classical approximation for atomic electron motion. The elliptic orbit of the electron evolves slowly under the influence of the time-dependent electric field exerted by the incident ion. The quantum electron state is represented by an ensemble of classical trajectories. Within the dipole approximation extremely simple analytical formulas for the final-state l-distribution function are obtained for a fixed value of the impact parameter. The influence of the non-Coulomb core is taken into account approximately. The results of our calculations compare favorably with recent experimental data for the ${\mathrm{Na}}^{+}$(26d, 28d) Rydberg atom. The method can be extended to the calculation of distributions over various observables other than l.

An alternative technique of coincidence between energy-selected electrons and mass- and energy-selected photoions, combined with angle-resolved photoion spectroscopy, has been applied to investigate the state-selected dissociation dynamics of the B 1s core-excited ${\mathrm{BF}}_3$ molecule. Dissociation from the spectator Auger final states both above and below the double-ionization threshold produces energetic ${\mathrm{B}}^{+}$ in the secondary processes of stepwise dissociation after the molecular deformation (${\mathit{D}}_{3\mathit{h}}$→${\mathit{C}}_{3\mathit{v}}$), in marked contrast to dissociation following B 1s ionization in which energetic ${\mathrm{F}}^{+}$ is ejected within the ${\mathit{D}}_{3\mathit{h}}$ plane of the parent ${\mathrm{BF}}_3$ molecule.

The probe-transmission spectrum of a one-dimensional optical lattice is calculated. The optical lattice consists of atoms that are cooled by a pair of counterpropagating, linearly polarized fields, whose frequency ω is detuned to the blue side of an atomic transition. A weak probe field of frequency ${\mathrm{\omega }}^{\prime }$ is assumed to be propagating in the same direction as one of the cooling fields. It is shown that, owing to the existence of dark and gray states in the lattice, the probe-transmission spectrum exhibits interesting features that are qualitatively different from those of a ‘‘normal’’ optical lattice with red-detuned cooling fields. Examples of these features include subrecoil linewidths and reversed absorption-amplification sidebands. It is shown that by monitoring the magnitudes of resonance signals in the spectrum, one can gain information on the evolution of the dark-state population in the lattice.

Through numerical simulations we show that the propagation of pairs of optical pulses in a double-Λ configuration is favorable for the attainment of electromagnetically induced transparency with matched pulses, even through a long absorbing sample. The double-Λ configuration allows a flexible and precise control of the amplitudes and phases for the propagating pulses. Different atomic and field configurations based on a double-Λ system in rubidium atoms have been explored.

Experimental results of quasielastic light scattering on a water-HCl mixture at T=297 K are reported, which demonstrate the existence of a different kind of nonclassical two-photon (fourth-order) correlation, in the absence of second-order interferences. The normalized two-photon correlation function ${\lambda }^{\mathrm{}\left(2\right)\mathrm{}}$(1,2) shows an oscillation with an amplitude of about 25%, depending on the relative position of the two detectors and the scattering source. The equivalent measurement on ${\mathrm{CS}}_2$ shows no such effect. The possible physical significance of the observations is briefly mentioned.

Four electronic states of ${\mathrm{H}}_3$ have been studied using a multiple-reference double-excitation configuration-interaction method with an extensive basis set of 75 Gaussian-type atomic orbitals. A total of 1340 ab initio points were calculated over a wide range of ${\mathrm{H}}_3$ molecular geometries. These four states include the ground state and the Rydberg 2s ${\mathrm{A}}_1^{2\prime }$ and ${2\mathrm{p}}_{\mathrm{z}}$ ${\mathrm{A}}_2^{2\mathrm{″}}$ states, as well as the state that in equilateral triangular geometry is related to the ground state by a conical intersection. Electric-dipole transition moments were also obtained between these states. The results show that the atomic and diatomic energetic asymptotes are accurately described. The barriers, wells, and energy differences also show good agreement compared to literature values, where available. The potential energies of the ground state and the ${2\mathrm{p}}_{\mathrm{z}}$ ${\mathrm{A}}_2^{2\mathrm{″}}$ Rydberg state display smooth and regular behavior and were fitted over the whole molecular geometries using a rotated Morse curve-cubic spline approach. The other two potential-energy surfaces reveal more complicated behaviors, such as avoided crossings, and will require a different fitting procedure to obtain global fitting. Finally, dynamical implications of these potential surfaces and electric-dipole transition moments are discussed.

The low-lying electronic states of the ${\mathrm{S}}_2^{\mathrm{-}}$ anion have been investigated by quantum-chemical methods incorporating an extensive treatment of electron correlation. All excited doublet states that can be reached in spin- and dipole-allowed transitions from the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ ground state of the anionic disulfur molecule as well as the lowest quartet state ${}_{}{}^4{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{\mathrm{-}}{}_{}{}^{}$ are characterized by their spectroscopic constants, excitation energies, and transition dipole matrix elements with the ground state. Furthermore, an accurate calibration of the employed theoretical methods with respect to the electron affinity of the sulfur atom, the potential energy curves for the ground states of ${\mathrm{S}}_2$ and ${\mathrm{S}}_2^{\mathrm{-}}$, the electron affinity of ${\mathrm{S}}_2$, and the binding energies of the neutral and anionic ${\mathrm{S}}_3$ clusters is presented.

Ab initio calculations of the static longitudinal polarizability of different molecular hydrogen model chains have been carried out at different levels of approximation to investigate the effects of including electron correlation as well as the variation of these effects as a function of the bond-length alternation of the systems. First, the coupled and uncoupled Hartree-Fock schemes have been employed. To assess the electron-correlation effects, the size-consistent Mo/ller-Plesset treatments limited to second (MP2), third (MP3), and fourth (MP4) order in electron-electron interactions, as well as the coupled-cluster techniques including all double substitutions (CCD), all single and double substitutions (CCSD), and all single and double substitutions with a perturbational estimate of the connected triple excitations [CCSD(T)] have been used. Within the MP4 treatment, a decomposition of the electron-correlation corrections according to the different classes of substitutions and different order highlights the relatively greater importance of the double substitutions at second and third orders. The main findings are that (i) the coupled Hartree-Fock (CHF) technique overestimates the asymptotic static longitudinal polarizability per unit cell for the three types of ${\mathrm{H}}_2$ chains under investigation; (ii) larger basis sets have to be employed when including electron correlation effects, otherwise, the correction is overestimated; (iii) these basis-set effects on the electron-correlation correction are enhanced in the case of the less alternating chains; (iv) using a sufficiently large atomic basis set, at the Mo/ller-Plesset or CCSD(T) levels, the more conjugated the chains, the less the relative magnitude of the electron-correlation correction to the CHF value, whereas using the CCD and CCSD techniques, these relative electron-correlation corrections slightly increase in the case of the less alternating molecular hydrogen chains; and (v) the more conjugated the systems, the higher order the treatments of electron correlation required to get suitable values but the smaller the magnitude of electron-correlation correction.

We have derived an expression in terms of eigenvalues and eigenfunctions of the no-pair Hamiltonian for the sum over the generalized oscillator strength distribution for the relativistic, positive-energy solutions for a many-electron system. Formally, it looks very much like the corresponding nonrelativistic sum. However, only in the nonrelativistic limit is the sum equal to the number of electrons (the Bethe sum rule). We have determined the leading (1/${\mathit{c}}^2$) relativistic correction to the nonrelativistic Bethe sum rule and we argue that this correction is more in accordance with relativistic quantum mechanics than is a previous suggestion. The same statement holds for relativistic corrections to the Thomas-Reiche-Kuhn sum rule, previously derived only for one-electron systems. We discuss the problem that the explicit summation of the generalized oscillator strengths and calculation of the sum as a ground-state average of a comutator, while formally equivalent, may not give identical results in approximate calculations.

In this study we carried out a 1/Z expansion of the ground-state correlation energies for He through Ar isoelectronic systems based on the data of S. J. Chakravorty et al. [Phys. Rev. A 47, 3649 (1993)]. From this expansion, we determined the changes of the average electron-nuclear (〈${\mathit{V}}_{\mathrm{en}}$〉) and electron-electron (〈${\mathit{V}}_{\mathit{e}\mathit{e}}$〉) potentials in these systems due to electron correlation. The unique features of Δ〈${\mathit{V}}_{\mathit{e}\mathit{n}}$〉 in the O, F, and Ne isoelectronic series have been linked to their electronic structures. Also, the 1/Z expansion allows us to predict the electron affinities (EA’s) of stable first- and second-row negative ions. The predicted EAs compare favorably with those from photodetachment experiments.

Methods of the statistical theory of spectra are applied to the description of the vibronic spectra of molecules and solids. Explicit expressions for envelopes of electronic bands are derived. Several examples are elaborated to illustrate the theory.

A systematic x-ray absorption study to detect atomic background features at the K edges of fifth-period elements is reported. Samples of ${\mathrm{MoC}}_{\mathit{x}}$ (Z=42) and pure Rh (Z=45), Pd (Z=46), Ag (Z=47), In (Z=49), and Sn (Z=50) are measured at high temperature, mostly in the liquid phase, to reduce the intensity of the structural extended x-ray absorption fine structure (EXAFS) contribution. Main anomalies, showing a regular trend as a function of Z, are identified in the region around 100 eV and in the range 200–800 eV above an edge. They are assigned to the opening of absorption channels creating double-hole configurations such as [1s4p], [1s,3d], and [1s,3p]. Differences of self-consistent calculations in the Dirac-Fock approximation have been performed and the dominant transitions unambiguously identified. The results are relevant for the improvement of the EXAFS analysis at these edges.

A simplified calculation of the radiative recoil correction to hydrogenic energy levels in ${\mathit{m}}^2$/M[α(Zα${)}^5$/${\mathit{n}}^3$] order is presented. The method is based on evaluation of the proton kinetic energy term in the electron state. The result obtained is in disagreement with a previous calculation of Bhatt and Grotch [Ann. Phys. (N.Y.) 178, 1 (1987)]. We also analyze the nuclear self-energy contribution and the corresponding definition of the nuclear mean square charge radius.

When perturbation theory is applied to a quantity for which a variational principle holds (eigenenergies of Hamiltonian, Hartree-Fock or density-functional-theory, etc.), different variation-perturbation theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when constraints are present, is provided here. Explicit formulas for these variational principles for even orders of perturbation, as well as for the ‘‘2n+1 theorem,’’ to any order of perturbation, with or without constraints, are also exhibited. This approach is applied to the case of eigenenergies of quantum-mechanical Hamiltonians, studied previously by other methods.

The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green’s function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ‘‘parallel-transport-gauge’’ and a ‘‘diagonal-gauge’’ perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.

Absolute partial cross sections from threshold to 1000 eV are reported for the production of ${\mathrm{Ar}}^{\mathit{n}+}$ (n=1–4) by electron-impact ionization of argon. The total cross sections, obtained from an appropriately weighted sum of the partial cross sections, are also reported. These results are obtained with an apparatus incorporating a time-of-flight mass spectrometer with position-sensitive detection of the product ions. The simple apparatus design embodies recent developments in pressure measurement and particle detection and is believed to yield more reliable results than those previously reported. For singly charged ions, the overall uncertainty in the absolute cross section values reported here is ±3.5%. Previous measurements of absolute partial and total cross sections are reviewed and compared with the present results.

L-shell x-ray production and subshell ionization cross sections have been measured for 0.4–1.8-MeV/amu carbon and nitrogen ions for selected heavy elements with 72≤${\mathit{Z}}_2$≤90. The results are compared with the predictions of the ECPSSR theory [perturbed-stationary-state (PSS) theory with energy-loss (E), Coulomb deflection (C), and relativistic (R) corrections] describing both direct ionization and electron-capture processes and the semiclassical approximation (SCA) calculations for direct ionization. For both theories significant deviations are found for ${\mathit{L}}_2$-subshell ionization in the low-energy range. The multiple ionization of outer shells was studied by comparing L x-ray intensity ratios measured for heavy ions and protons. The ionization probabilities of the ${\mathit{N}}_4$ subshell at zero impact parameter was extracted from these data. Measured ionization probabilities are compared with the predictions of the SCA theory and the ‘‘geometrical model.’’ The influence of multiple ionization on the measured L-subshell cross sections is discussed.

A 15-state diabatic molecular expansion, covering channels up to 2s and 2p excitations, has been used to study single and double charge transfer in ${\mathrm{He}}^{2+}$-He(1${\mathit{s}}^2$) collisions at kilo-electron-volt energies. The aim of the work has been to explore the usefulness of this type of diabatic molecular basis for eventual use in benchmark calculations, electron translation factors not being included in this low-energy calculation. Our results for single and double electron capture agree very well with experiment up to relative velocities of ∼0.5–0.6 a.u. For single capture into the ground state the series can be truncated early with very little effect, but for double capture the truncation cannot be done. A probable connection with correlated two-electron motion is discussed.

A theoretical study is made of the absorption cross section by a finite width laser pulse for atoms or negative ions in external fields. A modified closed-orbit formula for the cross section is derived. It is shown that the finite width of the laser pulse reduces the contributions from the short closed orbits and completely eliminates the contributions from the long closed orbits whose transit times are much greater than the pulse width. The theory is applied to study the photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ in the presence of a static electric field by a laser pulse.