A first-principles relativistic many-body investigation of magnetic hyperfine fields has been carried out for the ground states 4${\mathrm{}}^2$ ${\mathrm{S}}_{1\mathrm{/}2}$ of the alkali atom K and doubly charged ion ${\mathrm{Sc}}^{2+}$ completing the investigation over the three members of the isoelectronic series K, ${\mathrm{Ca}}^{+}$ , and ${\mathrm{Sc}}^{2+}$ with a single valence electron in the 4s state, since ${\mathrm{Ca}}^{+}$ had been investigated by us previously. This allows one to study both the nature of agreement with experiment over this series as the charge increases and the trends in the contributions from the major mechanisms responsible for the hyperfine fields in these systems. The calculated magnetic hyperfine fields in tesla for K, ${\mathrm{Ca}}^{+}$ , and ${\mathrm{Sc}}^{2+}$ are 56.81, 135.90, and 239.29, respectively. These agree very well with the measured values of 58.02 T for K and 140.30 T for ${\mathrm{Ca}}^{+}$ . No experimental data are available for the ${\mathrm{Sc}}^{2+}$ system. The exchange core polarization (ECP) and correlation contributions, as fractions of the valence contribution, are found to decrease rapidly as one goes to systems with higher ionic charges, the decrease being more drastic for correlation effects. The trend of the ratios of ECP and correlation contributions to the valence contribution for both K and ${\mathrm{Sc}}^{2+}$ were compared with those calculated for the neighboring alkali-metal systems, sodium and rubidium. The physical explanations for the results and the observed trends in the contributions from the different mechanisms are discussed.

A relativistic Sturmian analytic basis set representation for the Coulomb-Dirac Green function, previously studied by Zapryagaev, Manakov, and Pal'chikov [Opt. Spectrosc. 52, 248 (1982)], is investigated for application to high-Z atomic QED calculations. This pseudoeigenfunction representation follows from exact identities starting from the Whittaker function representation. It eliminates the radial ordering problem of that representation, and so is particularly useful for numerical calculation of the perturbation theory Feynman diagrams with more than one electron Green function. While the Green function represents discrete bound states, and both positive and negative energy continuum states, the Sturmian (bound-state-like) form for the pseudoeigenfunctions makes it possible to more analytically calculate matrix elements for full photon exchange, reducing numerical problems for high photon frequency. For He-like Fm (Z=100) we calculate the perturbation theory equivalent of the Dirac-Fock-Breit ground-state energy, agreeing well with the Grant code and with the numerical B-spline basis set approach results of Blundell, Mohr, Johnson, and Sapirstein [Phys. Rev. A 48, 2615 (1993)]. Preliminary results on the relativistic and QED correlation are also reported.

The bound-state spectra of the positronium hydrides ${}_{}{}^{\mathrm{\infty }}{}_{}{}^{}\mathrm{HPs}$, TPs, DPs, ${}_{}{}^1{}_{}{}^{}\mathrm{HPs}$, and MuPs are considered. The properties of the bound ground S states (L=0) in these systems and the ${\mathrm{Ps}}_2$ molecule have been determined by extensive variational calculations. The hyperfine structure of these states is also investigated. The positron annihilation rates have been evaluated for the positronium hydrides, the ${\mathrm{Ps}}_2$ molecule, and the ${\mathrm{Ps}}^{\mathrm{-}}$ ion and compared. The positron annihilation rates ${\mathrm{\Gamma }}_{\mathrm{n}\gamma }$ (where n⩾2) in the positronium hydrides are significantly closer to those in the ${\mathrm{Ps}}^{\mathrm{-}}$ ion (the three-body system) than in the ${\mathrm{Ps}}_2$ molecule.

The standard adiabatic hyperspherical approach to the description of doubly excited two-electron systems is adapted to the special case of ridge states. The two electrons are treated as a pair throughout the whole range of the adiabatic variable R. Diabatic corrections to the adiabatic potential curves are determined that are similar to the diabatic-by-sector method. The evolution of the correlation patterns (correlation diagram) is investigated and the most appropriate sets of coordinates and corresponding quantum numbers are identified for three different regions of the adiabatic variable.

The coupled cluster method (CCM) introduces a linked-cluster parametrization for the many-body wave function. The method can be formulated through an action principle, which introduces a symplectic structure into the CCM phase space. We study the phase spaces of the normal and extended coupled cluster methods (NCCM and ECCM, respectively) with a special emphasis on the ensuing characteristic non-Hermiticity of the action and the average-value functionals. By introducing the complex conjugates of the usual CCM cluster amplitudes the phase space is enlarged into a genuine complex manifold. The extra degrees of freedom are then eliminated by the Dirac bracket method, leaving as independent coordinates a minimal set of complex conjugate (eventually, real) coordinate functions. The constraint functions performing this elimination are shown to be of second class. The induced symplectic structure in the physical submanifold (or the constraint surface) is derived, and the physical shell itself found to be a Kähler manifold. Furthermore, the significance of the CCM star product in generating the average-value functionals of compound operators is emphasized. It is proven that the star product can also be defined on the constraint surface in both the NCCM and ECCM cases. The results suggest that Hermiticity-preserving truncation schemes based on the on-shell star product may become feasible.

The hydrogen molecular ion in a strong external magnetic field parallel to the molecular axis is investigated using a semianalytical method based on the presentation of the wave function in the form of a double power series in nonseparable space variables. The solution is determined from the requirement for the coefficients of the series to obey linear relations imposed by the Schrödinger equation. For the ground state, the method provides accuracy ${10}^{\mathrm{-}8}$ hartree and higher for magnetic fields from 0 up to ${10}^4$ T; the applicability of the technique to excited states is limited to lower field strengths.

Stark shifts were determined using an electro-optically modulated laser beam. The voltage required for atoms excited by the laser beam in an electric field, to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region, was measured. The scalar ${\mathrm{\alpha }}_0$ and tensor ${\mathrm{\alpha }}_2$ polarizabilities of the cesium 11D state were found to be ${\mathrm{\alpha }}_0$(${11\mathrm{D}}_{3\mathrm{/}2}$)=-2694.6±2.7, ${\mathrm{\alpha }}_2$(${11\mathrm{D}}_{3\mathrm{/}2}$)=2107.5±2.7, ${\mathrm{\alpha }}_0$(${11\mathrm{D}}_{5\mathrm{/}2}$)=-3379.5±5.4, and ${\mathrm{\alpha }}_2$(${11\mathrm{D}}_{5\mathrm{/}2}$)=4242.1±11.4 MHz/(kV/cm${)}^2$. The tensor polarizabilities are the most accurate yet determined for any atomic state.

A theory for natural circular dichroism (CD) in x-ray Raman scattering from molecules is presented. Analytical formulas are given for the CD effect and for the angular dependence of this effect in the electric dipole and in the electric- and magnetic-dipole approximations. It is demonstrated that the CD effect can be observed for randomly oriented molecules even assuming the pure electric-dipole approximation. The effect can only be described by a one-step model for x-ray Raman scattering, while in the two-step model the electric CD contribution is identically zero. The effect is intimately connected to the molecular point-group symmetry and to channel interference, and, contrary to optical CD, it will preferentially be observed for 'achiral' molecules. It is shown that it acts as a unique experimental tool to identify the degree of dynamic localization of core excited states. Sample calculations indicate that the electric contribution to the molecular CD effect can be very large and about one order of magnitude larger than the magnetic-dipole contributions.

Oscillator strengths for the three lowest ground-state transitions ${3\mathrm{p}}^6$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$-${3\mathrm{p}}^5$4s ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$, ${3\mathrm{p}}^6$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$-${3\mathrm{p}}^5$4s ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$, and ${3\mathrm{p}}^6$ ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$-${3\mathrm{p}}^5$3d ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ in argonlike K II are reported. The values were determined by lifetime measurements made using foil excitation of a fast ion beam, which yielded values τ(4s ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$)=8.4±1.6 ns, τ(3d ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$)=2.4±0.4 ns, and τ(4s ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$)=0.43±0.04 ns. Application of these results to the development of extreme ultraviolet lasers is discussed.

A systematic calculation of the hyperfine structure of 2${\mathrm{}}^3$P levels of heliumlike ions is presented. Reduced matrix elements of the magnetic-dipole hyperfine operator between substates of the 2${\mathrm{}}^{1,3}$P states are evaluated using relativistic configuration-interaction wave functions that account for both Coulomb and Breit interactions. These matrix elements, together with the energy intervals Δ${\mathrm{E}}_{10}$=E(2${\mathrm{}}^3$${\mathrm{P}}_1$)-E(2${\mathrm{}}^3$${\mathrm{P}}_0$), Δ${\mathrm{E}}_{20}$=E(2${\mathrm{}}^3$${\mathrm{P}}_2$)-E(2${\mathrm{}}^3$${\mathrm{P}}_0$), and Δ${\mathrm{E}}_{\mathrm{st}}$=E(2${\mathrm{}}^1$${\mathrm{P}}_1$)-E(2${\mathrm{}}^3$${\mathrm{P}}_0$), are tabulated for ions with nuclear charges in the range Z=2–100. For Z=2, the matrix elements are in close agreement with precise nonrelativistic variational calculations, but as Z increases from 2 to 10, the present values deviate smoothly from the variational values owing to relativistic corrections. Applications are given to determine the hyperfine structure of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^{6,7}{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{2+}{}_{}{}^{}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{7+}{}_{}{}^{}$. Hyperfine quenching rates of 2${\mathrm{}}^3$${\mathrm{P}}_0$ states are calculated using a radiation-damping formalism for all stable isotopes in the range Z=6–92. Quenching rates of 2${\mathrm{}}^3$${\mathrm{P}}_2$ states are also calculated for selected ions. For Z=9–29, the 2${\mathrm{}}^3$${\mathrm{P}}_0$ quenching rates are in good agreement with relativistic 1/Z calculations. For Z>40, the diagonal hyperfine matrix elements disagree in sign with previously published multiconfiguration Dirac-Fock values. In view of these differences, the present matrix elements are used to reevaluate the fine-structure intervals Δ${\mathrm{E}}_{10}$ inferred from hyperfine quenching experiments for the ions ${\mathrm{Ni}}^{26+}$, ${\mathrm{Ag}}^{45+}$, and ${\mathrm{Gd}}^{62+}$.

Fully relativistic, all-electron self-consistent-field calculations, based on the Dirac-Coulomb(-Gaunt) Hamiltonian, have been performed on the ground state and the three Cl 2p–ionized states of HCl. The calculations are done by the Dirac-Fock method and correlation is included through relativistic configuration-interaction calculations. The core-orbitals of HCl are shown to have a relativistic character and a description of the Cl 2p–ionized states in terms of ωω-coupling is found to be crucial. Calculated Cl 2p–ionization energies and energy splittings are in very good agreement with recent experimental, high resolution results. For the ionization energies, relaxation dominates correlation, and the effect of correlation are found to be neglible. Furthermore, the combined effects of the Gaunt term and core-valence correlation brings the calculated energy splittings in excellent agreement with experiment.

Vibrational fine structure in the C 1s photoelectron spectra of methane, ethene, propene, and 2-methylpropene has been observed using high-resolution synchrotron radiation. The degree of vibrational excitation is found to increase with the number of hydrogens attached to the core-ionized carbon atom, and this observation can be rationalized using a linear coupling intensity model. The vibrational structure can be accounted for almost quantitatively with the assumption that the primary vibrational excitation is stretching of the CH bond attached to the core-ionized carbon atom, using the results from methane to establish the intensities of the CH stretching vibrations in the other molecules. Ab initio calculations of the geometrical changes accompanying C 1s core ionization support this picture. The high resolution in these experiments makes it possible to determine the core-ionization energies of the inequivalent carbons in propene and 2-methylpropene, as well as the difference between the adiabatic and vertical ionization energies in all four molecules. Ab initio calculations of vertical binding-energy shifts using hole-state calculations show good agreement with those determined experimentally.

In this paper we apply the single-particle Green's-function method to the atomic many-body perturbation theory. We present an all-order evaluation scheme for the proper self-energy operator based on the systematic use of Dyson's integral equations. The method is complete to third order in perturbation theory and, in addition, large classes of higher-order effects are included by solving the Dyson equations. Certain classes of many-body correlation effects beyond the pair-correlation approximation are included. The proposed method is tested by calculating the ground-state valence-electron binding energy for the alkali-metal atoms Li, Na, and K. Agreement with experimental results corresponds to an error in the correlation energy contribution of 3–4%. If certain three-particle effects, not evaluated in this work, are added, the agreement with experiments is, for sodium and potassium, approximately within 1% of the correlation energy.

Contributions of the electron-electron and electron-nucleus interactions to the ionization of ${\mathrm{O}}^{7+}$ by He are experimentally separated using recoil momentum spectroscopy. The electron-electron contribution is found to produce much smaller recoil momenta, both longitudinal and transverse. The momentum distributions of the two mechanisms are in good agreement with theoretical predictions. The comparison between the experiment and the theory suggests that electron-electron interactions in the projectile ionization can be understood in terms of free-electron impact ionization of the projectile ions.

Electron capture in collisions of C, N, O, and Si atoms with ${\mathrm{H}}^{+}$ ions is studied theoretically based on a molecular representation within a fully quantum framework by including six molecular channels both for the ground and excited states for the [${\mathrm{H}}^{+}$+C] system, and four channels for the ground-state [${\mathrm{H}}^{+}$+N] and [${\mathrm{H}}^{+}$+O] systems. For the [${\mathrm{H}}^{+}$+Si] system, we employed the molecular representation both in fully quantum and semiclassical frameworks to investigate electron capture at higher energy as well. The ab initio potential curves and nonadiabatic coupling matrix elements for all these systems are obtained from multireference single- and double-excitation configuration interaction calculations. For all systems, the effect of excited atoms on electron capture is examined in addition to that from the ground state. Because of a small asymptotic energy defect (near-resonant processes) between the initial and closest electron capture channels for almost all systems, electron capture cross sections from the ground-state atoms are large with values of approximately ${10}^{\mathrm{-}16}$-${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ for all systems at above 100 eV. Corresponding rate coefficients are found to be much smaller than those previously reported for the ${\mathrm{NH}}^{+}$ and ${\mathrm{OH}}^{+}$, but, on the contrary, found to be larger by a few orders of magnitude than the previously estimated value for the ${\mathrm{SiH}}^{+}$ system. Those from excited states are also found to be extremely efficient for all cases.

The calculation of electron-molecule cross sections at scattering energies well below 0.1 eV using conventional algorithms for solving the Schrödinger equation is often rendered problematic by severe numerical problems. Here we describe and implement an alternative procedure that combines known analytic properties of the body-frame electron-molecule scattering matrix, as codified in the modified effective range theory, with an analytic correction that imposes physically correct threshold laws. This approach eliminates completely the need for numerically solving the Schrödinger equation at energies below about 0.1 eV. Instead, one uses scattering matrices above this energy to determine parameters for an extrapolation to subthermal energies. We apply this method to the calculation of e-${\mathrm{N}}_2$ momentum-transfer and rotational excitation cross sections from threshold to 1.25 eV. The results resolve a long-standing apparent anomaly in the analysis of experimental data for very low-energy electron scattering from ${\mathrm{N}}_2$. Finally, we use linear regression to present our theoretical results in a user-friendly form.

The cross sections for dissociative recombination (DR) and dissociative excitation (DE) have been measured for the H^n+>₂ and HD⁺ molecular ions in the energy range from 0 to ∼30 eV. An imaging technique that provides a measure of the kinetic energy release in the DR process was used to yield information about the initial vibrational distribution of the molecular ions and the final atomic states of the DR reaction. The results for DR with HD⁺ in the vibrational ground level, ν=0, are compared with other measurements and recent multichannel quantum defect theory calculations. Significant deviations that appear at high energy ∼5–10 eV are discussed. The present work reports on an absolute DE measurement with HD⁺ . The vibrational distribution of H^n+>₂ was manipulated by photodissociation of ions in vibrationally excited levels. We obtained DE and DR cross sections for H^n+>₂ ions populating primarily the two lowest vibrational levels ν=0,1 and H^n+>₂ ions in a broad vibrational distribution. It is found that DR of H^n+>₂ with zero energy electrons results in the H(n=1)+H(n=2) final channel, open for all vibrational levels, and in the H(n=1)+H(n=3) channel, which is energetically open for initial vibrational levels ν⩾5.

We present an approximate solution of the Schrödinger equation for the three-body Coulomb problem. We write the Hamiltonian in parabolic curvilinear coordinates and study the possible separation of the wave equation as a system of coupled partial differential equations. When two of the particles are heavier than the others, we write an approximate wave equation that incorporates some terms of the Hamiltonian that before had been considered as a perturbation. Its solution can be expressed in terms of a confluent hypergeometric function of two variables. We show that the proposed wave function includes a correlation between the motion of the light particle relative to the heavy particles and verifies the correct asymptotic behavior when all particles are far from each other. Finally, we discuss the possible uses of this function in the calculation of transition matrices and differential cross sections in ionizing collisions.

In recent years there has been renewed interest in semiclassical methods of modeling atomic structure and collision dynamics. A class of many-body models applied to these problems are descendants of the original work by Kirschbaum and Wilets [Phys. Rev. A 21, 834 (1980)], who used momentum dependent pseudopotentials to exclude particles from quantum mechanically forbidden regions of phase space. These methods have been used for static, ground-state calculations for increasingly complex atoms, but the calculation of collision cross sections has to date been limited to fairly simple systems. This paper will consider the dependence of collision cross-section calculations on the parameters of the Kirschbaum-Wilets semiclassical model, present a general method for calculation of proton stopping powers by atomic targets, and present results for proton stopping by atomic targets ranging from He to Ne which agree quite well with experiments over a wide range of proton energies. A simple extension of the method to multicenter molecular targets will then be discussed, illustrated by the case of proton stopping by water.

We present a theoretical approach to the ab initio calculation of single or multiphoton double electron ionization cross sections, ${\mathrm{\sigma }}^{++}$(E), of polyelectronic atoms, near (Wannier region) and far from threshold. The overall computational method is variational, uses functions of real as well as of complex coordinates, and follows the many-electron, many-photon theory proposed by Mercouris and Nicolaides [J. Phys. B 21, L285 (1988); 23, 2037 (1990)]. It incorporates the electronic structure and the pair correlations in the continuum via configuration-interaction techniques. ${\mathrm{\sigma }}^{++}$(E) is obtained as the imaginary part of a complex eigenvalue that is computed by diagonalizing a state-specific non-Hermitian matrix constructed from separately optimized function spaces Q and P representing the field-induced resonance state. Q contains correlated wave functions of bound or quasibound states expanded over numerical and analytic orbitals of real coordinates. P is composed, in principle, of subspaces ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$, representing the one- and the two-electron channels, respectively, which are optimized separately and then are allowed to mix via the construction of the total non-Hermitian matrix. Both are spanned by basis sets of real coordinates for the ionized core and of complex coordinates for the outgoing part of the one- and the two-electron resonance state. The two-electron square integrable 'continuum' function space is made orthogonal to the available single electron channels in order for ${\mathrm{\sigma }}^{++}$(E) not to include portions of the single electron ionization cross section ${\mathrm{\sigma }}^{+}$(E). Application is made to the single photon ${\mathrm{\sigma }}^{++}$(E) of the prototypical systems ${\mathrm{H}}^{\mathrm{-}}$ and He, but without the mixing of ${\mathrm{P}}_2$ and ${\mathrm{P}}_1$, due to numerical instabilities. The two-electron ionization channels were composed of Slater-type orbitals, symmetry-coupled according to (sp), (pd), and (df ). Higher symmetries would also be needed at higher energies, with corresponding increase of angular correlation terms in the initial-state wave function. The continuous energy ranged from E=0 to E=250 eV. In the threshold region E=0–2 eV, the length and velocity results are in good agreement with experiment for ${\mathrm{H}}^{\mathrm{-}}$ and in reasonable agreement with experiment for He. Far from threshold, there is discrepancy between length and velocity forms in this as well as in previous works by other methods. Apart from whatever inadequacies of the basis functions, this is possibly due to the exclusion of mixing of the single electron open channels into the correlated wave function of the two free electrons. By comparing the results from the use of correlated wave functions with those obtained when the calculation of the transition matrix element is done with wave functions of real coordinates, where the initial state is correlated but the final one is only a product of Coulomb wave functions, the effect of correlation of the two free electrons is deduced for the case of He, without considering the mixing of one- and two-electron channels. Finally, a by-product of the present development was the calculation of the He ${\mathrm{\sigma }}^{+}$(E) to the n=1 single ionization threshold. Comparison with previous accurate experimental results reveals very good agreement.