We present ab initio calculations of the complete gauge invariant set of the self-energy screening diagrams for the ${2p}_{1/2}-2s$ transition in Li-like ions. The calculation was performed for extended nuclei in the range $Z=18\mathrm{}–100.$ Various contributions to the transition energy are collected. The accuracy of theoretical predictions is discussed.

Recently, a great deal of attention has been devoted to the near-exact Kohn-Sham (KS) atomic potentials, mainly obtained from quantum Monte Carlo (QMC) calculations for a few significant test cases. We show that the potential of the highest occupied orbital in the self-interaction corrected local-density approximation (SIC-LDA) approach provides an excellent approximation for the QMC potentials, far better than the commonly used ones. Moreover, near-exact KS potentials of the same quality as the QMC ones can be obtained from the SIC-LDA potentials of the highest occupied and lowest empty orbitals, by a simple two-parameter fitting procedure to reproduce the experimental values of the ionization and first excitation energies. This has been demonstrated by a quantum-defect analysis of the empty states of Ne and Be atoms, for which QMC potentials are available to us. The introduced method is used to construct a near-exact KS potential for Ar.

The hyperfine constants for the ground states of ${\mathrm{Be}}^{+}$ and ${\mathrm{F}}^{6+},$ and for the two lowest excited states of ${\mathrm{Be}}^{+},$ are calculated in a multiconfiguration Dirac-Fock model. Convergence of the calculated magnetic dipole constants is studied as the active set of orbitals is systematically increased. The final results are compared with experimental data and theoretical values obtained from other methods.

The ground and a few excited states of the carbon atom in external uniform magnetic fields are calculated by means of our two-dimensional mesh Hartree-Fock method for field strengths ranging from zero up to $2.35\times {10}^9$ T. With increasing field strength the ground state undergoes six transitions involving seven different electronic configurations which belong to three groups with different spin projections $S_z=-1,-2,-3.$ For weak fields the ground-state configuration arises from the field-free ${1s}^2{2s}^2{2p}_0{2p}_{-1},$ $S_z=-1$ configuration. With increasing field strength the ground state involves the four $S_z=-2$ configurations ${1s}^2{2s2p}_0{2p}_{-1}{2p}_{+1\mathrm{}},$ ${1s}^2{2s2p}_0{2p}_{-1}{3d}_{-2},$ ${1s}^2{2p}_0{2p}_{-1}{3d}_{-2}{4f}_{-3},$ and ${1s}^2{2p}_{-1}{3d}_{-2}{4f}_{-3}{5g}_{-4},$ followed by the two fully spin-polarized $S_z=-3$ configurations ${1s2p}_0{2p}_{-1}{3d}_{-2}{4f}_{-3}{5g}_{-4}$ and ${1s2p}_{-1}{3d}_{-2}{4f}_{-3}{5g}_{-4}{6h}_{-5}.$ The last configuration forms the ground state of the carbon atom in the high-field regime $\gamma >\mathrm{18.664.}\mathrm{}$ The above series of ground-state configurations is extracted from the results of numerical calculations for more than 20 electronic configurations selected due to some general energetic arguments.

Radiative lifetimes have been measured for fine-structure transitions in the intercombination ${2s2p}^2{}^4\overrightarrow{P}{2s}^{2}2p$${}^2{P}^o$ decay in ${\mathrm{C}}^{+}.$ Use was made of a Kingdon ion trap installed on a beam line for highly charged ions. The radiative rates $A_J$ derived from the lifetime measurements are $130.0\pm 5.5{\mathrm{s}}^{\mathrm{-}1}$ for the ${}^4{P}_{1/2}$ sublevel, $9.0\pm 1.0{\mathrm{s}}^{\mathrm{-}1}$ for the ${}^4{P}_{3/2}$ sublevel, and $50.0\pm 2.5{\mathrm{s}}^{\mathrm{-}1}$ for the ${}^4{P}_{5/2}$ sublevel. Comparisons with other measurements and results of theories are given.

The “molecular” values of the quadrupole moment of the Rb and Na nuclei have been obtained by using spectroscopic values of nuclear coupling constants and high-level-correlated relativistic calculations of the electric-field gradients in fluorides and chlorides. The recommended value for the ${}^{85}\mathrm{Rb}$ nucleus which follows from the present study is about 276 mb, with expected error bars of the order of about 1 mb. This value agrees with the atomic spectroscopy data, and suggests that the quadrupole coupling constant measured for the RbCl molecule is in error. The present calculations for ${}^{23}\mathrm{Na}$ confirm the earlier molecular result for its electric quadrupole moment, and combined with recent atomic calculations lead to the recommended value in the range 104–105 mb. The molecular results for nuclear quadrupole moments of the alkali-metal nuclei are reviewed leading to a list of the corresponding recommended values.

We present a method for evaluating resonances and bound states present in any one-dimensional potential. Semiclassical theory (WKB) provides a fast estimate of resonance positions, but it can be off in calculating resonance lifetimes. Conversely, there are a multitude of numerical techniques, solving the one-dimensional Schrödinger equation, that give precise resonance energies and widths, but they are much more difficult to apply. The phase-amplitude method presented here yields accurate resonance energies and widths and is as easy to apply as semiclassical theory. Long-lived vibrational states of ${\mathrm{He}}_2^{2+}$ and ${\mathrm{CO}}^{2+}$ molecular ions are computed for demonstration.

Proton structure effects, including finite size, polarizability, and self-energy are considered and their influence on energy levels of muonic hydrogen is recalculated. A theoretical prediction for the Lamb shift is presented together with improved values of all known QED contributions for muonic hydrogen. This would allow for the substantial improvement of the proton charge radius determination.

van Leeuwen and Baerends proposed a Becke-like nonlocal correction to the local-density-approximation (LDA) exchange-correlation potential so that its asymptotic structure becomes exact i.e., $-1/r$ [Phys. Rev. A 49, 2421 (1994)]. They showed that it significantly improves the value of the highest occupied orbital eigenvalue of atoms and molecules. However, the correction is exchangelike in nature. With this in mind, in this paper we investigate how this correction affects the total energies and highest eigenvalues within the exchange-only approximation. We show that the potential also corrects the LDA errors substantially within this approximation, and leads to total energies and high eigenvalues which compare well with their Hartree-Fock counterparts. Improvement in the asymptotic behavior of the potential should also result in better values of the response properties of these systems. We show that with this correction one obtains better estimates, both within the exchange-only approximation and with correlation included, of the linear and nonlinear polarizabilities of inert gas atoms. This is quite significant, since the LDA is known to overestimate the nonlinear polarizabilities of these atoms by roughly 100%. On the other hand, for alkaline-earth atoms the values of polarizabilities obtained with this correction are not satisfactory. Nonetheless, hyperpolarizabilities show a marked improvement over the LDA results.

We revisit the ${\mathrm{HD}}^{+}$ molecular ion by starting from a definition of the nonrelativistic adiabatic Hamiltonian that recovers the isotopic splitting. The Hamiltonian is written in prolate spheroidal coordinates with the origin at the nuclear center of mass. This prescription for the adiabatic Hamiltonian implicitly contains the symmetry-breaking effects arising from the mass difference between the proton and the deuteron, and gives the correct asymptotic atomic reduced masses. We calculate potential-energy curves, vibrational energies, transition dipole moments, and coupling matrix elements for ${\mathrm{HD}}^{+}.$ In our adiabatic approximation, the isotopic splitting is recovered to nine significant digits at a value of ${R=750a}_0.$ We investigate the dependence of the vibrational energies on the number of coupled electronic states, and compare with other calculations.

The solution of N-representability for the two-particle reduced density matrix (2-RDM) is intimately connected through the contracted Schrödinger equation with the problem of reconstructing the 3- and 4-RDM’s from the 2-RDM [D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998)]. We derive an explicit formula for building the 3-RDM from the 2-RDM which significantly improves the accuracy of the 3-RDM cumulant expansion. Calculations indicate that the improvement is better than that achieved by the correction of Nakatsuji and Yasuda (NY) [Phys. Rev. Lett. 76, 1039 (1996); Phys. Rev. A 56, 2648 (1997)]. We also present a more efficient formulation of the NY correction. Both the present and NY reconstructions are shown to satisfy the particle-hole duality. Comparison of the reconstruction methods is made through several molecules LiH, ${\mathrm{BeH}}_2,$ ${\mathrm{BH}}_3,$ ${\mathrm{H}}_2\mathrm{O},$ and ${\mathrm{CH}}_4,$ as well as systems with more general pairwise correlation.

Long-lived metastable states of ${\mathrm{N}}_2^{\mathrm{-}}$ are generated by sputtering surfaces of TiN or BN with keV ${\mathrm{Cs}}^{+}$ ions. The lifetimes of the metastable ions have been measured at the storage ring ASTRID. Experimental investigations of the charge exchange of ${\mathrm{N}}_2^{+}$ ions in alkali-metal vapor and theoretical calculations support the conclusion that the long-lived ${\mathrm{N}}_2^{\mathrm{-}}$ species are sextet states, originating from the attachment of an electron to a quintet state of the ${\mathrm{N}}_2$ molecule.

We report density-functional studies of several small molecules $({\mathrm{H}}_2,$ ${\mathrm{N}}_2,$ CO, ${\mathrm{H}}_2\mathrm{O},$ and ${\mathrm{CH}}_4)$ within the Krieger-Li-Iafrate (KLI) approximation to the exact Kohn-Sham local exchange potential, using a three-dimensional real-space finite-difference pseudopotential method. It is found that the exchange-only KLI approximation leads to markedly improved eigenvalue spectra compared to those obtained within the standard local-density approximation (LDA), the generalized gradient approximation (GGA), and the Hartree-Fock (HF) method. For structural properties, exchange-only KLI approximation results are close to the corresponding HF values. We find that the addition of LDA or GGA correlation energy functionals does not lead to systematic improvements.

A relativistic method for the calculation of positron binding to atoms is presented. The method combines a configuration-interaction treatment of the valence electron and the positron, with a many-body perturbation-theory description of their interaction with the atomic core. We apply this method to positron binding by the copper atom and obtain a binding energy of 170 meV $(\pm 10\%).$ To check the accuracy of the method we use a similar approach to calculate the negative copper ion. The calculated electron affinity is 1.218 eV, in good agreement with the experimental value of 1.236 eV. The problem of convergence of positron-atom bound-state calculations is investigated, and means to improve it are discussed. The relativistic character of the method and its satisfactory convergence make it a suitable tool for heavier atoms.

We provide a detailed description of our fast-beam laser lifetime measurements in atomic cesium. Selective excitation of the neutral ${}^{133}\mathrm{Cs}$ $6p{}^2{P}_{1/2}$ and $6p{}^2{P}_{3/2}$ states is accomplished with resonant diode laser light directed transversely to the atomic velocity. The in-flight decay of the excited-state fluorescence is observed with a position-correlated single photon-counting detector. The Doppler-shifted $6p{}^2{P}_{3/2}$ resonance, when probed with longitudinally propagating laser radiation, provides a precise means for determination of the beam velocity, and converts the position scale to a time scale. Our lifetime results are $35.07\pm 0.10\hspace{0.5em}\mathrm{ns}$ for the $6p{}^2{P}_{1/2}$ state and $30.57\pm 0.07\hspace{0.5em}\mathrm{ns}$ for the $6p{}^2{P}_{3/2}$ state. These results represent a data set larger than in our previous work, and include beam divergence corrections which have been evaluated by two different methods. We present comparisons of our results with previous measurements and with relativistic many-body calculations of atomic transition matrix elements in this neutral alkali system.

The time-dependent flux redistribution analysis is applied to model simulations of selective breaking of the ON single bond in the excited electronic state of ${\mathrm{HONO}}_2$ and control of vibrational state redistribution of the OH fragment by infrared-laser pulses. Control over vibrational state redistribution of the $\mathrm{OH}\mathrm{}\left(v\right)\mathrm{}$ fragment is demonstrated, with the $\mathrm{OH}\mathrm{}(v=0\mathrm{})/\mathrm{OH}\mathrm{}(v=1\mathrm{})\mathrm{}$ branching ratio being changed by about a factor of 30 and the dissociation probability approaching 100% on a picosecond time scale.

We present an ab initio scheme for computing the wave function of the pair of electrons projected into the double continuum of the helium atom by a one-photon dipolar excitation. The scheme uses the Floquet approach to convert the time-dependent Schrödinger equation into an infinite set of coupled time-independent equations. The latter reduces to a single stationary inhomogeneous Schrödinger equation in the weak-field limit, which is relevant here. This equation is solved using an $\mathcal{R}$ matrix approach to combine a quantum treatment of all variables within the hypersphere $R<~R_0$ with a semiclassical treatment of the R motion outside this hypersphere. We apply this approach to a model helium atom where $r_1{=r}_2.$ We thus demonstrate the feasibility of the method, and obtain insights into the dynamics of the double photoionization of helium at equal sharing of a low excess energy.

The effect of a long-range polarization force on the low-energy scattering of an electron by a neutral atom may be accounted for by adopting a form of distorted-wave theory in which the phase shift is represented as the sum of a polarization phase and a relative phase. From this latter phase an effective-range function is formed having a smooth energy dependence in the neighborhood of threshold. Multichannel extensions of this approach have been described. For highly polarizable targets, and for scattering energies sufficiently removed from threshold, the polarization phase takes on complex values. The relative phase, and hence the effective-range parameters, must then be complex as well since unitarity requires that the physical phase shift be real. For scattering by short-range potentials unitarity is preserved by formulating approximation procedures in terms of a Hermitian reaction matrix. This standard approach is generalized here in the context of effective-range theory involving strong polarization forces. The hermiticity condition on the reaction matrix is replaced by a more general requirement relating its Hermitian and anti-Hermitian components. Methods for imposing unitarity constraints in approximation procedures are described and illustrated, for resonant and nonresonant systems, in numerical examples.

In this paper, we show elastic and rotationally inelastic cross-section calculations of low-energy electron scattering by ${\mathrm{CF}}_4,$ ${\mathrm{CCl}}_4,$ ${\mathrm{SiCl}}_4,$ ${\mathrm{SiBr}}_4,$ and ${\mathrm{SiI}}_4.$ The fixed-nuclei static-exchange scattering amplitudes were obtained with the Schwinger multichannel method with soft norm-conserving pseudopotentials. We show elastic integral and differential cross sections and discuss the role of the basis set on the nature of some structures seen in a previous publication [A. P. P. Natalense et al., Phys. Rev. A 52, R1 (1995)]. We have attributed these structures to linear dependency in the basis set caused by the symmetric combination ${(x}^2{+y}^2{+z}^2\left)\exp \right(-\alpha r^2).\mathrm{}$ The rotational cross sections were calculated with the help of the adiabatic-nuclei-rotation approximation. Our results are in good agreement with available experimental data. The sums of $\overrightarrow{0}0,3,4,6$ rotational cross sections in general show good agreement with the elastic (rotationally unresolved) ones. The rotationally summed integral cross section agrees within 0.3% with the elastic integral cross section for ${\mathrm{CF}}_4$ at 7.5 eV, and within 26% for ${\mathrm{SiI}}_4$ at 30 eV. It was found that rotationally inelastic cross sections are considerably large for such molecules, because the heavy peripheral atoms play a significant role as scattering centers.

Single and double electron capture in ${\mathrm{C}}^{5+}+\mathrm{H}\mathrm{e}$ collisions at energies ranging from 9 to 90 keV have been investigated using recoil ion momentum spectroscopy. Doubly differential cross-section measurements allow the identification of the processes involved in the electron transfer. For single capture, n-state relative populations and projectile scattering angle distributions are given and compared to previous calculations. A satisfying simple model calculation is proposed. The cross sections for the transfer excitation process are found to be smaller than the calculated cross sections. In the case of double capture, the autoionizing double capture dominates and populates the symmetric state ${\mathrm{C}}^{3+}{(2l2l}^{\prime }),$ while the true double capture mainly gives rise to ${\mathrm{C}}^{3+}{(2\mathrm{lnl}}^{\prime })$ $\mathrm{}(n>\mathrm{}2\mathrm{})\mathrm{}$ configurations. In addition to experimental relative populations and stabilization ratios, the Q-value resolution enables us to show the processes involved in the population of the different ${(2l2l}^{\prime })$ terms. These processes, which are correlated double capture and correlated transfer excitation, are found to depend strongly on the collision energy.