Maxwell coils are solenoids of spheroidal shape which produce a constant magnetic field inside the coil; at large distances the field of a Maxwell coil becomes that of a magnetic dipole. The current in systems consisting of several confocal Maxwell coils can be adjusted in such a way that the magnetic field inside the smallest coil is constant and the back flux is confined to the interior of the largest coil. Quantum-mechanical scattering of charged particles by Maxwell coils, or systems thereof, is first formulated as a three-dimensional problem and then treated within a two-dimensional approximation. The evolution in time of wave packets, which are Gaussian wave packets in the beginning, is calculated numerically. In all cases an Aharonov-Bohm effect is observed in the angular distribution of the scattered wave packets. The back flux results only in an additional deflection of the packets, which corresponds to the classical deflection caused by the Lorentz force.

The accelerated clock principle in special relativity and possible alternatives are investigated. Alternative clock rates are proposed and their implications on the proper time of an observer with constant proper acceleration considered. The effect such alternatives have on the synchronization of spatially separated accelerated clocks is discussed and a review of experimental work is used to establish an upper bound on the magnitude of acceleration-dependent contributions to the rate.

A numerical method is developed to obtain convergence to the eigenfunctions of the Schrödinger operators associated to singular potentials whose asymptotic behavior is of the Coulomb type. The method consists in solving the Dirichlet problem in a box with radius n by the Ritz method, whose convergence to the eigenfunctions in the norm of the Hilbert space ${\mathit{L}}_2$(0,n) is provided. Using a physical argument, we show that the solutions of the Dirichlet problem converge to those of the unbounded system in the norm of the Hilbert space ${\mathit{L}}_2$(0,∞) as n→∞. This last property guarantees the accurate computation of the expected values for a symmetric operator. The method is applied to the hydrogen atom, Yukawa potential, and Hulten potential; in each case we show the numerical convergence of the eigenfunctions, eigenvalues, and density moments.

We develop in this paper a consistent superoperator-resolvent-based propagator theory using the extended coupled-cluster (CC) parametrization [Phys. Rev. A 36, 2519 (1987); Ann. Phys. 151, 311 (1983)] of the ground state. The method exploits the underlying non-Hermitian nature of the transformed Hamiltonian appearing in the extended coupled-cluster method. In this method, we obtain finite expressions in powers of cluster coefficients for both the transition amplitudes as the residues and the elements of the effective matrix contributing to the poles of the propagator. There is a natural ‘‘resolution of identity’’ involving consistent basis constructed by us, which leads to the biorthogonal sets of ket and bra functions used in the representation of the intermediate states in the inner projection of the propagator. The manifold of operators generating these states satisfies the ‘‘vacuum-annihilation condition’’ on the ground state and is thus consistent. There is a natural decoupling of the forward and backward components of the propagator even under the uneven truncation of the CC expansion of the ground state and the operator basis, which should be convenient for practical applications. We have discussed in detail the realization of the consistent representation of the ionized or excited states by taking as illustrative examples the case of one-electron and polarization propagators and have suggested practical truncation schemes for their implementation. An order-by-order perturbative analysis has been made to indicate the relation of our formalism to some of the more recent theories. We have also shown that the now established coupled-cluster-based linear-response theory can be viewed as an approximate version of the consistent propagator theory, which furnishes the same poles as the latter but nonconsistent residues.

Recently Davidson et al. [Phys. Rev. A 44, 7071 (1991)] have estimated nonrelativistic correlation energies and relativistic corrections to ionization potentials for atomic ions with up to 10 electrons. In this work, this approach is extended to atomic ions with 11 to 18 electrons. The correlation energies for 3- to 10-electron atomic ions are also recomputed using more recent experimental and theoretical data. Unlike other work the method focuses on the correlation contribution to the individual ionization energies which are obtained by comparing experimental data with relativistic complete-valence-space energies. Ab initio estimates of correlation contributions to the ionization energies with extensive configuration-interaction calculations of 3- to 10-electron atomic ions with nuclear charge from 4 through 10 and 18, 36, 50, 72, 100, and 144 have been obtained. The correlation energies obtained from some density-functional models are also compared to these correlation energy data.

Nonadiabatic variational calculations are described for dipositronium (${\mathit{e}}^{+}$,${\mathit{e}}^{+}$,${\mathit{e}}^{\mathrm{-}}$,${\mathit{e}}^{\mathrm{-}}$) using explicitly correlated Gaussian basis functions with angular momentum zero. An improved rigorous upper bound for the ${\mathit{A}}_1$ ground-state energy for dipositronium is achieved (-0.515 976 7 a.u.) leading to a corresponding bound for the binding energy, Δ${\mathrm{\varepsilon }}_0$>0.435 eV, which is greater than previous estimates by 0.024 eV. This improved energy is obtained by exploiting the full permutational symmetry of the Hamiltonian including charge-reversal symmetry which was ignored in recent calculations. The first excited ${\mathit{A}}_1$ state, and the lowest ${\mathit{B}}_1$ and ${\mathit{A}}_2$ states of dipositronium are found to be unbound while the ${\mathit{B}}_2$ and E states appear to be metastable. For comparison, by the same method, the ${}_{}{}^2{}_{}{}^{}$S ground-state energy of the lithium atom is found to be -7.476 716 1 a.u., which lies 0.001 343 a.u. above the accepted true energy. Expectation values for individual terms of the Hamiltonian along with moments of interparticle distances 〈${\mathit{r}}^{\pm 1}$〉, 〈${\mathit{r}}^{\pm 2}$〉, and 〈δ(${\mathit{r}}_{\mathit{i}\mathit{j}}$)〉 are also reported.

Measurements have been made of the total decay rates of the 14.4-keV level in the ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ nucleus in highly charged Fe ions having one to six electrons outside the nucleus. Results are 10.0(9), 7.06(18), 7.36(14), 7.16(11), 7.10(23), 7.28(25), and 6.92(46), in units of ${10}^6$ ${\mathrm{s}}^{\mathrm{-}1}$, for ions of charge states q from 25 to 19, respectively. For the q=25 single-electron ion the result quoted is for the ion in which the spin of the 1${\mathit{s}}_{1/2}$ electron and the excited nuclear state are coupled to give quantum number F=1. Measurements have also been made of the K-shell fluorescent yields for ions in charge states q (before K-vacancy production) from 22 to 19. Results are 0.62(1), 0.50(1), 0.48(2), and 0.50(6), respectively. These data are discussed and compared with theoretical predictions.

Eigenfunctions and eigenvalues of the relativistic no-pair Hamiltonian are determined for n=2 triplet states of heliumlike ions with charges in the range Z=5–100. The eigenfunctions are expanded in a basis of two-electron wave functions constructed from Dirac-Coulomb orbitals restricted to a finite cavity. The Hamiltonian matrix is evaluated and Davidson’s method is then used to determine the lowest few eigenfunctions and eigenvalues. These calculations, which include the Coulomb interaction and the retarded Breit interaction, are corrected for QED and mass-polarization effects using values from Drake’s unified method and are compared with other calculations and with experiment. For low-Z ions, the present calculations agree well with many-body perturbation theory and with the unified method, but disagree substantially with multiconfiguration Dirac-Fock (MCDF) calculations corrected for correlations. At Z=36, our term energies are lower than the unified method by λ${\mathrm{\alpha }}^4$${\mathit{Z}}^4$ a.u., where λ=0.033, 0.51, 0.16, and 0.003 for the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$, and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ states, respectively. For Z=47 and 64, the present values of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ fine structure agree better with MCDF predictions than with the unified method. The energy intervals 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$-2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$-2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$-2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$, and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$-2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ are consistent with experiment throughout the entire range of Z.

We present some systematic calculations of dynamic multipole polarizabilities and van der Waals dispersion coefficients for the helium atom and ${\mathrm{H}}_2$ molecule with a quantum Monte Carlo calculation. Using an original method based on a gauge-invariant formalism we also report some ab nitio results of the same quantities. In light of the results we discuss the advantages and drawbacks of both approaches in comparison to prior theoretical results.

Autoionization rates of the 1s2s2p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{5/2}$ level are computed for ${\mathrm{He}}^{\mathrm{-}}$, Li i, and Be ii, using the golden-rule formalism in the multiconfiguration Hartree-Fock approximation. The main objective is to clarify ambiguities concerning the metastable ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{5/2}$ component in ${\mathrm{He}}^{\mathrm{-}}$, whose lifetimes differ significantly in various works. The present calculations reveal a much shorter lifetime, 345 μs, than predicted in earlier theoretical works. Our result for ${\mathrm{He}}^{\mathrm{-}}$ is in perfect agreement with recent measurements, and for Li i and Be ii we agree well with other theoretical predictions.

Experimentally determined differential cross sections are presented for the (e,2e) process in helium, in which the two outgoing electrons have the same energy and the same scattering angle with respect to the incident beam. At four incident energies from 20 to 50 eV above the ionization threshold the detection plane defined by the outgoing electrons was varied from being coplanar with the incident beam to being perpendicular to the beam. The differential cross section evolves from a two-peak structure in coplanar geometry to a three-peak structure in the perpendicular plane. At the lowest energy the forward-scattering coplanar peak is smaller than the backscatter peak, in contrast to the results at higher energies. A deep minimum is seen at an intermediate plane angle of 67.5°, this minimum being deepest at 40 eV above the ionization threshold. The results are normalized to an absolute scale using previous coplanar measurements as discussed in the text. The spectrometer used to collect these results is fully computer controlled and real-time computer optimized.

The angular-distribution parameters of the resonant Auger transitions induced by photoexcitation have been calculated for the ${\mathit{L}}_{23\mathrm{-}}$${\mathit{M}}_{23}$${\mathit{M}}_{23}$, ${\mathit{M}}_{45\mathrm{-}}$${\mathit{N}}_{23}$${\mathit{N}}_{23}$ and ${\mathit{N}}_{45\mathrm{-}}$${\mathit{O}}_{23}$${\mathit{O}}_{23}$ transitions in Ar, Kr, and Xe, respectively. The calculations are carried out using the multiconfiguration Dirac-Fock method in intermediate coupling with configuration interaction. A two-step model is employed to describe the resonant Auger process. As in the case of normal Auger decay, inclusion of the effect of intermediate coupling removes the major discrepancy between theory based on the spectator model and experiment.

Single and double K-K-electron transfer and the K-shell-vacancy production cross sections for Ti bombarded by ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ beams at energies varying between 1.25 and 4.7 MeV/amu have been determined, in the limit of zero target thickness, from the thickness variation of the Ti K x-ray yield with ion beams having 0, 1, or 2 vacancies in their K shell. From the measured energy shift and the intensity ratios of Kα, Kβ lines, the average number of 2p and 3p vacancies were determined from which the average value of the fluorescence yield ${\mathrm{\omega }}_{\mathit{K}}$ was deduced using the statistical scaling procedure of Larkins [J. Phys. B 4, L29 (1971)]. The single-electron transfer cross sections are compared with the calculations of Brinkman and Kramer as formulated by Nikolaev [Sov. Phys. JETP 24, 847 (1967)] and those of Lapicki and McDaniel [Phys. Rev. A 22, 1896 (1980)] and the modified two-center atomic-orbital-expansion model (AO+) of Fritsch and Lin [J. Phys. B 15, 1255 (1982)]. The double-electron transfer cross sections are also compared with the AO+ predictions. The K-shell-vacancy production data are compared with calculations based on the perturbed-stationary-state approach with the Coulomb-deflection, binding-energy, and relativistic corrections (ECPSSR) included. In addition, the projectile cross sections for single-electron capture and loss have also been deduced at a few energies.

The cross sections of the different breakup channels of ${\mathrm{CH}}_4$, produced by 4-MeV proton impact, have been measured using the coincidence time-of-flight technique. The relative abundances of the different breakup channels were evaluated for collisions in which the molecule broke into two charged fragments as well as for collisions where only a single charged molecular ion or fragment was produced. These relative abundances are compared to the ones measured for photodissociation, and for electron and proton impact. Only the ${\mathrm{CH}}_4^{+}$ ion survives long enough to be detected as a molecular ion, while the doubly charged ${\mathrm{CH}}_4^{2+}$ ion dissociates rapidly. The most probable final product of the fragmentation of doubly charged methane as formed by fast-proton impact is ${\mathrm{H}}^{+}$+${\mathrm{CH}}_2^{+}$+H. The abundance of ${\mathrm{H}}_{\mathit{m}}^{+}$+${\mathrm{CH}}_{\mathit{n}}^{+}$ (m+n≤4) ion pairs decreases rapidly with increasing m, as suggested by Siegbahn [Chem. Phys. 66, 443 (1982)]. The momentum of neutral fragments, in channels where they are produced, is small in comparison with the momentum of the charged fragments so that two-body breakup holds approximately. The deviation from two-body breakup increases with increasing number of neutral hydrogen atoms produced. The sensitivity of the experimental method enabled us to extend the study of the fragmentation pattern of ${\mathrm{CH}}_4^{2+}$ to include small breakup channels such as ${\mathrm{CH}}_4^{2+}$→${\mathrm{H}}_3^{+}$+${\mathrm{CH}}^{+}$. Furthermore, some breakup channels of the triply charged ${\mathrm{CH}}_4^{3+}$ have been detected as triple coincidences.

Absolute values for the total and one- and two-electron transfer cross sections for ${\mathrm{Ar}}^{\mathit{q}+}$ ions (8≤q≤16) colliding with helium and molecular hydrogen at 2.3q keV laboratory energy were measured by the growth-rate method. The He and ${\mathrm{H}}_2$ total cross sections as a function of Ar-projectile L-shell occupation number increase monotonically from ${\mathrm{Ar}}^{8+}$, 2p shell full, to ${\mathrm{Ar}}^{16+}$, 2s shell empty. The ${\mathrm{H}}_2$ one-electron capture cross section scales approximately as [${\mathit{E}}_{\mathrm{IP}}$ (He)/${\mathit{E}}_{\mathrm{IP}}$(${\mathrm{H}}_2$)${]}^2$ times the corresponding He cross section, but the shapes of the two cross sections differ in detail. The ${\mathrm{Ar}}^{\mathit{q}+}$ ions were produced by the Cornell superconducting-solenoid, cryogenic electron-beam ion source (CEBIS) and extracted at 2.3 kV. Selected charge states traversed a gas cell, after which they were detected and charge-state analyzed by the energy-retardation method and by a π/ √2 cylindrical electrostatic analyzer. The target-gas pressure in the cell was measured directly by the orifice-flow method used for absolute-pressure gauge calibration. The overall error in the ${\mathrm{Ar}}^{\mathit{q}+}$ on ${\mathrm{H}}_2$ cross-section measurements is ±10%, and ±15% in the He measurements.

Different aspects of relativistic distorted-wave models for electron capture in ion-atom collisions are analyzed. In particular, the nonrelativistic limit of the matrix continuum distorted-wave approximation is studied for reactions with or without change in the electron spin.

We have measured the integrated Stokes parameters of the light emitted following the impact excitation by polarized electrons of the ${\mathit{np}}^5$ (n+1)p[5/2${]}_3$ states in Ne (n=2), Ar (n=3), Kr (n=4), Xe (n=5), and the ${\mathit{np}}^5$ (n+1)p[5/2${]}_2$ state in Kr. The near-threshold linear-polarization fractions ${\mathrm{\eta }}_1$ were consistent with zero for all of the J=3 states measured, providing no evidence of Mott scattering. For J=2 excitation, ${\mathrm{\eta }}_1$ shows the clear influence of the intermediately coupled nature of the state. At threshold, the measured circular polarization ${\mathrm{\eta }}_2$ and linear polarization ${\mathrm{\eta }}_3$ for the J=3 states agree well with the LS-coupled threshold predictions. These results provide the basis for optical measurements of electron polarization.

The optimal values of the scattering and the ejection angles and energies are studied in the case of the double ionization of the helium atom by fast-electron impact (5 keV) using a recently developed procedure based on the first Born approximation. This calculation includes several correlated initial-bound-state wave functions and the correlated-double-continuum wave function satisfying the exact asymptotic boundary conditions. Besides its interest for (e-3e) measurements which are in preparation in Orsay, and its utility for supplying immediate results needed for the verification of the different hypotheses of the ionization mechanisms, this work collects information which is potentially important for future calculations of the total cross section for the double ionization of helium.

Total electron-detachment and charge-transfer cross sections for collisions of ${\mathrm{O}}^{\mathrm{-}}$ and ${\mathrm{S}}^{\mathrm{-}}$ with atomic hydrogen have been measured for relative collision energies E ranging from 0.1 to 15 eV. At low collision energies these results are fairly well described by a simple Langevin orbiting model and, in the case of ${\mathrm{O}}^{\mathrm{-}}$ (where intermolecular potentials are available), a simple curve-crossing model is also in reasonable accord with the measurements. Neither ${\mathrm{O}}^{\mathrm{-}}$+H nor ${\mathrm{S}}^{\mathrm{-}}$+H displays an energetic barrier to associative detachment. Charge-transfer cross sections are small for both systems for the range of collision energies sampled in the experiment. Associative detachment cross sections are also reported for ${\mathrm{S}}^{\mathrm{-}}$+${\mathrm{H}}_2$ for E<2 eV; the results appear to resolve an apparent discrepancy between previous measurements.

Experimental resonant transfer and excitation (RTE) cross sections were measured for lithiumlike carbon ions in the energy range 5–9 MeV incident on a lithium vapor target. Transfer excitation populates the 1s2s2${\mathit{p}}^2$ ${}_{}{}^3{}_{}{}^{}$D state predominantly. Subsequent Auger decay of this state to the ground state is studied in high resolution using a 0° electron spectrometer. The measured single-differential cross sections at different projectile energies were compared with theoretical calculations based on the impulse-approximation formulation of RTE. The results of these experiments show that while the contribution of the target valence electron is consistent with impulse-approximation theory, no contribution to RTE by the core electrons is seen.