A generalized gradient approximation (GGA) for the exchange energy functional of relativistic many-electron systems, including both a longitudinal and a transverse contribution, is presented. The resulting longitudinal exchange energies for atoms reproduce the corresponding exact values, obtained via the relativistic optimized-potential method, with the same accuracy that has been found for GGAs in the nonrelativistic context. In addition, it is shown that transverse contributions to the self-consistent exchange potential should not be neglected in the case of gradient-corrected functionals. © 1996 The American Physical Society.

Polarizabilities of ions of the helium isoelectronic sequence with nuclear charges in the range 2≤Z≤30 are evaluated starting from the relativistic no-pair Hamiltonian and including both the Coulomb and Breit interactions. The ground state and perturbed wave functions are expanded in two-electron basis functions constructed from B splines. For each ion, the ground-state wave function is determined by a configuration interaction calculation; the perturbed wave function is then found by solving an inhomogeneous algebraic equation. Nonrelativistic calculations are carried out in parallel with the relativistic calculations, permitting relativistic corrections to be isolated. The present nonrelativistic calculations are found to be in good agreement with other precise calculations. For the experimentally interesting case of heliumlike lithium, we obtain the value Δ${\mathrm{\alpha }}_{\mathrm{Rel}}$=-(4.50±0.05)×${10}^{\mathrm{-}5}$ a.u. for the relativistic correction to the ground-state polarizability. © 1996 The American Physical Society.

A theory for nonradiative decay of molecular-field-split states is presented. It is shown that the relative inner-shell sublevel cross sections for Auger transitions are sensitively dependent on the matching of spin-orbit and molecular-field interactions. This can lead to suppression of particular sublevel Auger transitions and to a breakdown of the constant core-hole lifetime approximation. The investigated effects are caused by a strong dependence of the Auger intensity on the mutual local space orientation of initial- and final-state orbitals. These features are illustrated for S 2p (${\mathit{L}}_{\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$VV) Auger spectra of ${\mathrm{H}}_2$S, and explain the apparent mismatch of 2p spin-orbit energies observed in Auger and photoelectron spectra of this molecule. © 1996 The American Physical Society.

Starting with the equations for the total molecular wave function that describe the self-consistent coupling of electrons and nuclei over time, we consider the case of one active electron outside closed shells and apply the formalism to ion-atom collisions. We discuss the need for electron translation factors, basis set type and size, and the choice of effective potentials in the calculation of the total integral cross section, the state-to-state integral cross section, and the differential cross sections for electron transfer and excitation. Atomic orbital alignment is considered here as well. We concern ourselves with the ${\mathrm{H}}^{+}$-H and ${\mathrm{He}}^{2+}$-H systems and the lower end of collision energies, 10 keV and below, down to several eV. We emphasize the study of time-dependent populations and properties to provide a deeper understanding of the dynamics of slow ion-atom collisions. Numerical results for cross sections and polarization parameters are in good agreement with other theories and experiments. © 1996 The American Physical Society.

In this paper we use the Schwinger multichannel method (SMC) to calculate several types of cross sections related to the elastic electron scattering by NO. We show through the NO system that the elastic scattering of an electron by an open shell molecule is a much richer process than the corresponding scattering by closed shell targets. We present cross sections for unpolarized electron scattering by (oriented and nonoriented) molecules, spin-flip cross sections (in the form of polarization fractions), and zero-energy electronic excitation cross sections (due to orbital degeneracy of the NO ground state). Our results agree well with published experimental values for elastic unpolarized data as well as recent polarized electron-NO scattering. We also present a detailed study of the dependence of the polarization fraction on molecular orientation. Our results also show a shape resonance which is also seen experimentally around 18 eV, and we suggest its symmetry.

Ion-branching ratios following the relaxation of C (1${\mathit{s}}^{\mathrm{-}1}$${\mathrm{\pi }}^{\mathrm{*}}$,nlλ,${\mathit{v}}^{\prime }$) synchrotron light-excited, vibrationally resolved resonances in CO have been measured using a time-of-flight spectrometer at high extraction voltages. Additional measurements at low extraction voltages (higher kinetic-energy resolution) have enabled an estimate of the kinetic-energy distributions (KED’s) of the emitted ${\mathrm{C}}^{+}$, ${\mathrm{O}}^{+}$, ${\mathrm{C}}^{2+}$, and ${\mathrm{O}}^{2+}$ ions. Large differences in these distributions are observed at various resonances and, for instance, a doorway-state dependence of the KED has been found for the 3sσ and 3pπ Rydberg resonances. While the results give some different information concerning the involved relaxation processes, more theoretical calculations are needed to get a more quantitative understanding. © 1996 The American Physical Society.

We have measured the dielectronic recombination cross section of ${\mathrm{Se}}^{25+}$ ions at center-of-mass energies from 1 to 1800 eV using merged electron and ion beams in the Heidelberg heavy-ion Test Storage Ring (TSR). All dielectronic resonances involving changes of ΔN=0 and ΔN=1 of the core principal quantum number N are covered with high-energy resolution (ranging from <0.6 eV at <90 eV to ≊6 eV at 1600 eV). A strong contribution of ΔN=1 Rydberg resonances at 1200–1700 eV is observed. The results are compared with isolated-resonance intermediate-coupling calculations of the cross section. Good agreement is found for the ΔN=0 and the low-lying ΔN=1 resonances. For the ΔN=1 Rydberg series the resonant pattern continues to be well reproduced by theory, whereas the total energy-integrated cross section significantly exceeds the theoretical prediction. From experimental and theoretical results rate coefficients for isotropic plasma temperatures between 100 and 2000 eV are also derived. © 1996 The American Physical Society.

We describe extensive results on the ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ double-excitation resonances of He below the N=2–9 ionization thresholds obtained recently by high-resolution photoionization measurements using synchrotron radiation from the SX700/II monochromator at the Berliner Elektronenspeicherring für Synchrotronstrahlung (BESSY). The resonance energies, linewidths, Fano-q parameters, and quantum defects of the various Rydberg resonances, derived from the experimental data, are compared in detail with the results of ab initio calculations employing the complex-rotation method. All three optically allowed Rydberg series below the N=2 ionization threshold were identified. For 3≤N≤8, the two most intense Rydberg series were resolved below each threshold, and for N=3, one state of a third series could be identified. For the higher Rydberg series (N≥5), the two neighboring series, N and N+1, generally interfere, which has a strong influence on the transition intensities, linewidths, and quantum defects of the principal series. All together, states of 18 different Rydberg series in the ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ double-excitation resonance region of He were observed. © 1996 The American Physical Society.

The retardation long-range potentials between two 1${\mathrm{}}^1$S (or 2${\mathrm{}}^3$S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1${\mathrm{}}^1$S and 2${\mathrm{}}^3$S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1${\mathrm{}}^1$S–2${\mathrm{}}^3$S ${\mathrm{He}}_2$ state is estimated. © 1996 The American Physical Society.

We calculate the rates of elastic and inelastic collisions in a gas of spin-polarized triplet helium ${(}^4$${\mathrm{He}}^{\mathrm{*}}$↑) in a wide range of temperatures (0<T<0.5 K) and magnetic fields (0<B<100 kG), which includes all values of T and B relevant for trapped ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{\mathrm{*}}{}_{}{}^{}$↑. At densities n≲${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$, where three-body recombination is not important, the main inelastic processes are spin relaxation and relaxation-induced ionization, both induced by the spin-dipole interaction in pair collisions. For ultralow temperatures T≲10 mK and low magnetic fields B≲100 G, the leading decay channel is relaxation-induced ionization. If either T or B is higher, the gas decays through spin relaxation. The ratio of elastic to inelastic rate is found to be large even in the nanokelvin regime, which is promising for evaporative cooling of ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{\mathrm{*}}{}_{}{}^{}$↑. © 1996 The American Physical Society.

Experimental data on the spectroscopic and dynamic properties of the 2${\mathit{p}}^4$${(}^1$S)ns,md series between the ${}_{}{}^1{}_{}{}^{}$D and ${}_{}{}^1{}_{}{}^{}$S thresholds of atomic fluorine are presented. These series are observed through their decay into the allowed 2${\mathit{p}}^4$${(}^3$P)εl and 2${\mathit{p}}^4$${(}^1$D)εl ionization channels. The ${(}^1$S)ns${\mathrm{}}^2$S resonances are broad windows, and the ${(}^1$S)${\mathit{md}}^2$D resonances are narrow peaks in the principal 2${\mathit{p}}^4$${(}^1$D)εl channel. The 2s2${\mathit{p}}^6$${\mathrm{}}^2$S resonance is located at 20.99(1) eV and is seen to interact strongly with the nearby 2${\mathit{p}}^4$${(}^1$S)4s${\mathrm{}}^2$S resonance. The resulting structure can serve as a sensitive marker for this interchannel mixing. Except for the interacting resonances, the data are found to be in satisfactory accord with eigenchannel R-matrix results for the total cross section. © 1996 The American Physical Society.

The elastic differential electron cross section of ${\mathrm{CH}}_3$I molecules, state selected with an electrostatic hexapole and oriented in an electric field by the linear Stark effect, was measured as a function of the transferred momentum at electron energies of 700, 1000, and 1250 eV. The molecular-state ensemble was oriented with a preferential direction of the molecular symmetry axis parallel or antiparallel to the electron beam. By switching the orientation on and off, the orientation-dependent interference contribution M¯, normalized to the differential cross section of unoriented molecules, was determined, independently of a model, for scattering angles of 4°–15°. The results, which can be divided into pure orientation and alignment parts, display different dependences on the electron energy and the degree of orientation. Model calculations based on the independent atom model (IAM) were carried out for the state mixture present in the scattering region. They reproduce the orientation contributions fairly well, but show some deviations for the stronger alignment contributions. Assuming the validity of the IAM, a Legendre expansion analysis was carried out to extract the leading Legendre moments characterizing the oriented molecular-state ensemble. © 1996 The American Physical Society.

A solution is presented for the problem of interpreting measurements of data from many degrees of freedom where binning is prohibitive. A binninglike procedure is introduced in which data and theory are represented by a set of independent expectation values. A comparison between theory and experiment is then performed by a conventional procedure together with an additional test of the independence of the expectation values. Associated uncorrelated errors are derived as well. The application of this method to Coulomb-explosion imaging is discussed. The method is illustrated by the analysis of the bending angle distribution of the ${\mathrm{CH}}_2^{+}$ molecule from Coulomb-explosion imaging measurements. © 1996 The American Physical Society.

Absolute generalized oscillator strengths (GOSs) of valence-shell electronic transitions of ${\mathrm{CHF}}_3$ and ${\mathrm{CHCl}}_3$ as functions of energy loss (0–150 eV) and momentum transfer (i.e., the Bethe surfaces) have been determined using angle-resolved electron energy-loss spectroscopy at an impact energy of 2.5 keV. The assignments for the prominent low-lying preionization-edge energy-loss features of ${\mathrm{CHF}}_3$ and ${\mathrm{CHCl}}_3$ were inferred from the term values reported previously and from their characteristic experimental GOS profiles. In particular, the GOS profiles of the low-lying Rydberg transitions (which originated from the nonbonding highest occupied molecular orbitals) below the ionization edge at 11.1, 11.9, 12.7, and 13.7 eV in ${\mathrm{CHF}}_3$ and at 8.5, 9.6, and 10.6 eV in ${\mathrm{CHCl}}_3$ were determined. These GOS profiles were found to be dominated by a strong maximum at zero-momentum transfer, which is characteristic of dipole interaction. Weak secondary maxima (and minima) were also observed and could be interpreted qualitatively in terms of the spatial overlaps between the initial-state and final-state orbital wave functions.

In addition, the low-lying feature at 7.2 eV in ${\mathrm{CHCl}}_3$ could be attributed predominantly to electronic excitations from the Cl 3p nonbonding (n) orbitals (2${\mathit{a}}_2$, 9e, 9${\mathit{a}}_1$, and 8e) to a C-Cl σ* antibonding orbital (10${\mathit{a}}_1$), according to a single-excitation configuration-interaction (CI) excited-state calculation. The experimental GOS profile of this low-lying feature was found to have a shape that is characteristic of a mixture of dipole-allowed and nondipole interactions, with maxima at momentum transfers of 0 and ∼0.9 a.u., respectively. Furthermore, the CI calculation indicated that some of these n(Cl 3p)→σ*(C-Cl) excitations in ${\mathrm{CHCl}}_3$, like other Cl-containing freons [${\mathrm{CF}}_{\mathit{n}}$${\mathrm{Cl}}_{4\mathrm{-}\mathit{n}}$ (n=0–3) and ${\mathrm{CHF}}_{\mathit{m}}$${\mathrm{Cl}}_{3\mathrm{-}\mathit{m}}$ (m=1,2)], could also lead to dissociation of the C-Cl bond. © 1996 The American Physical Society.

The charge-transfer cross section between a gadolinium atom and its positive ion has been measured with a crossed-beam apparatus that features primary ion production by photoionization with a tunable dye laser. The initial states of the Gd ions were controlled to be in the ground state by tuning the photon energy to be close to the ionization potential energy. The Gd ions in the ground states were collided with the Gd atoms in the ground and some excited states. The cross sections as a function of impact energy (30–1000 eV) were successfully obtained. The cross section at 1000 eV was 3.3×${10}^{\mathrm{-}14}$ ${\mathrm{cm}}^2$. The obtained cross sections were larger than those of other elements obtained experimentally in the past. © 1996 The American Physical Society.

We investigate the deviations from the dipole approximation for the two-photon bremsstrahlung cross section ${\mathrm{\sigma }}_4$, corresponding to the observation of the emitted photons (but not the scattered electron) in coincidence, which has been the subject of recent experiments. Our analysis is for the Coulomb field, and it is done in the Born approximation. We find that retardation effects are important, even in the lower energy range (8–12 keV) of the Hippler experiments, but not in the particular configuration for which experiments were performed. Using the simple analytic expression that we derive, including retardation, in the nonrelativistic Born approximation, we show that, in the incident electron energy range 10–50 keV, the differences between the relativistic Born (Smirnov’s approach) and nonrelativistic dipole approximation results are mainly retardation effects. © 1996 The American Physical Society.

We have developed a nonperturbative treatment of bound-free lepton-pair production caused by the strong and sharply pulsed electromagnetic fields generated by heavy ions in peripheral, relativistic collisions based on the solution of the time-dependent Dirac equation using lattice techniques. In this paper, we discuss refinements and extensions of our numerical methods for this problem and demonstrate convergent calculations, with respect to the parameters of the lattice, for bound-free muon-pair production in collisions near grazing incidence of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}_{}^{92+}{}_{}{}^{}$${+}^{238}$${\mathrm{U}}^{92+}$ and beam kinetic energies of 30 GeV per nucleon in the fixed-target frame. © 1996 The American Physical Society.

Absolute direct cross sections for electron excitation out of the 2${\mathrm{}}^3$S level and into the 3${\mathrm{}}^3$D, 4${\mathrm{}}^3$D, and 3${\mathrm{}}^3$S levels of the helium atom from threshold to 500 eV and into the 3${\mathrm{}}^3$P level over a more limited energy range have been measured using a fast metastable atomic beam target. We produce the metastable atoms via near-resonant charge exchange between a 1.6-keV ${\mathrm{He}}^{+}$ ion beam and Cs vapor. Because this reaction is highly nonresonant with the ground state of helium, the charge-transfer process yields a primarily metastable beam. We use a thermal detector which we calibrate with ions to measure absolutely the neutral beam flux. The atomic beam is crossed by an electron beam, and we collect the resulting fluorescence at right angles to both the electron and atomic beams. We obtain the cross sections for excitation out of the 2${\mathrm{}}^3$S level into the various excited levels by monitoring the emission out of the excited level of interest. © 1996 The American Physical Society.

We obtain the quantal zero-energy-loss limit of the radial integrals arising in the nonrelativistic atomic excitation of electric-hexadecapole transitions. We compare these results to the classical limit and the WKB approximation. We show the different behavior of the Coulomb integrals in the WKB approximation in the cases of repulsive and attractive potentials as functions of the Sommerfeld number η. © 1996 The American Physical Society.

Electron-impact ionization of atomic hydrogen is studied by direct solution of a set of time-dependent close-coupled partial differential equations. The close-coupled equations describe the propagation of a time-evolving wave packet on a two-dimensional radial lattice. Following the collision, the wave packet is projected onto stationary states of the target to obtain probabilities for elastic and inelastic scattering processes. Ionization cross sections are calculated for various LS partial waves and compared with previous theoretical methods. © 1996 The American Physical Society.