An exact expression for the exchange kernel (the frequency-dependent functional derivative of the exchange potential with respect to the electron density) is derived. For the correlation kernel a coupling-constant expansion is presented. A modified coupled Kohn-Sham equation for an efficient “exact-exchange” calculation of dynamic polarizabilities and excitation energies is suggested.

Nuclear motion of a plane polyatomic molecule ${\mathrm{BF}}_3$ is theoretically investigated under the core excitation of the B $1s$ electron to the antibonding ${2a}_2^{″}$ unoccupied molecular orbital. The B atom starts to move in the direction out of plane immediately after the core excitation. Owing to the finite core-hole lifetime comparable to a vibrational period, the B atom can move around the new equilibrium position of the core-excited state and the Auger decay occurs while this nuclear motion is going on. The x-ray absorption spectra and the resonant Auger emission spectra are calculated quantum mechanically. The calculated results are in reasonable agreement with the recent experimental results, illustrating that the dynamical aspect in the nuclear motion in the core-excited state is directly reflected in the resonant Auger emission spectrum.

Natural radiative lifetimes have been measured in the odd-parity Rydberg series $6pns$ $(n=7\mathrm{}–13)$ and $6pnd$ $(n=6\mathrm{}–13)$ of neutral lead using time-resolved UV laser-induced fluorescence from a laser-produced plasma. A relativistic Hartree-Fock calculation taking configuration interaction into account in a detailed way has also been performed for odd- as well as even-parity states for testing the ability of this approach to correctly predict radiative properties of heavy atoms. A generally good overall agreement between experimental and theoretical lifetimes has been achieved except for a few levels.

The Pauli repulsion between closed shells of two interacting systems induces structure in the exchange-correlation Kohn-Sham potential ${\nu }_{\mathrm{xc}}.$ This effect has been studied by the construction of ${\nu }_{\mathrm{xc}}$ from the ab initio correlated density ρ for the ${\mathrm{Ne}}_2$ dimer. Pauli repulsion manifests itself in the formation of a characteristic bond midpoint peak of ${\nu }_{\mathrm{xc}}.$ The behavior of ${\nu }_{\mathrm{xc}}$ has been analyzed by means of a partitioning into various components: the potential of the exchange-correlation hole ${\nu }_{\mathrm{xc}}^{\mathrm{hole}},$ the kinetic component ${\nu }_{c,\mathrm{kin}},$ and the “response” component ${\nu }_{\mathrm{resp}}.$ These components have been constructed from ab initio first- and second-order density matrices. All the components display bond midpoint peaks that contribute to the corresponding peak of ${\nu }_{\mathrm{xc}}.$ The peaks of ${\nu }_{\mathrm{xc}}^{\mathrm{hole}}$ and ${\nu }_{c,\mathrm{kin}}$ have been interpreted in terms of localization and mobility of the exchange-correlation hole, while the peak of ${\nu }_{\mathrm{resp}}$ is related to the Pauli repulsion with the help of the approximation of Krieger-Li-Iafrate for this potential. The results obtained have been compared with those for the ${\mathrm{N}}_2$ molecule.

Based on a theorem of Theophilou [Philos. Mag. B 69, 771 (1994)], the total electron density in a central field atom is determined from the Kohn-Sham $s$-electron density. Exchange-only density-functional calculations for atoms are presented.

Negative ions of the nitrogen atom have yet to be observed. We estimate the electron affinity of the ${\mathrm{N}}^{-}$ system to be approximately $-0.181$ eV using the multiconfiguration Dirac-Fock method. Similar calculations for the neighboring (same row) ${\mathrm{C}}^{-}$ and (same column) ${\mathrm{P}}^{-}$ system yield, respectively, 1.210 eV and 0.702 eV, in good agreement with measurements: respectively, 1.263 eV and 0.746 eV. The discrepancies that remain are primarily due to core-core and core-valence correlation effects that have been neglected. The improbability of the existence of a stable ${\mathrm{N}}^{-}$ system is already evident from a comparison of much simpler calculations with measurements for systems in the same row and neighboring row of the Periodic Table.

Differential coherent scattering cross sections for 11 moderate- to high-atomic-number elements have been experimentally determined with $O$(10%) error at the photon energies 13.95, 17.75, 26.36, and 59.54 keV, corresponding to major photon-emission intensities of the radionuclide ${}^{241}\mathrm{Am}.$ The measurements were performed using a standard backscattering geometry setup to obtain scattering angles of 145°, 154°, and 165°, with resulting photon momentum transfers in the range $1.07<~x<~4.76{\mathrm{\AA }}^{\mathrm{-}1}.$ High-purity (better than 99%) foils of Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Ta, and W were used as targets. A hyperpure germanium detector completed the arrangement. Measurements for Mo and Zr using the 17.75-keV photon-energy emission of ${}^{241}\mathrm{Am}$ were not possible due to the fact that for these targets at this photon energy, intense fluorescence overlapped significantly with the coherent scatter. At 26.36 keV the coherent scatter from Cd was similarly dominated by fluorescence. Experimental data have been compared with predictions from relativistic form factors (RFFs), modified relativistic form factors (MRFFs), and counterpart RFF and MRFF approximations with anomalous corrections using angle-independent scattering factors.

The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ $(j=\pm \frac{1}{2},\pm \frac{3}{2},\dots )$, $n_j,$ to the phase shifts ${\eta }_j(\pm E_k)$ of scattering states at zero momentum as follows: ${\eta }_j\left(\mu \right)+{\eta }_j(-\mu {)=n}_j\pi$.

Relativistic calculations are made for photoionization of the ground state of neonlike Fe XVII, using the Breit-Pauli Hamiltonian within the $R$-matrix method. Relativistic effects are clearly revealed by comparing the results with those obtained in the nonrelativistic $\mathrm{LS}$ coupling approximation.

Ab initio calculations of the total dielectronic recombination (DR) rate coefficient for Ar-like tungsten $\left({\mathrm{W}}^{56+}\right)$ are performed using the relativistic HULLAC code package based on the parametric potential method. The high efficiency of HULLAC compared to other codes enables us to perform extensive DR calculations for highly complex atomic systems such as Ar-like tungsten. The present work provides a general procedure for computing the DR rate coefficients for multielectron high-$Z$ ions. This procedure is applicable to DR computations for other Ar-like ions, as well as for ions in neighboring isoelectronic sequences. In the present work level-by-level calculations are performed for evaluating the contributions to DR through all the relevant K-like autoionizing inner-shell excited configuration complexes: ${3p}^5{4ln}^{\prime }{l}^{\prime }$ $(4\mathrm{}<~n^{\prime }<~17),$ ${3s3p}^6{4ln}^{\prime }{l}^{\prime }$ $(4\mathrm{}<~n^{\prime }<~12),$ ${3p}^5{3dn}^{\prime }{l}^{\prime }$ $(8\mathrm{}<~n^{\prime }<~18),$ ${3s3p}^6{3dn}^{\prime }{l}^{\prime }$ $(7\mathrm{}<~n^{\prime }<~18),$ ${2p}^5{3s}^2{3p}^6{3dn}^{\prime }{l}^{\prime }$ $(3\mathrm{}<~n^{\prime }<~8),$ ${2s2p}^6{3s}^2{3p}^6{3dn}^{\prime }{l}^{\prime }$ $(3\mathrm{}<~n^{\prime }<~5),$ and ${3p}^5{5l5l}^{\prime }.$ In addition, extrapolation methods are developed to calculate the contributions of even higher $n^{\prime }$ complexes along each complex series. In the case of ${3p}^5{3dn}^{\prime }{l}^{\prime },$ the usual complex-by-complex extrapolation method based on the $n^{\prime -3}$ scaling law is found to be inaccurate; thus, a more detailed level-by-level procedure is discussed. All calculations are carried out assuming no electron collisions occur after the initial electron capture. Although the dominant DR contributions come from ${3p}^5{4ln}^{\prime }{l}^{\prime }$ and ${3p}^5{3dn}^{\prime }{l}^{\prime },$ the contributions of the other complex series cannot be neglected. A comparison between the present results and the Burgess-Merts (BM) approximation shows that at low electron temperatures the BM approximation greatly underestimates the DR rate coefficients, whereas at high electron temperatures this approximation is fairly good.

Elastic differential, integral, and momentum-transfer cross sections are reported for electron scattering by ${\mathrm{C}}_2{\mathrm{H}}_4$ at impact energies ranging from 1 to 50 eV. The Schwinger iterative variational method in the fixed-nuclei, static-exchange plus correlation-polarization approximation is used to calculate the scattering amplitudes. Integrated cross sections are also calculated below 1 eV, showing the existence of a Ramsauer-Townsend minimum in this region. Our calculated cross sections are compared with recent experimental data and other theoretical results.

An extension of the Kohn variational method for computing scattering amplitudes is demonstrated that requires only matrix elements of the resolvent of the Hamiltonian between energy-independent test functions. Scattering boundary conditions are imposed by expanding the resolvent in a basis of square-integrable functions and outgoing-wave continuum functions. By employing several continuum basis functions with overlaps defined by suitable analytic continuation, the scattering amplitude can be expressed efficiently over a continuous range of energies. The method described here differs from previous approaches using time-independent wave packets in that the wave packets which generate the initial and final states in this approach can lie within the interaction region.

The ${}^{2}S$ and ${}^{2}D$ photoionization cross section (PICS) of lithium from the ${1s}^{2}2p$ state is calculated for photon energies below the ${\mathrm{Li}}^{+}$ $1s2s{}^{1}S$ threshold. Forty-seven resonances are predicted. All the important PICS peaks predicted are found to be associated with the spectral lines observed in the high precision experiment. Although the agreement between theory and experiment is excellent in most cases, there are some interesting exceptions. The possible sources of these discrepancies are discussed. An important discrepancy in the earlier experiments is resolved. Several new identifications are made. Some of the observed lines are reassigned.

The $4d$ photoelectron spectra of atomic lanthanides Ce, Pr, Nd, Sm, and Eu have been measured using synchrotron radiation. The multiplet structure of the ${4d}^{-1}$ hole states has been investigated by applying the electron-ion coincidence technique in the form of final ion-charge resolving electron (FIRE) spectroscopy. FIRE spectroscopy is a spin-sensitive method for the study of ${4d}^{-1}$ decay processes. Photoelectron spectra have been calculated in the one-configuration approximation for the rare-earth atoms from Ce to Gd and FIRE spectra have been calculated for Ce, Pr, Nd, Sm, and Eu. Comparing theoretical and experimental results, we discuss the trend of the development of the ${4d}^{-1}$ multiplet structure from Ce to Gd.

In 1929, von Neumann and Wigner [Phys. Z. 30, 465 (1929)] demonstrated the existence of local potentials which support a bound state with energy embedded in the continuous spectrum. In this paper, we study the $s$-wave scattering produced by a class of von Neumann–Wigner potentials which are perturbed by truncating them at some large radius $r=a.\mathrm{}$ For the class of potentials considered, we obtain an analytic expression for the Jost function. The original continuum bound state is replaced by a well isolated complex zero of the Jost function (equivalent to a pole of the $S$ matrix), but this does not produce a conventional Breit-Wigner resonance. Instead, we find twin peaks in the cross section, separated by a very narrow gap associated with the Jost function zero. Our study continues with an account of bound states and virtual states supported by the potential, and with an investigation of the form of asymptotically large zeros of the Jost function. We compare the results of this paper with the significantly different results we obtained using a different perturbation [Phys. Rev. A 52, 3932 (1995)].

The method of high-resolution Auger spectroscopy was used to study mechanisms for double-electron capture producing the projectile configurations ${3lnl}^{\prime }$ and ${4lnl}^{\prime }$ $(n>~4)$ in ${\mathrm{Ne}}^{10+}+\mathrm{He}$ collisions. Emphasis was given to slow collisions with projectile energies near 1 keV. At low collision energies the production of the configurations ${3lnl}^{\prime }$ $(n>~6)$ of nonequivalent electrons is found to become dominant. It is shown that dielectronic processes produced by the electron-electron interaction play a major role in the creation of the ${\mathrm{Ne}}^{8+}{(3\mathrm{lnl}}^{\prime })$ states.

The time-dependent Schrödinger equation is solved numerically for scattering of several model potentials. The time evolution operator is approximated to a Chebyshev polynomial expansion and the spatial derivatives are evaluated using the fast-Fourier-transform algorithm. Such a scheme is found to be highly accurate and effective. The results are in excellent agreement with exact values.

We have observed linearly polarized components of the foil-excited hydrogen Balmer $\alpha$ line and the neutral helium $2^1\mathrm{P}-3^1\mathrm{D}$ line from beams of 5–55 $\mu {\mathrm{A}/\mathrm{c}\mathrm{m}}^2$ current density at 150 keV. The intensities and the linear Stokes parameter of both the lines changed with the total beam charge density irradiated to the carbon foil (beam dose) and then saturated. These changes are attributed to changes of the state of the carbon foil caused by the irradiation by the ion beam. The dose dependence of the linear Stokes parameter was fitted with an exponential curve. The values at saturation for both the lines showed an increase with an increase in the current density, which is similar to the previous reports. The initial value for the helium line depended little on the beam current density, while that for the hydrogen line showed substantial increase. Both the behaviors are consistent with the explanation in terms of the Stark effect by the macroscopic electric field of the order of 10 V/cm extending downstream from the foil.

Triple differential cross sections (TDCS) of the argon $3s$ and $3p$ outer shells were obtained from electron-impact ionization $\mathrm{}(e,2e)\mathrm{}$ experiments with coplanar equal-energy sharing scattering geometries. The advantages of a new asymmetric equal-energy-scattering geometry are described. Data are reported for incident electron energies of 2020, 1220, 620, and 420 eV. Measurements extend to the high-binding momentum region of the TDCS. The data are compared with recent distorted-wave calculations, with a view to determining the range of validity of the models for coplanar equal-energy-sharing kinematics.

A prior form of boundary corrected continuum intermediate state approximation has been employed to calculate charge-transfer cross sections involving different degree ions of berryllium and boron with atomic hydrogen in the energy range of 25–200 keV/amu. In this formalism, interactions of the active electron with the partially stripped ions have been estimated by a model potential. Results agree favorably well with the available results in some processes. In other processes results have been reported.