The hyperfine fields in the noble-metal atoms Cu, Ag, and Au have been calculated by means of a relativistic many-body perturbation-theory technique. The resulting hyperfine fields for these atoms were 256±11, 531±22, and 1997±92 T, respectively, in good agreement with the experimental results of 259.95, 499.12, and 2085.1781 T. The reasons for the error bars in the theoretical results are discussed and are associated with the substantial sizes of the third- and higher-order correlation effects, which are found to be of great importance in these atoms. We will discuss the contributions to the total field from various one- and two-body interaction mechanisms and compare these contributions to those in related systems. Our results for the Cu and Au systems will also be compared with those available from other calculations reported in the literature.

A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yields substantially better results than alternative widely used semiclassical analyses.

By diagonalizing the diamagnetic Hamiltonian, with a basis set composed of potential-model eigenstates of field-free alkali-metal atoms, we have calculated the quasi-Landau resonances (QLR) of sodium (even parity, magnetic quantum number m=-2,-1) and obtained results which agree remarkably well with the experiment of Castro et al. [Phys. Rev. Lett. 45, 1780 (1980)]. The agreement suggests that, up to a close vicinity of the ionization threshold, the continuum states contribute little to the shaping of quasi-Landau modulations. Fourier transforms of our numerical QLR reveal two energy spacings which correspond, respectively, to 1.5ħ${\mathrm{\omega }}_{\mathit{c}}$ and 0.64ħ${\mathrm{\omega }}_{\mathit{c}}$ at the ionization threshold.

A technique is proposed for the excitation of coherent cyclotron motion of ions undergoing a relativistic mass increase. The equations of relativistic-ion cyclotron motion excited by an rf electric dipolar field of fixed peak-to-peak amplitude and a phase that exactly matches the ion cyclotron orbital phase during the excitation process are solved analytically. The resonant cyclotron-motion excitation method is well-suited for bringing ions of low mass-to-charge ratio coherently to a large cyclotron orbital radius for detection or ejection. The method is demonstrated for the excitation of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{3+}{}_{}{}^{}$ ions up to about 1% of the speed of light in the cubic ion trap of a Fourier-transform ion cyclotron-resonance mass spectrometer.

The recently developed explicit formalism of orthogonally-spin-adapted, Hilbert-space (or state-universal), multireference (MR), coupled-cluster (CC) theory, exploiting the model space spanned by two closed-shell-type reference configurations, is applied to a simple four-electron model system consisting of two interacting hydrogen molecules. Four planar minimum-basis-set ${\mathrm{H}}_4$ models are examined, each characterized by a single parameter that fully determines its geometry, assuming the trapezoidal (H4 model), rectangular (P4 model), linear (D4 model), and square (S4 model) nuclear configuration. Varying this geometry-determining parameter, in each case we obtain different cross sections of the ${\mathrm{H}}_4$ potential-energy hypersurface, involving the dissociation of one, two, or all four H-H ‘‘bonds.’’ Comparing the resulting CC energies with exact values that are easily obtained for this model using the full configuration-interaction method, we can assess the performance of various MRCC Hilbert-space approaches at both the linear and nonlinear levels of approximation, while a continuous transition is being made between the degenerate and nondegenerate regimes. This enables us to elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, to examine the role played by various intruder states, the existence and types of multiple solutions and their ability to describe various excited states, and, by performing a cluster analysis of the exact solutions, to assess the quality of the MRCC wave functions as well as the energies.

The formal structure of density-functional theory in the constrained-search formulation is analyzed and a theory is derived which is symmetrized with respect to the symmetry group of the Hamiltonian operator. This theory is valid for an arbitrary given electronic system and takes into account symmetries in spin as well as in ordinary space. The symmetrized theory is based on the totally symmetric part of the density instead of the density or spin density itself. In the corresponding symmetrized Kohn-Sham formalism no symmetry dilemma can occur. The concepts of symmetrized N-representability and symmetrized v-representability are defined. Known examples of non-v-representable densities are shown to be symmetrized v-representable. The related question of the convexity of the universal functionals involved is discussed. The computational demands of this symmetrized formalism are on the level of non-spin-polarized calculations for all systems, independent of their actual spin structure. The usual treatment of symmetry within density-functional theory is investigated. The widespread usage of non-symmetry-dependent density functionals in cases when it is formally not justified is identified as a possible source of errors.

We present accurate optimized-potential-model (OPM) results for spherical spin-polarized atoms emphasizing the precise construction of the OPM exchange potential from the numerical solution of the OPM integral equation, especially for large r. The results are used to discuss the quality of the local spin-density approximation (LSDA) and a generalized-gradient expansion (GGA) [A. D. Becke, Phys. Rev. A 38, 3098 (1988)] for describing these atoms. It is shown that the LSDA can produce substantial errors (beyond what is known from unpolarized atoms) for quantities which are directly related to the spin polarization of these systems. In particular, the LSDA overestimates the magnetization density in the interior of Cu by a factor of 2. While the GGA improves integral quantities like total ground-state and exchange energies, remarkably it is less successful for energy differences like ${\mathit{E}}_{\mathit{x}\mathrm{\uparrow }}$-${\mathit{E}}_{\mathit{x}\mathrm{\downarrow }}$. Most important, however, it is not able to reduce the LSDA’s errors for local quantities like the difference between spin-up and spin-down exchange potentials and magnetization densities significantly nor does it reverse the LSDA’s incorrect ordering of the two highest occupied majority-spin eigenvalues of Cr and Cu.

The calculation of diamagnetic Rydberg eigenfunctions described in paper I [Phys. Rev. A 45, 4776 (1992)] has been extended to radial distances of 1600 a.u. for a 5-T field, thus affording a far more detailed view of the nonperturbative evolution of each channel. Particularly notable is the emergence of an approximate block diagonalization of the reaction matrix ${\mathrm{K}}_{\mathrm{ll}\prime }$(r), which illustrates the sequential isolation of eigenvectors localized along and across the magnetic field (Landau and quasi-Landau states). This evolution is viewed as a prototype for many-body processes.

Two-photon coincidence yields have been measured in thick targets of C, Al, Ag, and Ta for 70 keV incident electrons and photons radiated at ±45° to the incident beam. A theoretical model, which is more rigorous, has been developed to simulate the two-photon processes of coherent thick-target double bremsstrahlung (TTDB) and the incoherent emission of two single-bremsstrahlung (SBSB) photons in a thick-target environment. The model is based on an integration of the thin-target cross sections over the target thickness taking into account electron energy loss, electron backscattering, and photon attenuation. It predicts a yield that is much lower than that of the previous model. The prediction of the model fits the present experimental data well by adjusting the relative weight of the two competing processes, and we find that TTDB dominates at low Z and incoherent SBSB dominates at higher Z.

Multiple-electron removal from and molecular fragmentation of carbon monoxide molecules caused by collisions with 1-MeV/amu ${\mathrm{F}}^{4+}$ ions were studied using the coincidence time-of-flight technique. In these collisions, multiple-electron removal of the target molecule is a dominant process. Cross sections for the different levels of ionization of the CO molecule during the collision were determined. The relative cross sections of ionization decrease with increasing number of electrons removed in a similar way as seen in atomic targets. This behavior is in agreement with a two-step mechanism, where first the molecule is ionized by a Franck-Condon ionization and then the molecular ion dissociates. Most of the highly charged intermediate states of the molecule dissociate rapidly. Only ${\mathrm{CO}}^{+}$ and ${\mathrm{CO}}^{2+}$ molecular ions have been seen to survive long enough to be detected as molecular ions. The relative cross sections for 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 were produced. The average charge state of each fragment resulting from ${\mathrm{CO}}^{\mathit{Q}+}$→${\mathrm{C}}^{\mathit{i}+}$+${\mathrm{O}}^{\mathit{j}+}$ breakup increases with the number of electrons removed from the molecule approximately following the relationship i¯=j¯=Q/2 as long as K-shell electrons are not removed. This does not mean that the charge-state distribution is exactly symmetric, as, in general, removing electrons from the carbon fragment is slightly more likely than removing electrons from the oxygen due to the difference in binding energy. The cross sections for molecular breakup into a charged fragment and a neutral fragment drop rapidly with an increasing number of electrons removed.

A path-integral formulation of resonant electron-molecule scattering is developed within the framework of the projection-operator formalism of scattering theory. The formation and decay of resonances is treated in real time as a quantum-mechanical electronic-tunneling process, modified by the coupling of the electronic motion with the nuclear degrees of freedom. It is shown that the electronic continuum can be summed over in the path-integral formulation, resulting formally in the path integral for an effective two-state system with coupling to vibrations. The harmonic-oscillator approximation is adopted for the vibrational motion in the present work. Approximation methods are introduced which render the numerical evaluation of the sum over paths feasible for up to ≊${10}^3$ elementary time slices. The theory is numerically realized for simple but nontrivial models representing the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ d-wave shape resonance in ${\mathit{e}}^{\mathrm{-}}$+${\mathrm{N}}_2$ collisions and the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ p-wave shape resonance in ${\mathit{e}}^{\mathrm{-}}$+${\mathrm{H}}_2$ collisions, respectively. The accuracy of the path-integral results is assessed by comparison with exact numerical reference data for these models. The essential virtue of the path-integral approach is the fact that the computational effort scales at most linearly with the number of vibrational degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates.

A method of dealing with hypergeometric functions to obtain closed expressions for partial-wave components of photoelectron spectra in terms of elementary functions is presented through an example of a hydrogen atom struck by a temporal δ-function pulse. Based on this method, angular distributions of photoelectrons with various energies are presented for a wide range of field strengths from a perturbative (field strength∼0.05 a.u., 1 a.u.=5.14×${10}^9$ V/cm) to a superintense regime (field strength∼5 a.u.).

The polarized orbitals produced by simultaneous optimization of both bound and continuum multiconfiguration Hartree-Fock wave functions at each kinetic energy of the scattering electron in low-energy electron-atom collisions are used to calculate the frequency-dependent dipole polarizability of the ground state of atomic oxygen. Excellent agreement is obtained with experiment and other theoretical calculations, indicating that this ab initio approach is a powerful tool for determining accurate frequency-dependent atomic dipole polarizabilities.

The total and angular differential excitation cross sections for the transitions 3${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S→3s3p ${}_{}{}^3{}_{}{}^{}$P, 3${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S→3s3p ${}_{}{}^1{}_{}{}^{}$P, and 3s3p ${}_{}{}^3{}_{}{}^{}$P→3s3p ${}_{}{}^1{}_{}{}^{}$P in the Mg-like ions ${\mathrm{Si}}^{2+}$ and ${\mathrm{Ar}}^{6+}$ are determined in the threshold energy region using the close-coupling R-matrix method. The total cross sections for all three transitions in both ions exhibit strong resonance structures near threshold. We focus our analysis on the angular distribution of the scattered electrons. The differential cross sections are found to undergo rapid and strong variations when the incident energy is tuned through the autoionizing resonance transitions. In ${\mathrm{Ar}}^{6+}$, we also examine the angular distribution of the scattered electrons associated with the nonresonant background cross sections for the two transitions from the ground state. For the dipole-allowed transition, the electrons are preferentially backscattered near the excitation threshold; however, the fraction of electrons scattered in the forward direction increases dramatically with energy. The corresponding behavior for the spin-forbidden transition is quite different. We discuss the implications of these results to possible excitation measurements in which the scattered electrons are collected.

In this paper we report measurements of photoelectron angular distributions for two-photon ionization of atomic rubidium. These measurements are carried out over a range of laser wavelengths from 591 to 532 nm. Relative cross sections for the various photoionization channels and continuum-wave-function phase differences are derived from the data. These phase differences are not in good agreement with calculations of phase differences based on quantum-defect data and Coulomb phase shifts.

Crossed beams of electrons and ions have been used to measure absolute cross sections for single ionization of ${\mathrm{Si}}^{6+}$ and ${\mathrm{Si}}^{7+}$ ions from below threshold to 1400 eV. The measurements for ${\mathrm{Si}}^{6+}$ and ${\mathrm{Si}}^{7+}$ agree with distorted-wave calculations for direct ionization within 20% and 5%, respectively, suggesting that this mechanism is the dominant contribution to the cross section. The bulk of the measurements were performed with the more abundant ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ isotope; however, due to beam impurities, measurements with ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ were used to correct the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ data.

In this paper we present an analysis of the Feshbach resonances located below the first inelastic threshold in helium, neon, argon, krypton, and xenon. The measurements were made with an electron-scattering spectrometer called MAPDESS capable of simultaneous measurements at up to 19 angles, ranging from 18° to 162°. Data are analyzed using single-phase-shift formalism to evaluate the angle-dependent form factors of the resonances, describing the interference of the resonant amplitude with the nonresonant one. For each gas, the use of data at many angles enables a precise evaluation of the first three or four phase shifts and the resonance width. In some cases, the agreement of the analyzed experiment and theory is not perfect at small and large scattering angles.

We present a method which allows the efficient calculation of the amplitudes for two-photon processes based on variations of the eigenchannel R-matrix method and of the multichannel quantum-defect theory (MQDT). This method contains the flexibility to describe structure due to intermediate- as well as final-state Rydberg series, autoionizing series, and continua. Because the method is based on MQDT, we would be able to describe easily two-photon processes in negative ions as well as in any of the situations previously described by the generalization of MQDT in one-photon processes. We present calculations for two-photon absorption from the ground state of Mg and Ca.

Stopping powers of the noble gases for 300-keV to 10-MeV nitrogen ions were measured using a time-of-flight technique. The stopping power was directly determined from changes in ion time of flight over a fixed distance as a function of the target-gas pressure of a differentially pumped, windowless gas cell. The measured stopping-power values are compared to predictions of the modified Firsov theory of Land and Brennan (FLB) [At. Data Nucl. Data Tables 22, 235 (1978)] and to values compiled by Ziegler et al. [Stopping and Range of Ions in Solids (Pergamon, New York, 1985)]. The measured values are close to the FLB values at v=${\mathit{v}}_0$ for low target atomic number Z but are somewhat lower at higher Z. They are systematically smaller than those of Ziegler et al. at nitrogen energies below 2.5 MeV and larger from 2.5 to 10.0 MeV. For projectile velocities greater than ${\mathit{v}}_0$ the stopping in general is found not to be proportional to velocity.