Relativistic distorted-wave electron-collision strengths have been calculated for transitions from the ground state to the 36 n=3 excited states of neonlike barium. These theoretical results are compared with recent experimental results obtained with the Electron Beam Ion Trap (EBIT) at Lawrence Livermore National Laboratory. Overall good agreement between our calculated results and the experimental results underscores the effectiveness of the new EBIT method for measuring electron-collision cross sections and supports confidence in the theoretical methods used to calculate these cross sections for highly charged ions.

The 3p photoionization cross section and asymmetry parameter of the excited state 2$p^2$3p ${}_{}{}^2{}_{}{}^{}S_{1/2}^{}{}_{}{}^{}$ of nitrogen have been calculated within the Hartree-Slater approximation over a broad energy range. A Cooper minimum at photoelectron energy 1.4 eV is found to drastically affect the asymmetry parameter values near threshold. A recent experimental measurement by Pratt et al. [Phys. Rev. A 36, 1702 (1987)] found an anisotropic angular distribution of the photoelectrons emitted from that state by 4.61-eV photons. Our calculated result of the asymmetry parameter β=-0.25 at the above energy is in excellent agreement with the experimental value of -0.2(1).

The 2p electrons of Ar have been excited selectively to the 2$p^5$3$s^2$3$p^6$nl (nl=4s,5s,3d,4d) states by synchrotron radiation. The resulting Auger-like spectra have been measured for the first time with high resolution and analyzed in detail. The structures in the experimental spectra have been identified by comparing the experimental Auger energy shifts due to various nl spectator electrons with the corresponding calculated values. Anomalously high intensities have been found for the transitions corresponding to simultaneous shake up of the spectator electron.

We demonstrate a new form of interferometry which is independent of Maxwell’s equations and measures optical frequency differences rather than wavelength ratios. Stable laser and electro-optic FM sideband techniques make a direct measurement of the mode spacing of a high finesse cavity with subhertz precision (0.4 Hz rms) over a 50-THz region. Experiments indicate errors below ${10}^{\mathrm{-}10}$ over a 50-THz bandwidth and that improvements of several orders of magnitude are possible. New variables for interferometry simplify the use of multilayer dielectric mirrors and are directly measurable in situ. .AE

Finite input laser bandwidths alter the output quantum statistics in an intracativity parametric oscillator. We show that in an above-threshold experiment, the obtainable squeezing can be greatly reduced by these laser fluctuations. The effect is not eliminated just by reducing the laser bandwidth to less than the cavity bandwidth. Instead, the cavity/laser bandwidth ratio must be improved to the order of the intracavity photon number. Thus, highly stabilized lasers are essential in above-threshold squeezing experiments.

We consider phase conjugation via degenerate four-wave mixing in photorefractive crystals when more than one grating mechanism is operative. A method for exact solution of the steady-state wave equations which include pump depletion is presented. It is discovered that equal-strength multigrating operation does not allow signal amplification.

We present the first calculations, by computer simulation, of the Frank elastic constants of a liquid crystal composed of freely rotating and translating molecules. Extensive calculations are performed for hard prolate ellipsoids at a single density, and for hard spherocylinders at three densities. For ellipsoids, the resulting Frank constants are of the same order of magnitude as those found experimentally, and in the expected ratios. For spherocylinders, elastic constants increase rapidly with density. Existing density functional theories are only moderately successful in predicting elastic constants.

Numerical simulations of two-dimensional thermosolutal convection in a long box of aspect ratio d=16, with free but impenetrable boundaries, reveal solutions in the form of traveling, standing, and modulated waves. These nonlinear solutions are closely related to the theoretical predictions for an unbounded layer. An unexpected feature is that the traveling waves reverse their direction of propagation in an episodic manner; this is not the case for the modulated waves. The calculations are related to recent experiments on convection in binary fluid mixtures.

We study diffusion of hard-core particles in linear chains where disorder arises from two distinct sources, (i) random bias fields and (ii) random transition rates. In the case of random bias fields, the step probability to the left and right is randomly chosen to be (1+E)/2 and (1-E)/2 with equal probability. Using Monte Carlo simulations and scaling arguments we find that the mean-square displacement is given by 〈$x^2$(t)〉∼[A(c)(lnt${\left)\right]}^4$, and the probability density P(x,t) scales as P(x,t)∼<${\mathit{x}}^2$(t)${>}^{\mathrm{-}1/2}$G(x/${\mathit{x}}^2$(t)${>}^{1/2}$). Here c is the concentration of particles; for c→0 〈$x^2$(t)〉 reduces to the Sinai result for noninteracting particles. We find that the scaling function G(u) has the form G(u)∼exp(-$u^{\alpha }$), with α=1.5, a value distinctly different from the value for noninteracting particles (α=1.25) and from the value for zero-bias field (α=2). In contrast, in the case of random transition rates with a power-law distribution, we find that the asymptotic behavior of 〈$x^2$(t)〉 as well as P(x,t) is changed by the hard-core interaction.

Evidence of a first-order smectic-A–smectic-$C^{\mathrm{*}}$ (SmA-Sm$C^{\mathrm{*}}$) transition is presented. Detailed x-ray studies on 4-(3-methyl-2-chloropentanoyloxy)4’-heptyloxybiphenyl show that the SmA-Sm$C^{\mathrm{*}}$ transition in this material is characterized by a discontinuous jump in the layer spacing (and hence in the tilt angle) and by a narrow two-phase region in which the density modulations due to the smectic-A and the smectic-$C^{\mathrm{*}}$ phases coexist. Addition of a second compound drives the SmA-Sm$C^{\mathrm{*}}$ transition towards second order.

The wave number for one-dimensional maps is introduced. For unimodal maps this new concept is a counterpart to the winding number for circle maps. Its dependence on the tuning parameter, in particular, some scaling behavior, is discussed.

A concentration dependence of elastic and viscous properties of nematic poly-γ-benzyl glutamate (PBG) was studied experimentally. The splay and bend constants are similar in magnitude, both linear in concentration. The twist constant is much smaller and constant. Viscosities exhibit large anisotropies. ${\gamma }_1$ and ${\eta }_c$ are roughly quadratic in concentration, ${\eta }_a$ is linear, while ${\eta }_b$ is constant. The data are self-consistently interpreted in terms of the theoretical models for nematics of semi flexible chains rather than those of rigid rods.

Molecular-orbital calculations of ${\mathrm{TiF}}_4$, ${\mathrm{TiCl}}_4$, ${\mathrm{TiBr}}_4$, and ${\mathrm{TiI}}_4$ molecules have been made with use of self-consistent local-density theory with the discrete variational (DV-Xα) method. Core-level excitation energies corresponding to x-ray photoelectron spectroscopy (XPS) measurements are calculated. Spectral peaks associated with metastable final states of the core ionized atom that include relaxation and charge transfer processes are calculated. XPS spectra of Ti core levels in these compounds show that binding energies of both main lines and satellites clearly depend on the ligated anion. The observed systematic behavior of ionization potentials and satellite separation energies for the halide series is calculated with reasonable accuracy. With use of the single-determinant formalism, contributions to the intensity of the main line and satellites are examined.

In this work relativistic and many-body effects in transition-metal ions are treated independently. For the former, we have written an automated program which provides level-dependent (J) structure input (for both the electrostatic and the magnetic portion of the Breit operator) to Desclaux’s multiconfigurational Dirac-Fock program. Also, the nonrelativistic treatment of many-body effects for these atoms via the configuration-interaction (CI) technique has been made much more efficient, in part by the removal of unnecessary (through first-order) parents, so as to make computational costs competitive with those associated with smaller species. We predict that all levels of ${\mathrm{Zn}}^{\mathrm{-}}$ 3$d^9$4s4${p^3}^6$${\mathrm{D}}_{\mathrm{J}}$ are bound, with the lowest J=(9/2 bound by 0.810 eV and the highest J=1/2 by 0.511 eV, that ${\mathrm{Zn}}^{\mathrm{-}}$ 3$d^{10}$4s4${p^2}^4$${\mathrm{P}}_{\mathrm{J}}$ is bound by 0.169 eV (J=1/2) and 0.136 eV (J=(5/2), and that ${\mathrm{Zn}}^{\mathrm{-}}$ 3$d^{10}$4$p^3$ ${}_{}{}^4{}_{}{}^{}S_{3/2}^{}{}_{}{}^{}$ is bound by 0.566 eV. The complete fine structure is given as well as the electric dipole oscillator strength for the ${}_{}{}^4{}_{}{}^{}\to _{}^4{}_{}{}^{}$S° transition. All states are found to consist of at least 90% pure LS coupling. Finally, the configuration-interaction program referred to above will soon be modified to do relativistic CI calculations, thus removing the separability assumption.

We show that a representation-independent, spectrum-generating algebra for the Coulomb problem in an angular momentum basis can be obtained by quantizing two complex, time-dependent, classical vectors, ${\mathrm{D}}_c$${=\mathrm{F}}_c$+i${\mathrm{G}}_c$ and ${\mathrm{D}}_c^{\mathrm{*}}$. The approach is based on an analogy with a treatment of the isotropic harmonic oscillator [A. J. Bracken and H. I. Leemon, J. Math. Phys. 21, 2170 (1980)], and on work in which classical constants of the motion were quantized to yield shift operators for angular momentum in the Coulomb problem [O. L. de Lange and R. E. Raab, Phys. Rev. A 34, 1650 (1986)]. By construction ${\mathrm{F}}_c$ and ${\mathrm{G}}_c$ are orthogonal to the orbital angular momentum L, their moduli have equal, constant magnitude, and they rotate about L. In this construction we use ${\mathrm{A}}_c$ (the Laplace-Runge-Lenz vector) and ${\mathrm{A}}_c$×L^ as basis vectors. ${\mathrm{F}}_c$ and ${\mathrm{G}}_c$ contain an undetermined phase factor exp(iδ). ${\mathrm{D}}_c$ and ${\mathrm{D}}_c^{\mathrm{*}}$ are quantized by requiring that the resulting operators should be shift operators for energy and angular momentum in the bound-state kets ‖nlm〉. This determines the operators ${\Delta }^{\pm }$ corresponding to the classical phase factors exp(±iδ). In the coordinate and momentum representations of wave mechanics respectively, ${\Delta }^{\pm }$ are the dilatation operators for coordinate-space and momentum-space wave functions. The shift operators can be factorized to yield 20 abstract operators. Apart from their dependence on ${\Delta }^{\pm }$ and constants of the motion, ten of these are linear in p, eight are linear in r, and two are quadratic in r. Apart from ${\Delta }^{\pm }$, these operators can be linearized by replacing constants of the motion with their eigenvalues: In the coordinate and momentum representations of wave mechanics they are first-order differential operators. The shift operators are part of a Hermitian basis for a spectrum-generating algebra which is shown to be SO(2,1)⊕SO(3,2).

The idea of generating a relativistic electron density from knowledge of the nonrelativistic limit is illustrated by examples from two areas: (i) independent electrons moving in a fixed one-body potential energy and (ii) two-electron atomic ions treated in a model with δ-function interactions.

The problem of calculating transition rates between atomic fine-structure levels is considered. Nonrelativistic configuration-interaction calculations of terms of interest are performed and the terms are then mixed by the relativistic couplings of the Breit-Pauli Hamiltonian. Frequently it turns out that the mixing components of the Breit-Pauli matrix are larger than the relative term energies. This leads to sensitivity of the level eigenvectors to small errors in the energies and thus to errors in the transition rates among the levels. A nonperturbative method for correcting the level vectors for cases involving any number of strongly mixed terms is developed. The method is based on solving the inverse eigenvalue problem for a matrix using the observed spectrum to correct the diagonal matrix elements of the Breit-Pauli matrix. It is applied in the present work to calculate level wave functions and transition rates for the 1$s^2$2$s^2$2$p^5$3s, 3p, and 3d levels of the Ne i–Si v ions of the neon isoelectronic sequence.

Electric dipole and quadrupole transitions probabilities between two atomic Rydberg states νl,ν’l’ have been calculated using three methods. From comparison of results we deduce a new method from which any radial integrals may be obtained very easily using only two functions of the difference s=ν-ν’. These functions are $g_0$(s) and $g_1$(s) which have been calculated in the dipole case [J. Picart, A. R. Edmonds, N. Tran Minh, and R. Pullen, J. Phys. B 11, L651 (1978); A. R. Edmonds, J. Picart, N. Tran Minh, and R. Pullen, J. Phys. B 12, 2781 (1979)].

In this paper we perform a configuration-space analysis of the local-density approximation (LDA) for the exchange-correlation energy functional of Kohn-Sham density-functional theory in terms of the corresponding average exchange-correlation charge (hole) and energy densities. According to our analysis, the explanation for the quantitative success of the LDA based on the hole charge-conservation sum rule and the assumed consequent cancellation of errors in the spherical averages of the hole is inadequate. The principal conclusion of our work is that the constraint of charge neutrality is a necessary but not sufficient condition for an approximate energy functional to lead to accurate ground-state energies and ionization potentials. The significant additional requirement for the functional is that it must, at least qualitatively, reproduce correctly the structure of the hole as a function of electron position. We perform our calculations within the exchange-only approximation as applied to atoms and jellium metal surfaces. In atoms the Fermi hole is localized about the nucleus; as a consequence the LDA Fermi hole is accurate only for electron positions close to it.

However, we show that the spherically averaged LDA hole is accurate for electron positions in the shell regions; it is substantially in error in the intershell and classically forbidden regions. The fact that the principal contribution to the exchange energy comes from the inner-shell region of the atom, where the LDA hole is accurate, explains why the errors in the LDA ground-state energies are small. However, the ionization potential, which depends on the structure of the hole in the outer regions of the atom, is substantially in error in the LDA since here the LDA hole differs significantly from the exact one. For metallic surfaces, on the other hand, as an electron is pulled from within the metal to infinity outside, the Fermi hole is delocalized and spread throughout the crystal. As a consequence, the planar-averaged LDA hole, which is accurate for electron positions inside the metal, bears little resemblance to the exact hole for electron positions outside the surface. Thus the planar-averaged LDA energy density in the regions at and outside the surface, from which there is a significant contribution to the energy, is poor, and consequently so is the surface exchange energy. However, the LDA work function is accurate since the surface dipole barrier is fairly insensitive to the choice of the approximate energy functional.

Finally, our calculations exhibit a striking similarity in the structure of the exact spherically averaged Fermi holes for the few-electron-atomic and many-electron-metallic-surface nonuniform systems, thus demonstrating the truly universal nature of the exact energy functional.

A detailed and systematic presentation of algebraic and diagrammatic techniques introduced in paper I [L. Z. Stolarczyk and H. J. Monkhorst, Phys. Rev. A 32, 725 (1985)] is given. Performing a similarity transformation of an operator in Fock space, e.g., a Hamiltonian in the generalized coupled-cluster method (see paper I), leads to lengthy algebraic formulas for the linear parameters (amplitudes) of the transformed operator. These formulas can be expressed in a compact form by means of the so-called reduced diagrams. Precise rules are given for constructing such diagrams (related to the so-called directed graphs of the graph theory) and the algebraic expressions corresponding to them. In particular, rules for generating a connected-diagram expansion of the amplitudes of the transformed operator are formulated. Several examples illustrating the use of this diagrammatic-algebraic approach are considered.