A self-consistent mode-coupling theory is used to calculate the coefficient of self-diffusion in a three-dimensional classical one-component plasma subjected to an external magnetic field. For asymptotically large fields a Bohm-like behavior is found for diffusion in the plane perpendicular to the magnetic field. The experimental consequences of these results are discussed.

We investigate density expansions for the configurationally averaged Green's function for a random walk on a (site) disordered lattice. Two-point Padé summation techniques are used in conjunction with scaling arguments to examine behavior near the percolation density. Recent proposals for the structure of the percolation cluster are discussed in light of the results.

The irreversible accretion of diffusing particles onto a large cluster results in a tenuous aggregate characterized by a fractal dimension $D_0$ smaller than that of space. The rate of aggregation onto the fastest-growing sites in such a process must not increase indefinitely as the cluster grows. This fact sets a lower limit on the fractal dimension, viz., the dimension $d$ of space minus 1. For aggregation of ballistically moving particles, this bound implies that the aggregate must be compact: The fractal dimension must equal that of space. In general, if the aggregating particles follow trajectories of fractal dimension $D_1$, the bound implies $D_0>~d-D_1+1\mathrm{}$.

The characteristic frequency of the $E\parallel n$ dielectric relaxation in three compounds of the $p$- pentoxybenzylidene alkylaniline is directly related to the squared nematic order parameter in the nematic, smectic-$A$ and smectic-$C$ phases. In the crystalline smectic-$B$ phase the relaxation frequency depends on the molecular length.

The dipole polarizability of ${\mathrm{F}}^{-}$ and the electron affinity of F are studied using full fourth-order many-body perturbation theory (MBPT) and the infinite-order coupled-cluster single- and double-excitation model (CCSD). It is shown that the fourth-order correlation corrections for the polarizability of ${\mathrm{F}}^{-}$ are larger than second-order, raising questions about the suitability of finite-order methods for including electron correlation effects on the polarizability of this system. MBPT-CC results in a variety of basis sets suggest that the experimentally unknown polarizability of ${\mathrm{F}}^{-}$ is ∼ 18-20 a.u., of which a large percentage is due to the inclusion of triple-excitation effects.

We apply displacement operator coherent-state (DOCS) methods to calculate coherent states of systems subject to the potential $V(x,t)=g_2\mathrm{}\left(t\right)\mathrm{}{x}^2+g_1\mathrm{}\left(t\right)x$. We call states which are initially coherent and which preserve their coherence with time nondispersive, in contrast to those coherent states which lose their coherence which we denote as dispersive or dissipative. We report necessary and sufficient conditions for the time-dependent coefficients $g_1\mathrm{}\left(t\right)\mathrm{}$ and $g_2\mathrm{}\left(t\right)\mathrm{}$ for the DOCS to be nondispersive. We also show that there is no necessary connection between the nondispersive character of coherent states and the ability of the DOCS to provide the quantum analog of the corresponding classical dynamical problem. A number of simple examples are treated.

The quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of motion of a quantum particle in a one-dimensional lattice in the presence of a static-random potential. Classically, the first problem is nonintegrable and, for certain values of the parameters, exhibits chaos and diffusion in phase space; in the second problem, diffusion takes place in configuration space. Quantum phase interference, however, is known to suppress diffusion in Anderson's problem and to produce quasiperiodic motion. By establishing a mapping between the two systems we show that a similar effect determines the dynamics of the quantum rotator. As a result its wave functions are localized in phase space and their time evolution is quasiperiodic. This result explains the quantum recurrences and boundedness of the energy found in recent numerical work.

The Kohn-Sham method for energy calculation in inhomogeneous electron systems relies on a comparison of functionals describing interacting and noninteracting electrons. An alternate approach draws the link between interacting and noninteracting systems explicitly, via an adiabatic connection of eigenstates. This adiabatic-connection scheme eliminates the "Fermi-statistics" problem and provides partial answers to some other conceptual difficulties that arise when the Kohn-Sham method is applied in practice. In addition, dimensional arguments can be given that justify the use of local-density approximations for exchange and correlation within the adiabatic connection framework. These arguments do not involve a "slowly varying" assumption and are valid for any system, however inhomogeneous.

The parity-violating $E1\mathrm{}$ transitions between the $n=2\mathrm{}$ levels of atomic helium, induced by the electron-electron neutral weak interaction have been computed by using Coulomb-type wave functions and (up to 84 parameter) Hylleraas wave functions. The parity-violating matrix elements turn out to be of the same order of magnitude as those due to the electron-nucleus weak interaction, thus allowing one to conclude that the relative importance of both effects is to be traced to their corresponding effective coupling constants.

This paper analyzes the dynamics of two-level systems from a new perspective. The notion of eigenvalues (EV) of the pulse area squared, which was introduced in a previous paper, is developed further. Integral expressions for the eigenvalues in terms of eigenfunctions are exhibited, and it is pointed out that these formulas also enable one to estimate EV variationally. Examples are given of how the method may be used to predict qualitative features of two-level spectra without solving equations of motion. Finally, an expression for the transition amplitude in terms of an eigenfunction expansion is derived. It is suggested that this expansion may be useful for both numerical determinations of transition probabilities and for analytic, variational calculations of these parameters. As an application, an expression for the transition probability at small detunings for a rather general class of coupling functions is derived, and its predictions compared to exact numerical calculations in a specific case.

An integral representation of the Coulomb Green's function is expressed in the form of a Fourier transform with respect to the quantum-number variable. The inverse transform leads to the function $S({\overrightarrow{\mathrm{r}}}_1,{\overrightarrow{\mathrm{r}}}_2,q)=-\left(\frac{k^2}{4\pi }\right){csc}^2{\mathrm{qe}}^{\mathrm{ik}\xi cotq}{J}_0\left(k\eta cscq\right)$ which is shown to represent a propagator in the domain of a complete set of Coulomb Sturmian eigenfunctions: $S({\overrightarrow{\mathrm{r}}}_1,{\overrightarrow{\mathrm{r}}}_2,q)=\Sigma \stackrel{}{n,l,m}{\phi }_{\mathrm{nlm}}\left({\overrightarrow{\mathrm{r}}}_1\right){\phi }_{\mathrm{nlm}}^{*}\left({\overrightarrow{\mathrm{r}}}_2\right)e^{-2\mathrm{inq}}$. The analogous Sturmian propagator for continuum eigenstates is also derived. Various aspects of these propagators are developed, including reduction to a quasi-one-dimensional form, partial-wave expansion, and connection to a harmonic-oscillator propagator.

In the $\Xi$ method, the self-interaction part of the total exchange-correlation potential in atoms is evaluated exactly and the remaining "pure exchange" is approximated using a Fermi-hole formalism. A theoretical derivation of an ab initio exchange potential for atoms using a simple model of this pure exchange hole is presented. This model of the exchange hole satisfies, unlike an earlier treatment, the necessary condition that the total charge removed from the exchange hole is zero. The orbital eigenvalues and the total energies of the ground-state multiplets for various atoms and ions are reported and found to be in close agreement with the Hartree-Fock values.

The Klein-Nishina formula describes the scattering of transversely polarized electromagnetic radiation from relativistic electrons. In this work the Klein-Nishina amplitude is generalized to include the scattering of electromagnetic radiation of any polarization. Potential applications of these new results are found in plasma physics and solid-state physics.

We extend the linear algebraic method to the calculation of molecular photoionization cross sections. The formulation is primarily developed in the fixed-nuclei, Hartree-Fock, and frozen-core approximations, although correlation effects in the scattering solution are introduced through an effective optical potential. The single-center expansion and close-coupling approximations are invoked to give converged scattering solutions. Cross sections and asymmetry parameters are reported for photoionization from the ground state of ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, NO, and C${\mathrm{O}}_2$. We obtain very good agreement with the Schwinger variational results of McKoy and co-workers for all molecular systems. For NO and C${\mathrm{O}}_2$, we find substantial disagreements with the Stieltjes calculations for some symmetries.

Absolute optical-emission excitation functions have been measured for the $D {}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to B {}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ fourth positive system bands ($0,v^{\prime \prime }$) with $v^{\prime \prime }=0,1,2,3,4,5,6\mathrm{}$ and for the $c_4^{\prime } {}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to a {}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ Gaydon-Herman singlet system bands ($0,v^{\prime \prime }$) with $v^{\prime \prime }=0,1,2,3,4,5\mathrm{}$ produced by electron-impact excitation of the ${\mathrm{N}}_2 X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\mathrm{}(v=0\mathrm{})\mathrm{}$ ground state, for incident electron energies ranging from threshold to 440 eV. We find that the $D\to B$ emission has a principal maximum at 14.1±0.3 eV, a smaller maximum (83% of principal maximum) at 23 eV, and an $E^{-3\mathrm{}}$ energy dependence for incident electron energies $E>\mathrm{}65\mathrm{}$ eV. Measurements over the energy range 13.5-31 eV indicate the $D\to B$ emission is unpolarized. The sum over $v^{\prime \prime }$ of the $D\to B (0,v^{\prime \prime })$ optical-emission cross sections gives a maximum value 1.27 × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ for the apparent cross section for the $v=0\mathrm{}$ vibrational level of the $D {}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state excited by electron collision with the ${\mathrm{N}}_2 X {}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\mathrm{}(v=0\mathrm{})\mathrm{}$ ground state. The appearance of two maxima in the $D\to B$ optical emission is qualitatively confirmed by other experimental work. This point is discussed. For the $c_4^{\prime }\to a$ emission we find a single very broad maximum near 80 eV and for $E>\mathrm{}110\mathrm{}$ eV an energy dependence described by the form $\left(\frac{C_1}{E}\right)\ln \left(\frac{E}{C_2}\right)$. The $c_4^{\prime }\to a$ optical-emission cross sections were obtained by extrapolating measurements to low pressure (<0.1 mTorr) in order to account for the nonlinear pressure dependence of the $c_4^{\prime }\to a$ emission caused by absorption of the very intense $c_4^{\prime }\to X \mathrm{}(0,0)\mathrm{}$ band radiation. The sum over $v^{\prime \prime }$ of our measured optical-emission cross sections for the $c_4^{\prime }\to a (0,v^{\prime \prime })$ bands has a maximum value 1.0 × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$. This result, when combined with the absolute $c_4^{\prime }\to X \mathrm{}(0,0)\mathrm{}$ band-emission cross section of Zipf and McLaughlin and the $c_4^{\prime }\to X \mathrm{}(0,1)\mathrm{}$ cross section of Aarts and DeHeer, yields an upper bound of 0.006 for the $c_4^{\prime }\mathrm{}\left(0\right)\mathrm{}\to a$ optical branching ratio, i.e., more than 99.4% of $c_4^{\prime } {}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\mathrm{}(v=0\mathrm{})\mathrm{}$ molecules will decay to the ground state.

The distorted-wave approximation and electron-ion crossed beams have been employed to complete a theoretical and experimental study of electron-impact ionization along the Xe isonuclear sequence. Experimental results are given for ${\mathrm{Xe}}^{2+}$ through ${\mathrm{Xe}}^{6+}$ and the results of theoretical calculations are presented for ${\mathrm{Xe}}^{+}$ through ${\mathrm{Xe}}^{6+}$. The data reveal large contributions due to indirect ionization processes. Theoretical cross sections include the contributions of inner-shell excitations to autoionizing levels of the types ${\mathrm{Xe}}^{q+}\left({4d}^{10}{5s}^2{5p}^{6-q}\right)\to {\mathrm{Xe}}^{q+}\left({4d}^9{5s}^2{5p}^{7-q}\right)$ and ${\mathrm{Xe}}^{q+}\left({4d}^{10}{5s}^2{5p}^{6-q}\right)\to {\mathrm{Xe}}^{q+}\left({4d}^9{5s}^2{5p}^{6-q}nl\right)$ with $nl=4f,5d,\mathrm{and} 5f$. Hartree-Fock structure calculations for the ${4d}^9{5s}^2{5p}^{6-q}\mathrm{nf}$ configurations are highly term dependent and this has a pronounced effect on the magnitude and energy dependence of indirect contributions to the cross sections. Model calculations indicate that resonant-recombination double autoionization also contributes to the ionization cross sections of ${\mathrm{Xe}}^{2+}$ through ${\mathrm{Xe}}^{5+}$.

A model potential that includes both correlation and polarization effects is proposed for electron-molecule collisions. It is based, as suggested by O'Connell and Lane, on a hybridization of local electron-gas theory for short distances and the asymptotic form of the polarization potential. It is energy independent and very simple to apply, depending only on the molecular charge density and polarizabilities. The potential has been calculated for several molecules (${\mathrm{H}}_2$, ${\mathrm{N}}_2$, C${\mathrm{O}}_2$, HF, HCl, and CO); the crossing point between the correlation and polarization potentials is remarkably constant, averaging 0.96 eV. Application in scattering calculations for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ yields very encouraging results.

Cross sections for the removal of two electrons from rare-gas ions by single collisions with incident electrons have been both measured using crossed beams of ions and electrons, and calculated using Hartree-Fock distorted-wave theory. For initial ions ${\mathrm{Ar}}^{4+}$, ${\mathrm{Kr}}^{4+}$, and ${\mathrm{Xe}}^{4+}$ the measured peak cross sections are 1.4 × ${10}^{-18\mathrm{}}$, 6.5 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$, respectively. These measurements confirm and extend the measurements of Müller and Frodl and of Achenbach et al. Calculations were performed for the charge-state-4 + ions and for ${\mathrm{Xe}}^{+}$, ${\mathrm{Xe}}^{2+}$, and ${\mathrm{Xe}}^{3+}$. Comparison of experiment and theory indicates that the double ionization of rare-gas ions is dominated by the indirect mechanism of inner-shell single ionization followed by autoionization. The distorted-wave calculations for the $4d$ ionization cross section of ${\mathrm{Xe}}^{q+} (q=1\mathrm{} \mathrm{to} 4)$ ions are strongly influenced by term dependence in the ejected-electron continuum, and by ground-state correlations.

Previously we have discussed the shell corrections to electronic stopping which may be calculated from momentum distributions obtained from numerical atomic wave functions. In that case, the lower limit for particle velocity was determined by the largest orbital mean excitation energy for the system. Here we discuss the extension of these calculations to the kilovolt region of projectile velocity, and report stopping powers, stopping numbers, and shell corrections for various cases. Trends across the first two rows of the periodic table are discussed, and the low-velocity limiting behavior of the stopping power and stopping number is considered.

Equilibrium charge-state distributions of F ions have been measured in the collisions of (1) (29-108)-MeV F+C and (2) 30- and 60-MeV $F+{}_{Z_2}{}^{}{}_{}{}^{}X$ foils. Measurement (1) is done to investigate the projectile-velocity dependence of the mean charge state, distribution width, and charge-distribution function. Measurement (2) is done to investigate the $Z_2$ (target atomic number) dependence of F-ion charge states using 20 kinds of foils with different $Z_2$. Contrary to the $Z_2$ oscillation of mean charge states of swift Si and Cl ions, obvious $Z_2$ oscillatory behavior has not been observed in 30- and 60-MeV F ions. Generally, higher-charge states are observed after passage through lower-$Z_2$ foils, which follows a trend similar to the $Z_2$ dependence of effective charges estimated from stopping powers.