$M_{4,5}{N}_{6,7}X$ ($X=N_{6,7} or O_{2,3}$)-type normal and vacancy satellite Auger spectra of atomic ytterbium have been measured with the use of electron impact excitation. The main Auger spectra have been analyzed and compared with the calculated results. The relative energies and intensities of the lines have been calculated in the nonrelativistic mixed-coupling scheme applying $\mathrm{jj}$ coupling to the initial and the intermediate coupling to the final states of the Auger transitions. The kinetic energies have also been calculated in the relativistic intermediate coupling with the use of the Dirac-Fock program of Grant . The experimental intensity ratio between the $M_5$ and $M_4$ line groups is found to be 3.0, which deviates strongly from the statistical ratio 1.5 due to $M_4{M}_{5}X$ Coster-Kronig processes. For the same reason, a strong satellite structure appears also at the low-energy side of the main $M_5{N}_{6,7}{N}_{6,7}$ line group.

The problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schrödinger equation, is reformulated as a variational problem. By means of Gaussian trial functions and a Ritz optimization procedure, approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp. Comparisons with results from inverse-scattering theory and/or numerically obtained solutions show very good agreement.

Analytical and numerical solutions are presented to elucidate the important physical aspects of the incoherent nonlinear interaction and propagation of high-intensity radiation in an absorbing (or amplifying) medium. The properties of radiation-driven one-dimensional density discontinuities or wave fronts are examined for monochromatic and broadband radiation sources, and for a nonlinear absorbing medium characterized by a spectral absorption cross section that is square, Gaussian, or Lorentzian. The effect of the angular distribution of the radiation source is considered in detail. The results of the analysis show that the propagation behavior of the radiation-driven wave front depends strongly on the spectral dependence of the absorption cross section. The wave front propagates with a constant shape and at a constant velocity $v_b$ only for monochromatic radiation or a square absorption cross section. For a Lorentzian, $v_b\sim x^{\frac{1}{2}}$ at large values of the propagation distance $x$. The absorption of intense radiation in a medium generally causes local heating, which can introduce hydrodynamic disturbances that propagate behind, along with, or ahead of the radiation-driven wave front. Conditions are derived for the amount of heat addition that is required to produce these disturbances for a given velocity of the wave front.

The wavelength- and frequency-dependent linear transport coefficients and the wavelength-dependent thermodynamic properties have been determined for hard spheres at three different densities and over a region of wavelengths and frequencies that range from the hydrodynamic to the free-streaming regime. The molecular-dynamics calculation involves the evaluation of correlation functions from which the generalized properties can be simply derived consistent with their hydrodynamic definitions. The results are compared with generalized kinetic theory and, except for the viscosity at high density and small wavelength, the predictions of that theory are accurate within a few percent. For the viscosity, mode-coupling theory improves upon the predictions of kinetic theory. A single application is given in which the dependence of the Stokes friction coefficient on the size of the massive Brownian particle is determined using the generalized viscosity. This illustration leads one to believe that generalized hydrodynamics quantitatively applies on the molecular scale.

Density, longitudinal, and transverse-current correlation functions for hard spheres at various densities and wavelengths have been generated by computer simulation and compared with both the generalized Enskog kinetic theory and wavelength-dependent hydrodynamics. It is shown that even for dense gases the generalized Enskog kinetic theory is quantitatively accurate in describing the thermal fluctuations at finite wavelengths and frequencies, as is wavelength-dependent hydrodynamics, as long as the wavelength is greater than the mean free path. At liquid densities neither theory can account for the viscoelastic relaxation effects, directly observed in the transverse-current correlation function by shear-wave propagation, at a wavelength somewhat above the first diffraction maximum. However, wavelength-dependent hydrodynamics quantitatively describes the neutron scattering function at wavelengths from this point (above the first diffraction maximum) through the diffraction maximum (where the de Gennes narrowing occurs) to the mean-free-path limit. Furthermore, viscoelastic effects in the long-wavelength regime can be accounted for by introducing into hydrodynamics time-dependent transport coefficients. At still longer wavelengths, viscoelastic relaxation times become short compared with hydrodynamic relaxation times and ordinary hydrodynamics with constant transport coefficients describes the neutron scattering function.

A previously developed extension of the quasistatic approximation which allows for the broadening of hydrogen lines by low-frequency fields is applied to the first four Lyman lines of hydrogen, ionized helium, CVI, and ArXVIII. It is demonstrated numerically that the low-frequency Stark broadening is Gaussian in the case of relatively small dynamical corrections. Extrapolation of this Gaussian approximation to cases with large corrections leads to good agreement with measurements of the Lyman-$\alpha$, -$\beta$, and -$\gamma$ lines of hydrogen and allows the prediction that the Lyman-$\delta$ should retain its central dip.

Alternate paths to chaos are observed experimentally in a hybrid optically bistable system with delayed feedback. The waveforms observed on these alternate paths are the frequency-locked waveforms seen in an earlier experiment which we find to be modified versions of the typical period-doubled waveforms. The transitions between these waveforms are discontinuous and show hysteresis loops. By the introduction of an external locking signal we are able to stabilize waveforms in the neighborhood of the discontinuous transitions. By so doing we show that the transitions among the branches are due to their lack of stability. The transition are thus not strictly first-order nonequilibrium phase transitions, since in that case the branches cease to exist at the transition point.

We have obtained predictions for free-free Gaunt factors, using a full relativistic numerical partial-wave and multipole calculation of the bremsstrahlung process as a single electron transition in a potential. We study hot dense cesium plasmas, at various densities and temperatures, using the finite-temperature and -density Thomas-Fermi potential. We consider incident electron energies in the range 1-50 keV. Our results show that use of isolated neutral or ion Gaunt factors has only limited applicability in this environment, while use of the Elwert-Born approximation can lead to a factor-of-3 discrepancy for low incident electron energies.

The evidence for long-time tails as a part of the velocity autocorrelation function for a classical particle is examined. Computer simulations, theoretical treatments, and light-scattering experiments are discussed. It is argued that numerical error propagation in the computer simulations may give rise to long-time tails as an artifact which is of hydrodynamic character. The theoretical treatments of physicists, whether avowedly phenomenological or putatively rigorous, all rely on a hydrodynamic mechanism. The usual theoretical treatments by mathematicians, based on the differential topology of "dynamical systems," appear not to be in agreement with long-time tails. Recent experiments with polystyrene spheres, observed by light scattering, claim to see the effect of long-time tails. These experiments may be interpreted as observations of the Stokes-Boussinesq effect expected for "macroscopic" spheres, but not justified for truly microscopic, molecular-sized, particles. While long-time tails may yet be rigorously established by computer simulation, theory, and experiment, it is argued in this paper that this has not happened yet. Moreover, a firm basis for serious doubt is raised.

High-resolution ac calorimetric, x-ray, and light-scattering measurements have been made on $\mathrm{N}-[4-(n-\mathrm{butyloxy}\left)\mathrm{benzylidene}\right]-4^{\prime }-(n-\mathrm{heptyl})\mathrm{aniline}$ (4O.7) near the nematic-smectic-$A$ phase transition. This transition is second order, with a variation in $C_p$ which is well described by a critical exponent $\alpha ={\alpha }^{\prime }=-0.026\mathrm{}$ corresponding to the three-dimensional $\mathrm{XY}$ model. The longitudinal and transverse correlation lengths exhibit single-power-law divergences over the reduced-temperature range ${10}^{-2\mathrm{}}$ to 3×${10}^{-5\mathrm{}}$ with exponents ${\nu }_{\parallel }=0.78\mathrm{}\pm 0.02$ and ${\nu }_{\perp }=0.65\mathrm{}\pm 0.02$, respectively. The anisotropic hyperscaling relation ${\nu }_{\parallel }+2\mathrm{}{\nu }_{\perp }+\alpha =2\mathrm{}$ is satisfied to within the errors. A dynamical-scaling analysis of light-scattering measurements of the bend-mode director fluctuations with elastic constant $K_3$ yields values for ${\xi }_{\parallel }$ which agree absolutely with the x-ray measurements. Thus the data are all internally consistent, and they appear to exclude all current theories of the nematic-smectic-$A$ transition. It is observed that the overall critical behavior in smectic liquid crystals is sensitive to the width of the nematic range; this may offer an explanation for the apparent nonuniversality of the exponents.

Multiparticle correlations in dense plasmas are analyzed in terms of the density-functional formalism; theoretical schemes of improvement over the hypernetted-chain (HNC) approximation are thereby advanced. The proposed schemes contain no adjustable parameters; the computational difficulties associated with these schemes are no greater than those involved in the solution of the ordinary HNC equations. The validity and accuracy of those improved HNC schemes are examined through numerical comparison with the exact Monte Carlo (MC) simulation data; significant improvement over the HNC scheme and close agreement with the MC results are thereby demonstrated.

We have studied theoretically and experimentally the nonlinear Fabry-Perot transmission of a cavity with a thin nematic liquid-crystal film. Various modes of operation have been observed, using a moderate-power cw laser. In the limit of small reorientation angles, the optically induced molecular reorientation of the birefringent crystal and the nonlinear phase shift is solved for a homeotropically aligned crystal. Multiple-valued Fabry-Perot transmission is obtained by solving the nonlinear equations that couple the optical phase shift with the cavity transmission. The time-independent nature of the process and the explicit quantitative expressions involving the nematic liquid-crystal parameters allow a direct comparison between the thoery and experimental results. Good quantitative agreement is demonstrated.

Ion diodes suited to inertially confined fusion research must conduct very high currents. The magnetic fields due to these currents are comparable to the fields used to provide magnetic insulation of electrons. Because these self-fields are necessarily high at the diode boundary where the power is applied, and are zero at some other part of the diode away from the power feed, these diodes have generally been treated theoretically by two-dimensional particle-in-cell computer simulations. There is a special class of ion diodes employing series magnetic field coils which can be described by a one-dimensional model. These diodes are highly amenable to treatment by analytic theory, and therefore are easily designed and scaled to multiterawatt systems. Many features of these diodes make them very attractive as drivers for inertial-confinement fusion research. Theoretical analysis of this class, including magnetic field configuration and field coil design, electron drifts, diode efficiency, and ion focusing, is presented. Also presented is analysis of a plasma-filled version which provides ion bunching and filtering of light ion species which might otherwise have detrimental effects on target experiments.

Our theoretical procedure for calculating thermalization times and the evolution of the process of electron thermalization in rare gases and diatomic molecules has been extended to the case of mixtures of Ar and ${\mathrm{N}}_2$ and of Xe and ${\mathrm{N}}_2$. The results are compared with the time delays for the recombination luminescence decay measured in Ar-${\mathrm{N}}_2$ and Xe-${\mathrm{N}}_2$ mixtures. Calculated values of thermalization times agree well with the experimental time-delay data.

The negative-glow plasma of an inverse-brush-cathode discharge has been studied by laser-induced fluorescence and absolute emission spectroscopy. The fluorescence saturation curve is shown to give directly the ratio of the populating source terms for the two coupled levels. The fluorescence and absolute density measurements of excited atoms are consistent with the production of excited species via molecular reactions involving the energetic primary electrons and the secondary electrons. A rate-equation model including several molecular processes has been developed and is found to give relatively good agreement with the experimental results.

A general theory of the light propagation in periodic structures characterized by a uniform rotation of the dielectric tensor about a given axis is presented. Starting from a fundamental approach of Dreher and Meier, which is mostly numerical, an analytical solution of the characteristic equation has been found which can be used to calculate the wave vectors as a function of $\omega$ and of the incidence angle ${\theta }_i$. The electromagnetic wave is described as a superposition of elementary modes having the form of Bloch waves. Each elementary mode is represented by a sum of plane waves elliptically polarized, whose wave vectors are the roots of the characteristic equation. The analysis of the solutions of such an equation allows us to draw a more complete map of the stability and instability regions for light propagation in helical structures than the ones currently available in the literature. The coexistence of two distinct modes, with different polarization states, determines the shape of the stability map. Each mode presents a series of Bragg instabilities. Between the two Bragg instabilities of the same order a further instability exists which is common to both modes and does not satisfy the Bragg conditions. All instability bands, with the exception of only one of the first order, vanish at normal incidence. This occurs for any value of the optical anisotropy and is a peculiarity of perfectly ordered helical structures. The bandwidth increases with ${\theta }_i$, and overlapping may occur. Typical plots of dispersion curves and attenuation constants are reported. Finally, we compute the intensity and the polarization state of the light reflected from a thin film, in order to clarify the controversial point about the structure—doublet or triplet—of the higher-order reflection bands.

Recent experiments show that the translational temperature of clusters in a beam expansion increases with cluster size. We present a general theory for steady-state nucleation of pure gases, explaining this observation as a combination of two effects: the heating of the clusters by condensation and an induced Maxwellian motion by rocketlike emission of fast monomers from clusters.

This work deals with the evaporation of clusters in their flight from the condensation zone in the nozzle until their detection. This time is of order ${10}^{-5\mathrm{}}$ - ${10}^{-3\mathrm{}}$ sec, depending on the experimental setup. It is shown that the cluster concentrations converge to a characteristic distribution in a short time (∼ ${10}^{-8\mathrm{}}$ sec) independently of the initial conditions. It is also concluded that both Ar and Xe small clusters arrive solid at the detection zone.

We present a detailed derivation of the one-particle-irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order ${\epsilon }^2$ the characteristic time exponent $z$ for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both $z$ and $\eta$ to order ${\epsilon }^2$ by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator.

A modification of the Burkhardt, Kónya, Coulson, and March (BKCM) procedure [Phys. Rev. A 24, 2906 (1981)], enabling an estimation of electron momentum density exclusively from the knowledge of an atomic electron density, has been presented. A known value of the electronic energy has been employed as a constraint in effecting this modification without loss of simplicity of the BKCM procedure. These electron momentum densities are seen to be more physical than their unmodified counterparts.