Deviations from Kleinman symmetry for the second hyperpolarizability tensors of some simple atoms and molecules (He, Ar, Kr, Xe, ${\mathrm{CH}}_4$, ${\mathrm{CF}}_4$, ${\mathrm{SF}}_6$, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{CO}}_2$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, ${\mathrm{CHF}}_3$, and ${\mathrm{C}}_2$${\mathrm{H}}_4$) have been measured down to the 0.1% level of accuracy at several frequencies far below the first strong electronic resonance, by means of dc-electric-field–induced second-harmonic generation (ESHG). The results of the experiment are discussed within the framework of several models. The observed Kleinman-symmetry deviations are small compared to the electronic dispersion, and appear to be dominated by electronic rather than vibrational contributions. However, vibrations are shown to play a role in the case of ${\mathrm{H}}_2$, and the results observed for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ differ significantly. The observed deviation for He is relatively large and should provide a sensitive test of ab initio calculations.

We use techniques of singular perturbation theory to investigate the scattering of nonrelativistic charged particles by a standing light wave (Kapitza-Dirac scattering). Unlike previous treatments, we give explicit results for the effects of the time-dependent part of the field. For low field intensity or low particle energy, we show that the leading-order effects can be found from an averaged equation, and we compute corrections. For the strong fields that can be produced by modern lasers and/or high particle energies, we show that the time dependence of the potential leads to focusing. Our methods can be applied to other problems with time-periodic potentials.

A method for exact solution of the stationary holographic degenerate four-wave mixing in reflection geometry in photorefractive media is presented. The effects of pump depletion and light absorption in the nonlinear dynamic medium are rigorously taken into account. Numerical steps in the procedure are reduced to the solution of one simple nonlinear first-order differential equation, or are absent altogether when the equation is linearized, or for the case of no absorption. The method of solution is applicable to other wave-mixing geometries as well.

The dynamical behavior of a two-level system in an intense frequency-modulated field is obtained without recourse to the weak-modulation assumption. Solutions to the optical Bloch equations are expressed in terms of continued fractions involving 2×2 matrices. Such matrix-continued fractions are numerically evaluated to obtain a wide variety of absorption and fluorescence spectra in frequency-modulated fields. Results in various special cases involving combinations of weak fields, weak modulation, strong modulation, and strong fields are given. Analytical results for weak fields but with an arbitrary degree of modulation are also presented. The spectra exhibit additional resonances for strong modulation. The main resonance shifts and broadens considerably due to strong modulation and saturation effects.

Apertured cross-correlation functions (ACCF’s) are proposed and demonstrated to be useful constructs in the study of local structure in disordered systems. A formal expression for the apertured intensity cross-correlation function is obtained in terms of multiparticle ACCF’s. This expression is examined in several limits and is seen to be related to a variety of correlation functions which can be studied via present or proposed intensity cross-correlation experiments. A two-dimensional hard-disk system is investigated by computer simulation to demonstrate the use of ACCF’s. It is found that three- and four-body correlations must, in general, be included to give accurate representation of the apertured intensity cross-correlation function. A harmonic-model calculation is reviewed, and possible uses of the cross-correlation technique are discussed.

Calculated values of the stopping power of ions in superheated liquid have been used in predicting the minimum neutron energy that will nucleate vapor bubbles in a superheated liquid. Such predictions are useful in understanding the behavior of a new class of neutron detectors based on superheated halocarbon or hydrocarbon drops suspended in aqueous gel.

The finite-size effect is studied in the Kasteleyn model of dimers on the brick lattice. This model is isomorphic to an anisotropic domain-wall model. Asymptotic analysis of the exact Pfaffian solution for the specific heat establishes that finite-size-scaling theory is valid near the critical point of this model. The finite-size-scaling function is a function of a scaled temperature variable τ and a shape factor scrr=$N^2$/M, where 2N is the number of lattice points in the direction perpendicular to the preferred axis for the domain walls and 2M is the number of lattice points parallel to the preferred axis. The scaled temperature variable τ is given by ${\mathrm{MN}}^2$t/(M+$N^2$), where t is the reduced temperature. As a function of τ the scaling function scrP(τ,scrr) is a sequence of δ functions in the limit scrr=0 and a smooth single-peaked function in the limit scrr=∞. In the latter case the specific heat per lattice site can be written as &,∞), where α is the bulk specific-heat exponent with the known value of (1/2) and ${\nu }_M$ is found to have the value of 1. In the case scrr=0, the specific heat per lattice site can be written in an equivalent form by replacing M by N and ${\nu }_m$ by ${\nu }_N$ which takes the value ${\nu }_N$=(1/2). According to finite-size-scaling theory ${\nu }_M$ and ${\nu }_N$ may be interpreted to be the critical exponents ${\nu }_{\mathrm{y}}$ and ${\nu }_{\mathrm{x}}$, respectively, of the divergent length scales in the two principal directions. Our exact values of ${\nu }_m$ and ${\nu }_N$ are in agreement with the values of ${\nu }_{\mathrm{y}}$ and ${\nu }_{\mathrm{x}}$ predicted for general anisotropic domain-wall models.

Molecular-lattice-theory results for rigid cores having partially-flexible tails reveal that it is not necessary to invoke dipolar forces to have stable smectic-$A_1$, smectic-$A_d$, and low-temperature nematic (including reentrant-nematic) liquid-crystal phases. However, dipolar forces increase the stability of these phases in systems with Lennard-Jones interactions. Dipolar forces also shift the temperature ranges of these phases closer to ambient, thus making them easier to discover and observe experimentally.

Energy transport and photon emission are theoretically investigated in laser-heated foil targets at medium laser irradiance, with use of a numerical model which treats hydrodynamics, ionization, and radiation in a completely self-consistent manner. The radiation model is a detailed, collisional radiative scheme which calculates explicitly the line, recombination, and bremsstrahlung emission in concert with a probabilistic photon transport method. The role of radiation transport in thin-foil targets was studied as a function of target thickness, target-Z, laser intensity, laser wavelength, and laser pulse width. Significant differences were found in the radiation preheat, x-ray conversion efficiency, and broadband frontside emission spectrum, as these parameters were varied. It is also demonstrated that photon emission, absorption, and transport play an important role in the accurate calculation of heat penetration, plasma temperature and density gradients, and ablation-surface–to–critical-surface separation distance, and that radiation can constitute a major energy-loss mechanism even in a low-Z target such as carbon.

We investigate the dynamical behavior of a classical harmonic-oscillator chain with periodic and fixed-end boundary conditions. The displacement and velocity autocorrelation functions are obtained by a recurrence relations method. We show that the finite diffusion constant and the divergence in the mean-square displacement of a tagged oscillator arise from the zero-frequency mode present in the chain with periodic boundary conditions. For the chain with fixed-end boundary conditions, the diffusion constant vanishes and there is no divergence in the mean-square displacement. These results should hold for the harmonic-oscillator model in higher dimensions.

The product of the rms fluctuations of an extensive thermodynamic variable with that of its conjugate intensive thermodynamic variable is bounded below by k in the entropy representation and by kT in the energy representation. The uncertainty relations of statistical mechanics are equivalent to the stability relations of equilibrium thermodynamics.

Relaxation times in chlorine near its liquid-vapor critical point have been studied after thermal and chemical perturbations. The chemical perturbation was by photolysis with ultraviolet light, to dissociate the chlorine molecules. The chemical relaxation was very fast, contrary to earlier reports. The relaxation after a thermal perturbation was very slow (${10}^3$ s). The thermal relaxation time near the critical point behaved as τ=${\mathrm{Ct}}^{\mathrm{-}0.94\pm 0.10}$ [where t≡(T-$T_c$)/$T_c$ and $T_c$ is the transition temperature], in contrast to the expectation that τ would be determined by the thermal diffusivity and have a critical exponent (-0.63).

The density and parallel temperature of an electron beam passing through a magnetic guide field and a linear wiggler are determined as functions of distance from the anode. Starting with a given beam emittance and phase-space distribution at the anode, single-particle orbits are employed to propagate the beam along the drift tube. Finite-gyro-orbit effects induce substantial modulation in density. Additionally, the evolution of an initial spread in the parallel speed of the electrons is sensitively dependent on the wiggler strength and contributes to further density fluctuation. The beam’s parallel temperature, a critical factor in determining laser efficiency and gain, is found to increase significantly when the wiggler strength is raised.

In this paper we study the topological entropy and the metric entropy of one-dimensional maps. Let T(x,s) be a map with a parameter s. Introduced in the paper is a class of maps defined over a special set of parameter values. These maps are characterized by possession of generating partitions and will be referred to as generating maps. They have some very attractive properties. According to their topological properties and with the aid of kneading sequences, the generating maps may be classified in a systematic way and their topological entropy values can be determined readily by using a theorem on kneading determinant by Milnor and Thurston. The generating partitions also allow us to compute the metric entropy of the maps with relative ease. After some general discussions this method of entropy evaluation is applied to the tent map, the logistic map, the spike map, and a discontinuous map. For the logistic map, the topological entropy values for a set of 306 generating maps and the metric entropy values for a set of 244 generating maps have been computed. The data show that the topological entropy never decreases with an increasing s, and that the computed metric entropy of each map agrees with the Liapunov number of the map. From the results given in this paper one sees that the generating maps can play a significant role in delineating the ergodic properties of maps.

We have analyzed, in the context of a boundary-layer model, the problem of pattern selection in dendritic growth in a situation where impurities are present in the undercooled liquid. We find that the tip-velocity selection criterion that has been proposed recently for the geometrical model and the boundary-layer model of a pure substance can be extended, in a nontrivial way, to this more complex situation where two coupled diffusion fields (temperature and solute) determine the interface dynamics. Our model predicts a sharp enhancement of tip velocity in good qualitative agreement with experiment. This agreement is consistent with the conjecture that a solvability condition can be used to determine the operating point of the dendrite in the full nonlocal problem.

Effective rate coefficients for dielectronic recombination and ionization were derived for argon ions from the time-histories of lines emitted by the respective ions in various transient plasmas. They were produced in a theta-pinch discharge at different hydrogen filling pressures; argon was added as small admixture.

The motion of a charged particle in a modulated electrostatic wave is studied with special emphasis on a standing wave. It is shown numerically that the trajectories of particles which make transitions from being trapped to untrapped are always chaotic on a sufficiently long time scale, while the trajectories of particles which do not make transitions are regular. It is shown how to calculate the adiabatic invariant for this system using Lie perturbation techniques. Finally, the time scale on which large-scale chaos is visible is determined by calculating Lyapunov exponents.

Densities of C, O, and Si impurities during the steady-state portion of Alcator-C discharges have been computed from spectroscopic measurements of the absolute brightnesses of visible and uv emission lines in combination with a one-dimensional transport calculation which models the charge-state and emissivity profiles. Profiles of all the charge states of a particular impurity were calculated by utilizing independent measurements of plasma density and temperature and by solving the coupled system of transport and rate equations connecting the ionization states. These profiles were then used to calculate emissivity profiles by solving the matrix equation relating the level populations through collisional excitation, collisional deexcitation, spontaneous emission, inner-shell ionization, and cascades from upper levels. Three different types of limiters (molybdenum, graphite, and SiC-coated graphite) have been used on the Alcator-C. It was observed that the principal impurities in the plasma, under most conditions, were determined by the type of limiter material being used. However, the source of the impurities could be either the wall or the limiters, since it has been shown that the wall becomes coated with limiter material. A significant influx of impurities directly from the limiters was often seen during the application of lower-hybrid-frequency rf power to the plasma.

Kβ x-ray lines from partially M-shell-ionized ions of titanium through nickel which are produced in vacuum-spark plasmas have been observed systematically for the first time, using a high-resolution curved-crystal spectrometer. Each Kβ line is clearly separated into its corresponding charge state. As a result, it is possible to measure the Kβ-type transition energies of the M-shell-ionized ions. The transition energies accurately determined are compared with those calculated for iron ions, and the agreement is excellent except for ions having some additional 3d outer-shell electrons or 3s inner-shell vacancies. The square root of the Kβ transition frequency is expressed as a linear function of the nuclear charge for isoelectronic sequences. The effective nuclear charges have been also determined for each Kβ transition. The 3p electrons do not affect the effective nuclear charges.

Scattering theories for the time-independent Schrödinger equation and for the plasma wave equation in $R^3$ are compared. If V-Δ has no point eigenvalues, the relevant quantities in both theories are simply related by Fourier transformation, but if V-Δ has eigenvalues, then retarded pulse solutions of the plasma wave equation are shown to grow exponentially with time and no physically meaningful scattering theory appears possible for that equation.