We calculate the exact lowest-order collisional contribution to the polarizability of a one-component classical plasma. Both approximate analytic and numerical solutions are obtained over a wide range of frequencies and at long wavelengths, with a full taking into account of previously ignored dynamical effects in the screening. We have established a reliable standard against which plasma approximation schemes can be compared in order to assess their accuracy in the weak-coupling limit. We compare the exact solutions with those calculated in our earlier velocity-average-approximation scheme updated to take account of dynamical effects in the screening.

Ionic recombination in a dense plasma is studied by the application of molecular dynamics and Monte Carlo simulations and through the development of transport theory. For charge densities exceeding ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the modification of the effective interaction between positive and negative ions leads to a significant reduction in the recombination rate at pressures below 1 atm. At higher pressures the rate is less sensitive to the ion density. The presence of an external field also inhibits the recombination rate. This latter effect may be especially important in rare-gas—halide discharge laser plasmas.

The Boltzmann equation for a uniform gas in an electric field is immediately soluble if we neglect the scattering in, and these solutions will be termed SOO functions (for scattering out only). They are complementary functions to the conventional $P_1$ approximation, and for isotropic scattering they satisfy all the Legendre component equations except the zero-order equation. With the taking of the Legendre components of the complete Boltzmann equation, the zero-order equation determines the ratio $\frac{f_1}{f_0}$ and no more, and shows this to be an increasing function of the energy $u$ so that $f_1$ crosses $f_0$ at $u_1$. Above $u_1$, the behavior of the Legendre expansion is defined as semidivergent. The first-order equation relates $f_2$, $f_1$, $f_0$, and as $\frac{f_2}{f_1}\to 0$ at low energies the $P_1$ approximation is valid there, whereas when $\frac{f_0}{f_1}\to 0$ at high energies a SOO function is valid there. This is illustrated by an analytical solution of a simple model in the integral-equation form of the Boltzmann equation.

A path-integral calculation of the shear viscosity of a dilute gas in a thermal gradient shows that it depends on the thermal gradient. We have taken into account terms contributing to the molecular distribution function up to third order in the collision time. We have shown that not only terms proportional to $\frac{\partial u_x}{\partial z}$ and $\frac{{\partial }^3{u}_x}{\partial z^3}$, but also terms proportional to $\frac{{\partial }^2{u}_x}{\partial z^2}$ contribute to the viscosity, where $u_x\mathrm{}\left(z\right)\mathrm{}$ is the velocity of a fluid layer and $z$ is the coordinate along an axis $z$ defined by the velocity gradient. Here we have analyzed the dependence of viscosity on the thermal gradient in the weak-thermal-gradient case. We have found that this dependence becomes quite strong as one approaches the transition regime. For gases in the continuous regime our model predicts an effect of the thermal gradient on viscosity, opposite and of a much smaller magnitude than the one reported in liquids by Gaeta, Migliardo, and Wanderlingh.

It is shown that the concept of fractal dimensionality, recently proposed by Mandelbrot, provides a useful characterization of the configurational properties of a single polymer. From numerical studies of self-avoiding walks, computer generated by Monte Carlo methods, we find that a single-chain configuration possesses a statistical self-similarity property and therefore has a well-defined fractal dimensionality. The fluctuations in fractal dimensionality measured on a single-chain configuration vanish as the number of steps increases. It is shown that renormalization-group theory provides a theoretical basis for the concept of fractal dimensionality in polymers, as well as for its relation to the end-to-end exponent $\nu$.

A model is proposed which interpolates between the diffusive picture for particles adsorbed on a surface and the full hydrodynamics of a compressible fluid. The model is the Navier-Stokes equations modified by a friction term. When the friction parameter $\sigma$ is set equal to zero, the Navier-Stokes equations obtain, but for large $\sigma$, Fick's law and diffusive behavior for the density emerge. It is found that for $\sigma$ small enough, the dynamic structure factor should display sound peaks in a certain wave-number range. It is also shown that the infrared divergences that signal the breakdown of hydrodynamics for two-dimensional fluids are regulated by the frinction term. The possibility of observing the sound modes and the nonlinear corrections to the transport coefficients is discussed.

The anisotropic conductivity of a semi-infinite free-electron solid-state plasma having a sharp boundary is calculated assuming specular electron surface scattering. Explicit expressions for the conductivity-tensor components are presented for a fully degenerate plasma with special emphasis on the near-local regime. With the assumption that the monochromatic electromagnetic plane wave penetrates the surface at an oblique angle the reflected and transmitted fields are determined. By combining Maxwell's equations and the nonlinear Boltzmann equation the energy transport in the plasma is studied. With spatial dispersion effects taken into account, the cycle-averaged Poynting vectors of the plasma, originating in the induced dc mass transport of the conduction electrons, and of the electromagnetic field are determined. A particular investigation is devoted to the case of TE-mode propagation in the near-local regime, with emphasis on (i) a discussion of the angular deviation of the plasma Poynting vector from the electromagnetic Poynting vector and (ii) a calculation of the ratio between the magnitudes of the energy flows. The "problem" of the violation of the principle of energy conservation at a sharp boundary is considered.

A simple formula is given for the energy levels of a particle bound by a Yukawa potential which is accurate at the 1% level over the entire range of $Z$ for a large range of $n$ and $l$.

The ground-state wave function of a heliumlike atom is assumed to be $\Psi =N(1+\mu \lambda r_{12})\times \exp [-\mu (\beta r_{>}+r_{<}\left)\right]$, where $r_{<},r_{>}=\mathrm{m}\mathrm{i}\mathrm{n},max(r_1,r_2)$, $r_1$ and $r_2$ are the distances of the electrons from the nucleus, and $r_{12}$ is the distance between the electrons. The parameters $\mu$, $\beta$, and $\lambda$ are determined by minimizing the energy of the system and it can be reduced to a two-parameter problem. Numerical results are presented to show the improvement for the groundstate energy from the two- or three-parameter calculations.

A procedure has been suggested to evaluate the dissociation energies of diatoms by fitting empirical potential functions to the true Rydberg-Klein-Rees (RKR) curves using the correlation coefficient as the criterion for the selection of the best fit. It has been applied to the CN radical after the testing of the method by evaluating the dissociation-energy values of some molecules for which near-accurate values are available.

The $〈r^n〉$ expectation values have been extracted from the known electron momentum distributions for hydrogen, helium, argon, and krypton atoms with the use of a semiclassical approach. These values compare fairly well with their Hartree-Fock counterparts. This procedure provides a link between the distribution of electrons in the momentum space and that in the coordinate space.

Differential and integrated cross sections for the elastic process ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ were calculated with the use of results of coupled-state calculations in the energy range 15-200 keV. Results are presented and, at 60 keV, compared favorably with preliminary experimental data. The asymptotic form of the elastic amplitude for $b\gg a_0$ (where $b$ is the impact parameter) is derived for the two cases $\lambda \ll 1$ and $\lambda \gg 1$, where $\lambda$ is the ratio of the collision duration to the orbital period. The asymptotic form for $\lambda \gg 1$ provides a useful test on the numerical accuracy of the amplitudes.

We present an analytical solution for the nonrelativistic Stark effect in hydrogen separated in parabolic coordinates. The solution is given in terms of elliptic integrals and is obtained in a first-order WKB approximation. In addition, by a suitable approximation, we extend the WKB results to autoionizing states, above the threshold barrier. A short comparison of the present results with exact numerical calculations is also presented.

Diffusive processes in one-dimensional discrete chaotic systems are considered. Drift and diffusion coefficients are calculated, which show critical behavior including logarithmic corrections. A Kubo formula for the diffusion coefficient in terms of the time-correlation function is given. Nondiffusive states may exist in certain parameter windows showing drift with broken symmetry or strict localization. Period-doubling bifurcations and states of periodic chaos describing chaotic but nondiffusive drift occur.

It is shown by explicit calculation that there are 12 bulk elastic constants and 3 surface terms in the elastic energy of biaxial nematics.

Doolittle's law relates a kinetic property such as viscosity or dielectric relaxation to the free volume. In nematogens the volume expansion is discontinuous at the nematic-isotropic transition temperature $T_c$ and nonlinear at $(T_c-20\mathrm{} \mathrm{K})\lesssim T<~T_c$. This makes a test of Doolittle's law possible.

A new secondary instability has been found for nearly parallel rolls that eliminates all wavelengths previously thought to be stable for Prandtl numbers less than 0.301 or 0.782, depending on the circumstances. There is currently no known counterpart to this instability between rigid boundaries.

The asymptotic behavior of the total number of treelike clusters (lattice trees) on the hypercubic system is investigated for $d>~4$ by the method of series expansions. Interest centers on ascertaining the critical dimension, $d_c$, at which the prefactor exponent $\theta$ attains its mean-field value. We present results for $\theta$ and for the cluster growth parameter $\lambda$ for $d=4\mathrm{} \mathrm{to} 9$. The $\lambda$ values are close to within a few percent of those found for the general animal case. Results for $\theta$ have large uncertainties in the dimensions of interest, and the mean-field value is approached very gradually with $d$, so that the possibility of a lower value for $d_c$ cannot be completely discarded. Nevertheless, the available evidence suggests that $d_c=8\mathrm{}$ for lattice trees. This supports the findings of Lubensky and Isaacson in their recent work on lattice animals and dilute branched polymers.

The absolute values of the ground-state ($n=1\mathrm{}$) levels of positronium and of $\Delta E(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{})$ are given through order ${\alpha }^3$ Ry.

Arguments are given in support of a remark made by Mandel, that Maxwell's equations are not consistent with the multipolar form of the Hamiltonian for the electromagnetic field interacting with nonrelativistic electrons.