We derive and discuss the dispersion relation and polarization of waves in a one-component, cold, homogeneous plasma moving at arbitrary speed. The relevance to wave propagation (both low frequency and radio) through the pulsar magnetosphere is briefly discussed.

By observing the orientation dependence of the recoil-free fraction for three Sn-bearing solute molecules, we have determined the lattice contribution of a smectic $B$ glass (at 77 °K) to the anisotropy of the nuclear vibrational amplitude for the Sn-119 nucleus. The measured anisotropy depends on the solute shape and length and is explained in terms of the layered smectic structure and the difference between the character of the central core and the end-chain regions of the host liquid-crystal molecules. The resonant line position for the solute, 4-trimethyl-tin-benzylidene-4′-$n$-butylaniline (Sn-BBA), was found to be dependent on the angle ($\theta$) between the preferred direction of the aligned liquid-crystalline glass and the Mössbauer $\gamma$ beam. We interpret this in terms of an unresolved quadrupole splitting ($\Delta E_Q$) for this molecule. The line-shift data are shown to yield the sign of $V_{\mathrm{zz}}$ and the magnitude of $\Delta E_Q$ for the Sn-BBA molecule.

With the use of expressions for the nonlinear current density derived previously, the generation of the third harmonic in a collisional plasma by a Gaussian electromagnetic beam has been studied when the power of the beam exceeds the critical power for self-focusing. The self-focusing is caused by the nonuniform heating and redistribution of electrons. It is seen that the self-focusing of the main beam enhances the power of harmonic output by about three orders of magnitude in a typical case in the paraxial-ray approximation. The treatment is applicable after a time on the order of the energy relaxation time [$\sim {\left(\frac{2m\nu }{M}\right)}^{-1\mathrm{}}$].

Results are reported of measurements of the long-range correlation length $\xi$, made along the critical isochore. The measurements were made using two different light-scattering techniques and cover the temperature range $4.0\times {10}^{-6\mathrm{}}\le \frac{T}{T_c}-1\mathrm{}\le 3.1\times {10}^{-2\mathrm{}}$. All of the results are accurately fit by the expression $\xi =2.016\mathrm{}{(\frac{T}{T_c}-1)}^{-0.621\mathrm{}}$ Å. Measurements of the isothermal compressibility ${\kappa }_T$, in the temperature range $1.5\times {10}^{-4\mathrm{}}\le \frac{T}{T_c}-1\mathrm{}\le 3.1\times {10}^{-2\mathrm{}}$ are also reported and yield the result ${\kappa }_T=1.327\mathrm{}\times {10}^{-9\mathrm{}}{(\frac{T}{T_c}-1)}^{-1.223\mathrm{}}$ ${\mathrm{cm}}^2$/dyn. From these measurements the value of the exponent $\eta$ may be deduced as 0.03 ± 0.03. The measured values of $\xi$ are used to interpret existing measurements of the Rayleigh linewidth in terms of mode-mode coupling theories. Experimental results are also presented which indicate that stirring may be used to eliminate gravitationally induced density gradients near the critical point without affecting the fluid's critical properties.

The number-density fluctuation spectrum, $S_n(\overrightarrow{\mathrm{K}}, \omega )$, of xenon has been studied in the dilute-gas limit. Spectra of He-Ne laser light scattered through an angle of 10.58° at room temperature were measured for pressures ranging from 0.02 to 0.6 atm. Over this range $S_n(\overrightarrow{\mathrm{K}}, \omega )$ evolves from the Gaussian kinetic form to three peaked hydrodynamic form. Measured spectra were used to evaluate various kinetic and hydrodynamic calculations of $S_n(\overrightarrow{\mathrm{K}}, \omega )$ through this transition. Spectra obtained from the Boltzmann equation using the Gross-Jackson kinetic modeling procedure, for both Maxwell and hard-sphere intermolecular potentials, are in excellent agreement with the measurements. Among the hydrodynamic theories tested only the generalized hydrodynamics of Selwyn and Oppenheim satisfactorily provides the initial nonhydrodynamic corrections to the Navier-Stokes equations.

A molecular theory of two-dimensional liquid crystals is developed. Taking short-range correlations explicitly into account, we show that in addition to isotropic and nematic phases, solutions representing smectic and crystalline phases can also be constructed as the number density increases beyond certain critical values. Relevant order parameters defined in a canonical ensemble are obtained as functions of density at fixed temperature.

A dynamical equation for simple classical liquids is presented which is obtained by a systematic approximation for the memory function of the conventional, equilibrium-averaged, phase-space correlation function. This "kinetic" equation is non-Markovian and spatially nonlocal. It agrees with the known limiting behavior at high and low frequencies $\omega$ and wave vectors $\overrightarrow{\mathrm{k}}$ even for dense liquids. For intermediate $k$ and $\omega$, our equation represents an explicit interpolation model from which virtually all measurable dynamical properties of the simple one-component fluid can be obtained. This equation can be solved analytically. As an example, the dynamical structure factor $S_{\mathrm{nn}}(k, \omega )$ for liquid argon near its triple point was calculated. Our results are in excellent agreement with both coherent-neutron-scattering experiments (for $k=1-4\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$) and computer-dynamics results (for $k<\mathrm{}1\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$). We want to emphasize that no adjustable parameters are introduced. We believe that this is the first kinetic theory which gives satisfactory results for $S_{\mathrm{nn}}(k, \omega )$ for the full range $k$, $\omega$ for which data are available.

The x-ray spectra produced by the bombardment of thick targets with monoenergetic electrons between 10 and 30 keV have been determined as a function of the incident and emission angles. Spectra have been obtained for Al, Cu, Mo, and W using a Si(Li) detector. The electron current absorbed in the target was measured and corrected for backscattering, allowing a determination of absolute x-ray emission. A modified least-squares procedure was used to represent the spectra as analytical functions while taking into account the efficiency and resolution of the detector. The spectra show the effects of both target absorption and angular distribution of the thin-target bremsstrahlung production. Agreement with the Kramers formula is only moderate.

The 180° rule restricting the disposition of phase boundaries at triple points is generalized to a class of triple points involving transitions of higher than first order. At the triple point considered, two Ehrenfest second-order transition lines meet a first-order line. The recently discovered "polycritical point" in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is an example of such a triple point. It is shown, subject to certain explicit assumptions, that none of the three phases may occupy more than 180° of angle at the triple point. Our assumptions are weaker and our results stronger and more general than those in a recent treatment of the rule by Leggett. We show that each of our assumptions is essential: If any one is relaxed, a counterexample to the 180° rule can be exhibited.

Further results of a "molecular dynamics" simulation of liquid nitrogen are described. These results have been obtained under triple-point conditions. A molecular-pair distribution function which depends on the radial distance, plus three angular variables, has been computed. Partial averages of this function are depicted. These functions show an angular structure up to about 9 Å, but are not sharply peaked. It seems that the orientation of a molecule is more influenced by the positions of its neighbors than by their orientations. The dynamics of the orientational motion has also been further studied. The coupling between the environment and the orientational behavior of a given molecule has been examined through both cross-correlation functions and selectively sampled correlation functions. These results are the following: (i) An initial high rotational temperature of the molecule facilitates its reorientation. (ii) An initial fluctuation of the local density affects the reorientational behavior of the molecule only if this fluctuation persists for a sufficiently long time. (iii) By contrast, there is little coupling between the behavior of a molecule and the rotational temperature of its interacting partners. (iv) Individual samples of the motion indicate that a molecule shares its time about equally between periods of orientational trapping, with erratic librational motion, and periods of continuous nonuniform rotation.

The molecular dynamics method is used to simulate a fcc solid of 500 nitrogen molecules interacting by an atom-atom potential. Translational and rotational order parameters are computed, showing the existence of a crystal plastic phase not far from the coexistence line of the $\alpha$ and $\beta$ phases. Molecular pair distribution functions are calculated, and it is shown that thermodynamics quantities cannot be given with precision by the molecular dynamics method. Correlation functions are described. A link is established between the correlation functions and the language of phonons. The spectrum of the phonon frequencies is computed for six thermodynamic states, and the domain of validity of the harmonic approximation is discussed.

The short- and long-time behavior of the velocity-correlation functions characteristic for the coefficient of self-diffusion, and the kinetic parts of the coefficient of viscosity, and thermal conductivity, respectively, are computed approximately as a function of the density for a gas of hard disks or hard spheres on the basis of kinetic theory. The results obtained here are a generalization to higher densities of those obtained in an earlier paper, and reduce to them in the low-density limit. The density dependence is obtained by taking into account a larger number of dynamical events than previously considered. It is found that for short times the correlation functions decay exponentially, but that for longer times $t$, the correlation functions decay $\sim {\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(n\right)\mathrm{}{\left(\frac{t}{t_0}\right)}^{\frac{d}{2}}$ where $n$ is the density, $t_0$ the mean free time between collisions, and $d$ is the number of dimensions. The coefficient ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(n\right)\mathrm{}$ is determined by the transport coefficients of the Enskog theory for a dense gas of hard disks or hard spheres and is in very good agreement with existing computer experiments.

Because mixtures containing arbitrary ratios of ortho ($J=1\mathrm{}$) and para ($J=0\mathrm{}$) concentrations can be prepared, the condensed phases of hydrogen afford a unique opportunity to study interactions between isotropic and anisotropic molecules which are chemically identical. Detailed measurements are reported here of the rotational Raman spectra in the liquid and solid phases of ortho-para hydrogen mixtures, with para concentrations between 25% and 96% at temperatures between 10 and 23°K. Changes in the configuration and dynamics of the molecular environment with temperature and ortho concentration are clearly reflected in the rotational Raman line shapes. Logarithmically recorded spectra, covering an intensity dynamic range of typically ${10}^4$, reveal two relatively independent types of interaction which respectively govern the near (<30 ${\mathrm{cm}}^{-1\mathrm{}}$) and far (>30 ${\mathrm{cm}}^{-1\mathrm{}}$) wings. Quantum calculations of the low-frequency mechanism, electric quadrupole-quadrupole molecular pair interactions, are presented. They are found to produce values for the second frequency moments for all three ($J=1\mathrm{}\to 1$, $J=1\mathrm{}\to 3$, and $J=0\mathrm{}\to 2$) rotational transitions which agree well both in absolute magnitude and in concentration dependence with experimental observations. The far wings in the solid spectra consist of phonon sidebands whose structure is in good agreement with the phonon density of states previously observed by neutron scattering. In the liquid mixtures the far-wing line shapes are insensitive to temperature or concentration variation and are very similar to the solid wings.

Ionic conduction in the nematic phase of $p-n$-nonyloxybenzoic acid can be a maximum in a direction parallel (positive conductivity anisotropy) or perpendicular (negative anisotropy) to the nematic director. The presence of acetone can change a sample which exhibits a positive conductivity anisotropy to negative anisotropy. Experimental evidence indicates that there are many other dopants that can change the sign of anisotropy. It is suggested that the dopant may disrupt one of the hydrogen bonds of the dimer in some of the molecules, which makes it easier for trimers and higher polymers to form. This process should favor a smecticlike structure.

A previous derivation of the generalized Auger transition for inner-shell multiplets is shown to be incorrect. The previous derivation was based on deducing a coupling scheme from $6-j$ symbols in the transition-rate expression, then transforming the coupling coefficients. It was expected that the transformed transition rate would be correct up to a phase factor. It is shown here that this expectation is incorrect. The transformed transition-rate expression is structurally incorrect (i.e., incorrect irrespective of phase factor). Correct expressions are obtained by direct manipulation of $6-j$ and $9-j$ symbols. It is shown that the correct expression can be found using the coupling transformation provided a modified matrix element expression is used.

The multiconfiguration-variation approach to the problem of the hyperfine pressure shift for interacting atoms is analyzed with respect to some recent criticisms.

The recently calculated decay rate of orthopositronium differs with the experimental value by 2½ standard deviations. This communication reports a 100-fold improvement in the numerical error estimate for the double-vertex diagram contribution to the decay rate. This improvement reduces the numerical error estimate of the previously calculated decay rate of orthopositronium by 20%. This improvement of the double-vertex diagrams alone does not bring the experimental and calculated values into good agreement; however, the discrepancy is reduced.

The localization of atoms in solids leads, in principle, to changes in the electron distribution compared with the free-atom state. The effect of such changes on the calculation of the He-ion stopping cross section $S_e$ in solids has been investigated for an energy range 0.4-4.0 MeV. It is found that at low energies with free-atom wave functions, a large part of the calculated $S_e$ arises from regions at large distances from the target atom where the electron density is low compared to that in solids. The experimentally observed oscillations in $S_e$ as a function of target atomic number, which have been calculated from stopping-power theory by other authors, are also obtained in the present work with simple modifications of the electron density distributions. However, the detail of the structure of the stopping curves is altered. In addition, the use of an effective charge to account for electron capture by the He ion at low velocities, without a corresponding modification of the basic stopping-power theory to take into account the departure from point-charge behavior, leads to discrepancies from the experimental data.

Seiler, Oberoi, and Callaway first located resonances in the positron-hydrogen system below the $n=2\mathrm{}$ inelastic threshold, using the algebraic close-coupling method without including the open positronium channel. Several other calculations including both open channels have failed to find any resonances. In an attempt to clarify the situation, a calculation has been performed which is an extension of the work of Seiler, Oberoi, and Callaway. A wave function including the $1s$, $2s$, and $2p$ eigenstates of hydrogen and the $\overline{1s}$ ground state of positronium was used in a calculation that is a simplification of the usual close-coupling technique and that resembles the optical-potential method. In this approximation it is found that the lowest resonance of Seiler, Oberoi, and Callaway is destroyed by opening the $\overline{1s}$ channel. It is concluded that any resonances which may occur in this system must lie closer to the $n=2\mathrm{}$ threshold than do the corresponding electron-hydrogen resonances.