An anomalous effect owing to electric fields has been found in the nematic phase of a liquid crystal exhibiting positive dielectric and negative conductivity anisotropies. The preferred direction for the long axes of the molecules is perpendicular to a dc or very low-frequency ac electric field but parallel to a field for frequencies of a few thousand Hz. A sizable change in the average value of the dielectric loss was observed at the nematic-liquid transition temperature. This is explained by assuming that the nematic phase, which is believed to be a doubly-hydrogen-bonded dimer, contains a small percentage of monomer or dimer with one hydrogen bond broken. A small change in the percentage of normal dimer at the transition temperature could account for the change in loss. The effect of magnetic fields up to 68 000 G on the molecular alignment in the smectic $C$ phase is discussed.

Average-electron-density measurements in a neon discharge afterglow have been made using a T${\mathrm{M}}_{010}$ microwave cavity. The quartz and Pyrex tubes have a 2.18-cm inner diameter and are 90 cm long (${\Lambda }^2=0.206\mathrm{}$ ${\mathrm{cm}}^2$) with hollow nickel and molybdenum cylindrical electrodes. The gas pressure is 0.5 Torr at 300°K for the majority of our measurements, although some results are given at 1.5 and 5.0 Torr. Radiation-temperature measurements are made under identical experimental conditions using a 3.0-GHz microwave radiometer. Three ambient gas temperatures are used: 300, 500, and 673°K. The density decay measurements give an indirect indication of the supercooling of the electrons. The radiation measurements clearly show that the electron temperature falls below the ambient temperature of the gas and the discharge tube. A simple theory for the density and temperature decay compares reasonably well with the measured results.

The behavior of interacting electrons is dominated by the Coulomb repulsion in the limit of zero interparticle separation. Hence, in this limit the derivative of the two-particle correlation function is equal to the two-particle correlation function itself divided by the Bohr radius. Because correlation functions can be obtained from linear-response functions, the relation between the correlation function and its derivative can be used as a criterion for the validity of approximate linear-response functions. Some of the more familiar dielectric functions and spin susceptibilities are discussed in this context. For these response functions it is shown that the electric and magnetic response should approach the same ($q\to \infty$) asymptotic limit.

The ground-state energy of the $``X_g=\frac{1}{3}"$ and $``X_g=\frac{1}{4}"$ superlattice states of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ adsorbed on graphite is calculated via a variational wave function incorporating Jastrow factors. The single-particle factors in the wave function are constructed as an expansion in an orthogonal basis set and the Jastrow terms incorporate only lateral correlations. The ground-state energy is calculated using the Nosanow cluster expansion. The stability of the superlattice states is examined and both are found to be unstable at zero pressure. Estimates of the stability of these states to "melting" indicate the $``X_g=\frac{1}{3}"$ state is stable and the $``X_g=\frac{1}{4}"$ state is less stable or possibly unstable. The sensitivity of the results to reasonable substrate-induced many-body corrections to the adatom-adatom potential is found to be significant.

A quasilattice model for liquid water is formulated which in first approximation is based on the ice VII and ice $\mathrm{I}c$ structures. Values of the work required to create a molecular vacancy are computed from the observed density and scaled particle theory of liquids. The isothermal compressibility of water is computed and is in good agreement with experiment. A modified Stokes-Einstein relation for the nuclear relaxation time is shown to give good agreement with recent deuteron relaxation data.

The self-consistent harmonic theory of lattice dynamics for a crystal whose interatomic potential includes a hard core is developed in systematic fashion by application of point-transformation methods. In order to show the essential structure of the theory without undue complication, the many-body point transform is truncated by the assumption of pairwise additivity. A flexible class of healing functions is introduced. The variational energy in terms of the harmonic-pair-density distribution is then derived, followed by the development of the self-consistent dynamical matrix. The latter is found to be of much more complicated structure than that met in the usual self-consistent harmonic theory, and a discussion of that structure is given. A comparison of the present theory with some aspects of various other methods of handling hard-core quantum crystals is given.

A measurement is presented of the anisotropic liquid-structure factor of $p-n$-octyloxybenzylidene-$p^{\prime }$-toluidine in the nematic phase using monochromatic Cu $K\alpha$ radiation. This material has a smectic $A$ phase at lower temperature and exhibits strong pretransition scattering in the nematic phase. The experimental results are used to test the Landau theory of the smectic $A$ phase recently proposed by McMillan and by de Gennes. The experimental peak in the structure factor is approximately Lorentizian in two dimensions and a Lorentzian fit determines the Landau-theory parameters versus temperature. The small deviations from a Lorentzian may be due to higher-order terms in the Landau theory or to thermal fluctuations of the nematic director.

We have investigated the phase behavior that results when an infinitely weak and long-range attractive potential is added to the following hard-core lattice gases: the triangular-lattice gases with exclusions up to first, second, third, and fourth neighbors, and the square-lattice gases with exclusions up to first, second and third neighbors. Three of the systems considered have realistic (i.e., argonlike) phase diagrams, complete with a first-order solid-fluid phase change, a first-order liquid-gas phase change (with a critical point), and a triple point. Three other systems have a first-order solid-fluid phase change. The remaining system has a first-order liquid-gas phase change along with a higher-order transition that is not of the typical solid-fluid type. We find that when the hard-core system has a second-order or first-order phase change to begin with, the addition of the attractive potential spreads the transition out into a first-order phase change with temperature-dependent coexistence densities that bracket the density at which (or density interval over which) the original transition takes place. We also find that the presence or absence of realistic phase behavior for the combined system appears to be dependent upon the shape of the hard core as well as its range.

A molecular-dynamics "experiment" was performed for a system of 864 particles interacting through a Lennard-Jones potential. The state considered was in the immediate neighborhood of the triple point. The total duration of the "experiment" was quite large: It corresponds to ${10}^{-9\mathrm{}}$ sec in the case of argon. Transport coefficients were calculated using the standard Kubo formulas. They are compared with the prediction of a simple hard-sphere model. It is shown that, as in the case of the hard-sphere fluid near solidification, the Kubo-correlation function relative to the shear viscosity presents a tail extending at large time. The inclusion of this tail turns out to be essential in explaining the transverse-correlation function and the dynamical-structure factor, which shows, for the lowest wave vectors accessible in this study, a characteristic Brillouin doublet structure. Using the hydrodynamical model of Zwanzig and Bixon, it is shown that the introduction of the long-time tail in the Kubo-correlation function for the viscosity explains the negative plateau of the velocity-autocorrelation function observed near the triple point by Rahman and others.

We study the phase-space density-correlation function $S(\overrightarrow{\mathrm{r}}t; \overrightarrow{\mathrm{p}}{\overrightarrow{\mathrm{p}}}^{\prime })$ for a dense classical gas with repulsive interaction using the language of memory functions. We derive the kinetic equation for $S$ which is valid at all wavelengths and frequencies but limited to second order in the density (triple collisions). This model equation is, on the one hand, an extension of the earlier work of Mazenko to the next order in density and, on the other hand, an extension to arbitrary wavelengths and frequencies of some suggested generalizations of the linearized Boltzmann equation. The memory function for this kinetic equation is shown to be compatible with symmetry properties, sum rules, and the conservation laws. As an illustration of the hydrodynamics, we calculate the shear viscosity and show that the term linear in density agrees with an earlier calculation by Kawasaki and Oppenheim. We also give the analogous kinetic equation for the single-particle correlation function.

Continuous-wave NMR was used to study the temperature dependence of the static nuclear magnetic susceptibility of solid ${\mathrm{He}}^3$ and solid mixtures of ${\mathrm{He}}^4$ in ${\mathrm{He}}^3$. Measurements were performed in the purest sample (3.7×${10}^{-5\mathrm{}}$ ${\mathrm{He}}^4$ in ${\mathrm{He}}^3$) at four molar volumes (21, 22, 23, and 24 ${\mathrm{cm}}^3$/mole) in the bcc phase, and at several ${\mathrm{He}}^4$ concentrations ranging from 3.7×${10}^{-5\mathrm{}}$ to 2.0×${10}^{-2\mathrm{}}$ at 21 and 23 ${\mathrm{cm}}^3$/mole. The temperature range of the measurements was from 0.95 to 0.32 K. The data were fitted to a Curie-Weiss law with an rms deviation from best fit of less than ${10}^{-3\mathrm{}}$ and best values of the Weiss constant $\theta$ were obtained. Susceptibilities and temperatures were measured to better than 0.1%. The temperature scale was based upon the susceptibility of the purest, most-dense sample. The desired accuracy in the susceptibility measurements necessitated a new method of data reduction. The accuracy in the extracted values of $\theta$ was better than ±1 mk. The values of $\theta$ in the purest sample (-0.24±0.82 mK at 21 ${\mathrm{cm}}^3$/mole, -1.03±1.06 mK at 22 ${\mathrm{cm}}^3$/mole, -1.49±0.27 mK at 23 ${\mathrm{cm}}^3$/mole, and -3.07±0.78 mK at 24 ${\mathrm{cm}}^3$/mole) agreed within experimental uncertainty with those of earlier workers, operating at lower temperatures. They provide a high-temperature check on those measurements. The measured effects on $\theta$ of the ${\mathrm{He}}^4$ impurity are consistent with the work of Richards and Homer, but the measurements show an improved accuracy. The data, as a function of $x$, the atomic fraction of ${\mathrm{He}}^4$, have been fitted to the equation $\theta \mathrm{}\left(x\right)={\theta }_0\mathrm{}(1+Kx)\mathrm{}$. Values of $K$ of -430±450 and -19±10 were obtained at 21 and 23 ${\mathrm{cm}}^3$/mole, respectively.

The order-disorder theory of a classical lattice model is used to obtain both the solid-solid phase transition and fluid-solid phase transition in a single system. In this model, the range of the interatomic potential is extended up to the fourth-neighbor distance. If the potential is suitably chosen, it is shown that the phase transitions between the bcc solid and fcc solid, between the bcc solid and fluid, and between the fcc solid and fluid occur within the Bragg-Williams approximation. The results are shown by the phase diagrams.

Two descriptions of light passed through a random medium (the turbulent atmosphere), as recently proposed by Diament and Teich and by Tatarski, are derived from a unified approach based on the coherent-state technique. The photon counting distributions for both descriptions are numerically compared for special states of the field (chaotic and coherent radiation and their superposition); it is found that these distributions lie very close to each other for non-vacuum-states while they precisely coincide for the Fock states.

Continuum theory is used to calculate the molecular alignment and the elastic deformation energy in a nematic layer containing a circular-loop thread. In agreement with experiment, planar solutions are found, with the thread being the boundary between regions of different pitch. It is shown that threads in nematics and Grandjean lines in cholesterics are equivalent-alignment structures and that a thread located in the midplane of the layer is in equilibrium with respect to displacements normal to the layer. From an analogy to the case of magnetic fields general conclusions are drawn as to the alignment near threads of general shape outside the core. A model of a nonsingular core is given for threads of type $\mathrm{}\left|s\right|=1\mathrm{}$ and the alignment near point singularities is calculated.

It is shown that the scattering of neutrons at large momentum transfers can provide information on the detailed shape of the distribution of atomic kinetic energies. An expansion of the kinetic-energy distribution function $n\left(E\right)\mathrm{}$ leads to a corresponding expansion of the large -$k$ limit of the scattering function $S(\overrightarrow{\mathrm{k}}, \omega )$. Deviations of the latter from a Gaussian shape reflect deviations of $n\left(E\right)\mathrm{}$ from a Maxwellian. Corrections for finite $k$ are also derived. An application to the scattering data of Harling for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ leads to estimates of the condensate fraction and average kinetic energy for liquid temperatures in the range 1.27 to 4.2 °K.

Electrons injected into structurally disordered materials may occupy free-electron-like states in a conduction band, band-tail states, some of which will be nondiffusing and are thus localized in the Anderson sense, and, finally, self-trapped states. Eggarter has recently described the first two types of states with specific application to He gas. In the present work, the self-trapped states are discussed. Specific calculations are carried out for He, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and Ne in the ideal-gas approximation. Virial corrections are demonstrated for He gas at 4.2 K. Available experimental results, for the four materials mentioned, are discussed in the context of the theory presented and it is shown that for certain regimes of density and temperature self-trapped states exist and play an important role in determining the observed transport parameters. Further calculations and experiments are suggested to probe in detail the characteristics of all the states available to electrons in the type of disordered materials discussed.

The neoclassical or semiclassical theory (NCT) of the radiative decay of an isolated atom predicts that the decay rate of an excited state is proportional to the atoms's population in the state to which the atom is decaying. For weak excitation of a two-level system, this prediction is consistent with observations and with the Weisskopf-Wigner theory of decay, which assumes a quantized electromagnetic field as in quantum electrodynamics (QED). But for weak excitation of a system with three or more levels, there can be gross disagreements between NCT and QED. NCT predicts that the lifetime of an excited state depends on the nuclear spin which determines the number of ground states between which the atom's unity population density is divided. Also NCT predicts no fluorescence to a third level not initially populated, even though the transition is highly allowed. Observations in Pb vapor are inconsistent with NCT and consistent with QED. The oscillator strengths of the 2833-, 3640-, and 4058-A transitions were determined to be 0.167(20), 0.061(04), and 0.146(10), respectively, by measuring the ratios of oscillator strengths and using the lifetime measurements of Happer and Saloman.

A quantum-lattice-gas model of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures is proposed which includes the effects of the Bose and Fermi statistics. The effect of the hard-core interaction between all particles is included by altering the commutation relations of the field operators. The phase diagram of the model is obtained within mean-field theory under conditions of constant normal density and constant pressure. The diagram shows many of the features of the physical system. However, within mean-field theory, the phase separation is complete at the absolute zero of temperature.

A molecular theory of collective modes in liquid crystals is developed in the large-wave-vector regime with the use of a self-consistent-field method. The effects of orientational ordering on the translational collective modes are derived. A soft mode is obtained.

Previous theories of laser radiation have described the electromagnetic field in terms of a discrete set of quasimodes (Fox and Li "modes") of the laser cavity. Each quasimode was assumed to have a finite quality factor Q. In steady state (when gain due to lasing atoms cancels the losses) and in the absence of noise sources, the semiclassical theory predicts a $\delta$-function line shape. In the present semiclassical analysis (fluctuations are ignored), this theory is generalized for a maser with a cavity having a semitransparent wall as one of the mirrors so that there are now many modes of the universe corresponding to each Fox-Li-type quasimode. It is demonstrated that the normal modes of the universe associated with a single Fox-Li "mode" may, under proper conditions, lock together and the $\delta$-function laser line shape may be regained. Specifically, we investigate the conditions under which the coupled multimode equations associated with laser oscillation can be reduced to an equation of the form found in the usual single-quasimode theory.