We report new experimental observations on a cholesteric planar texture of pitch $P$ and thickness $L$ submitted to a static magnetic $\overrightarrow{\mathrm{H}}$ or a high-frequency electric field $\overrightarrow{\mathrm{E}}$. Two configurations are considered: (a) $\overrightarrow{\mathrm{H}}$ parallel to the helical axis: if ${\chi }_a>0\mathrm{}$, $L\sim P$, an array of stripes is observed at threshold. This is to be compared to the case ${\chi }_a>0\mathrm{}$, $L\gg P$, where a square gridlike pattern is nucleated in the same conditions. (b) $\overrightarrow{\mathrm{E}}$ perpendicular to the helical axis: if ${\epsilon }_a<0\mathrm{}$, $L\gg 0$, a static array of stripes is again observed, the stripes being perpendicular to $\overrightarrow{\mathrm{E}}$. This configuration is equivalent to the configuration ${\chi }_a<0\mathrm{}$, $\overrightarrow{\mathrm{H}}$ perpendicular to the helical axis. The threshold conditions derived by Helfrich and Hurault in the case $L\gg P$, ${\chi }_a>0\mathrm{}$, $\overrightarrow{\mathrm{H}}$ parallel to the helical axis seem to be also valid in those two cases. A more detailed theoretical treatment is devoted to the second geometry.

A theoretical calculation of the chemical potential, spreading pressure, and inverse compressibility at $0^{\mathrm{o}}$K is reported for ${\mathrm{He}}^4$ adsorbed on a graphite-like substrate for monolayer densities of 0.10 to 0.13 ${\mathrm{\AA }}^{-2\mathrm{}}$. These functions are obtained from a ground-state variational wave function constructed of single-particle functions multiplied by Jastrow correlation factors. Use was made of a cluster expansion in the calculation of the ground-state energy. The theoretical results agree quite well with the empirical values.

The Lamb semiclassical laser theory is developed uniformly for multimode unidirectional ring, two-mirror, and bidirectional-ring lasers. Equations are given which determine the mode amplitudes and frequencies to third order in the electric-dipole interaction energy. A diagram technique called the perturbation tree is used to bypass most of the algebra for the complicated multimode bidirectional-ring case. Numerical results are given for a variety of multimode laser configurations in the free-run approximation. In particular it is shown that the multimode, two-mirror gas laser exhibits an asymmetric spectrum in agreement with the experimental observations of Garside. This asymmetry is found to be absent in the unidirectional-ring case and is attributed to mode competition for the same pairs of velocity ensembles (an origin related to that for the Lamb dip). The coupling role of population pulsations is discussed with numerical illustrations. Treatment of mode locking is deferred to a forthcoming companion paper.

The density of liquid ${\mathrm{He}}^3$ along the melting curve below 3 mK and through the transitions to the $A$ and $B$ phases has been studied using a parallel-plate capacitor in a Pomeranchuk cell. It is found that the density varies smoothly in this region with no discontinuity larger than $\frac{\Delta \rho }{\rho }=5\mathrm{}\times {10}^{-5\mathrm{}}$. The existence of a latent heat demonstrates that the $B$ transition is first order; however, the jump in density must be minute.

The equilibrium properties of a classical one-component plasma, in a uniform background of opposite charge, are computed for systems of various sizes by the Monte Carlo method of Metropolis et al. Following the work of Brush, Sahlin, and Teller, the periodicity of the system is accounted for by replacing the long-range Coulomb potential by an effective Ewald sum. Thermodynamic properties are computed over the whole density range of the fluid phase of the system, and their $N$ dependence is carefully investigated. A semiempirical equation of state is proposed from which all thermodynamic properties can be easily derived. Quantum corrections to these properties are calculated to first order in the Wigner expansion. Radial distribution functions, direct-correlation functions, and structure factors at various densities are tabulated. It is shown that at all densities, the direct-correlation function tends rapidly towards its Debye-Hückel form, in contrast to the radial distribution function. The behavior of the structure factor at small wave vectors is also shown to be in good agreement with the Debye-Hückel predictions at all densities.

A study of the crystalline phase of a one-component plasma in a uniform background is reported here. Extensive Monte Carlo computations of the equilibrium properties in the classical region are presented and a value of the melting parameter ${\Gamma }_m=155\mathrm{}\pm 10$ is obtained. These results are extended into the quantum region in the framework of conventional lattice dynamics to estimate the solid-fluid coexistence curve in conjunction with the Lindemann melting criterion. A preliminary investigation is made of the effect of allowing the charge neutralizing background to respond to the ionic motion and it is concluded that the melting curve will be unaffected for ions with $Z\ge 2$.

Experimental investigations of the behavior of the Kr $1s_2$ excited-state population in after-glow discharge plasmas are described. The number density of Kr $1s_2$ atoms was obtained by performing resonant absorption measurements at 8509 Å $(\mathrm{Kr} 1s_2\to 2p_4)$ with a tunable GaAs laser diode. The narrow-width laser was tuned and swept through the entire resonant transition. The decay of the $1s_2$ species in the late afterglow was found to depend primarily on the decay processes for the $1s_3$ species. Analysis of the pressure-dependent decay curve in the late afterglow has been carried out to derive the diffusion coefficient as well as two-body and three-body destruction frequencies for Kr $1s_3$ excited species. The diffusion coefficient was found to be 49 ${\mathrm{cm}}^2$${\mathrm{s}}^{-1\mathrm{}}$. The two-body collisional destruction rate was found to be 9×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^3$/s. The three-body collisional destruction rate, which presumably indicates the rate of formation of the excited dimer $\mathrm{Kr}_2^{}{}_{}{}^{*}$, was found to be 53.6×${10}^{-33\mathrm{}}$ ${\mathrm{cm}}^6$/s.

The bound state of a ${\mathrm{He}}^3$ atom trapped in the free surface of ${\mathrm{He}}^4$ is studied, using a trial function suggested by Lekner. The effective potential which determines the bound-state wave function is calculated from first principles, and results in a binding energy 20% larger than the observed value.

We present the first completely quantum-mechanical calculation of the Kapitza resistance for the solid-liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ interface. By using a realistic model of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, processes involving phonons and rotons in the liquid helium are treated in a unified manner. The coupling of the phonons in the solid to the excitations in the helium is derived in the form of a transfer Hamiltonian. In the long-wavelength limit the classical acoustic-mismatch theory is reproduced by transmission processes involving single phonons, but the coupling Hamiltonian also includes roton emission and higher-order processes involving two or more excitations in the helium. As in the theory of electron tunneling, the transfer-Hamiltonian formalism can serve as a basis for further studies taking account of many-body interactions in the solid or liquid, scattering by defects or surface structure, and the influence of attractive van der Waals forces at the interface.

A new formula for induced transition amplitudes in intense photon beams is derived which relates the photon-number description to the coherent-field description. According to this formula transition amplitudes describing processes in which $m$ photons are added to the intense one-mode beam or subtracted from that beam are equal to the Fourier coefficients of the corresponding amplitude in the external field, expanded with respect to the phase of the classical field. The same formula is used to study the expectation values of dynamical variables in $n$-photon states leading to the conclusion that for large $n$ such states are very much like classical statistical states with a given amplitude and evenly distributed phase.

The self-consistent random-phase approximation is used to derive an integral equation for the quasiparticle energy of a charged Bose gas near a critical point. An approximate analytical solution, valid at long wavelengths, is used to compute the critical exponents which are those of an ideal Bose gas with the single-particle spectrum $\epsilon \mathrm{}\left(p\right)=A{p}^{2-\eta },\eta \simeq 0.2$. The accuracy of the analytical solution is checked by an exact numerical solution which is also used in a calculation of the transition curve. A necessary condition for the correctness of the theory is found to be $\frac{(T-T_c)}{T_c}\gg 0.01$.

Magnetic-susceptibility measurements around the apparent very low transition temperatures of liquid ${\mathrm{He}}^3$ will be shown to be indicative of the role played by the spin system in the transformation process. This phenomenon is found to be depressed toward lower temperatures on application of external, constant, and uniform magnetic fields, with the ordered modification of the liquid confined to a limited region of its magnetic phase diagram.

We measure the incoherent quasielastic scattering of thermal neutrons from hydrogen gas at 85°K and various pressures up to 140 atm. The observed Van Hove self-correlation function (or the self-part of the dynamic structure factor) shows a narrowing effect as the ratio of the observational wavelength to the collisional mean free path increases. The resulting line shape and linewidths are analyzed using an appropriate kinetic equation. The theoretical prediction agrees with experiment when the only parameter in the theory, namely, the self-diffusion coefficient, is properly calculated in the Enskog approximation. We demonstrate experimentally that the linearized Boltzmann equation gives an accurate description of the dynamics of the single-particle motion at moderately high density and in the range of wave vectors and frequencies comparable to inverse collision mean free paths and collision frequencies of the molecules.

The first two terms in the density expansion of the autocorrelation-function expression for the self-diffusion coefficient of a fully ionized plasma are obtained. The expression for the self-diffusion coefficient $D$ is $D={\mathrm{}\left[A\right(T)\mathrm{}\rho \ln \rho +B(T\left)\mathrm{}\rho \right]}^{-1\mathrm{}}$ The technique employed is that due to Zwanzig and Kawasaki and Oppenheim, suitably modified to remove the divergences due to the long-range Coulombic interactions. The pertinent expansion parameter is the plasma parameter ${\left(4\mathrm{}\pi \rho {\beta }^3{e}^6\right)}^{\frac{1}{2}}$. The dynamical operators appearing in the final expression are the linearized Lennard-Balescu operator, a Fokker-Planck operator, and a Boltzmann operator with the Coulomb potential replaced by a Debye-Hückel potential. The technique is easily generalized to obtain density expansions of the other plasma transport coefficients.

A treatment of the steric model of nematic liquid crystals based on the empirical equation of state is presented. The steric model of the nematic state assumes that the orientationally dependent molecular repulsive barrier potential is responsible for the isotropic-nematic phase transition. An examination of previous treatments of this model identifies one of the sources of computational difficulty as the need to calculate the form of the equation of state. A method is found which avoids this problem by use of an ansatz. The order parameter is found to be a function of a reduced temperature which depends on parameters which may be found by measuring the equation of state of the isotropic phase outside the transition region. The influence of short-range orientational order may be estimated in a more straightforward manner than possible in previous treatments. Theory and experiment are found to agree on two important aspects of this model.

A brief review of the current state of understanding of the vortex-ring transition in superfluid helium leads to a reexamination of the early suggestion that the critical velocity for vortex-ring creation is determined by energy and momentum conservation. The energy and impulse of a sphere and a vortex ring moving coaxially through an ideal fluid are evaluated. This allows an approximate determination of the velocity at which a moving sphere can create a vortex ring with a given size and location. By minimizing this velocity with respect to the size and location of the ring, one finds that the ring first appears girdling the sphere in the plane perpendicular to the direction of motion. The critical velocity when this ring appears is evaluated for sphere radii and masses derived from the usual models of the charge carriers in helium. The results are in good qualitative agreement with the experimentally observed critical velocities.

The properties of ${\mathrm{Xe}}^{+}$ and Xe${\mathrm{H}}^{+}$ ions were studied in xenon and helium-hydrogen-xenon mixtures, respectively, by means of the stationary-afterglow method. The time dependence of the number density of these ions was measured by mass-spectrometric techniques. The temporal behavior of the intensity of the 4671-Å spectral line of xenon was determined by light-spectrometric techniques. The studies established for the first time the occurrence of the collisional recombination process ${\mathrm{Xe}}^{+}+2e\to {\mathrm{Xe}}^{*}+e\to \mathrm{Xe}+e+h\nu$ and that of the dissociative recombination process $\mathrm{Xe}{\mathrm{H}}^{+}+e\to {\mathrm{Xe}}^{*}+\mathrm{H}\to \mathrm{Xe}+\mathrm{H}+h\nu$.

Thermodynamic properties of the liquid metals Li, Na, K, and Al are calculated using a pseudopotential model together with an application of thermodynamic perturbation theory based on the Gibbs-Bogoliubov inequality. The theory is used to predict many properties associated with the melting phenomenon; for example, the melting temperature and density as a function of temperature, and the latent heat of fusion. It is found that the theory reproduces the trend in latent heats between the alkali metals, in contrast to previous work, although quantitative agreement with experiment is no better than has been obtained before. The theory is also applied to the prediction of thermodynamic properties on and away from the melting curve; in particular, the specific heat and velocity of sound of sodium are calculated over a wide range of temperature. Agreement with experiment is found to be good.

A generalized correction to the $N$-photon transition amplitude proposed by Reiss is calculated. The corrected amplitude reduces to the perturbation-theory result in the limit of a low-intensity photon beam.

A hydrodynamic model is used to describe the condensation of a supersaturated vapor near its critical point. Calculations are based on a statistical theory of nucleation previously developed by one of the authors (J.S.L.). The method permits careful study of various statistical corrections and a quantitative treatment of the thermal nonaccommodation effect. Although the theory developed here is based on assumptions which are quite different from the classical Becker-Döring theory, numerical predictions of the critical supersaturation in Xe and C${\mathrm{O}}_2$ turn out to be very nearly the same as the classical results.