We use the equations proposed by Gaudin for the free energy of the Heisenberg-Ising ring for $\left|\Delta \right|\ge 1$ to obtain the first temperature-dependent term in a systematic low-temperature expansion of the free energy.

We report on recent measurements of the ultrasonic velocity in the binary mixture nitrobenzene-$n$-hexane in the homogeneous phase above $T_c$. The observed dispersion in the range 5-55 MHz has been compared with the prediction of a modified form of the Fixman-Kawasaki theory.

Simultaneous measurements of both viscosity and light scattering are performed on two critical mixtures. The first one is a triethylamine-water solution, which exhibits a lower consolute point, the second one a methanol-ciclohexane mixture with an upper consolute point. It is found that the singular behavior of viscosity cannot be fitted by a simple power law, nor by a logarithmic one, in the entire range of temperature. The asymptotic behavior, however, tends to become logarithmic as the critical temperature is approached. The simultaneous observation of scattered light allows one to exclude the intervention of spurious processes, like a breaking of correlations because of impurities. In addition, it is shown that the correlation length seems to depend mainly on the reduced temperature, irrespective of the system under examination.

The results of an experimental determination of the statistical properties of radiation from OH maser sources are reported and interpreted. The radiation is found to have Gaussian statistics with no deviations greater than 1%.

The densities at which monolayers of ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$ on graphite are completed are calculated. as are their compressibilities. In addition, the binding energy of the first few atoms on the second layer is obtained.

In this work the electron energy distribution functions and the anisotropic drift term of the velocity distribution functions in non-self-sustaining (Townsend) discharges in argon were determined by direct measurement for a range of $\frac{E}{N}$ (electric field strength per gas-atom concentration) from 70 to 407 townsends (Td) (1 Td=${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$). Some structure in the form of the distribution functions is observed, but the prediction of Heylen and Lewis for argon is not fully supported. The experimental method employed is to energy analyze electrons effusing from apertures in the anode of a discharge cell with a spherical retarding electric field. The experimental energy distributions were used along with cross-section data from the literature to compute the electron mobilities, diffusion constants, mean energies, and Townsend's first-ionization coefficients. Combination of the data with results from kinetic theory permitted evaluation of the anisotropic part of the velocity-distribution function.

Steric effects and compressibility appear to be important in determining the effective Kerr constant of liquids for short laser pulses, and also the saturation of the Kerr constant. Their influence may explain the relatively high threshold power and large diameters of self-trapped light filaments which are observed in many liquids.

We have extended the theory of the roton lifetime to include two-roton resonances in the final-state interaction. When resonances are taken into account, the final density of states ${\rho }_2$ exhibits a complicated energy dependence and bears little resemblance to the noninteracting roton density ${\rho }_2^{\mathrm{}\left(0\right)\mathrm{}}$ used in the Landau-Khalatnikov theory. Using a point-interaction model for the roton coupling and including only direct roton-roton scattering, we obtain a single-roton linewidth which is consistent with the upper bound given by other authors; we then obtain a linewidth for the two-roton resonance which is smaller than the experimental value. In contrast to previous work, we have proceeded to include roton hydridization in the lifetime theory. The effect of hybridization is twofold: (a) The final density of states ${\rho }_2$ is markedly altered, and (b) the hybridization opens new scattering channels involving a single quasiparticle in the final state. Although the net effect of mechanism (a) on the roton lifetime seems to be small, the additional scattering (b) gives a non-negligible contribution. Furthermore, we discuss the importance of self-consistency and roton scattering in nonzero angular momentum channels. Our theory predicts an unusual pressure dependence for the roton linewidth which may be checked experimentally. We conclude that further experiments, such as light and neutron scattering, are needed to resolve the strength of the various contributions to the linewidth and thereby provide a truly quantitative analysis of the roton lifetime.

We have solved the boundary-value problem associated with the electro-optic mode which appears in a nematic liquid crystal subjected to a dc electric field parallel to the nematic director. Above a critical voltage, the liquid breaks up into a series of cylindrical lenses similar to those observed in the Williams domain mode. The dispersion relations for $p$-azoxyanisole and $p$-methoxybenzylidene-$p-n$-butylaniline were calculated using the known material constants for these two nematogens. We show that the critical voltage is caused by the dielectric torque opposed by the bend distortion torque; the critical voltage is not sensitive to the various viscosity parameters nor the conductivities. The dispersion relation at higher voltages does involve these constants.

A recent theorem by Ruelle is shown to be applicable to the calculation of lower bounds on the radius of convergence of activity expansions for lattice gases. Systems with nearest-neighbor repulsive interactions are used as examples. Special consideration is given to systems whose molecules possess infinitely repulsive potentials.

The angular distribution of electrons elastically scattered from ${\mathrm{N}}_2$ as a function of energy has been measured utilizing a crossed-beam technique. Measurements have been made of monoenergetic electrons with energies between 5 and 90 eV scattered from a collimated beam of ${\mathrm{N}}_2$ at angles from - 114° to + 160°. The wide angular range of the measurements has enabled the determination of the total elastic-scattering and momentum-transfer cross sections. The measurements are relative and have been normalized to Fisk's theoretical calculation at 5 eV. The results generally agree well with other published measurements and with theory.

Born-approximation calculations of the ionization of aluminum $L$-shell electrons have been performed using Hartree-Slater wave functions. Generalized oscillator strengths and proton energy-loss cross sections from threshold to ionized-electron energies of 128 Ry have been calculated. The results show a delayed maximum above threshold, and the ramifications of this phenomenon are discussed. Comparison is made with hydrogenic results and good agreement is found at intermediate and large energy loss, but the hydrogenic calculation is totally inadequate near threshold. The implications of this for stopping-power calculations and subshell corrections is discussed. The Bethe asymptotic cross section is obtained and the variation of parameters therein is investigated.

Absolute cross sections for the deexcitation of $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ and of $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ metastables by ${\mathrm{N}}_2$ and Ar have been measured over the energy interval from 150 to 1600 eV using an optical technique. The $2{}_{}{}^1{}_{}{}^{}S$ cross sections are found to be as much as 50% larger than the $2{}_{}{}^3{}_{}{}^{}S$ cross sections for deexcitation by ${\mathrm{N}}_2$, while for Ar the two cross sections are nearly equal at these energies. The cross sections all lie in the range of 7-20 ${\mathrm{\AA }}^2$ and decrease with increasing energy. Deexcitation cross sections have also been measured by collecting slow ions for mixed beams of He metastables in ${\mathrm{N}}_2$, Ar, and ${\mathrm{C}}_2$${\mathrm{H}}_2$ and for mixed beams of Ar metastables in ${\mathrm{C}}_2$${\mathrm{H}}_2$ and Ne metastables in Ar. These measurements are in the energy range from 50 to 600 eV. They do not discriminate between different metastable states, but the results exhibit an energy behavior similar to that of the state-separated measurements and are consistent with those measurements when comparison can be made.

The ionization (associative and Penning) total cross sections for ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+\mathrm{Ar}$ and ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)+\mathrm{Ar}$ have been calculated from ${10}^{-3\mathrm{}}$ to ${10}^4$ eV and compared with experimental data. The classical calculations used interaction potentials that agreed with ab initio theoretical calculations for the repulsive wall, possessed the correct long-range energy dependence, and were in agreement with glory-scattering experiments. The coupling width was an exponential with its free parameter determined by the thermal-energy ionization cross section for each system. The calculations were then extended over a wide range of energies. It was found that as the collision energy increased at the very low energies, the cross sections decreased until about 0.1 eV where they began slowly to rise. As the collision energy is further increased, the cross sections reach a maximum of about 15 ${\mathrm{\AA }}^2$ around 10 eV, and then decrease again at higher energies. The cross sections predicted by the high-energy results, 100-1500 eV, are compared with the data of Moseley, Peterson, Lorents, and Hollstein (preceding paper) and are found to agree within 20% and to have a similar energy dependence.

Optical studies of spectral lines produced in collisions of ${\mathrm{He}}^{+}$ + ${\mathrm{H}}_2$ have been made at energies below 700 eV. Lines of atomic hydrogen and helium are the only features observed. Emission cross sections have been measured for Lyman-$\beta$, Balmer-$\alpha$, Balmer-$\beta$, and for the following He i lines: $5876 \AA (3\mathrm{}{}_{}{}^3{}_{}{}^{}D\to 2{}_{}{}^3{}_{}{}^{}P)$, $6678 \AA (3\mathrm{}{}_{}{}^1{}_{}{}^{}D\to 2{}_{}{}^1{}_{}{}^{}P)$, $4471 \AA (4\mathrm{}{}_{}{}^3{}_{}{}^{}D\to 2{}_{}{}^3{}_{}{}^{}P)$. Emission cross sections are also listed at certain selected energies for all spectral lines which have been observed. Polarization measurements have been performed on the Balmer-$\alpha$, the Balmer-$\beta$ and the visible helium lines. Only the Balmer-$\alpha$ line exhibits significant polarization, and the results have been interpreted as indicating that the excited hydrogen atoms dissociate primarily in a direction perpendicular to the ion beam.

The author has calculated contributions to the total photoionization cross section of Fei in which the remaining Fe ii ion is left in a low-lying excited state. The excited states considered are ${\mathrm{}\left(3d\right)\mathrm{}}^7{}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}F$ and ${\mathrm{}\left(3d\right)\mathrm{}}^6{}_{}{}^5{}_{}{}^{}D4p{}_{}{}^6{}_{}{}^{}D$, ${}_{}{}^6{}_{}{}^{}F$, ${}_{}{}^6{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}F$, ${}_{}{}^4{}_{}{}^{}D$, and ${}_{}{}^4{}_{}{}^{}P$. We used the velocity form for the dipole-matrix elements and calculated the cross sections by means of many-body perturbation theory. Our results are compared with the cross section for photoionization of Fei without excitation which we calculated recently. Near threshold the contributions to the total photoionization cross section involving excited ${\mathrm{}\left(3d\right)\mathrm{}}^7$ and ${\mathrm{}\left(3d\right)\mathrm{}}^6{}_{}{}^5{}_{}{}^{}D4p$ excited states of Fei are approximately 20% of the cross section without excitation.

A study has been made of the angular distribution of scattered particles induced by proton impact on a target of helium. Cross sections are presented for scattering of protons, of neutral hydrogen atoms, and of metastable hydrogen atoms. Impact energies range from 4 to 20 keV; scattering angles are from 0° to 2.0°. Measurements of the fractional metastable content of the scattered neutral flux rise from 1% or less at 0° to as much as 8% at angles of 1°. Theoretical predictions of the cross sections for scattering of all particles, neutrals and protons, show reasonable agreement with experiments. Theoretical predictions, by Colegrave and Stevens, of the probability for forming a neutral atom disagree with the experimental values by a constant phase factor. Measurements of the probability for forming a metastable atom do not agree with available theoretical predictions.