The collisional depopulation rate of the $2{}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ triplet levels of Cv, Nvi, Ovii, Fviii, and Ne ix was determined from measured $2{}_{}{}^3{}_{}{}^{}S-2\mathrm{}{}_{}{}^3{}_{}{}^{}P$ line intensity ratios. The triplet lines were observed in a hot $\theta$-pinch deuterium plasma seeded with a few percent of the element to be examined. The plasma electron temperature and density were known from laser-light-scattering experiments. The total depopulation rate of the $2{}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ levels is mainly due to the $2{}_{}{}^3{}_{}{}^{}S-2\mathrm{}{}_{}{}^3{}_{}{}^{}P$ collisional deexcitation rate. The measured rate agrees well with calculations by Blaha based on the Coulomb—Born approximation. With these depopulation rates known, the electron density of the plasma can be determined just by measuring the triplet-line intensity ratios.

We have measured thermal-relaxation times ($\tau$) near the critical point of ${\mathrm{He}}^3$. $\tau$ remains small in one-phase states throughout the critical region. In two-phase states, $\tau$ increases as the critical temperature ($T_c$) is approached in proportion to ${(T_c-T)}^{-1.0\mathrm{}}$ at all densities. An extra increase in $\tau$ occurs in two-phase states very near the phase boundary. These observations suggest to us that the diffusion of matter across the liquid-vapor interface is a bottle-neck for equilibration. Our data are of value in interpreting puzzling features of several other experiments near critical points.

Franzen's approximation for the relaxation time of an optically pumped vapor is shown to yield effective values of diffusion coefficients and relaxation cross sections which differ by small predictable amounts from the true values of these parameters. The appropriate correction factors have been calculated. Relaxation at cell walls is shown to be approximated well by an additive relaxation rate, allowing a simple description of the relaxation of the electronic spin polarization of atoms subject to collisions both with cell walls and with buffergas atoms.

The radiation emitted by an electron traversing an output cavity tuned to a single frequency after having traversed an excited input cavity is calculated using quantum field theory. It is found that the emission has maxima when the output cavity is tuned to a harmonic of the inputcavity frequency, the result being very similar to classical klystron theory. The emitted power is independent of the state of the field in the input cavity under any realizable conditions, so that this provides no mechanism for determining the state of this field.

The motion of the nucleus yields numerically important order $\frac{m}{M_{\mathrm{He}}}$ corrections to the fine structure of the helium atom. We present here the derivation of such corrections applied to the $2{}_{}{}^3{}_{}{}^{}P$ fine-structure splittings in ${\mathrm{He}}^4$.

The electron-ion recombination coefficient measured in a cryogenic helium afterglow at a constant gas temperature of 4.2 °K at pressures between 0.075 and 1.25 Torr (neutral densities ranging from 1.7 to 28.7×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$) and at an electron temperature of 10 °K is (40 ± 6) × ${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$. It varies with the electron temperature as $T_e^{-\chi }$, where $\chi =1\mathrm{}\pm 0.2$, and shows no dependence on electron density over the range we have covered from 5×${10}^8$ to 2.5×${10}^{10}$ ${\mathrm{cm}}^{-3\mathrm{}}$.

Expressions for the diffusion coefficient of ions in gas mixtures are obtained from momentum-transfer theory, and are given in terms of the diffusion coefficients and drift velocities of the ions in the pure component gases. Blanc's law holds exactly at all field strengths if the mean free time between collisions is independent of velocity (Maxwell model), but otherwise there may be either positive or negative deviations from Blanc's law at high fields. Such deviations are of comparable magnitude for the diffusion coefficients and the mobility, but are not identical. Specific cases of inverse-power potentials are treated in further detail, and some numerical examples are given for rigid-sphere interactions.

In the interest of understanding the nature and properties of physically adsorbed helium monolayers in the mobile limit, we study the ground state of a two-dimensional helium liquid, using integral-equation techniques which have been thoroughly tested in connection with bulk helium. Our results are compared to those of computer experiments by Hyman and by Campbell and Schick, and to actual experimental data obtained by Dash and co-workers.

Measurements were made of the mobility of positive and negative charge carriers in ${\mathrm{He}}^4$, for ${\mathrm{He}}^3$ impurity concentrations ranging from 10 to 1800 ppm and temperatures in the range $0.3<T<\mathrm{}1.0\mathrm{}°$K. The excess inverse mobility $\frac{e}{\mu }-\frac{e}{{\mu }_0}$ was everywhere found to vary linearly with concentration, as expected. For negative carriers, the data are well explained by a hardsphere scattering model with a collision radius of 21 Å. For positive carriers, the polarization-deficit potential proposed by Bowley and Lekner gives reasonable agreement with experiment, provided a collision radius of 7.0 Å is assumed.

In this paper we investigate the mathematical validity of Bogoliubov's functional assumption. For this purpose, we analyze a model for a system in which light particles scatter against fixed centers. We compare the exact solution for the one-body distribution function and two-body correlation function with the results given by Bogoliubov's method. We find that Bogoliubov's functional assumption is too restrictive to allow proper initialization for both functions. As a consequence, the Bogoliubov result for the two-body correlation departs drastically from the exact solution. The results obtained here are fully consistent with previous asymptotic analysis of the one- and two-body equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarcy.

New resonances have been observed in the absorption spectrum of neutral cadmium vapor at wavelengths around 30 Å. These are believed to be at present the shortest-wavelength metal-vapor absorption features recorded optically. The 2.5-GeV electron synchrotron at Bonn University was used as a background source of continuous radiation. Hartree-Fock calculations enabled identification of the resonances as caused by excitation from the $3d$ shell, although somewhat larger differences between computed and observed wavelengths were found than were expected.

The problem of phonon scattering by charge carriers in superfluid helium is considered, with the aim of interpreting recent measurements of charge-carrier mobilities below 1 °K. The calculations are done in the hydrodynamic approximation, and explicitly include the effect of the electrostrictive variations in the fluid surrounding the core structures of the carriers. For the positive carrier, the necessary core properties are calculated, and in particular it is found that the core does not act like a hard sphere. The theoretically predicted phonon-limited mobility for positives is found to be in excellent agreement with experiment, provided a liquid-solid surface energy of order 0.1 erg ${\mathrm{cm}}^{-2\mathrm{}}$ for the core is assumed. In the case of the negatives, results are similar to those of previous workers. The mobility of the electron bubble is substantially explained by resonance scattering of phonons, but a significant discrepancy remains which probably arises from the use of the idealized bubble model. The changes in the theoretical mobility curves that can be produced by varying the bubble parameters $a_{-}$ and $V_1$ are of the order of this systematic discrepancy, so that the best values of these parameters cannot be determined from the data. Values of $a_{-}$ less than 15 Å can, however, be ruled out with some confidence. The roton contribution to the scattering is determined by subtracting the phonon part, and turns out to have some unexpected features. For the positives, $\frac{e}{{\mu }_{+}}\cong 1.34\times {10}^{-9\mathrm{}}{T}^{-\frac{1}{2}}{e}^{-\frac{\Delta }{\mathrm{kT}}}$. The temperature dependence of $\frac{e}{{\mu }_{-}}$ is not as clearly established, but the prefactor lies between $T^0$ and $T^{-\frac{1}{2}}$. The ratio of $\frac{e}{{\mu }_{-}}$ to $\frac{e}{{\mu }_{+}}$ is found to have a surprisingly small value of about 1.5, perhaps indicating that electrostrictive variations in the fluid surrounding the positive core scatter rotons strongly. No present theory of roton scattering explains the observed features.

Positron-annihilation lifetimes in nitrogen dioxide and nitric oxide gases are carefully determined. Nitrogen is used as a dilutant. The free-positron-annihilation rate in units of the effective number of electrons per molecule $Z_{\mathrm{eff}}$ for nitrogen dioxide as a mixture of dimers and monomers is determined to be 720 to 1090 and the free-positron-annihilation rate for nitric oxide is $Z_{\mathrm{eff}}=34\mathrm{}$. The positronium quenching rate in nitrogen dioxide gas is very high and the conversion reaction by N${\mathrm{O}}_2$ is found to be mainly responsible for the quenching. The quenching rate is determined to be $460D$ ${\mathrm{nsec}}^{-1\mathrm{}}$ ${\mathrm{amagat}}^{-1\mathrm{}}$, where $D$ is the partial density. The positronium quenching rate in nitric oxide is determined to be only about $0.15D$ ${\mathrm{nsec}}^{-1\mathrm{}}$ ${\mathrm{amagat}}^{-1\mathrm{}}$, and it changes with the concentration of nitrogen.

The present study concerns the evolution in time of explosively unstable systems under the influence of time-dependent dissipative and nonlinear coupling effects. Generalized criteria for instability as well as new mode solutions are constructed by introducing a suitable transformation in time.

Two rather unusual effects which are associated with the propagation of plane waves of constant amplitude in nondispersive isotropic nonlinear electromagnetic media are presented. One is the distortion-free transmission of information through a nonlinear medium, by "polarization modulation" of a plane wave of constant amplitude. The other is the reflection and refraction of a monochromatic wave, obliquely incident on the plane interface between a linear medium and a nonlinear one, so that the transmitted wave, in the nonlinear medium, is also monochromatic. These effects are described by exact solutions of the nonlinear system of equations and they should be of interest, in particular, in laser physics.

Density fluctuations in a moderately dilute gas of hard spheres are analyzed using a kinetic equation which is the generalization of the linearized Boltzmann equation to arbitrary frequencies and wave numbers. The phase-space memory function derived recently by Mazenko is evaluated for the hard-sphere interaction, and the result is shown to be explicitly frequency independent. In the case of the self-correlation function, the memory function is found to be identical to the collision operator in the appropriate Boltzmann equation, thus implying that in this special case the Boltzmann-equation description is valid at all frequencies and wavelengths. Wave-number-dependent matrix elements of the memory functions are calculated using the Hermite function as a basis, and a number of interesting features are observed. The matrix elements are utilized in a kinetic-model formulation of the initial-value problem of evaluating the spectral densities of thermal fluctuations. Numerically converged results are presented and compared with previous Boltzmann-equation calculations. While the qualitative behavior of the spectral distribution still can be characterized by the ratio of wavelength to collision mean free path, details of the line shape now depend on density and wave number. At reasonable density and wave-number values, a narrowing effect is observed. This effect, which is most pronounced at small and moderate wavelength-to-mean-free-path ratios, is sufficiently significant that further investigation is warranted.

Large scale configuration-interaction calculations are carried out on the $2sns{}_{}{}^1{}_{}{}^{}S$ series of Be i in an attempt to account for the anomalous behavior of the measured $f$ value for the 3455-Å line, which had been identified as the $2s2p{}_{}{}^1{}_{}{}^{}P-2\mathrm{}{p}^2{}_{}{}^1{}_{}{}^{}S$ transition. The calculations indicate that the series is very nearly purely Rydberg in character and that $2p^2{}_{}{}^1{}_{}{}^{}S$ is not embedded in the series between $6s$ and $7s$, as had been previously assigned. Additional variational calculations on the $2snp$ and $2p3p$ levels indicate that a reidentification of the 3455-Å line with the $2s3p{}_{}{}^1{}_{}{}^{}P-2p3p{}_{}{}^1{}_{}{}^{}P$ transition is consistent with both lifetime and wavelength measurements. These calculations also predict lines at 2148 and 4528Å, which have recently been found in beam-foil spectra.

A simple and direct procedure has been used to calculate the flux gradients inside Knudsen cells and the related effusive-flow patterns. Knudsen cells of simple geometries with knife-edge orifices and flat sources are considered. The calculated value of the Motzfeldt factor (1. 020) is in very good agreement with the literature value (1. 020) and the Monte Carlo calculations (1. 020) for a cell of reduced height $H=4.0\mathrm{}$ and the knife-edge orifice of reduced diameter=0.1064. It is suggested that an extension of these calculations has an importance in solving some of the problems encountered in determining the absolute total scattering cross section from scattering measurements.