A preliminary discussion is given of electron-positron pair production by means of electrons accelerated to relativistic velocities at the focus of a laser beam. First, the pair-production cross section was numerically evaluated near its energy threshold. Then, two methods of relativistic electron production by focused laser light were considered: the coherent oscillation of electrons, and the acceleration of a few high-velocity electrons by plasma waves excited by laser-driven instabilities. It was found that the first method would produce pairs for neodymium-laser light at intensities close to the achievable limit (${10}^{19}$ - ${10}^{20}$ W/${\mathrm{cm}}^2$). The second method, however, may be capable of producing pairs at lower intensities.

Heat capacities of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ monolayers adsorbed on "Grafoil" graphite substrates at low temperatures are qualitatively different from previous results using other adsorbents. The present study consists of a detailed survey of many samples conducted in two similar but independent calorimeters: the fractional coverages ranged from 5 to 115% of a completed first layer and the temperature range extended from 0.04 to above 10° K. Several distinct thermodynamic regimes are seen, some of which correspond closely with well-known theoretical models as well as others that had not been predicted. At moderate densities and temperatures the behavior resembles that of two-dimensional gases. Departures from ideality are correlated with quantum-mechanical virial corrections for interacting molecules. In this range of coverages the ${\mathrm{He}}^4$ specific heats begin to rise at $T\lesssim 3^{\circ }$ K, forming strong rounded peaks near 1°K. ${\mathrm{He}}^3$, on the other hand, shows a monotonic decrease with falling temperature until $T\simeq {0.2}^{\circ }$ K, then (for a narrow range of coverages) reversing the trend to form rounded maxima near 100 m°K. At the lowest temperatures the ${\mathrm{He}}^3$ appears to enter a two-dimensional ($2D$) Fermi-liquid regime. At higher coverage both ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ undergo second-order phase transitions to regular arrays in registry with the substrate. In the critical region that heat capacities have symmetric peaks of logarithmic shape, with coefficients in close quantitative agreement with exact $2D$ Ising models. Above critical density the ordering peaks disappear and $2D$ liquid and solid behavior is seen. ${\mathrm{He}}^4$ at high density and low $T$ is Debye-like, with characteristic temperatures ${\Theta }_{2D}$ equal to ${\Theta }_{3D}$ of hcp solid ${\mathrm{He}}^4$ of the same interatomic spacing. At higher $T$ the $2D$ solid appears to transform to a $2D$ fluid by a continuous process, and pronounced heat-capacity peaks associated with the transformation are located at temperatures near the melting points of hcp ${\mathrm{He}}^4$ having the same interatomic spacing. At very low coverage the $2D$ gas character gives way to a regime resembling a low-density $2D$ solid.

A general theory of wave propagation in helical structures is developed. It is shown that this problem is quite similar to the well-known wave propagation in solid crystal lattices. If energy dissipation is neglected there are shown to exist frequency bands for wave propagation without attenuation separated by frequency bands where waves are damped out and cannot propagate. Formally, the waves have the form of Bloch waves $e^{i\overrightarrow{\mathrm{k}}.\overrightarrow{\mathrm{r}}}u\left(\overrightarrow{\mathrm{r}}\right)$, having the character of plane waves modulated by a function $u\left(\overrightarrow{\mathrm{r}}\right)$ which is periodic with the structure. Based on this theory, for reflection of light by homogeneously ordered cholesteric liquid crystals the following results are obtained: For incident light parallel to the helical axis there exists only one band of selective reflection. For obliquely incident light, however, an infinite series of higher-order reflection bands occur. Each reflection band is split into two branches. The angular dependence of the reflection bands and the sequence of the higher-order reflections on the wavelength scale bear a certain analogy to Bragg reflection.

The noncharacteristic X-ray band produced by Ar bombardment of various targets has been investigated with a high-transmission window, gas-flow proportional counter, and Si(Li) detectors. We find (i) that the Ar bombardment of Si produces a continuum with monotonically decreasing intensity for increasing energy, extending from ≲250 eV to ∼1.2 keV; (ii) Ar-target interactions and Ar-Ar interactions produce distinctly different spectra; (iii) the band observed in the Ar-C system is inconsistent with a simple quasimolecular picture. The bearing of these results on the quasimolecular description is discussed.

The problem of obtaining the probability density of the fluctuating light intensity from the knowledge of photocounting statistics, when the detectors have a finite dead time, is considered. The integral relation for the probability of registering $n$ photocounts in the time interval $T$ in the presence of a dead time $\tau$ is inverted, and an expression is obtained for the probability density of the fluctuating intensity of the incident light radiation. The method is illustrated with a few specific examples.

In an applied magnetic field the "$A$" transition in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ (at 2.7 mK on the melting curve) splits into two discrete transitions, occuring at different temperatures. This effect has been observed both in pressure-versus-time measurements in two different compressional cooling cells and in the attenuation of 10-MHz zero sound. The magnitude of the temperature splitting, in units of pressure along the melting curve, is $0.20H$ mbar for $H$ in kOe. A third pressure-versus-time feature has been observed near $A$ at high fields, but is not accompanied by an attenuation peak.

Temporal measurements of the electron density and ion wall currents in helium-argon mixtures in which ${\mathrm{Ar}}^{+}$ is the dominant ion show that the transition from ambipolar to free diffusion is identical to that previously measured in pure helium by Gerber and Gerardo. This establishes that helium metastables did not influence the decay of the electrons and ions, as was suggested by Gerber and Gerardo, and thus cannot account for the difference between experiment and theory. The zero-field mobility of ${\mathrm{Ar}}^{+}$ in He was found to be ${\mu }_0=22.4\mathrm{}$ ${\mathrm{cm}}^2$${\mathrm{V}}^{-1\mathrm{}}$${\sec }^{-1\mathrm{}}$.

The behavior of photon echoes near level anticrossings is described in terms of the magnetic-field-dependent mixing parameters. The general features of level-crossing behavior are obscured for most cases in dilute ruby and are dominated instead by strong spin-dependent decay resulting from Cr-Al interactions. However, new experiments at short time separation ($\tau =32\mathrm{}$ nsec) between pulses have permitted observation of the predicted photon-echo anticrossing signals in ruby, and may be applied to other atomic systems.

The ionic beam—gas-target method was used to obtain intensity decay curves for some transitions of Ne I and Ne II. The mean radiative lifetimes of the upper levels were extracted by a computerized least-squares curve-fitting procedure. The lifetime of the $3p^{\prime }{}_{}{}^2{}_{}{}^{}D_{}^{\circ }{}_{}{}^{}$ level of Ne II was found in this way to be 5.2 ± 0.5 nsec. Somewhat less-reliable lifetimes were obtained for some $2p$ (Paschen notation) levels of Ne I. Those lifetimes $\tau$ in nsec are as follows: $\tau \left(2\mathrm{}{p}_1\right)=15.5\mathrm{}\pm 0.3$, $\tau \left(2\mathrm{}{p}_4\right)=24.8\mathrm{}\pm 0.7$, $\tau \left(2\mathrm{}{p}_6\right)=25.5\mathrm{}\pm 0.8$, and $\tau \left(2\mathrm{}{p}_9\right)=23.4\mathrm{}\pm 0.3$. Errors quoted for the Ne I lifetimes are standard deviations of several measurements. The error for the Ne II measurement represents a combination of statistical and possible systematic errors. Since the Ne I work may be affected by unresolved cascading, we do not claim an accuracy better than (15-20)% for those measurements. This paper completes the study of the ${\mathrm{Ne}}^{+}$ beam begun by Head and Head.

The first Born approximation with the incident-ion—electron interaction (OBK) was used to calculate cross sections for capture of electrons from Ar by multiply charged atomic-oxygen ions. This calculation was effected for five different incident ions. ${\mathrm{O}}^{i+}$, $i=8,7,6,5,4\mathrm{}$. Cross sections $Q_n$ were calculated for capture from each subshell of Ar into the ground state, and for a few of the excited states of the final ion ${\mathrm{O}}^{\mathrm{}(i-1\mathrm{})+}$. However, no cross sections were calculated for capture into excited states of ${\mathrm{O}}^{6+}$ by reason of the apparent lack of analytic wave functions for these states. The calculated ratios, $r_i=\frac{\left[{\Sigma }_n{Q}_n\right(i\to i-1\left)\right]}{\left[{\Sigma }_m{Q}_m\right(i-1\mathrm{}\to i-2\left)\right]}$, $i=8,7,6,5\mathrm{}$, are compared with the corresponding ratios of measured total cross sections for single electronic capture. The calculated $r_i$ do not predict the ratios of measured cross sections very well in the range of impact energies of the measurements, $10\le E\le 40$ MeV. For $i=7,6,5\mathrm{}$, all of the calculated $r_i$, except $r_6$ (10 MeV), underestimate by factors $F$ in the range $1<F\le 5.8$. For $i=8\mathrm{}$ the prediction overstimates by a factor of 9 at $E=10\mathrm{}$ MeV, but at $E=40\mathrm{}$ MeV the factor is 1.96. The greatest disagreement occurs for $i=8,7\mathrm{}$, this discrepancy perhaps indicating the importance of contributions for capture into excited states of ${\mathrm{O}}^{6+}$.

Estimates of the Lamb shift in bound states of two-electron ions reported by Kastner are discussed critically. A consistent treatment of the quantum-electrodynamical correction of order ${\alpha }^3$ to the relativistic potentials of ionization of atoms with two electrons is developed and convenient expressions for these corrections in a $|nLSJ〉$ state of the atom are obtained. The numerical results are in close agreement with the experimental data of Edlén and Löfstrand for C v.

For the propagation of an ion acoustic wave, we observed an amplitude oscillation of the second-harmonic ion acoustic wave, which is qualitatively explained by nonlinear wave-wave-coupled theory with a fluid model.

A microscopic calculation of the long-time tail in the autocorrelation function corresponding to the mutual diffusion coefficient is presented. Mode-coupling methods in the framework of a generalized Langevin equation are used to obtain the results. The calculation yields an expression for the mutual diffusion coefficient in terms of two quantities; a bare mutual diffusion coefficient $D^{*}$ and a complicated nonlinear transport coefficient $\alpha$. Density expansions of these transport coefficients are carried out in order to elucidate their structure. In particular, we investigate, for dense gases, the conditions under which $\alpha$ reduces to a factored form involving the kinematic viscosity and diffusion coefficient, and the relation between $D^{*}$ and the usual mutual diffusion coefficient.

The results of an analytical treatment of the local low-frequency stability of weakly ionized molecular-gas mixtures consisting of a diatomic molecular species and an atomic diluent are presented. Plasma conditions typical of high-power electric-discharge-laser technology are emphasized. The calculations indicate that small-amplitude fluctuations present within these discharges excite several different wave modes. These have been identified as a space-charge relaxation mode, an electron thermal mode, an ionization mode, a negative-ion-production mode, an electronically-excited-species-production mode, a sound mode, a vibrational-energy relaxation mode, a heavy-particle thermal mode, and a vorticity mode. The stability of these modes is treated in detail with particular emphasis placed on illustrating the influence on stability of charged-particle kinetics, energy transfer, and transport processes. The influence of auxiliary ionization and aerodynamic techniques is also considered.

The drift velocities of $\mathrm{O}_2^{}{}_{}{}^{+}$, C$\mathrm{O}_2^{}{}_{}{}^{+}$, and C$\mathrm{O}_4^{}{}_{}{}^{+}$ ions in their parent carbon dioxide gas have been measured using the "four-gauze" electrical shutter method of Tyndall et al. with a glow-discharge ion source. Measurements were made at 29-32°C gas temperature over a range of $\frac{E}{p_0}$ from 20 to 250 V/cm torr and in a pressure range of from 0.5 to 1.3 torr. The ions have been identified mass spectrometrically during the process of measurement of the drift velocity. The predominent ions were $\mathrm{O}_2^{}{}_{}{}^{+}$ and C$\mathrm{O}_2^{}{}_{}{}^{+}$. In addition, ${\mathrm{C}}^{+}$, ${\mathrm{O}}^{+}$, C${\mathrm{O}}^{+}$, ${\mathrm{C}}_2$${\mathrm{O}}^{+}$, ${\mathrm{C}}_2$$\mathrm{O}_2^{}{}_{}{}^{+}$, C$\mathrm{O}_3^{}{}_{}{}^{+}$, ${\mathrm{C}}_3$$\mathrm{O}_2^{}{}_{}{}^{+}$, C$\mathrm{O}_4^{}{}_{}{}^{+}$, and ${\mathrm{C}}_2$$\mathrm{O}_4^{}{}_{}{}^{+}$ molecular ions have been observed. The mobility, extrapolated to zero field and atmospheric pressure, is about 1.32 ${\mathrm{cm}}^2$/V sec for $\mathrm{O}_2^{}{}_{}{}^{+}$ and C$\mathrm{O}_4^{}{}_{}{}^{+}$ ions and 1.13 ${\mathrm{cm}}^2$/V sec for C$\mathrm{O}_2^{}{}_{}{}^{+}$ ions.

It is shown that one can take advantage of total neutron reflection at a free surface to eliminate volume-proportional terms in inelastic neutron scattering. When this is done, the neutron inelastic-scattering cross section for superfluid ${\mathrm{He}}^4$ with a free surface is found, within an ideal-fluid model, to contain only ripplon peaks distinctly separated from a smooth background due to nonresonant single-phonon processes occurring near the surface of the liquid. Some numerical results are given for the predicted cross section.

The behavior of a simple theoretical model of a quantum-frequency converter with a time-dependent pump amplitude and phase is analyzed quantum mechanically. A sufficient condition ensuring periodic frequency conversion between the modes is found and exact solutions are given in these cases. The complete time-dependent density matrices which give the most complete statistical description of the system are presented for a variety of initial states of the system. In the general case where the sufficient condition is not satisfied, time-dependent-perturbation-theory results give corrections to the amplitude and the period of the energy exchange between the modes. Comparisons are made between these results and those of other authors.

A quantum-statistical-mechanical formulation is developed for determining the equation of state of Coulomb gases. The procedure is to develop the activity expansion of the grand partition function into a true perturbation expansion in which the divergences present in the cluster expansion of the Coulomb gas have been eliminated. Ionization and dissociation appear quite naturally in this approach even though only the total number of nuclei and electrons in the system are specified. Considerable insight into the quantum-mechanical perturbation result is obtained from the classical perturbation theory. The form of the static screened Coulomb potential that replaces the classical Debye-Hückel potential is discussed. An application to the equation of state of gaseous hydrogen which takes account of all $e-e$, $p-p$, and $e-p$ interactions is given. The formation of higher clusters such as $\mathrm{H}-e$, $\mathrm{H}-p$, H-H, etc., can also be systematically included. Owing to the extensive numerical calculations required, this has currently only been done in an approximate way. It is shown that the simple one-level Saha equation, including Debye-Hückel corrections for the free charges, is fairly accurate for $\rho <{10}^{-3\mathrm{}}$ g/${\mathrm{cm}}^3$. At greater densities the differences become significant.

The time dependencies of the ${\mathrm{He}}^{+}$, $\mathrm{He}_2^{}{}_{}{}^{+}$, and ${\mathrm{Cs}}^{+}$ ion densities have been measured during the decay period of a plasma produced in helium containing from (${10}^{-6\mathrm{}}$-${10}^{-2\mathrm{}}$)% cesium. Analyses of the ion decay rates as a function of helium pressure indicate that ${\mathrm{Cs}}^{+}$ is produced in the afterglow by collisions between neutral ground-state cesium atoms and ${\mathrm{He}}^{+}$, $\mathrm{He}_2^{}{}_{}{}^{+}$, and $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$. The values of the rate constants measured at a gas temperature of $T_g=415\mathrm{}$ °K for these reactions are ${\mathrm{k}}_2$(${\mathrm{He}}^{+}$)=3×${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$/sec, ${\mathrm{k}}_3\left(\mathrm{He}2{}_{}{}^3{}_{}{}^{}S\right)=1\mathrm{}\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$/sec, and ${\mathrm{k}}_4$($\mathrm{He}_2^{}{}_{}{}^{+}$)=2×${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$/sec. The reduced mobility of ${\mathrm{Cs}}^{+}$ in helium at 415 °K was measured to be (15.5±1) ${\mathrm{cm}}^2$/V sec.