The optical excitation of a beam of ${\mathrm{Na}}^{+}$ ions by a thin carbon foil has been observed in the spectral range 1100-6000 Å. Ions with a charge state as high as $5^{+}$ were present in the beam after the foil. A large number of untabulated lines has been detected and several identifications are proposed mainly in the Na IV and Na V spectra. The decay along the beam of numerous transitions in Na II and Na III has also been recorded. In a few favorable cases, the resolution of the decay curve gives a useful estimate of the mean life of the corresponding excited state.

Gaseous Ar, Kr, and Xe are observed at room temperature to scatter light into a broad frequency band whose intensity varies as the square of the density at low densities. Such scattering is attributed to an incremental polarizability due to the distortion of the electronic distributions of colliding atoms. Studies of the depolarization ratio show that the collision-induced spherical polarizability is negligible with respect to the induced anisotropy. Within experimental error, the (relative) integrated depolarized intensity at low densities and the second virial Kerr coefficient, to which it is directly related, are in agreement. Studies made at wave-number deviations of about 5 - 100 ${\mathrm{cm}}^{-1\mathrm{}}$ from the laser frequency show that the spectral shape is exponentiallike and the bandwidth is of the order of the duration of collision.

Collisional excitation rates in N v, O VI, and Ne VIII have been derived from absolute line intensities emitted by these ions in a well-diagnosed plasma. The plasma was produced in a $\theta$-pinch device, and several plasma conditions were investigated. The electron density and temperature were obtained as a function of radius and time from the spectrum of scattered laser light. The experimental results are compared with Bely's calculations using the Coulomb-Born approximation. Although the maximum error of the individual rate coefficients is a factor of 2, the standard deviation of the experimental values from the theoretical ones is less than 30% for excitation to the $n=2\mathrm{}$ and $n=3\mathrm{}$ levels and less than 40% for excitation to the $4s$ level. The rates to the $4p$ and $4d$ levels are on the average ∼ 60% of the theoretical ones.

The velocity autocorrelation function $〈v\left(t\right)\mathrm{}v\left(0\right)\mathrm{}〉$ of a hard-sphere Brownian particle moving in an incompressible viscous fluid is calculated on the basis of hydrodynamics. The usually assumed exponential decay at long times is shown to be inconsistent with fluid mechanics. A $\mathrm{slower}\mathrm{decay}\propto t^{-\frac{3}{2}}$ as $t\to \infty$ is derived. This decay has been observed in molecular dynamic computations carried out by Alder and Wainwright.

The one-dimensional charged-particle continuity equation with recombination-volume loss terms has been solved in a negative-glow-Faraday-dark-space environment without the usual assumptions neglecting the dependence of electron transport and recombination coefficients on the electric field. It is concluded that such assumptions are in serious error in the one-dimensional case and this raises the question of their effect on a three-dimensional model.

The stability of a periodic large-amplitude electrostatic wave [Bernstein-Greene-Kurskal (BGK) mode] in a collisionless plasma is investigated. It is found that instability or damping can result whenever a wave has a frequency which is resonant with one of the natural frequencies of a particle in the BGK mode. The total growth or damping rate is expressed as a summation over these resonances. In appropriate limits, the growth rates are identical with those corresponding to linear and nonlinear Landau damping. Three specific problems are considered. Electron plasma waves in a plasma at thermal equilibrium are shown to be unstable toward decay into an ion acoustic wave. Plasma waves in an electron-beam plasma system are shown to be unstable toward decay into ion waves. Finally, an electron plasma wave at frequency ${\omega }_0$ is shown to be unstable toward decay into the lower sideband, that is a wave at ${\omega }_0-{\omega }_T$ where ${\omega }_T$ is the trapping frequency.

We describe a new approach to the understanding of the thermodynamic properties of a physical system near a critical point. The critical point is characterized by the peculiar dependence of various quantities on the size of the system, rather than by the mathematical singularities which appear in an infinite system. We indicate a very general method of obtaining scaling laws for the critical behavior of any thermodynamic system by considering its thermodynamic fluctuations. As an example, a new scaling law is obtained for the susceptibility at a gas-liquid critical point.

The thermodynamic equilibrium properties of strongly ionized multicomponent gas mixtures are investigated by application of the free-energy minimization method. For high-temperature regions where the Coulomb interaction is the dominant perturbation, the many-body partition function is developed from quantum cluster-expansion theory. The Coulomb free energy is given as the sum of the first- and second-order direct-interaction terms, plus the first three exchange-interaction terms. All five terms are exact in the classical limit, i. e., where Maxwell-Boltzmann statistics apply. The direct terms are correct for weak electron degeneracy and include wave-mechanical effects, while the first-order exchange term is exact for all degrees of degeneracy. The theoretical model is applied to multicomponent mixtures of hydrogen and of helium in the temperature range 50-2000 eV. The combination of the ring term plus higher-order terms significantly extends the region of applicability of the model over a classical electrostatic model. Specifically, electron degeneracy, the short-range cutoff in the ring term, and the three-rung ladder (second-order direct) term all operate to produce much less divergent thermodynamic results at a given density and temperature. First-order exchange is important even at moderate values of the electron-degeneracy parameter. The thermodynamic results indicate that evaluation of the exact quantum-mechanical ring term is essential for wider application of the perturbation-expansion theory, as is the development of a second-order exchange term for arbitrary degeneracy.

$A$ relativistic two-level model of a massive atom in the presence of an external plane-wave laser beam is solved. Using the resulting wave functions, the cross sections for the scattering of a photon of the laser frequency or one of its harmonics is calculated. Many interesting nonlinear effects are found, the most striking being the rapid change of the resonance frequency in the cross section for harmonic production as the intensity of the laser is increased. Both approximate and exact numerical results are presented.

Moments of the relativistic Vlasov equation were taken over a Maxwellian distribution. The resulting fluid equations were coupled with Maxwell's equations and solved for an axially uniform cylindrically symmetric electron beam in the steady state. Magnetic neutralization and thermal conduction were neglected, and the beam was assumed to be charge neutralized in the observer's reference frame. The equilibrium was supported by radial gradients in particle pressure balancing against magnetic forces. With no externally applied magnetic field, or for a beam propagating parallel to a magnetic field with no rotation, the total current carried by the beam was found to be significantly less than the Alfvén critical current $I_A$, the ratio of beam current to $I_A$ increasing with temperature and decreasing with increasing $\beta$. For a diamagnetic beam in an external field, a rigid-rotator model was assumed. Solutions of the steady-state equations were obtained for various values of rotation frequency $\omega$ and beam temperature. The radial density profiles were peaked on axis for small $\omega$ and became hollow as $\omega$ increased, because of centrifugal forces. For all $\omega$, the beam density was observed to exhibit radial oscillations which grew in amplitude and decreased in wavelength with decreasing temperature. Equilibria with magnetic field reversal were possible for all values of $\omega$. Purely rotational self-consistent equilibria of the rigid-rotor type were not possible for a charge-neutralized beam of the type considered.

Phonon dispersion in a weakly interacting Bose gas at low temperatures is investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a generalized dielectric formulation. The leading terms for the frequency and damping rate of phonons are evaluated exactly from the zero of the dielectric constant. These terms may be viewed as the extension of Belyaev's zero-temperature results to low temperatures.

Generalized hydrodynamics for classical fluids composed of structured molecules is discussed from a fundamental microscopic viewpoint. The analysis is concentrated on collective fluctuations of the intrinsic molecular angular momentum, and their coupling to the conserved densities of particle number, linear momentum, and energy. It is found from symmetry that the transverse components of linear and angular momentum are dynamically coupled, while the longitudinal angular momentum density moves independently of the other variables. By using the Zwanzig-Mori projection-operator technique, we derive closed and rigorous equations of motion for the set of fluctuations considered. For the case where the intrinsic angular momentum is not far from being separately conserved, approximations can be motivated which reduce these equations to simple relaxation equations, valid for small $k$ and long times. General, Kubo-type expressions for the relaxation coefficients are given. Finally, sum-rule considerations are presented from which these coefficients can be approximately calculated.

Recent light-scattering experiments which have investigated the splittings in the depolarized Rayleigh spectrum of certain nonassociated liquids are discussed in the context of generalized hydrodynamics. It is shown that a purely hydrodynamic or viscoelastic theory does not account for important features of the observed spectrum. However, if angular momentum fluctuations are considered, many of the features of the observed spectra can be accounted for. Moreover, a theory due to Rytov is discussed and studied in the context of generalized hydrodynamics.

A simple model of a traveling-wave parametric amplifier is discussed in quantum-mechanical terms. The amplifier consists of a slab of Raman-active material, illuminated on one face by an intense laser beam that serves as the pump mode; an optical-phonon oscillation serves as the idler mode, and the scattered Stokes light occupies the signal mode. With only a few simplifying assumptions, it is possible to solve the equation of motion for the signal field operator exactly. For large times, both an amplified steady signal and the quantum noise contributed by the material assume simple steady states in an amplifier of finite length. The transient and asymptotic behaviors of the signal and noise intensities are found, together with the corresponding first-order correlation functions. The quasiprobability distribution which specifies the complete density operator for the electric field strength of the amplified signal is also derived.

If the particle-foil interaction potential governing production of H atoms coherently excited by passage through thin foils obeys the $\mathrm{LS}$ coupling scheme applied by Macek (conservation of $z$ components of total orbital and spin angular momenta of the entire particle-foil system, and incoherence of final states of foil constituents), the ad hoc assumption that random phases prevail among the hydrogenic magnetic substate amplitudes invoked in the interpretation of certain recent experiments is avoided. Arguments concerning relative phases of states of different orbital angular momentum are unaffected.

For the positron-hydrogen scattering above the electron-pickup threshold, an improved upper bound on the lowest trajectory of the closed-channel Hamiltonian is obtained and its effect on the bounds on the scattering parameters is clarified.

The analysis of neutron spectra scattered from molecular solids and liquids presents a formidable problem which so far has been only slightly touched upon. For a period of ten years, the translational motions of atoms in monatomic liquids have been investigated by neutron spectroscopists; their theoretical interpretation has reached a certain degree of refinement. An understanding of the effects of rotational motions on the neutron spectra scattered from molecular liquids, however, has not been developed to the same degree. The aim of the present work is to use some simple but reasonable model for the translational motions and to investigate in more detail the effect of the various possible rotational motions on the observed neutron spectrum. The general principle used is that translational and rotational motions are statistically uncorrelated. Thus, when the molecule as a whole vibrates and diffuses, it is assumed that it can also perform librations, free rotations, or rotational diffusion. Phonon expansions are done for the molecular vibrations and librations. Sears's basic theory is used to describe the free rotations and rotational diffusion. A cross section is obtained which contains all the basic components in the scattered-neutron spectrum. A discussion of "good"- and "bad"-resolution measurements is carried through. The value of older neutron-linewidth determinations is discussed. It is concluded that the resolution width ought to be ≤ 0.1 × (the width of the rotational spectrum) if finer details of the rotational motion should be observed as resolved structure. With the aid of good-resolution data it is shown that the nature of the rotational motion changes drastically over the liquid range, from librations to almost free rotations. Comparison is made to changes of rotational motion of ions in the phase transition from the ferro- to the para-electric phase in the solid state. It is shown that from such observations of molecular motion the liquid appears as a phase transition or as a transient phenomenon.

The motion of the center of mass of atoms and molecules is described in the presence of external fields. In the case of electromagnetic radiation whose wavelength is much larger than the atom or molecule, we find that there will be a very small change in the component of the momentum of the center of mass which is in the direction of the polarization of the light. For ions we show that the integral over the perturbing potential yields $-Nqv$, where $N$ is the degree of ionization, $q$ is the elementary charge, and $v$ is the velocity of the center of mass in the direction which the light wave travels. If the wavelength of the light is large when compared with the size of the vessel which contains ionized atoms or molecules, the equation describing the motion of the center of mass is that of a damped harmonic oscillator. We show that in an external homogeneous electric field, the wave function of the center of mass of an ionized atom or molecule is an Airy function. In an external homogeneous magnetic field, we show that the motion of the center of mass of a neutral molecule is that of a harmonic oscillator with a frequency of $\omega ={\left(\frac{N_e{q}^2{H}^2}{4Mm{c}^2}\right)}^{\frac{1}{2}}$, where $N_e$ is the number of electrons in the atom or molecule, $H$ is the magnetic field strength, $M$ is the total mass, $m$ is the electronic mass, and $c$ is the velocity of light. If an oscillatory field polarized perpendicular to the steady field is introduced, we show that the transitions are restricted by the usual harmonic-oscillator selection rules, and that the emission rate for spontaneous emission is about ${10}^{-3\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ for the lighter atoms.

The Cohen-Lekner kinetic theory of electron transport in simple systems is extended to polyatomic systems. The single-scatterer approximation is used to construct differential scattering cross sections for electron-molecule scattering in which the dependence on certain internal parameters such as molecular orientations and conformations, which vary with periods short compared to the duration of an electron-molecule collision, is accounted for by a fixed-internal-coordinates approximation. The resulting differential cross section, unlike the case treated by Cohen and Lekner, does not factor into a product of the electron-single-scatterer cross section and the Van Hove spectral function. The most important consequence of the internal parameters of the scattering molecules is the appearance of an incoherent scattering effect. Such an effect can be very important in liquids and solids where, because of intermolecular order, the coherent part of the cross section may be very small. Boltzmann's equation for electrons moving in a constant electric field is derived, solved formally for arbitrary field strength, and solved explicitly for a low-field limit.