Resonances of quantum systems are associated with poles of the Green's function which occur at complex energies. The wave functions corresponding to such poles increase exponentially at large distances and so are very badly divergent. Nevertheless, these resonance wave functions have useful properties which can be exploited in cases where only their behavior at small distances is relevant. In this paper we construct and study such resonance wave functions for several illustrative quantum systems of theoretical interest. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, the renormalization which occurs here is entirely automatic and the theory has neither ad hoc procedures nor infinite quantities. In addition to other results, we obtain a representation of the Green's function in terms of the resonance wave functions; this representation appears likely to be useful because it has an energy dependence that is especially simple.

Parametric equations of state near the critical point of fluids are discussed with emphasis on their physical implications and potential applications. Two specific phenomenological proposals in which the "distance" parameter is directly related to singular thermodynamic functions are studied. One of these is shown to be obtainable from a general equation of state in which the isothermal compressibility is used as a scaling factor. Both proposals are found to be in agreement with the $\mathrm{PVT}$ data on ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$. Consistency checks between $\mathrm{PVT}$ and specific-heat data on these fluids are made using the parametric equations.

Landau's quantized hydrodynamics is derived from the microscopic Hamiltonian, which is written in terms of the density and velocity operators. In Euler's equation for the velocity operator, the force per unit mass has a form different from Landau's and is given explicitly in terms of the two-body potential. A quantum pressure term, which does not occur in Landau's theory, also appears. New realizations of the density and velocity operators are given which satisfy the commutation relations, but must act in a Hilbert space larger than Fock space. It is shown that the formalism is without meaning in Fock space owing to the nonexistence of certain operators.

The propagation of a strong coherent "pump" wave traveling through a resonant medium is discussed. The medium is assumed to consist of identical stationary atoms, and the pump-wave frequency is assumed to coincide exactly with the resonance frequency for transitions between a particular pair of atomic states. A previously developed theory of the response of a strongly driven atom to a weak nearly resonant "signal" field is used to deduce the existence of a coupling between any two waves travelling parallel to the pump wave whose (nearly equal) frequencies sum to twice the pump-wave frequency. In the limit of very intense (highly saturating) pump fields, the coupling between the two waves of nearby frequencies leads to amplification of both waves if their frequencies lie within an interval about the pump-wave frequency equal to the Rabi frequency of population inversion. The basic process, which is roughly described by travelling-wave parametric-amplifier equations of motion, consists of the absorption of two pump-field photons followed by their emission at different nearby frequencies, and thus implies a frequency instability of the initially coherent pump wave.

Jackson's model for adsorbed helium monolayers is suitable for studying thermodynamic properties in the mobile limit. In particular, low-temperature specific heats can be calculated over a range of areal densities. The dominant contributions come from longitudinal surface phonons. We report here (i) an extension of Jackson's model to account for surface-phonon—surface-phonon interactions, (ii) computations of low-temperature specific heats to several coverages, and (iii) a comparison of the computed results to experiment.

The systematic dependence of the magnitude of the self-generated magnetic fields of a laser-produced plasma on nitrogen background pressure has been investigated. At expansion distances of a few millimeters or more, the strongest fields were found to reside at the front of the streaming laser plasma. Magnetic fields were created in the laser plasma long after laser shut off by allowing the streaming plasma to impinge upon a glass plate.

The normal-mode decomposition of the spectral densities which play a role in the analysis of light-scattering spectra of fluids is treated. The inherent symmetry of the hydrodynamic matrix and the relative magnitude of its elements are utilized to develop a simple and systematic method for obtaining the eigenvalues and the required eigenvector elements. The scheme, which involves a partitioning of the hydrodynamic matrix, is shown to yield the eigenvalues correct up to terms of order $k^2$ and the eigenvectors correct up to terms of order $k$. The method is illustrated by application to a two-component fluid.

The electronic-recombination coefficient of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_2^{}{}_{}{}^{+}$ is shown to be ($1.23\times {10}^{-8\mathrm{}}+5.04\mathrm{}\times {10}^{-10\mathrm{}}p$) ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$, compared to that of ${}_{}{}^4{}_{}{}^{}\mathrm{He}_2^{}{}_{}{}^{+}$, which is ($1.15\times {10}^{-8\mathrm{}}+3.86\mathrm{}\times {10}^{-10\mathrm{}}p$) ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$, where $p$ is the gas pressure in Torr.

The energy distribution function for electrons in a Townsend discharge in argon is computed from a development of the Boltzmann equation. A wide range of elevated values of $\frac{E}{N}$ is treated. The results are compared with experimental findings and are used to calculate ionization coefficients, transport coefficients, and mean swarm energies.

The nonlinear limit of the resistive tearing-mode instability is investigated by a time-dependent solution of the Fourier-transformed magnetohydrodynamic equations. The calculation is started with the fastest-growing linear mode and assumes a constant (e.g., turbulent) resistivity. Attainable magnetic Reynolds numbers are limited by the steep spatial gradients developed and by the propagation of Alfven waves in the system. At the largest values used, 10% of the background energy is released in nonthermal forms. The time and energy scales found are consistent with the results of astrophysical observations and laboratory studies of solar-flare processes.

Radiative corrections to the Bohm-Pines dispersion equation and the Pines-Schrieffer-Drummond coupled pair of quasilinear equations are examined in the light of the Weisskopf-Wigner theory of line broadening. The principal results are the natural broadening and the Lamb shift of the particle-wave resonance condition. The dimensionless width of the nonresonant or adiabatic interaction is of the order of $\alpha \left(\frac{c}{\nu }\right)$ for electron-plasmon interaction and $\alpha \left(\frac{\nu }{c}\right)$ for electron-photon interaction, where $\alpha$ is the fine-structure constant. The Lamb shift of the resonance condition $\omega -\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{v}}\approx 0$ is of the order of $\frac{q^2{\omega }^2}{\pi \mu {\nu }^3}$ for electron-plasmon interaction and $\frac{q^2{\omega }^2}{\pi \mu c^2\nu }$ for electron-photon interaction. Here $\omega$ and $\overrightarrow{\mathrm{k}}$ are the frequency and wave vector, respectively, of the photon or the plasmon and $q$, $\mu$, and $\overrightarrow{\mathrm{v}}$ are the charge, mass, and velocity of the electron, respectively.

We have determined the molecular arrangement that results when the smectic $C$ liquid-crystalline phase is subjected to large magnetic fields. Furthermore, a simple technique which makes use of the free-induction decay is used to obtain a precise determination of the smectic $C$ tilt angle. Uniformly aligned smectic $C$ samples are obtained by cooling through the nematic phase into the smectic phase in the presence of a 14 000-G magnetic field. Once aligned, the samples are then oriented at various angles relative to the magnetic field direction and the absorption line shape is recorded. A model is developed to describe the molecular arrangement in the smectic $C$ which results from reorientation of the sample in the magnetic field. This model allows for the reorientation of the long molecular axes within the smectic layers subject to the constraint that a constant tilt angle be maintained. The experimental test of the model comes from its ability to predict NMR line shapes and second moments. In terephthal-bis-4(4-$n$-butylaniline), we measure the temperature dependence of the tilt angle to be a ${(T_c-T)}^{\beta }$ dependence, where $\beta =0.40\mathrm{}\pm 0.04$ and $T_c$ is the smectic $A$-smectic $C$ transition temperature. This is compared with de Gennes's prediction of $\beta =0.35\mathrm{}$. In addition, a tilt angle of 45° was obtained for 4, 4′-bis-(heptyloxy)azoxybenzene.

The ground-state energy of an interacting many-boson system obtained by Bogoliubov and Zubarev using the collective-coordinate method is shown to be equivalent through second order to the variation-perturbation energy evaluated in the uniform limit by means of the method of correlated basis functions. It is also shown that the wave function derived with a slight modification of the Bogoliubov-Zubarev approach is equivalent to that determined formally from the Rayleigh-Schrödinger perturbation theory in the uniform limit.

The long-time behavior of autocorrelation functions of conserved variables and of their corresponding dissipative fluxes is studied using the Mori formalism. A set of variables including linear and bilinear forms of the conserved variables is treated and consistent expansions to quadratic order in the wave-vector dependence of the appropriate correlation functions are carried out. The treatment is self-consistent and does not involve factorization of time-dependent correlation functions. Explicit calculations for the wave vector $\overrightarrow{\mathrm{k}}$ and the frequency-dependent shear-viscosity coefficient are carried out in two dimensions. The asymptotic time dependence of the shear-viscosity correlation function is proportional to $t^{-1\mathrm{}}$ when $k\to 0$. The effect of higher-order nonlinear forms of the conserved variables has not been studied; such a study is essential to ensure the validity of the asymptotic time dependence found here.

We present a general theory for the calculation of the single-particle time-correlation function $\alpha \mathrm{}\left(t\right)=〈[a,a^{†}\mathrm{}(t\left)\right]〉$ which is the canonical average of the commutator between the particle annihilation $a$ and creation $a^{†}\mathrm{}\left(t\right)\mathrm{}$ at time $t$. The theory is based on the projection-operator method. The complex spectral function $\hat{\alpha }\left(\omega \right)$ is expressed in terms of the natural frequency of oscillation $\Omega$ and the width function $\hat{\gamma }\left(\omega \right)$. From the analytical property of $\hat{\alpha }\left(\omega \right)$ in the complex $\omega$ plane for the weak-coupling limit, the long-time behavior of the correlation function $\alpha \mathrm{}\left(t\right)\mathrm{}$ and the relaxation functions is obtained. For a harmonic oscillator immersed in a heat bath, the perturbation calculations for $\Omega$ and $\hat{\gamma }\left(\omega \right)$ are given in the power of the coupling constant. By means of this series, the spectral function $\hat{\alpha }\left(\omega \right)$ for a single normal mode of an anharmonic system is explicitly calculated as a function of the frequency $\omega$ and the temperature $T$. As a possible application of the results the electrical conductivity due to a localized mode is discussed.

The three-body recombination coefficient has been measured in a partially ionized plasma jet mainly by using a spectroscopic technique. Experimental data were treated by the consideration that the net number of particles that were deexcited across a minimum in the total rate of deexcitation of atoms was substantially equal to the number of electronic recombinations. Experimental results are in good agreement with other investigated values and show $T_e^{-4.4\mathrm{}}$ dependence of the recombination coefficient.

The partitioning of ion energy among thermal energy, drift energy, and random-field energy is studied by solution of the Boltzmann equation. An expansion in powers of the square of the electric field strength is obtained by Kihara's method. Numerical calculations for several ion-neutral force laws show that Wannier's constant mean-free-time model gives a reasonable first approximation. The formal extension to multicomponent mixtures is also given. The matrix elements obtained are tabulated, and can be used to study the field dependence of other moments of the ion-distribution function.

We discuss the relation between the observed spectra in the Rayleigh—Brillouin light-scattering experiments for molecular fluids and the generalized transport coefficients. For a two-level molecular fluid undergoing thermal relaxation, we derive the generalized hydrodynamic equations for the conditions when translational motion is hydrodynamic. For two explicit examples of parahydrogen and sulphur hexafluoride, we numerically evaluate the wave-number- and frequency-dependent transport coefficients implied by the generalized hydrodynamic equations. We then critically examine the implication of these results for the phenomenological analysis of the polarized-light-scattering spectra, which is commonly employed by most workers in the field. We find that the most important quantity for the description of such experiments on intermediate-density fluids is a frequency- and wave-number-dependent bulk viscosity rather than a frequency-dependent thermal conductivity.

The anisotropic liquid-structure factor of $p$ -cyanobenzylidene-amino-$p$-$n$-octyloxybenzene has been measured in the nematic phase using $\mathrm{Cu} K\alpha$ x rays. This material exhibits a second-order phase transition to the smectic $A$ phase at $T_c=82.8\mathrm{}$ °C. The liquid-structure factor shows a non-Lorentzian peak at a wave number of $q_0=0.179\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ (equivalent $d$ spacing 35.0 Å) of the following form: $S_q=1+{\{3.5\mathrm{}{\epsilon }^{\gamma }+10\mathrm{}{\left[\frac{(q_{\parallel }-q_0)}{q_0}\right]}^2+0.6\mathrm{}{\left(\frac{q_{\perp }}{q_0}\right)}^{\eta }\}}^{-1\mathrm{}}$, where $\epsilon =\frac{(T-T_c)}{T_c}$, $\gamma =1.49\mathrm{}\pm 0.1$, $\eta =2.5\mathrm{}\pm 0.2$, and $\hslash q_{\parallel }\left(\hslash q_{\perp }\right)$ are the momentum transfers parallel (perpendicular) to the orienting field.

We show that atomic-electron screening and subshell-ratio effects in single-quantum pair annihilation, reported by Broda and Johnson and by Sheth and Swamy, have a simple origin observed also in pair production and atomic photoelectric effect. In all three processes, the characteristic distances are small on an atomic scale, but large on a nuclear scale; wave functions have a point-Coulomb shape, but not the point-Coulomb normalization. Atomic-electron screening effects cause appreciable modifications of the total pair-annihilation cross section for positron energies below $1.5m_{ e}{c}^2$ in heavy elements ($Z>\mathrm{}47\mathrm{}$). For low-$Z$ elements, screening effects are always important. The $n^3$ rule of Bethe for subshell ratios is good only for low-$Z$ elements (where $n$ is the prinicipal quantum number); we find that the subshell ratio between the $K$ and $L_I$ single-quantum pair-annihilation cross sections is well predicted by the square of the ratio of the $K$ and $L_I$ bound-electron wave-function normalizations.