We consider the long-wavelength behavior of smectic liquid crystals (or any solid developing periodic order in only one direction) in the presence of anharmonic terms dictated by symmetry considerations. We analyze this anharmonic model of smectics with the use of analytic renormalization-group techniques directly in three dimensions. We find that the hydrodynamic description of smectics given by the harmonic theory is not valid at sufficiently small wave vectors. Instead, the elastic constants corresponding to the compression and undulation modes, respectively, vanish and diverge logarithmically at small wave vectors. Density correlations, which decay algebraically in the harmonic theory, are found to fall off with a distance-dependent power law at sufficiently long distances. Additionally, the system responds nonlinearly to applied stress at sufficiently small stress, i.e., Hooke's law is not valid. After presenting the calculations leading to the above results, we discuss the feasibility of experimental observation of these effects.

Hydrodynamic instabilities of a cylindrical plasma shell which is imploded by the pressure of an external massless fluid are considered. The plasma shell is assumed to be a compressible, isentropic fluid which is describable as an ideal gas ($p=a{\rho }^{\gamma },\gamma \ne 1$). The unperturbed plasma shell is assumed to undergo a self-similar motion. This assumption together with mass conservation determines the time-dependent pressure profile of the plasma shell. Linear stability analyses for this prescribed self-similar motion are carried out analytically. Stability criteria are obtained in terms of the ratio of specific heats $\gamma$ and an azimuthal mode number of perturbations. It is shown that the imploding plasma shell is unstable to compressible perturbations when $\gamma <2\mathrm{}$. In the case of incompressible perturbations, similar calculations show that the Rayleigh-Taylor instability occurs at the outer surface and, in addition, the unstable mode develops at the inner surface. A plausible mechanism for the development of the unstable mode at the inner surface is given.

Fluctuating hydrodynamics is used to calculate the density correlation function and light-scattering spectrum for a fluid in a stationary temperature gradient. The non-plane-wave nature of the light source in the direction of the temperature gradient is considered explicitly. Finite-size effects are shown to be important when the ratio of system size to dynamic correlation length is smaller than or equal to $O\left(1\right)\mathrm{}$. The magnitude and size of the asymmetry of the Brillouin peaks, as well as the line shapes, are found to depend strongly on the scattering wave vector, beam width, and system size, while the dependence on the surface reflection coefficient is much weaker than expected. The importance of including surface fluctuations when absorbing walls are used is discussed.

In this paper the correlation functions for fluctuations in a fluid kept in a nonequilibrium steady state are studied. Hydrodynamiclike equations for the unequal- and equal-time correlation functions of the microscopic densities of mass, momentum, and energy are derived both for a dilute gas on the basis of kinetic theory and for a fluid of arbitrary density from the Liouville equation. The connection of these equations with those of fluctuating hydrodynamics is discussed.

The equations derived in the previous paper for the unequal- and equal-time correlation functions of the microscopic densities of mass, momentum, and energy are solved and applied to light scattering for the case of a fluid subject to a small temperature gradient. The deviations of the dynamical structure factor $S(\overrightarrow{\mathrm{k}},\omega )$ and the intensities of the Rayleigh and Brillouin lines from their equilibrium behavior are computed to first order in the temperature gradient. The shape and intensity of the Rayleigh line remains the same as in equilibrium. The shapes and the intensities of the Brillouin lines deviate from their equilibrium values by terms proportional to the temperature gradient, leading to an asymmetry in the heights and intensities of the two lines. This asymmetry in the intensities is caused by a mode-coupling effect: the coupling of two sound modes to the heat flux. Owing to restrictions on the theory, the predicted change in the shape of the Brillouin lines is too small to be detected, but the change in their integrated intensities might be observable.

The equations derived in the first paper of this series for the correlation functions of mass, momentum, and energy densities are solved for a fluid subject to a large temperature gradient. The shape and intensity of the Rayleigh line show deviations from equilibrium that are proportional to the square of the temperature gradient. The deviations of the intensity of each Brillouin line from its equilibrium value as a function of the temperature gradient is obtained for the optimal scattering geometry. The intensity of one of these two Brillouin lines shows a maximum or minimum as a function of the temperature gradient, depending on the sign of the temperature derivatives of the coefficient of sound attenuation and thermal conductivity and on the orientation of the momentum transfer between fluid and light with respect to the temperature gradient. Further, the difference in intensity of the two Brillouin lines is found to be about three times smaller than predicted by the linear theory, consistent with the experiments of Beysens et al. Since all these results are due to mode-coupling effects, an experimental verification would constitute the first observation of mode-coupling effects away from criticality. The connection between (a) the mode-coupling effects responsible for the changes in the intensities of the Rayleigh and Brillouin lines, (b) the long-time tail contributions to the transport coefficients, and (c) the nonexistence of a virial expansion of the transport coefficients is discussed.

The $Z$ dependence of the total electronic energy for an atomic isoelectronic series, was investigated in several different ways, first by the consideration of a Taylor-series expansion of ${\overline{V}}_{\mathrm{en}}$, the average electron-nuclear attractive potential energy, used in conjunction with the virial and Hellmann-Feynman theorems and, secondly, a Taylor-series expansion of ${\overline{V}}_{\mathrm{ee}}$, the average electron-electron repulsive potential energy, used in conjunction with the same two theorems. A direct Taylor-series expansion of the total energy $E$ was also studied. Convergence of these expansions was inferred from the rate of convergence of least-squares fits of tabulated values of the total electronic energies as a function of the increasing number of terms in the expansion. Theoretical nonrelativistic Hartree-Fock energies, accurate theoretical nonrelativistic energies, and experimental total energies, the latter approximately corrected for relativistic and quantum electrodynamic effects, were used in the fits. These expansions were compared with $\frac{1}{Z}$ expansion results. All Taylor-series variants studied showed comparable or superior convergence properties to the $\frac{1}{Z}$ expansion. The choice of a ${\overline{V}}_{\mathrm{en}}$ or a ${\overline{V}}_{\mathrm{ee}}$ expansion forces certain behavior on the total electronic energy $E$ as a function of $Z$. From a least-squares rate-of-convergence criterion and other considerations it appears that the Taylor-series expansion of ${\overline{V}}_{\mathrm{en}}$ offers slightly better results. It is pointed out that by the use of the virial and Hellmann-Feynman theorems it is possible to obtain accurate estimates of ${\overline{V}}_{\mathrm{ee}}$ and ${\overline{V}}_{\mathrm{en}}$ from a knowledge of total electronic energies of isoelectronic series alone. The technique is applied to accurate values for the He isoelectronic series and experimental data corrected for relativistic and radiative contributions for the He through Ne isoelectronic series in order to determine the effect of electron correlation on the quantities ${\overline{V}}_{\mathrm{en}}$ and ${\overline{V}}_{\mathrm{ee}}$. Comparisons are made with available experimental and theoretical results in the case of Ne. The $Z$ expansions for the energy were also used to fit individual ionization potentials across an isoelectronic series. These fits were used to predict electron affinities and improved values for certain ionization potentials.

Cross sections for one-electron transfer from a He atom into the fully stripped, hydrogenlike, heliumlike, and lithiumlike ${\mathrm{B}}^{q+}$, ${\mathrm{C}}^{q+}$, ${\mathrm{N}}^{q+}$, ${\mathrm{O}}^{q+}$, ${\mathrm{F}}^{q-}$, ${\mathrm{Ne}}^{q+}$ ions, and also highly stripped ${\mathrm{S}}^{q+}$ ions have been measured at the energy range of $1.5q-3.0q$ keV. The measured cross sections are nearly independent of the collision energy with a few exceptions, and most of the cross sections measured are about (1∼4)×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$, but the cross sections for ${\mathrm{B}}^{4+}$, ${\mathrm{C}}^{4+}$, and ${\mathrm{N}}^{4+}$ ions are very small in the energy range studied. When the cross sections measured are plotted as a function of the ionic charge $q$ of isoelectronic projectile ions, strong oscillations in the cross sections are observed. As a first approximation, this oscillatory behavior can be explained in terms of the classical one-electron model.

With the use of the comparison-equation method, asymptotically exact analytical expressions are derived for the molecular-energy splittings of highly excited states of the one-electron two-Coulomb-center system ($Z_{1}e{Z}_2$). Both the symmetrical ($Z_1=Z_2$) and non-symmetrical ($Z_1\ne Z_2$) cases are studied. The physical implications of our results are discussed, and their relationship with the expressions corresponding to low-lying states is analyzed.

A technique for modifying the laser power spectrum by use of an acousto-optic modulator is described. The theory of the power spectrum resulting from frequency modulation by Gaussian noise is reviewed, and several examples of broadened laser power spectra are presented.

Generalized oscillator strengths (GOS) for excitation and ionization of all occupied shells of ${\mathrm{Al}}^{n+} \left(0\mathrm{}\le n\le 11\right)$, and the Mg, Si, Ni, and Zn ions of the sodium isoelectronic sequence were calculated. The Al-ion GOS were used elsewhere to compute proton stopping power. There were no measurements or other calculations on stopping power with which to compare our calculations. Here the Al-ion GOS are used to calculate electron-ion ionization cross sections, including the effects of excitation followed by autoionization. The cross sections agree to 20% or better with measurements and other calculations, except near threshold. Calculations are also performed for five ions of the Na isoelectronic sequence to examine the relative importance of direct ionization versus excitation followed by autoionization. Comparison with recent measurements on three of these ions (${\mathrm{Mg}}^{1+}$, ${\mathrm{Al}}^{2+}$, and ${\mathrm{Si}}^{3+}$) shows agreement to better than 10% in some cases, and no worse than 20% in any case.

The theory of scattering of a charged particle in the presence of a laser field is formulated variationally. If the field is slowly varying, its dominant effect over a wide range of field intensities will be to modify the asymptotic motion of the projectile. A trial function is chosen which correctly accounts for the projectile-field interaction in asymptotic states. It leads to a variational approximation for the transition amplitude which generalizes earlier versions of the low-frequency approximation in two respects. Firstly, the field is not restricted to be of the form of a monochromatic plane wave but, more realistically, is taken to be a pulse of finite length. Secondly, the target may carry a net charge. The dependence of the transition amplitude on the variable $\Delta E$, which represents the energy transferred to the field, is modified by the presence of the long-range Coulomb interaction; additional terms which depend logarithmically on $\Delta E$ are found. The variational expression for the transition amplitude consists of two factors, one depending only on the external field and the other representing the amplitude for single-photon spontaneous bremsstrahlung. The present analysis of this bremsstrahlung amplitude is based on the assumption that $\Delta E$ is sufficiently small so that the dominant contribution to the spatial integration comes from the asymptotic domain. The low-energy approximation obtained in this way provides a generalization of Low's theorem on spontaneous bremsstrahlung to include the effect of the Coulomb tail.

Total cross sections for the ionization of atomic hydrogen by the impact of bare ions with charge $Z_1=1-6\mathrm{}$ evaluated in the Glauber approximation are presented and compared to recent data for $Z_1=1-3\mathrm{}$ and to other theoretical predictions. At projectile velocities $v<\mathrm{}{Z}_1$ (in atomic units) the Glauber results lie below data observed. For $v>\mathrm{}{Z}_1$ the Glauber results converge to observed results better than other theoretical calculations now available.

A cascade-free determination of the polarization fraction of $2{}_{}{}^1{}_{}{}^{}P$ line radiation excited by electrons in the energy range from 30 to 500 eV has been made from electron-photon angular-correlation and differential-cross-section data. The present results are, in general, larger than previous results and are in good agreement with Glauber-approximation calculations. Evidence is also given to show that the polarization fraction of the $3{}_{}{}^1{}_{}{}^{}P$ state is larger than that of the $2{}_{}{}^1{}_{}{}^{}P$ state at 80 and 100 eV.

The x rays from radiative electron capture (REC) have been observed under single-collision conditions for ${\mathrm{F}}^{8+}$ and ${\mathrm{F}}^{9+}$ ions incident on a He-gas target in the collision energy range 15 to 40 MeV. The peak energies of the REC x rays have been found to change linearly with the projectile ion energies. From extrapolation to the zero projectile energy, the binding energies of the $s$-shell electrons have been estimated to be 0.97±0.02 keV for ${\mathrm{F}}^{7+}$ and 1.08±0.02 keV for ${\mathrm{F}}^{8+}$ ions. These values are in agreement with theoretical predictions. It is found that the width of the REC x-ray peak for ${\mathrm{F}}^{9+}$ ions is broader than that for ${\mathrm{F}}^{8+}$ ions in contrast with a model for REC. The production cross sections of the REC x rays for ${\mathrm{F}}^{9+}$ ions are in reasonable agreement with the Bethe-Salpeter calculation. The total REC x-ray-production cross sections for ${\mathrm{F}}^{8+}$ and ${\mathrm{F}}^{9+}$ are compared with the total electron-capture cross sections.

With increasing nuclear charge $Z$ (and finite nuclear size), the lowest bound-state solution of the Dirac equation changes into a resonance located in the positron continuum (supercritical atom). We develop a formalism which enables us to treat this resonance explicitly in the manner of a quasibound state. The processes of electron and positron production in heavy-ion collisions of total charge $Z_1+Z_2\gtrsim 170$ can then be formulated analytically in such a way that all the rapid energy dependence due to this resonance is made explicit. The definition of the resonance wave function involves some ambiguity. As a consequence, the decomposition of the transition amplitude for positron production into a "spontaneous" and an "induced" part cannot be given unambiguously. The coupled time-dependent equations for the occupation amplitudes of the adiabatic single-particle states contain matrix elements which are smooth functions of the energy, and which can be calculated easily. The application of this formalism to positron production in supercritical atoms is presented in the following article by one of us (T.T.).

The method developed in the preceding paper is applied to the calculation of the spectra of positrons produced in the U + U collision. Matrix elements of the radial derivative operator between adiabatic basis states are calculated in the monopole approximation, with the finite nuclear size taken into account. These matrix elements are then modified for the supercritical case with the use of the analytical method presented in paper I of this series. The coupled differential equations for the occupation amplitudes of the basis states are solved and the positron spectra are obtained for the U + U collision. It is shown that the decomposition of the production probability into a spontaneous and an induced part depends on the definition of the resonance state and cannot be given unambiguously. The results are compared with those obtained by Reinhardt et al.

High-energy-electron-impact-spectroscopy experiments and exact-Hartree-Slater theory show the existence of Compton defects and asymmetries (nonimpulse effects) in helium and neon and are in good agreement with one another.

Coulomb-exploded fragments of ${\mathrm{C}}_3^{+,0,-}$, ${\mathrm{C}}_4^{-}$, ${\mathrm{C}}_5^{-}$, ${\mathrm{C}}_6^{-}$, and ${\mathrm{NCO}}^{+,0,-}$, following stripping of high-energy molecular ions in a thin carbon foil, were recorded, first in plastic sheet detectors, and in later experiments with a new image-intensifying and digitizing system. All of the ions studied in detail, ${\mathrm{C}}_3$ and ${\mathrm{NCO}}^{+,0,-}$, appear to be formed in states of high bending excitations perhaps close to the dissociation limit. The intranuclear separations for the ${\mathrm{C}}_3$ species were found to be similar to that of normal neutral ${\mathrm{C}}_3$, 2.5(1) Å; and for the NCO species, rather small, 2.0(1) Å.

Theoretical expressions for the electric and magnetic susceptibilities and shielding factors of closed-shell atoms and ions are derived from the point of view of the relativistic random-phase approximation. These expressions are evaluated to determine electric-dipole, electric-quadrupole, and magnetic-dipole susceptibilities, and shielding factors for ions of the noble-gas isoelectronic sequences, as well as for selected ions having closed $s$, $d$, and $f$ shells. Comparisons are given with previous theoretical work and with experiment.