The dielectric function $\epsilon (k,\omega )$ of an electron plasma in thermal equilibrium is calculated for all degrees of plasma degeneracy. Previous results for degenerate and nondegenerate plasmas, based on quantum-mechanical, classical, or semiclassical approaches, are contained in this analysis. Expressions for the real and imaginary parts of $\epsilon (k,\omega )$ are given for the cases of low and high frequencies and long and short wavelengths. In particular, the roles of thermal and quantum effects on screening, collective plasma resonance, and single-particle behavior are discussed.

Kramers' theory of activated processes yields expressions for the steady-state escape rate in the large- and small-friction limits and for Markovian dynamics. The present work extends this theory to non-Markovian dynamics and to the whole friction range. Kramers' results are recovered in the appropriate limits.

Application of the critical dynamics to the nucleation process results in a Langevin-type equation for the radius of the nucleus, which is transformed to a Fokker-Planck equation for the distribution function. The time-dependent solution of this equation is shown to be crucially dependent upon the initial conditions. The time lag associated with the establishment of the steady state following a fast quench is exponentially larger than that for a slow quench. Numerical estimates of the time lag are presented.

A study of anharmonic effects in the presence of shear flow in the liquid layers of smectic-$A$, hexatic-$B$, and cholesteric liquid crystals is presented. It is shown that the nonlinear coupling of the velocity field to thermally excited undulations of the layers gives rise to a singular $\frac{1}{\left|\dot{\gamma }\right|}$ dependence of the viscosities ${\eta }_i$ on the shear strain rate $\dot{\gamma }$ at small $\dot{\gamma }$. In addition, the coefficient of this anomaly is found to diverge as ${\left(\ln L\right)}^2$ where $L$ is the size of the system. The $\frac{1}{\left|\dot{\gamma }\right|}$ divergence of ${\eta }_2$, which governs shear flow in the layers, is shown to imply that a minimum applied stress is required in order to set up such a flow. It is demonstrated that this effect provides a straightforward explanation of the puzzling non-Newtonian "plastic" behavior widely observed in experiments on capillary flow in the liquid directions of smectics. The magnitude of the observed yield stress is shown to be consistent with the predictions of this work. Further experimental tests of the theory presented here are suggested.

The transition from Taylor to wavy vortex flows is described by an amplitude equation for the vortices. In agreement with experimental data, finite-size effects are shown to select azimuthal wave numbers greater than 1 at the onset and to modify the position of the transition. Moreover, the onset of wavy flows is also much more sensitive to end effects than the onset of Taylor vortex flows.

A scheme for current generation based on a stochastic driving mechanism is proposed. The current in this approach is generated by launching into the plasma two lower-hybrid waves having appropriate different frequencies, wave numbers, and amplitudes. The phase-space analysis of the electron motion in such a configuration reveals the existence of a relatively broad stochastic layer far away from the separatrix, allowing for diffusion in velocity space of high-velocity electrons. The diffusion coefficient of this process is evaluated and the solution of the Fokker-Planck equation for the electron velocity distribution function is used to calculate the current $J$ and the power dissipated $P_d$ in generating it. A favorable $J$-to-$P_d$ ratio for steady-current drive is found.

An explicit gauge-independent calculation of the bound-state Aharonov-Bohm effect is presented using the hydrodynamic formulation of quantum mechanics. It is pointed out that the Aharonov-Bohm effect is a genuine gauge-independent property of standard quantum mechanics. The statistics of the particle-vortex composites is also briefly mentioned.

The electron-capture processes of highly stripped ions of ${\mathrm{F}}^{q+} \mathrm{}(q=6,7,8\mathrm{})\mathrm{}$ and ${\mathrm{Ne}}^{q+} \mathrm{}(q=7,8,9\mathrm{})\mathrm{}$ in collisions with He atom were investigated using the energy-gain spectroscopy technique. A single dominant peak is observed in most of the energy-gain spectra except for the ${\mathrm{Ne}}^{7+}$ and ${\mathrm{Ne}}^{9+}$ spectra, in which two peaks are observed corresponding to the one-electron capture process into levels with different principal quantum number $n$.

The eikonal approximation taking into account the post-collisional Stark effect removes the shortcoming of the previous calculations of relative $l$ capture cross sections. We find good agreement between the calculated ${\sigma }_{2s}$ and ${\sigma }_{2p}$ cross sections and the available experimental data in $p+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions.

A quantum-mechanical treatment is used to determine the total differential cross section for collisions of excited sodium atoms with xenon. A rainbowlike structure in the angular distribution is predicted for collisions involving sodium in the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state.

Generalized oscillator strengths and integrated cross sections from threshold to 1000 eV are calculated in the Glauber approximation for $2s-3s$ and $2s-3d$ excitations. The calculations are carried out using the Hartree-Fock wave function of Weiss. The results are compared with the Born calculations using the same wave function and available experimental data.

The cross section ${\sigma }_{-+}$ for double-electron detachment from ${\mathrm{F}}^{-}$ ions in rare-gas targets has been measured between 25 and 125 keV under single-collision conditions. In contrast to the target dependence of single-detachment cross sections, the cross sections are largest for helium and neon and decreased with increasing target mass. The close similarity between the ${\sigma }_{-+}$ and ${\sigma }_{0+}$ cross sections suggest that double detachment is a sequential process where one electron is first detached and then the second electron is detached at a smaller interaction radius.

In this addendum to a previously published paper [Phys. Rev. A 22, 1563 (1980)] we clarify and correct our discussion of the anomalous-magnetic-moment contribution to the $1s2p{}_{}{}^3{}_{}{}^{}P$ fine structure, following a suggestion by Hata. The result of a reanalysis of our data is a slightly improved value for the $J$-independent $2P-2S$ differential Lamb shift: 1.2542(15) ${\mathrm{cm}}^{-1\mathrm{}}$.

Raman scattering by molecules embedded in microscopic particles is investigated, and a means for calculating the angular distribution is presented. The particle environment is shown to yield Raman-scattering angular distributions intrinsically different from those for fluorescence. The implications for surface-enhanced Raman scattering are discussed.

The transport of resonance radiation through an optically thick vapor of Sr atoms is studied. A pulsed dye laser tuned to the 461-nm resonance line excites a narrow (∼250-μm-diameter) column of Sr atoms along the axis of a cylindrical oven containing Sr vapor and Ar buffer gas. After a delay of ≤80 ns, a second dye laser excites the atom from the first excited state ($5s5p$) to a higher excited state ($5s7s$). The fluorescence from this latter transition is monitored as the second laser is translated parallel to the first. Since the excited-state-excited-state fluorescence is not trapped, the result is a plot of density of atoms in the $5s5p$ state as a function of position from the originally excited volume. The results are discussed qualitatively.

The Einstein-Milne relations for the continuum are generalized to a nondegenerate relativistic gas in thermodynamic equilibrium, using the relativistic ionization equation which has been recently established by us [J. Phys. A 16, 2347 (1983)] and which must replace the Saha equation at temperatures above ${10}^8$ K. The macroscopic continuum opacity and emissivity of this gas are also derived.

The static structure factor of liquid alkali metals is calculated using a classical one-component plasma as the reference system. The effect of electron-electron screening and the fluctuating dipole-dipole interaction (due to polarization of ion cores) is taken into account using low-order perturbation theory. The effect of the latter interaction is appreciable near the first two peaks and amounts to reducing the height of these peaks. The results obtained are in very good agreement with the experimental data for all the alkali metals.

Absolute values of excitation-rate coefficients for Fe viii, Fe ix, and Fe xi were obtained from measurements of relative excitation rates for these ions and the recent measurement of excitation rates for Fe X. With one exception, the results are within a factor of ∼2 of theoretical values. Observed deviations by factors less than 2 are probably not significant because the measurements were done under different plasma conditions and extrapolation of data was needed in their redution.

Time-dependent behavior of one-dimensional (1D) many-fermion models is obtained by a method of recurrence relations. The Hilbert space of the density-fluctuation operator is two dimensional ($2d$), resulting in a time-independent generalized random force. The relevant Hilbert spaces of 2D and 3D many-fermion models, however, are infinite dimensional and the generalized random forces are consequently time dependent. The structure of these Hilbert spaces provides a picture of time-dependent behavior for 1D models which is fundamentally very different from that for 2D or 3D models.

We have studied the period-doubling power spectrum of a class of area-preserving maps. The ratio of the successive average heights of the peaks in the spectrum is found to approach a universal limit $2{\beta }^{\mathrm{}\left(2\right)\mathrm{}}$ with ${\beta }^{\mathrm{}\left(2\right)\mathrm{}}\simeq 30.4$.