Existing ultrasonic and light-scattering data on sound propagation are analyzed, both in terms of a relaxing viscosity as calculated by Kawasaki, and in terms of relaxing heat capacities as calculated by Mistura. The two theories are examined and found to be quite different, but neither theory is found to be capable of accounting for the data, although disagreement with Kawasaki's theory is much more pronounced. Although not in agreement with theory, a frequency-dependent viscosity very similar to that required to account for the observed ultrasonic dispersion and attenuation is found to yield anomalous Brillouin spectra in excellent agreement with those observed near the critical point.

A unified theory is developed for describing dynamic and static properties of strongly correlated charged-particle systems, such as a high-density electron liquid and a strongly turbulent plasma, for which the correlation (or fluctuation) energy is comparable in magnitude to the kinetic energy. Based on the microscopic Klimontovich formalism, a systematic renormalization of the single-particle propagators is carried out and vertex corrections arising from strong correlations are taken account of. The resulting theory is examined, and found to be satisfactory, in the light of a number of rigorous criteria, such as explicit inclusion of statistical modification effects in the single-particle orbits, dynamic modification of effective particle interactions brought about by strong correlations, frequency-moment sum rules of the dielectric response function, and reproduction of exact results known in the static properties of the electron liquid; the theory is thus valid for all wave numbers and frequencies. With the aid of a velocity-average approximation, we show that the result can be expressed in a simplified form which still satisfies those criteria. Its relation with the polarization potential model in the theory of condensed matter is thereby noted; explicit expressions for the scalar and vector polarization potentials, the wave-number-dependent effective mass, and the collisional contribution to the response function are obtained.

The two-particle correlation function for the classical one-component plasma in the high-density fluid phase is calculated from the correlation function of a short-range reference potential by a perturbation method based on the hypernetted chain equation (HNC). It is shown thàt the long-wavelength correlations are correctly described by this method. A technique for extending $g\left(r\right)\mathrm{}$ to infinity is shown to be valid and useful. The results are in excellent agreement with those obtained from the "Ewald image" Monte Carlo method.

In this paper we present both the first realistic calculation of the spectrum of multiply scattered light near a critical point, and the first experimental determination of the corresponding spectrum. We assume the double scattering to be the dominant phenomenon, and we use the Ornstein-Zernike cross section and the Kawasaki dynamical structure factor. Experimental data, obtained in a critical mixture of nitrobenzene and $n$-hexane, are seen to be in good agreement with the calculated spectra. Both are clearly not Lorentzian.

Solutions to the initial-value problem of a weakly ionized rarefied gas in a uniform electrostatic field are found explicitly for the lowest three hydrodynamic levels indicated by a moment method previously described. The resulting sets of equations are solved by a completely implicit Crank-Nicholson scheme. For very light ions, or moderately inelastic electrons, a Monte Carlo solution is also found and compared to the moment solutions delineating their range of validity. The deviation of the higher-order theory from the diffusion theory is mapped on a parametric plane bounding the region of validity of the diffusion equation as derivable from the Boltzmann equation. The Hornbeck experiment is analyzed neglecting a cathode boundary, thus illustrating the effects of large initial density gradients on the transient current.

We describe an experiment to measure the specific heat of C${\mathrm{O}}_2$ to an accuracy of 1% along the critical isochore for $4\times {10}^{-5\mathrm{}}<\left|t\right|<3\mathrm{}\times {10}^{-2\mathrm{}}$, where $t=1-\frac{T}{T_c}$, giving details of the method and the analysis. After applying a correction term for the effect of gravity on the specific heat of the 1-mm-high sample, we fitted the data with functions of the form $C_v=A{\mathrm{}\left|t\right|\mathrm{}}^{-\alpha }+B$. With the constraint $\alpha ={\alpha }^{\prime }$ the optimum value of the exponent was $\alpha =0.124\mathrm{}\pm 0.005$. When this constraint was relaxed, we obtained $\alpha =0.124\mathrm{}\pm 0.014$ and ${\alpha }^{\prime }=0.124\mathrm{}\pm 0.012$. These results are in good agreement with predictions based on renormalization-group analysis and numerical estimates for the three-dimensional Ising lattice. For the ratio $\frac{A^{+}}{A^{-}}$ of the coefficients of the divergent term on each side of $T_c$, we obtained the value 0.54, which is within the range of predictions from scaling and the renormalization-group method, but disagrees with the estimate for the Ising model. We also present the results of measurements of the thermal relaxation time of the sample.

Starting from a novel exact expression for the dielectric constant of a classical one-component plasma, we study the important modifications of the plasma oscillation modes which appear when one progressively increases the plasma expansion parameter $\lambda$. For small $\lambda$ values the evaluation of the plasma mode requires a non-Markovian theory. We find good agreement between our results, recent computer findings, and known theoretical expressions. For instance, the dispersion of the plasma frequency is shown to take on values slightly above the mean-field prediction. For large $\lambda$ values the plasma mode is shown to be expressible in terms of hydrodynamical quantities. Here the dispersion of the plasma frequency is shown to be negative, while the damping of the plasma mode is given by the strong-coupling limit of the longitudinal viscosity from which the non-Markovian contributions to the bulk viscosity are to be deleted.

Concepts from the theory of dilatation analytic operators are applied to the problem of determining the radius of convergence of the $\frac{1}{Z}$ perturbation expansion for atomic bound-state energies. It is shown that if the radius of convergence is determined by a singularity on the positive real $Z$ axis, it will occur for a value of $Z$ such that $E\left(\frac{1}{Z}\right)$ becomes degenerate with a threshold. This result has serious consequences regarding conjectured bound states embedded in electronic continua of the same symmetry.

It is pointed out that Reinhardt's analysis assumes that wave-function normalizability persists up to the first real energy singularity. If this behavior is violated (as it is for the analogous square-well problem), then the analytically continued $E\left(\lambda \right)$ is neither prevented from crossing the first threshold, nor from exhibiting real singularities between thresholds.

The spin-orbit parameters for the sextet states of the $f^5$ configuration are computed using the Young-tableau techniques developed by Harter. The conceptual and computational advantages over traditional methods are discussed.

On the basis of improved multiconfiguration Hartree-Fock calculations for the ground states of Ca, Sr, Ba, Zn, Cd, and Hg it is confirmed that recent photoelectron satellite spectra obtained by Süzer, Lee, and Shirley do require for the interpretation of the observed satellite intensities knowledge of more than just the ground-state composition. The relevant dipole matrix elements between initial and final states are also needed. It is noticed that photoelectron spectroscopy allows the observation of the relaxation of atomic orbitals on a time scale determined by the kinetic energy of the photoelectron.

The intensity correlation functions $\mathrm{Tr}\left\{\rho \mathrm{}\right(0\left)\mathrm{}{s}^{+}\mathrm{}\right(t\left)\mathrm{}{s}^{+}\right(t+{\tau }_1\left)\cdots s^{+}\right(t+{\Sigma }_{i=1\mathrm{}}^n{\tau }_i\left)s^{-}\right(t+{\Sigma }_{i=1\mathrm{}}^n{\tau }_i\left)\cdots s^{-}\right(t+{\tau }_1\left)s^{-}\mathrm{}\right(t\left)\right\}$ associated with a two-level atom undergoing Markovian dynamics [$s^{\pm }\mathrm{}\left(t\right)\mathrm{}$ being the spin-½ operators for the atom] are shown to factorize in the form $f\left(t\right)\mathrm{}{\Pi }_{i=1\mathrm{}}^{n}g\left({\tau }_i\right)$ with $f\left(t\right)\mathrm{}$ [$g\left(t\right)\mathrm{}$] giving the probability of finding the atom in the excited state when initially it is in the state $\rho \mathrm{}\left(0\right)\mathrm{}$ [ground state].

Accurate and compact integral-transform wave functions are constructed for the $1{}_{}{}^1{}_{}{}^{}S$ state of the helium-like ions from ${\mathrm{H}}^{-}$ through ${\mathrm{Mg}}^{10+}$. The variational ansatz is of the form $\Psi (r_1, r_2, r_{12})={\left(4\mathrm{}\pi \right)}^{-1\mathrm{}}{\Sigma }_{k=1\mathrm{}}^N{c}_k(1+P_{12})\exp (-{\alpha }_k{r}_1-{\beta }_k{r}_2-{\gamma }_k{r}_{12})$ where the $c_k$ are found by solving the secular equation and the exponents ${\alpha }_k$, ${\beta }_k$, and ${\gamma }_k$ are chosen to be the abscissas of Monte Carlo and number-theoretic quadrature formulas for a variationally optimized parallelotope in $\alpha -\beta -\gamma$ space. A 66-term function of this type for the helium atom yields an energy of -2.903 724363 a.u. as compared with the 1078-term function of Pekeris which yields an energy of -2.903 724376 a.u. In order to test the accuracy of the wave functions a number of properties including $〈r^n〉$ and $〈r_{12}^n〉$ with $n=-2, -1, 1, \dots , 4$, $〈{\overrightarrow{\mathrm{r}}}_1·{\overrightarrow{\mathrm{r}}}_2〉$, $〈{cos\theta }_{12}〉$, $〈\delta \left({\overrightarrow{\mathrm{r}}}_1\right)〉$, and $〈\delta \left({\overrightarrow{\mathrm{r}}}_{12}\right)〉$ are computed and compared with the best available results. The electric dipole polarizability is computed from a simple formula due to Thorhallsson, Fisk, and Fraga. Comments on the limiting accuracy of this formula are made. Electron-nuclear and electron-electron cusp condition tests are made for the functions. Detailed convergence studies are presented for ${\mathrm{H}}^{-}$ and He in the form of a sequence of functions with increasing $N$. The functions are found to be rather accurate and more compact than any other functions available in the literature with the exception of those containing logarithmic terms. Possible refinements to the basis set used are discussed.

The noncoplanar symmetric ($e, 2e$) reaction is applied to the CO molecule at 1200 and 400 eV. The valence-state structure of the ion extends from 14 to 63 eV. Momentum profiles are measured for different fixed separation energies and shown to correspond closely to the plane-wave off-shell impulse approximation for electron orbitals given by self-consistent field calculations. Much structure is observed outside the main peaks. It is shown to be due mostly to configuration interaction of the $3\sigma$ hole state with core-excited states. Qualitative features of a configuration-interaction calculation are confirmed in terms of both momentum profiles and the spectroscopic strengths of ion states. The spectroscopic sum rule is satisfied within experimental error, confirming the validity of the analysis.

The differential cross sections for electrons scattered from atoms are determined in the first Born approximation by the Fourier transform of the sum of the first- (times $2Z$) and the second-order density matrix elements. When scattered intensities are measured with high accuracy, features such as electron correlation and relativistic effects can be studied. In the present experiment using 40-keV electrons, a precision of 0.1% in the count rates and 2 arc sec in the scattered angle has been achieved in the angular range of 7 to 200 mrad. The experimental data are matched at large scattering angles to theoretical cross sections based on Hartree-Fock potentials. The deviations between theory and experiment at small angles are discussed with respect to changes in the first- and second-order densities based on configuration-interaction wave functions.

With the use of recently proposed analytic methods, Glauber scattering amplitudes for the excitation of the $3d$ substates of atomic hydrogen by electron impact are obtained in closed form. The individual $n=3\mathrm{}$ cross sections and the Balmer-$\alpha$ cross section predicted by the Glauber theory in the range $18\le E_i\le 500$ eV are compared with experiments and with other calculations. The polarization fractions of $3p-2s$, $3d-2p$, and of the Balmer-$\alpha$ line are also calculated in the Glauber approximation, and comparison is made with the existing experimental data and with the Born predictions. The parameters ($\lambda , \chi$) predicted by the Glauber approximation are also given.

The elastic scattering of fast electrons and positrons by complex atoms is analyzed by using the basic ideas of the eikonal-Born series method within the framework of the optical-model formalism. This approach allows us to derive from first principles a local second-order pseudopotential which in addition to the static interaction also accounts for polarization, absorption, and exchange effects. A full wave treatment of this pseudopotential is then performed. Our ab initio optical-model theory is illustrated by a detailed analysis of the elastic scattering of electrons and positrons by helium and neon atoms for incident energies ranging from 100 to 700 eV. Our theoretical values for electron-helium and electron-neon differential cross sections are in excellent agreement with recent absolute experimental data.

We consider the deep-level absorption of x rays in atoms in the presence of an intense laser field. The laser field is considered to be small relative to atomic fields but strongly interacting with the outgoing electron, represented here by a plane wave. The general expression for the x-ray absorption cross section as a function of the laser field is obtained using the two methods of power-series expansion and asymptotically large fields. We find that for low fields, the cross section increases as the square of the field, while for large fields it decreases asymptotically as the inverse power of the field.

The relativistic random-phase approximation (RRPA) is applied to study radiative transitions from $n=2\mathrm{}$ states along the He isoelectronic sequence. The strengths of various decay modes and the energy splittings of the $n=2\mathrm{}$ multiplets are investigated. At low $Z$ the present results agree with earlier nonrelativistic studies, whereas, at high $Z$ our results provide new information about oscillator strengths, branching ratios, and multiplet structure for the $n=2\mathrm{}$ states.