Using a perturbation method based on a multiple scattering expansion of Maxwell's equations, we have analyzed the effect of multiple scattering on the polarized and the depolarized field-correlation (FC) functions of light scattered from independent Brownian particles. The results of a complete second-order (CSO) calculation are presented. The expression obtained for the polarized FC function includes double scattering as well as turbidity corrections to the single scattering. Such turbidity corrections strongly influence the static and dynamic properties of the polarized FC function. The results of the CSO calculation reproduce quite well published experimental data on the angular and concentration behavior of the decay time of the polarized FC function. However, for the polarized intensity there is only qualitative agreement between theoretical and experimental values. The CSO analysis does not introduce turbidity corrections to double scattering and hence leads to the same expression for the depolarized FC function as does a pure, double-scattering calculation.

Incoherent quasielastic scattering of neutrons from hydrogen gas has been measured at room temperature and 78°K in a range of pressures from 100 to 2000 atm. We present in some detail the data-reduction procedure which allows us to extract the van Hove self-correction function $S_s(Q, \omega )$. We then extract the linewidth of the self-correlation function by assuming a Lorentzian line shape. By extrapolating to the small-$Q$ limit, we obtain the macroscopic self-diffusion coefficient as a function of density and temperature. We compare the results with the hard-sphere Enskog theory and conclude that there is considerable enhancement over the Enskog values at higher densities.

The shear viscosity of binary liquid mixtures shows a weak anomaly in the critical region. Its empirical formula $\eta ={\eta }_{\mathrm{id}}{\epsilon }_{\mathrm{sp}}^{-\phi }$ is used first to determine $T_{\mathrm{sp}}$ and found to provide reasonable representations of the experimental results. The relevance of this equation to some current theoretical predictions and the general validity are discussed. In addition, it is shown that the shear viscosity satisfies scaling law relations similar to those previously established for equilibrium properties.

A previously developed novel theory for the formal canonical quantization of classically dissipating systems will be the starting point for a detailed discussion of the quantum statistical aspects of the simple linearly damped harmonic oscillator. The formalism essentially involves complex classical canonical coordinates and momenta, and thus quite naturally leads to the possibility of creation and annihilation operators. Furthermore, the occurrence of quantal noise operators appears to be of principal importance for the conservation of the fundamental commutator in the course of time, as will be expressed in a simple fluctuation-dissipation relation. Making a canonical transformation back to the real, Cartesian Hermitian position and momentum an "effective" Hermitian Hamiltonian will be derived, with which a transformation is made from the Heisenberg frame to the Schrödinger frame where the density operator equation will be computed. This will make it obvious that no proper Schrödinger equation exists for the dissipative subsystem on its own, thus reflecting an incomplete knowledge. The master equation will then be translated into its Wigner representation. The intimate connection between the diffusion coefficients in the resulting Fokker-Planck equation and the uncertainty relation will be demonstrated in a clear fashion.

A novel similarity solution in terms of a hyperelliptic integral is given for a magnetohydrodynamic flow across an azimuthal magnetic field in a diverging duct, under consideration of viscous stress relaxation. Velocity profiles and the critical duct angle for flow separation are calculated as a function of the Reynolds number and the Hartmann number. It is shown that viscous stress relaxation modifies the velocity distribution and reduces considerably the critical duct angle for flow separation at low Reynolds numbers. At large Reynolds numbers, viscous stress relaxation is less important, and the results approach asymptotically those of ordinary magnetofluiddynamics, which is based on a static relation between viscous stresses and the velocity component gradients.

A theory of surface tension is formulated for liquid microclusters which are so small that the homogeneous properties of the bulk liquid are not attained even at the center. The choice of the equimolecular dividing surface is made possible by employing a reference bulk liquid which possesses a different chemical potential from that of the real system. Cluster-size dependence of the surface tension is formulated in such a manner that the results of computer simulations for microclusters and for the bulk liquid may be employed, and it is found that for the size range relevant in nucleation the value of surface tension is appreciably greater than the bulk surface tension. The formalism is extended to noncritical microclusters, and the Gibbs-Thomson equation is derived in the present formalism to provide the size of a critical nucleus under a given supersaturation.

By solving the hypernetted chain (HNC) equation for the pair distribution functions, and by Monte Carlo simulations, we have calculated the equation of state and the pair structure of dense binary mixtures of classical point ions in a rigid, uniform background of opposite charge. All of our results indicate that the excess internal and free energies of mixing are negligible compared to the energies of the mixture or the pure phases, for ionic-charge ratios $\frac{Z_2}{Z_1}=2\mathrm{} \mathrm{and} 3$, in the strong coupling (high density or low temperature) regime. This feature allows us to write down a simple equation of state for such mixtures, which is used to determine the phase diagram of pressure-ionized H-He and H-Li mixtures in a rigid background of degenerate electrons. We then treat the polarization of the electron gas by the ionic-charge distribution by perturbation theory and include quantum corrections to the free energy of the ions. Both effects do not drastically modify the phase diagrams. The applicability of our results in astrophysical situations is discussed.

Theoretical results are presented for the bremsstrahlung spectra from 1-100-keV electrons incident on atomic ions, obtained with numerical relativistic partial-wave calculations based on a description of the process as a single-electron transition in a self-consistent screened central potential. Dependence on incident electron energy $T_1$, fraction of energy radiated $\frac{k}{T_1}$, atomic number $Z$, and degree of ionization $Z_i$, is discussed. The importance of screening is examined and comparisons are made with effective charge predictions.

Previous results concerning statistical errors due to finite-time $T$ averaging in many experiments are made more precise. In particular, we show that the error does not always decrease according to a $T^{-\frac{1}{2}}$ law as $T\to \infty$. In the case of power or correlation function measurements, the departure from a $T^{-\frac{1}{2}}$ law may be due to an unbounded spectral density for some frequencies, which appears for some physical noises.

A lattice model of a classical charged liquid originally proposed by Salpeter and Van Horn is found to solve the outstanding problems concerning the linear form of the screening potential known empirically in the Monte Carlo simulation of the classical one-component plasma in its liquid phase. This shows that the short-range order in the classical charged liquid is already very much like that in the lattice phase. Short-range contribution of the bridge diagrams is estimated with the aid of Hansen's computations of the direct correlation function.

Solitary wave solutions of an electric power envelope for two-photon pulse propagation in a resonant medium are given under limited conditions. In addition, we show new types of periodic solutions without Jacobian elliptic functions and the well-known Lorentzian-shape solutions for a coherent two-photon amplifier.

This paper comments on the recent observation of Rydberg "progressions" in atomic uranium. A multichannel quantum-defect analysis shows that the observed ion peaks are unresolved groups of levels with different total angular momenta $J$ and approximately the same effective quantum number ${\nu }_{\ln }$, and configuration interactions are apparent. The possible number of channels and their assignment are outlined.

$L$-subshell ionization cross sections have been measured for equal-velocity ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ projectiles on a gold target. The data are compared with the modified plane-wave Born approximation (PWBA) theory of Brandt and Lapicki. While the data are in excellent qualitative agreement with the theory, they exceed the theoretical predictions at low velocities by a factor of 1.4. Relativistic corrections do not improve the discrepancy.

A microscopic expression for the Maxwell relaxation time for the transverse mode in simple liquids has been derived on the basis of the generalized Langevin equation developed by Mori. For this, it is assumed that the correlation function of the second random force is a function of $t^2$. The derived expression does not involve any adjustable parameter and leads to a correct result for the shear-viscosity coefficient. Numerical predictions for the relaxation time in liquid argon are compared with other existing estimates. It is found that the present results are comparatively much better than some other existing estimates.

This paper examines the effect of velocity-dependent interactions in atoms on the form of the virial theorem and dipole sum rules. When the interactions are linear in the velocity components, the formulas closely resemble the applicable expressions for velocity-independent situations.

Ab initio self-consistent field calculations have been performed for $1s$-core-orbital ionization in the halogen atoms F, Cl, and Br, and their diatomic counterparts ${\mathrm{F}}_2$, ${\mathrm{Cl}}_2$, and ${\mathrm{Br}}_2$. It is found that $E_B\left(X_2\right)<\mathrm{}{E}_B\mathrm{}\left(X\right)\mathrm{}$ in all cases. This order is determined by the relaxation-energy corrections—Koopman's theorem predicts just the opposite shift. The calculations predict that an additional 7-14% of all $1s$-ionization events lead to multiple excitation (shakeup and shakeoff) in the diatomics relative to the free atom. Within a given series, however, the probabilities are fairly insensitive functions of atomic number. The corresponding orbital transformation of Amos and Hall is shown to have particularly useful features when applied to the ionization problem.

A rule is developed which predicts avoided crossings of resonance energy curves of long-lived states of one-electron atoms in an external electric field.

Accurate adiabatic potential curves are calculated for the ground state and 11 excited states of ${\mathrm{He}}_2^{++}$ using the James-Coolidge method. The values are the best of all existing results for this system. The number of basis sets used was 75 for ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ and 57 for ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$. The ground-state energy curve has both a dip and a peak. A dip is also expected for the lowest ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state.