For a classical fluid of hard spheres the nine hydrodynamic time-correlation functions between the microscopic density, longitudinal velocity, and temperature are calculated theoretically on the basis of the revised Enskog theory for all densities and wave numbers. It appears that a simplified description of these correlation functions is possible for small wave numbers in terms of extended hydrodynamic modes and for large wave numbers in terms of free streaming and a single binary collision.

In density-functional theory (DFT) of the ground state, a density distribution $n_o$(r) is called v-representable (VR) if it is the ground-state density in some external potential. [It is known that not all ‘‘reasonable’’ $n_0$(r) are VR.] In DFT of time-dependent linear response of a nondegenerate ground state, a similar question arises: Is a response density, $n_1$(r,ω)$e^{\mathrm{-}i\omega t}$, VR, i.e., is it the response to some perturbing potential $v_1$(r,ω)$e^{\mathrm{-}i\omega t}$ [E.K.U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985)]? In the present paper we show that (1) if the frequency ω<${\omega }_{\min }$ (the lowest excitation frequency), the answer is affirmative; and (2) if ω>${\omega }_{\min }$, the answer is not necessarily affirmative, as demonstrated by counterexamples. [We exhibit ‘‘reasonable’’ functions $n_1$(r,ω)$e^{\mathrm{-}i\omega t}$ which, at isolated frequencies, are not VR.] Implications for time-dependent DFT of linear response are discussed.

Smectic layering at the surface and smectic fluctuations in the bulk can be studied simultaneously by x-ray specular reflectivity and scattering measurements. There is a peak in the angular dependence of the specular reflectivity due to surface-induced smectic layering that penetrates into the bulk as exp(-z/${\xi }_{?}$) where ${\xi }_{?}$ is one of the nematic critical correlation lengths. This is illustrated by measurements of the liquid-crystal materials octyloxycyanobiphenyl (8OCB) and butyloxybenzyl- idene octylaniline (4O.8). In both cases the critical divergence of the intensity of the peak in the specular reflectivity is weaker than ${\xi }_{?}^2$, suggesting unexpected surface physics. The absolute value of the critical part of the density pair correlation function is determined by comparison to the Fresnel reflected intensity. Different geometries of the x-ray spectrometer are also discussed.

Scaling hypothesis on the ‘‘singular’’ part of the free-energy density of a finite system is examined in the context of a Bose gas confined to an enclosure of size $L^{d\mathrm{-}d\mathcal{’}}$×${\infty }^{d\mathcal{’}}$, with 2<d<4 and d’≤2, under periodic boundary conditions. Finite-size effects in the various thermodynamic properties of the system, such as the specific heat, the isothermal compressibility, and the condensate density, are predicted in the regions of both first-order (T<$T_c$) and second-order (T≃$T_c$) phase transition. To test these predictions, a detailed analytical study is carried out in the case of an ideal relativistic Bose gas, which includes the possibility of particle-antiparticle pair production in the system. The various predictions of the scaling hypothesis are fully borne out and the scaling functions governing the critical behavior of the system are found to be universal—irrespective of the severity of the relativistic effects. The influence of the latter enters only through nonuniversal parameters, C${̃}_1$t̃ and C${̃}_2$, which depend on the particle mass m and density ρ as well.

Theoretical calculations on the total (elastic plus inelastic) cross sections ${\sigma }_t$ for positron ($e^{+}$)-methane collisions are reported at 2–600 eV. We evaluate a complex optical potential (COP) for the $e^{+}$-${\mathrm{CH}}_4$ system and treat it exactly in a partial-wave analysis to obtain the S matrix. The real part is composed of an accurate repulsive static potential plus a parameter-free attractive correlation polarization potential. The imaginary part of the COP, $V_{\mathrm{abs}\left(\mathrm{r}\right)}$, is derived semiempirically in order to reproduce the sharp rise in ${\sigma }_t$ just above the positronium-formation threshold ($E_{\mathrm{Ps})}$. This form of $V_{\mathrm{abs}}$ is a function of target charge density, static plus polarization potential, local kinetic energy of the projectile, Fermi momentum, and the mean excitation energy of the system. Our final $e^{+}$-${\mathrm{CH}}_4$ ${\sigma }_t$ compare very well with measurements in the $E_{\mathrm{Ps}\mathrm{-}600}$-eV region. Below $E_{\mathrm{Ps}}$, the present results are in good accord with close-coupling calculations of Jain and Thompson and the measurements of Charlton and co-workers. We also test this absorption potential for the $e^{+}$-He system and find qualitative agreement with measurements. It is also possible from this model to extract approximate values of the Ps-formation cross sections in the ore gap.

Calculations of electron-capture cross sections are presented in the symmetrized strong-potential Born approximation for p+H. These calculations are complete through the third Born term. Our amplitudes may be expressed as a finite sum of hypergeometric functions and derivatives of hypergeometric functions. No evidence is found for new observable singular structure due to third Born contributions.

We have calculated corrections to the strong-potential Born approximation using the distorted-wave Born formalism of Taulbjerg and Briggs. In the sense of a plane-wave Born expansion, all terms of the third Born approximation, and all ‘‘single switching’’ fourth Born terms are included, but a peaking approximation is needed to reduce the calculation to tractable form. We believe this to be the first calculation to be so complete in the Born sense. Effects of the higher terms are most visible in the valley between the Thomas peak and the forward peak. The Thomas peak is visible in the correction term even though it includes no second Born contributions. We suggest that this may be interpreted as a third Born effect with two ‘‘hard’’ collisions followed by a ‘‘soft’’ collision.

Knowledge of the ratio of stopping cross sections may help in determining best values from measurements. The case of Ag and Au is discussed, where theoretical considerations show that this ratio always has a value smaller than 1. This is confirmed experimentally for proton energies larger than 70 keV, in contradiction to all published stopping-power tabulations.

The metastable highest-spin ${}_{}{}^4{}_{}{}^{}\mathrm{F}_{9/2}^{}{}_{}{}^{}$ state among 1s2p3d configurations of three-electron ions has unique characteristics. The decay rates of this state have been calculated relativistically by the multiconfiguration Dirac-Fock approach for ions with atomic numbers from Z=6 to 42. The major decay channels are found to be Auger transitions made possible by the Breit interaction, as well as 2s-2p and 3p-3d electric dipole, 2s-3d electric quadrupole, and 1s-2p magnetic quadrupole x-ray emission. The Auger rate scales as $Z^{4.6}$, the 2s-2$p_{3/2}$ E1 radiative decay rate as $Z^{2.8}$, the 2s-3$d_{5/2}$ E2 rate as $Z^{6.5}$, and the 1s-2$p_{3/2}$ rate as $Z^{8.5}$. The differential metastability among the 1s2p3d ${}_{}{}^4{}_{}{}^{}F$ fine-structure states caused by the effect of relativity is noted.

We present a theoretical work on non-Markovian effects in the time-resolved spectrum (TRS) of resonant light scattering caused by a short pulse excitation. It is found that when the off-resonance frequency becomes comparable or greater than the inverse of the reservoir correlation time ${\tau }_c$, the finiteness of ${\tau }_c$ reduces the luminescencelike component which is energetically and temporally uncorrelated with incident radiation. It is emphasized that this non-Markovian effect in TRS is essential for obtaining a full understanding of the resonant light scattering phenomena.

A four-wave mixer model is presented for which exact analytic results can be obtained in a regime where the usual perturbation procedures no longer apply. It is shown that under suitable conditions the output of such a four-wave mixer consists of a superposition of macroscopically distinguishable states. Such states can be identified with a homodyne detector which is able to observe the interference between the macroscopically distinguishable components. Further, it is shown that the device can act as an even-odd filter which will switch incoming pump light between two output ports depending on whether there is an even or odd number of pump photons.

It is shown that the shear-viscosity formulas derived by the modified moment method can adequately account for the shear rate and frequency dependence of the viscoelastic properties of a two-dimensional fluid computed by Evans et al. by a nonequilibrium molecular-dynamics method. The nonlinear shear viscosity computed from these formulas are positive everywhere for all values of shear rate and frequency.

A very-low-frequency oscillation has been observed in a Taylor-Couette flow. This oscillation corresponds to a periodic amplitude instability detected at any given point in the flow. This mode exists in a narrow range of Reynolds numbers between 183 and 190, provided that the flow has evolved very slowly. The frequency of this oscillation depends strongly on the Reynolds number and varies from 0.3 to 0.93 mHz.

The vector differential equation ∇×V=kV with constant k has been the subject of recent controversy. Some of its solutions lead to force-free magnetic fields or to standing electromagnetic waves having E parallel to B everywhere. Recent criticisms of this equation have been given based primarily on its transformation properties, especially under spatial inversions. Here we reformulate this equation so as to reconcile these criticisms.

A connection between entropy and parametrized time is established within the context of parametrized relativistic quantum mechanics. By recognizing the existence of three operationally distinct, and physically distinguishable, forms of time, it is shown that parametrized relativistic quantum theories have both an arrow of (parametrized) time and an equivalence between (coordinate) time and space in the relativistic sense.

Upper and lower bounds to the energy of quantum-mechanical parameter-dependent systems are obtained from variational functionals. Results are shown for the Zeeman effect in hydrogen and the anharmonic oscillator.

Cases of substantial term dependence are found in the Hartree-Fock approximation for heavy atoms that are not attributable to a large dipole exchange interaction. They may be associated with ‘‘giant resonances’’ in electron impact excitation and ionization.

We report results of the first ab initio, close-coupling calculations of the electron impact excitation of atomic copper in the 0.1–8.0-eV range. Integrated, inelastic cross sections are given for the low-lying ${}_{}{}^2{}_{}{}^{}\mathrm{°}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ excited states, which are important to the kinetics of the copper vapor laser. The calculated cross sections exhibit a rich resonance structure due to ${\mathrm{Cu}}^{\mathrm{-}}$ states, which have not been previously known.

We have calculated differential cross sections for positron-argon elastic scattering at intermediate energies, using an ab initio optical model potential which takes into account explicitly the static, polarization, and absorption contributions. Our results are compared with recent experimental data and demonstrate that absorption effects have an important influence on the angular distributions.