A theory of nonuniform liquids is presented which is based on the Yvon-Born-Green equation for the one-particle density and the Ornstein-Zernike equation of an inhomogeneous system. The necessary closure is effected by exploiting the solution of a modified hypernetted-chain equation and making a local approximation on the (highly universal) bridge function. The theory is successfully applied to model problems that have also been studied by direct-simulation methods. A brief generalization to quantum liquids is also given.

A theory that is suitable for the analysis of the nonlinear behavior at or very near to a far-from-equilibrium instability point is presented. The theory is based on the idea that far-from-equilibrium instabilities, like equilibrium critical systems, have a critical space dimensionality, $d_c$, above which a quasilinear treatment yields the correct values of the critical exponents. The results for physical systems (i.e., space dimensionality $d\le 3$) are obtained by an $\epsilon$ expansion, in a manner analogous to the one used in the dynamical renormalization group. We treat in detail a case model of a chemical instability. The main result is that the critical exponents differ from those predicted by the quasilinear approximation or by master equations (i.e., the so-called "classical" exponents). We show that great care must be taken with the correlation of random forces, since a faulty choice of this correlation can yield results that differ significantly from those obtained by using the correct correlation.

The nature of the threshold behavior of the Rayleigh-Bénard instability is investigated. It is shown that the physics of the convective transition depends crucially on the heat diffusivity of the material from which the horizontal plates of the Bénard cell are made. When the plates have a high heat diffusivity the critical fluctuations are two dimensional. A corresponding dynamical renormalization-group transformation is shown to possess no stable fixed point, indicating a "first-order" transition in agreement with recent experiments. In the case of poorly conducting plates the critical fluctuations are three dimensional outside a small region near the transition point. In this case the dynamical renormalization-group analysis yields a nontrivial fixed point and "nonclassical" critical exponents, whose numerical value is in excellent agreement with experiment. Our analysis indicates the existence of an interesting transition region between three-dimensional (3D) and two-dimensional (2D) behavior. The location of this transition region is estimated. An experiment to check this prediction is suggested. Finally, we address ourselves to the problem of the size of the "Ginzburg region." A mechanism for the amplification of fluctuations is suggested. A sizable enhancement of fluctuations compared to a "local-equilibrium" theory can be understood on the basis of a phenomenological model.

Calculations on the field-theoretic model of a planar fluctuating interface, recently proposed by Wallace and Zia, are extended to the four-loop order. This is greatly facilitated by a Ward identity and an additional simple but powerful theorem which we have found. Explicit results for the Wilson $\beta$ function and the correlation length exponent $\nu$ are given.

We report the observation of Ba $7snd \mathrm{}(n=29-85\mathrm{})\mathrm{}$ atoms in which the inner $7s$ electron is excited to a large enough orbit that the $7snd$ states are incompatible with the simple quantum-defect picture used to describe lower-lying doubly excited atoms. Rather, the observations are consistent with screening of the inner electron from the ${\mathrm{Ba}}^{2+}$ ion core by the outer Rydberg electron which penetrates its orbit. This leads to a shift of the ${\mathrm{Ba}}^{+}$ core energy from its unperturbed value.

A particularly simple instance of broken symmetry arises in the problem of a hydrogen atom in a uniform magnetic field. In a limited sense, the magnetic Hamiltonian nearly commutes with the unit projection of the Runge-Lenz vector upon the field direction.

Recently reported gas-ionization cross sections for ${\mathrm{C}}^{6+}$ projectiles at 4.75 MeV/amu, which were factors of 2-4 above the predictions of a semiclassical scaling model, are shown to be within 30% of Born and Bethe cross sections extracted from the literature.

Tunable coherent ultraviolet radiation has been used to excite selectively the $n=3\mathrm{}$ level in hydrogen and deuterium atoms via two-photon absorption from the ground state. The resulting Balmer-$\alpha$ fluorescence at 656 nm was observed as well as resonant three-photon ionization. This work demonstrates several advantages over other techniques for selective detection of neutral H and D atoms, including three-dimensional spatial resolution and a remote monitoring capability afforded by the use of laser-induced-fluorescence detection.

It is demonstrated that there are considerable differences between the inelastic (but nondetaching) scattering of ${\mathrm{Cl}}^{-}$ by ${\mathrm{N}}_2$ and C${\mathrm{O}}_2$ and that of the isoelectronic systems ${\mathrm{K}}^{+}$ + ${\mathrm{N}}_2$, C${\mathrm{O}}_2$. It is proposed that these differences arise from the fact that temporary negative-ion states of the target molecule serve as intermediaries in the inelastic scattering for the negative-ion—molecule systems.

Rydberg states of an atom in an electric field are represented in terms of hydrogen eigenfunctions for the same field but scattered by the ionic core of the actual atom. The effect of the Stark field on photoabsorption is expressed in terms of scattering and frame-transformation parameters.

We report observation of a pressure-induced extra resonance in four-wave mixing (PIER4 signal) using single-mode continuous-wave dye lasers. The narrow laser linewidth permits for the first time a quantitative verification of the frequency, intensity, and pressure dependence of the PIER4 signal predicted by the theory of the nonlinear susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$.

We consider an intracavity nonlinear medium interacting with two modes of the electromagnetic field via a two-photon process. The cavity is coherently driven at the frequencies of the two modes. We consider as the intracavity medium (a) a two-photon absorber, and (b) $N$ three-level atoms. These systems display a new class of bifurcations, and, in the case of the two-photon absorber, optical tristability is possible.

Multiconfiguration-Hartree-Fock wave functions for ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^1{}_{}{}^{}D$ states in Ca I and Sr I are compared with wave functions based on a multichannel-quantum-defect analysis. Discrepancies are found for all of the four series studied. In all cases the discrepancies pertain to perturbers which probably are located in the continuum.

Using Landau theory, we show that the red shift of the primary Bragg reflection in cholesteric blue phases and the appearance of more than one cubic structure can be understood by including harmonics of the basic spatial frequency in the order parameter. A new nonsymmorphic bcc structure, having $O^8\left(I{4}_{1}32\right)$ symmetry and no isotropic (defect) points, is found at intermediate chiralities.

The nonlinear wave equation and self-consistent pendulum equation are used to generalize free-electron-laser operation to higher harmonics; this can significantly extend their tunable range to shorter wavelengths.

The dynamic renormalization-group method is developed for investigation of correlations generated by the Kuramoto equation with random initial conditions. It is shown that elimination of modes from domain $\Lambda <k<\mathrm{}\infty$ generates the random force and "viscosity" which is positive in the $d=1\mathrm{}$ and negative in the $d\ge 2$ cases. The stable fixed point is found in the $d=1\mathrm{}$ system while the theory is asymptotically free when $d=3\mathrm{}$. No fixed point exists in the $d=2\mathrm{}$ case which explains the patterns formation obtained from computer simulations.