Observations of Cooper minima in excited-state photoionization cross sections for the Ne $3s$ and Ar $4s$ levels are reported. Prebreakdown Ne and Ar discharges under irradiation by light in the 200-400-nm wavelength range yield spectral dependences of photoionization cross sections with minima at the ionization threshold of these states in Ne and slightly distant from them in Ar. They are in close agreement with certain theoretical predictions. Autoionization structure which exists between the two ionization limits ${}_{}{}^2{}_{}{}^{}p_{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}p_{\frac{1}{2}}^{}{}_{}{}^{}$ was not observed in any of the Ne or Ar photoionization spectra due to both low spectral resolution and the high density of levels in this spectral region. Application of these measurements to ultraviolet-radiation detection is examined. High detection sensitivity of ultraviolet light is indicated.

Incoherent scattering functions have been experimentally determined for photon energies 84.4, 123.6, 145, and 320 keV in the angular range 30°-130° in the elements Sc, Y, La, Ce, Gd, Dy, W, Pt, and Pb with the use of the aluminum difference technique. The experimental values have been compared with those estimated on the basis of the nonrelativistic Hartree-Fock wave functions. Good agreement is observed between theory and experiment.

Čerenkov radiation is calculated for electron beams which exceed the velocity of radiation in a nondispersive dielectric medium. The electron beam is assumed to be bunched as emitted from a traveling-wave accelerator, and the emission region is assumed to be finite. Predictions include (a) emission at harmonics of the bunch rate, (b) coherence of radiation at low frequencies, (c) smearing of the emission angle for finite emission regions, and (d) explicit evaluation of the power spectrum in terms of bunch dimensions. The results apply to microwave emission from fast electrons in air or other dielectrics.

A preliminary experimental investigation of the generation of second-harmonic photons from the interaction of free electrons with an intense laser beam has been performed. Second-harmonic photons with a wavelength of 530 nm generated from the interaction of free electrons with 1060-nm photons from a neodymium-glass laser are implied by observing Doppler-shifted photons with wave lengths of 490 and 507 nm. The observed photon wavelengths result from a Doppler shift of the laser photon wavelength as viewed in the rest frame of the electrons, combined with a Doppler shift of the second-harmonic photon emitted from 1600- and 500-eV electrons. Comparison of experimental results with those predicted by cross sections, derived from classical and quantum electrodynamics, shows reasonable agreement with both theories. Although second-harmonic photons are created, the dynamics of second-harmonic-photon generation (accelerated electron motion due to the electromagnetic field or actual two-photon interaction with the electron) cannot be resolved without further experiment.

A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.

We present a quantum-statistical analysis of the steady-state light fields in driven parametric oscillation in a cavity. Using the solution of a Fokker-Planck equation for the generalized $P$ representation of the signal and idler modes, we calculate the mean photon numbers, second-order correlation functions, and intermode correlation function as functions of the driving field. The generalized $P$ distribution describes the signal and idler modes' statistics over the whole range of driving-field strengths except in the region far below the oscillation threshold. The second-order correlation functions are found to violate the Cauchy-Schwartz inequality, a violation allowed because the $P$ distribution is complex. Squeezing is also found in a linear combination of the signal and idler fields.

A closed-form approximant is proposed for the dynamic scaling function that characterizes the behavior of the wave-number—dependent diffusion of the order-parameter fluctuations in a fluid near a critical point. The expression contains two parameters that determine the expected behavior of the diffusion coefficient in the hydrodynamic and in the nonlocal critical limits. The proposed scaling function yields an accurate representation of our recent experimental data for the 3-methylpentane and nitroethane mixture near the critical mixing point with parameter values that are in good agreement with the values predicted from theory.

We derive an approximate closed form for the infinitesimal generator of the renormalization group for the interacting Bose fluid. The Bose-condensed phase is treated by the method of Bogoliubov, and a simple scaling law is found for the condensate density. It is shown that the quantum-mechanical features are irrelevant close to the $\lambda$ line. This is demonstrated by calculating the critical behavior in $4-\epsilon$ dimensions to order $\epsilon$.

Starting with a model intermolecular potential that includes $\hat{\Omega }·\hat{r}$ terms to account for anisotropic steric interactions, we carry out a statistical mechanical calculation in the cell approximation, and apply it specifically to the isotropic-nematic transition of methoxybenzylidene butylaniline (MBBA). The potential is determined to fit the experimental transition temperature $T_{\mathrm{IN}}$ and the discontinuity in the orientational order parameter $〈P_2〉$ at transition. $〈P_2〉$ and $〈P_4〉$ are then calculated from solving a set of coupled self-consistency equations for the orientational and spatial parts of the distribution function, as are other phase-transition properties. There are improvements over model calculations which do not account for anisotropic steric effects, but the improvements are generally less than significant. The most striking result is that a stable nematic phase requires $〈P_4〉$ to be negative at and near the transition. It is a theoretical result qualitatively consistent with experimental data but has not been attained until now.

The semiclassical impact-parameter method is used to calculate shifts of Lyman and Balmer lines from levels $n\le 6$ caused by electrons in a dense plasma. Comparison with measurements and estimates of shifts due to ion quadrupole interactions indicate that shifts from distant electron-atom collisions are the major cause of observed shifts of Balmer lines. Blue shifts from ion-atom quadrupole interactions are relatively small for low series members.

The hydrodynamic theory of the dynamics of equilibrium fluctuations in one-component fluid layers confined by two identical elastic solid boundaries is presented. The dynamic structure factor for a fluid layer and the interfacial modes are analyzed under assumptions of continuity of stresses (no interfacial stress) and velocities ("stick" boundary condition) across the fluid-solid interfaces. There are four interfacial modes in such a system with dispersion relations which depend on the component of the wave vector parallel to the interfaces, $k_{\parallel }$. In the limit of $\frac{\overline{\rho }}{{\rho }_s}\to 0$, where $\overline{\rho }$ and ${\rho }_s$ are the mean densities of the fluid and solid, respectively, two of these modes are just the well-known Rayleigh waves and the remaining two are the interfacial fluid modes found previously in the case of rigid solid walls [D. Gutkowicz-Krusin and I. Procaccia, Phys. Rev. Lett. 48, 417 (1982); Phys. Rev. A 27, 2585 (1983)]. For finite small values of $\frac{\overline{\rho }}{{\rho }_s}$ the attenuation of the interfacial fluid modes is due to dissipative interfacial transport and varies as $k_{\parallel }^{\frac{3}{2}}\frac{\overline{\rho }}{{\rho }_s}$, provided that $c<\mathrm{}{c}_t$, where $c$ is the speed of sound in the fluid and $c_t$ is the transverse sound speed in the solid. If, however, $c>\mathrm{}{c}_t$, the energy of the interfacial fluid mode is radiated into the solid and the resulting attenuation along the interface varies as $k_{\parallel }{\left(\frac{\overline{\rho }}{{\rho }_s}\right)}^2$, for small $k_{\parallel }$. Since the speed of the interfacial fluid modes is less than $c$, the corresponding peaks in the dynamic structure factor are better separated from the unbounded fluid Brillouin peaks and thus easier to observe experimentally than would have been the case with rigid solid walls.

The prediction of the stable configuration of an ideal uniformly volume-pumped electron-hole cloud involves the rationalization of a "free-boundary" problem. That is to say, there are an infinite number of degenerate steady-state solutions which satisfy the fluid-dynamical equations and the boundary conditions. If the stationary states are metastable due to isolation or freedom from large-scale fluctuations in the cloud, then all states are attainable via differing initial conditions (e.g., variable risetime of the laser pump). On the other hand, if configurational changes can occur by fluctuation, creation, and annihilation of drops at any "stationary" state, however slowly, then it is necessary to specify a global thermokinetic optimum if a unique stable solution is to be identified. Both the uniquely stable and hysteresis cases are experimentally observed. In this contribution we solve the fluid-dynamical equations for a cloud, explicitly demonstrating the degenerate nature of the boundary-value problem. The global dissipation rate is evaluated and shown to be a function of the exciton-gas density as a unique internal order parameter possessing two zeros and a maximum value, and free of explicit configurational parameters. The hypothesis of a stable maximal state in a topologically fluctuating milieu (already suggested by Onsager's dissipation principle) leads near the saturation line to strictly linear global and local flux-force relations as Euler-Lagrange equations and to explicit expressions for the drop density and exciton density which are in good functional and fair quantitative accord with conventional, low-excitation stripe and cylinder pumped experiments. Our theoretical expression for the drop radius is less successful, because, we believe, of the inappropriateness of the available experimental test and the strong experimental artifacts.

We present a detailed analysis of anharmonic effects on the viscous and elastic properties of various systems with one-dimensional order. We show that the nonlinear coupling of the velocity field to thermally excited undulation modes causes four of the five viscosities in these uniaxial systems (including one, ${\eta }_2$, governing shear flow in the layers) to diverge as $\frac{1}{\omega }$ when measured at small frequencies $\omega$. As a result, sound attenuations scale as $\omega$, rather than ${\omega }^2$ as in most materials. A simple algebraic relation between the divergent parts of three of the viscosities is derived. We argue that the divergence in ${\eta }_2$ leads to strongly non-Newtonian flow in the liquid layers of these materials. The calculations here extend the previous work of the authors to include an analysis of irreducible graphs to all orders in perturbation theory in the temperature. Some new results on the nonlinear elastic theory of these systems are also obtained, extending earlier work by Grinstein and Pelcovits. The existing experimental evidence for our predictions is discussed, and additional experiments are suggested.

We consider $N$ superimposed fluids, having arbitary initial perturbations at their $N-1\mathrm{}$ interfaces, undergoing a Rayleigh-Taylor instability with constant acceleration. The time evolution of these perturbations is described by a sum over normal modes and in general is a combination of oscillation and exponential rise. We derive the equation governing their growth, discuss the case $N=3\mathrm{}$ analytically, and give two numerical examples where we plot the time evolution of the perturbations at the four interfaces of five superimposed fluids. Our examples illustrate how the evolution depends on the density profile, on the wavelength of the perturbations, and on the initial conditions.

A computerized high-resolution ac calorimetric technique has been used to measure the heat capacity $C_{\mathrm{px}}$ of a critical 3-methylpentane + nitroethane binary-liquid mixture. An analysis of these results yields universal parameters in good agreement with those expected for the $d=3\mathrm{}$, $n=1\mathrm{}$ (three-dimensional Ising) universality class. The critical exponent $\alpha ={\alpha }^{\prime }$ lies in the range 0.11-0.12, the ratio $\frac{A^{\prime }}{A}$ of the amplitudes of the leading singularity in $C_{\mathrm{px}}$ above and below $T_c$ is 1.79±0.06. The ratio of the corrections-to-scaling amplitudes $\frac{D^{\prime }}{D}$ is ∼1. The quantity $\frac{A_v{\xi }_0^3}{k_B}$, which relates the critical amplitude of the heat capacity to that of the correlation length, is also in agreement with the renormalization-group value for the three-dimensional Ising model as expected from two-scale-factor universality.

Computer calculation for the numerical solution of Duffing's and generalized Duffing's equations shows global scaling properties for the bifurcation in parameter space. These scaling properties are discussed in terms of a one-dimensional map. The analysis based on a piecewise linear approximation gave results in good agreement with the experimentally observed scaling behavior.

The Milne problem for a hard-sphere Rayleigh gas is studied by solving the stationary Fokker-Planck equation according to the method of moments; the results, obtained with only a modicum of effort, are in excellent agreement with a recent treatment, based on the Boltzmann equation. The belief that the one-dimensional Fokker-Planck equation is appropriate for solving this problem is not supported by our analysis.

We analyze some general features of two models of coupled logistic equations. We find that, for selected values of the three control parameters, chaotic patterns may emerge out of an infinite sequence of period-doubling bifurcations. However, there exist large regions of control-parameter space where the approach to irregular behavior appears to be consistent with the Newhouse-Ruelle-Takens scenario, as evidenced by the appearance of two characteristic frequencies. As the ratio of these frequencies is varied, by changing the control parameters, phase locking and quasiperiodic motion are observed on the way to chaos.

A new method is developed for calculating electric microfield distributions in a plasma. The method uses a coupling-parameter integration technique to express the Fourier transform of the microfield distribution in terms of a special pair-distribution function. An approximation of this function yielding the exact second moment of the microfield distribution gives results which agree well with computer simulations for strongly coupled one-component plasmas.

A set of three coupled nonlinear equations describing electrostatic drift waves, drift Alfvén waves, convective cells, and magnetic drift modes has been derived for finite ion temperature. The reduction to simplified nonlinear model equations in different $\beta$ regimes and the consequences for transport properties are discussed.