A general expression for the shift in the average energy of an atomic electron configuration owing to configuration interaction is calculated in the second order of Rayleigh-Schrödinger perturbation theory, for arbitrary interacting configurations in either the relativistic (nlsj) or the nonrelativistic (nls) angular momentum classification scheme. This correction to the configuration-average energy is especially important for evaluating the effects of departures from pure j-j coupling when interpreting spectra from highly ionized atoms using the spin-orbit split array model. The total shift divides naturally into contributions from a set of distinct products of radial integrals, each multiply- ing the configuration average of a reducible four-body operator. For configurations that interact by single-electron excitation, $n_1$$l_1$$j_1$→$n_2$$l_2$$j_2$, the partial shift associated with each such product reduces to two terms, each proportional to a polynomial of degree 4 in the occupation numbers. The first & and is interpreted as a correction to the central potential. The second term contains the essential effects of configuration interaction, and vanishes unless the two spectator electrons (of the four-body operator) are equivalent. For two-electron excitations, only one term appears with no restrictions on the quantum numbers of the active electrons. Comparisons are presented with detailed level accounting results, and with experimental measurements.

Continuum electrons are produced in a specific l state with high-energy resolution using shake-off photoionization. This process is well characterized, so that the photoionization signal is an accurate measurement of the difference between the continuum electron’s wave-function phase and that produced by a hydrogenic interaction. Measurements are reported showing the phase of a ${\mathrm{Ba}}^{+}$+${\mathrm{e}}^{\mathrm{-}}$ in a d wave, in cases where it is well behaved, and in cases where doubly excited resonances produce rapid phase variations.

The ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ fine structure and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ hyperfine structure as well as the isotope shift between ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$→1snp (n=5–79) transitions have been measured using an atomic beam and an intracavity frequency-doubled coumarin ring dye laser near 270 nm. The observed 1snp ${}_{}{}^3{}_{}{}^{}P$ ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ fine structure is in agreement with (extrapolations of) existing experimental results and theoretical calculations. The 1snp ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ hyperfine structure has been analyzed using the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ fine-structure parametrization and the Fermi-contact interaction of the screened 1s electron. For n>35 hyperfine components of the 1snp ${}_{}{}^1{}_{}{}^{}P$ levels are also excited as a consequence of hyperfine-induced singlet-triplet mixing. Calculated hyperfine splittings agree with experiment for n<20. Deviations up to 50 MHz are observed for n>20. These are shown to be due to hyperfine-induced n-mixing effects. The experimental results are excellently reproduced in a three-channel two-limit quantum-defect model without any adjustable parameter. The observed 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$→1snp ${}_{}{}^3{}_{}{}^{}P$ isotope shifts can be fully explained using recent mass polarization calculations for the 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and 1snp (n=3–8) ${}_{}{}^3{}_{}{}^{}P$ levels and confirm an isotope dependence of 〈${\mathrm{p}}_1$⋅${\mathrm{p}}_2$〉 for the 1s2s ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ level.

The exact solution to the master equation of a nonlinear oscillator, subject to damping or amplification, is presented. The effect of such incoherent processes on the quantum-coherence properties and recurrences is obtained. It is shown that amplification destroys quantum coherence more rapidly than does attenuation.

We present a comprehensive theory for interference in an apparatus whose parts—source, detector, mirrors, beam splitters, and medium—are in general motion. Under the conditions prevailing in all practical cases, geometrical optics is fully adequate to give the phases of the interfering waves; therefore, our treatment is based on the Hamiltonian formalism. We assume that the speeds of all moving parts are small with respect to the velocities of the waves, so that their motions can be viewed as small perturbations to a stationary interferometer. A first-order perturbative expression is given for both the Hamiltonian and the ensuing phase shifts. The results are applied to a wide spectrum of cases, ranging from neutron interference experiments to gyro lasers.

A uv laser based on resonant photoexcitation is described. This type of laser is a prototype for soft-x-ray lasers in isoelectronic analogs. Intense, Mn vi–line radiation at 310 Å from a ${\mathrm{CO}}_2$-laser-produced plasma was used to resonantly pump Ciii ions, in an adjacent vacuum-arc discharge, from the 2$s^2$ ground state to the 2s4p upper level. Electron collisions rapidly redistribute the population of the pumped 4p level among other n=4 levels. Enhanced fluorescence coincident with the Mn vi–line radiation was observed on many 4-3 transitions in Ciii. To describe the kinetics in C iii ions, a 72-level collisional radiative model was constructed with up-to-date atomic data. Measured values of electron density and temperature in the C and Mn plasmas were used as inputs to the model. To verify this model, the populations of excited states in C iii ions were measured spectroscopically and compared with predictions. Gain coefficients of about 0.1 ${\mathrm{cm}}^{\mathrm{-}1}$ were predicted by the model. These gains were found to be consistent with the experiments. Single-pass gain measurements showed that the total gain-length product was 0.5 in two C iii lines at 2177 and 2163 Å. Laser action at these wavelengths was demonstrated in a resonant Fabry-Perot cavity. This C iii–Mn vi photoexcitation scheme is a prototype for soft-x-ray lasers in higher Z, isoelectronic analogs, such as Mg ix–Al xi and others.

Stochastic resonance was recently observed in a bistable ring laser. It is a phenomenon in which the response of a bistable system to a periodic modulation is enhanced by the injection of noise along with the modulation. So far, comparisons of the experimental observations with theory have been made only for models that are much simplified compared with the more realistic two-mode equations that describe the ring laser. We report here the results of numerical simulations of the stochastic differential equations for the laser with periodic modulation of the asymmetry between the two modes and injected noise. The simulations reveal the phenomenon of stochastic resonance in a manner closely resembling the experimental observations. The appearance of second-harmonic frequencies in the output power spectrum and the role of the colored nature of the pump laser noise are studied. Finally, we discuss the relation of the recent experimental measurements of hysteresis in a ring dye laser by Gage and Mandel [J. Opt. Soc. Am. B (to be published)] to the observation of stochastic resonance.

For the model of Drummond and Walls [J. Phys. A 13, 725 (1980)] describing dispersive optical bistability, the s-parametrized quasidistributions W(α,s) introduced by Cahill and Glauber [Phys. Rev. A 117, 1882 (1969)] are investigated. The equation of motion for W(α,s) generally has derivative terms up to third order. For the Q function (s=-1) and the P function (s=1) the third-order terms vanish. The equation of motion is then a pseudo-Fokker-Planck equation, i.e., a Fokker-Planck equation where the diffusion matrix is not positive definite or semidefinite. It is shown that the equation of motion with the inclusion of third-order-derivative terms can be solved by the matrix continued-fraction method. In particular, results for the Wigner function (s=0) are presented and compared with the results of the Q function (s=-1). Furthermore, the results are compared also with those obtained from the equation of motion for the Wigner function where the third-order-derivative terms have been neglected.

The structure factors S(Q) for gaseous deuterium at densities and temperatures in the critical region have been measured for the first time using time-of-flight neutron diffraction at the ISIS pulsed neutron source. The data, when inverted to real space, determine the site-site radial distribution function of the nuclei in the sample. The experimental results are compared with a classical Monte Carlo simulation of a monoatomic Lennard-Jones fluid under equivalent conditions. After correcting for the effects of the molecular form factor in modifying the static structure factor, the simulations reproduce the qualitative trends of the data with density and temperature, with quite good quantitative agreement as well. No evidence is found for the enhanced ordering near the critical point which had previously been predicted from Raman scattering data.

Within the framework of lattice-gas hydrodynamics, we study fluctuations of an interface separating two immiscible fluids. The static fluctuations show the random-walk behavior typical of systems with energies proportional to their lengths, whereas the time behavior of the interface can be described by a linear Langevin equation with noise. We discuss the thermodynamics of the interface fluctuating in the heat bath provided by the two fluids, measure and calculate the macroscopic and microscopic coefficients of surface tension, and numerically check the relevant fluctuation-dissipation relation.

A new formulation of the weighted-density approximation (WDA), as currently applied in the theory of nonuniform classical liquids, is presented. This modified weighted-density approximation retains a key feature of the original approximation by including correlations, at least approximately, to all orders in the functional expansion of the excess free energy. It continues to require as input only the two-particle direct correlation function of the uniform liquid. In contrast to the original WDA, however, practical implementation of the modified WDA demands considerably less computational effort. When applied to the freezing of the hard-sphere liquid, the results obtained previously with the original WDA, already in good agreement with simulation, are reproduced quite accurately. It is concluded that in its new formulation the WDA is now just as simple to implement as the widely used Ramakrishnan-Yussouff theory. But as with the original WDA the new formulation more accurately describes the freezing of hard spheres and is more soundly based in the sense of including correlations to all orders.

Fourteen realizations of Saffman-Taylor flow at small-viscosity contrast have been measured under nearly identical flow conditions. With control-parameter fluctuations ≲0.15%, we observe fluctuations of 20% in the crudest measures of the patterns and much larger fluctuations in the strengths of individual wave numbers of a modal analysis of the patterns for this broadband instability. The initial disturbance can be observed as it propagates toward the center of the cell from the side walls. As the patterns go over from the linear to the nonlinear regime, several quantitative measures show abrupt change. In the nonlinear regime the patterns not only fail to show progress toward a single-finger steady state but the individual fingers actually show a tendency to evolve toward a narrower distribution of lengths.

The thermal transport properties of mixtures can be formulated in a number of ways, depending on the choice of driving forces for the transport of heat and matter, without violating the Onsager conditions. Here we treat transport in mixtures based on the driving forces -∇ ln T and -T ∇(${\mu }_a$/T), with T the temperature and ${\mu }_a$ the specific chemical potential, to obtain the Green-Kubo expressions and the Enskog theory for the corresponding transport coefficients which seem most amenable to molecular-dynamics evaluation. The transport properties of a hard-sphere mixture (mass ratio of 0.1, diameter ratio of 1.0, at a volume of three times close-packed volume), calculated by a Monte Carlo, molecular-dynamics method based on the Green-Kubo formulas, are compared with the predictions of the Enskog theory. The long-time behavior of the Green-Kubo time-correlation functions for shear viscosity, thermal conductivity, thermal diffusion, and mutual diffusion are found to be in good agreement with the predictions of mode-coupling theory. Except for viscosity, the contribution of the long-time tails to the transport coefficients is found to be significant. We obtain values, relative to Enskog, of 1.016±0.007 for shear viscosity, 1.218±0.009 for thermal conductivity, 1.267±0.026 for thermal diffusion, and 1.117±0.008 for mutual diffusion.

The scintillation intensity S and the collected charge Q in liquid argon have been compared with each other for projectiles of relativistic protons and He, La, and Au ions. According to an elementary theory the quantity S/$S_0$ is a linear function of the quantity Q/$Q_{\infty }$, where $S_0$ is the scintillation intensity at zero electric field and $Q_{\infty }$ is the charge to be collected at an infinite field. The experimental results for protons and He ions lie between the line and the data for 1-MeV electrons. The results for La ions lie along the line. The results for Au ions show systematic deviations from the line and can be explained by quenching of scintillation.

A light particle (electron, positron, or positronium atom) thermalized in a dense fluid can, in certain instances, become localized in a region of altered fluid density. This process is known as self-trapping. In this paper we formulate a mesoscopic model for the evolution of translational degrees of freedom, which uses quantum mechanics to describe the light particle (LP) and classical mechanics for the fluid molecules. The model self-consistently takes into account the mutual influence between the LP and fluid and the large isothermal compressibility near the liquid-vapor critical point. The dynamical representation of this model leads to a set of hydrodynamic equations which couples the LP wave function to the local fluid density. The equilibrium representation takes the form of a Landau-Ginzberg functional in which the wave function plays the role of order parameter. Optimization of the probability density in state space generates a mean-field theory in which the wave function is coupled to the local fluid density via a local equilibrium condition.

The time-independent Schrödinger equation provides the second equation necessary to specify the local density and wave function. When the LP-fluid atom interaction is represented by a Fermi pseudopotential, the two coupled equations can be reduced to dimensionless form by scaling the position with respect to the scattering length and scaling the thermodynamic variables density (ρ) and temperature (T) with respect to their values at the critical point. Together with the principle of corresponding states, they provide a universal description of the trapped state. Scaling transforms the normalization integral into a universal constant which contains all system-specific parameters and determines the response of the gas to the presence of the light particle. The model was applied to the problem of computing the mean decay rate of a localized positronium atom. The van der Waals equation was used to approximate the equation of state. The decay rate and free energy were plotted versus density on isotherms. Trap formation was found to depend on the universal constant, scaled temperature, and density. The model provided good qualitative agreement with the results of experimental measurements of the decay rate of orthopositronium in ethane and argon.

In the wigglers of future free-electron lasers, the electron beam will be required to travel over a length of 10 m or more in pipes with small diameters. Transverse resistive wall effects could lead to beam breakup during this transport. To investigate this possibility, the equation of motion for a bunched beam is solved analytically. Results show that a steady-state solution is reached for times larger than the diffusion time. This solution can either oscillate or grow exponentially with the length of the pipe, depending on the relative magnitudes of the resistive wall effect and the focusing force in the wiggler. The magnitude of the resistive wall effect depends on the pipe radius b (it increases as 1/$b^2$) but is independent of the thickness and conductivity of the pipe. The thickness and conductivity affect only the time required to reach the steady-state solution. The possibility of a significant transient is also discussed.

Retaining the scalar as well as the vector nonlinearities on an equal footing in coupled nonlinear partial differential equations, it is shown that nonlinear magnetic-drift modes can propagate in the form of solitary pulses.

We extend our previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. [Phys. Rev. A 35, 2611 (1987)] yields for the surface tension τ=1.12×${10}^{-3}$($Z^2$$e^2$/$a^3$), where Ze is the ionic charge and a is the radius of the ionic sphere. For the fermion system, the absence of reliable correlation functions near the coexistence line makes it difficult to estimate the surface tension. We treat the Bose crystal-melt interface by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solid-superfluid interface at T=0, with a resulting surface tension τ≊0.085 erg/${\mathrm{cm}}^2$, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46–1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.

Chaotic dynamical systems are investigated, with the help of the Rényi information concept, both in their phase space and in their history space. Several phases are distinguished and their characteristics are discussed. Emphasis is put on two particular situations representing borderline cases of chaos: when an unstable periodic orbit exists in the system with a zero or an infinite Lyapunov exponent.

The temporal correlation in a steady time series experimentally observed is discussed by clarifying the direct interrelation between the double-time correlation function and the q→0 statistics of the order-q time correlation function introduced for the study of the overall characteristic motions embedded in the time series. As a workable method, we shall develop the continued-fraction expansion of the power spectrum. It turns out that it is especially efficient when the power spectrum consists of finite Lorentzians.