Collinear laser–ion-beam spectroscopy has been used to measure the hyperfine structure (hfs) of nine metastable even-parity levels (E<15000 ${\mathrm{cm}}^{\mathrm{-}1}$) and nine odd-parity levels (EV32000 ${\mathrm{cm}}^{\mathrm{-}1}$) in ${}_{}{}^{147}{}_{}{}^{}$,149Sm ii. The mass resolution of 1 part in 350 eliminates spectral congestion due to overlapping lines from neighboring isotopes. The kinematic compression of the Doppler width is essential to obtain the necessary spectral resolution (approximately 20 MHz) to completely resolve hfs. An optical pumping scheme is used to differentiate the upper and lower levels of the observed transitions. The resulting magnetic dipole hfs constants, A, for the even-parity states arising from the 4$f^6$${(\mathrm{}}^7$F)5d configuration that are nominally more than pure 90% LS coupled have been analyzed in terms of Sandars-Beck effective-operator theory. The analysis shows that these levels actually contain substantial admixture of open-shell s electrons.

We present the results of a numerical study of the invariant amplitudes of 1s-ns and 1s-nd two-photon transitions in hydrogenlike atoms in the nonrelativistic dipole approximation, based on compact analytic formulas. We report also results valid in the limit n→∞. The 1s-nd transitions with n>6 are studied for the first time. For other particular cases our numerical results are in agreement with previous calculations in the literature. The investigated energy region of the two-photon spectrum is extended. The position of the transparencies in the second half of the spectrum is found to be almost n independent.

It is shown that the electromagnetic vacuum in a cavity is squeezed if one or several charges are present. For a bright electron beam typical of present high-intensity free-electron lasers, the effect is not necessarily small.

Third-order dynamic hyperpolarizabilities (γ) for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are calculated using James-Coolidge-type wave functions for several internuclear distances and frequencies. From them, third-order susceptibilities (χ) relevant to dc Kerr, degenerate four-wave mixing, electric-field-induced second-harmonic generation and third-harmonic generation experiments are determined. Agreement with the electric-field-induced second-harmonic generation experimental data is very good: ${\chi }_{?}^{\mathrm{}\left(3\right)\mathrm{}}$=792, 821, and 959 a.u. for λ=6943, 6328, and 4880 Å, compared with the experimental values: 805, 828, and 973 a.u. Other aspects such as dispersion formulas, Kleinman symmetry, and vibrational contributions are also investigated and discussed.

The nonlinear evolution of the free-electron-laser (FEL) amplifier is investigated numerically for a configuration consisting of a planar wiggler with parabolically tapered pole pieces. A set of coupled nonlinear differential equations is derived in three dimensions which governs the self-consistent evolution of the TE and TM modes in a loss-free rectangular waveguide as well as the trajectories of an ensemble of electrons. The initial conditions are chosen to model the injection of a cylindrically symmetric electron beam into the wiggler by means of a region with an adiabatically tapered wiggler amplitude, and the effect of an initial beam momentum spread is included in the formulation. Both self-field and space-charge effects have been neglected, and the analysis is valid for the high-gain Compton regime. In addition, the phase stability of the FEL amplifier against fluctuations in the beam voltage, the enhancement of the efficiency by means of a tapered wiggler amplitude, and harmonic generation are also studied. Numerical simulations are conducted to model a 35-GHz amplifier with an electron beam energy of 3.5 MeV, and good agreement is found between the simulation and an experiment conducted by Orzechowski and co-workers. Significantly, the results indicate that a tapered wiggler configuration is somewhat less sensitive to the beam thermal spread than a uniform wiggler system.

The nonlinear analysis of the orbitron maser is studied numerically for an amplifier configuration in which an electron beam propagates through a coaxial wave guide with a voltage applied between the inner and outer conductors. A set of coupled nonlinear differential equations is derived in three dimensions which governs the self-consistent evolution of the TE, TM, or TEM modes in a loss-free coaxial waveguide as well as the trajectories of an ensemble of electrons. The saturation efficiency as well as the linear growth rate are calculated. The linear growth rate (∼1 dB/cm) is largest for the TEM modes but the efficiency (∼6.0%) is highest for the TE modes. Severe limitations arise in the high-frequency operation of the orbitron amplifier in the fundamental mode due to the breakdown electric field and the extremely small radius of the inner conductor.

Electric-field-induced second-harmonic generation experiments on polydiacetylene solutions in dimethylformamide and in chloroform at 1.064 μm fundamental wavelength are presented. The technique allows for the measurements of both modulus and phase of the cubic susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(-2ω;ω,ω,0). Influence of the phase on the measured harmonic intensities is discussed in detail as well as errors which can result when it is neglected. It is found that ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$(-2ω;ω,ω,0) is complex with negative real part. This result is discussed in terms of a two-photon resonance. A small solvatochromic effect is also observed.

The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in ${10}^{18}$. .AE

Using Stark-mixed laser-induced fluorescence, space-time–resolved maps of sheath electric fields in discharges through ${\mathrm{BCl}}_3$ and Ar are measured as a function of concentration, power density (0.14–0.41 W ${\mathrm{cm}}^{\mathrm{-}3}$), and frequency (dc to 10 MHz). Sheath oscillations are observed throughout this frequency range and are discussed qualitatively in terms of characteristic times for ion and electron transport. Double layers are observed in low-frequency discharges containing more than 5% ${\mathrm{BCl}}_3$ and are attributed to a buildup in negative-ion concentration; it is argued that different ratios of negative-ion to electron density in the plasma and sheath are responsible for double-layer formation at the plasma-sheath boundary. These maps should prove useful as input for particle transport simulations in plasma-processing and light-source applications. They also provide stringent tests for self-consistent sheath theories.

Some dynamical models in which there is a significant interplay between interfacial and bulk degrees of freedom are treated at the mean-field (or Van Hove) level from a coarse-grained microscopic viewpoint. Specifically, the near-equilibrium interfacial dynamics of two of the simplest models with conservation laws, models B and C, are studied with use of (as appropriate) variational techniques, perturbation theory, and (with certain additional simplifications) exact solutions. Use of these methods allows the dispersion relation for interfacial modes to be interpolated between the ‘‘hydrodynamical’’ and critical regimes. The crossover scaling behavior lends support to renormalization-group methods near d=1 which focus on the interfacial modes but nonetheless extract the bulk dynamical exponent as well as the crossover.

Within the hexagonal lattice-gas model, we obtain Darcy’s law for flow in the presence of scatterers. The associated momentum dissipation is described by an effective damping term in the Navier-Stokes equation, which we relate to the density of scatterers. The kinematic viscosity can be obtained from the Darcy velocity profile, once the permeability is determined. We also check that in the hexagonal lattice model, after coarse graining, velocity decay and plane-parallel Poiseuille flow occur as described by the macroscopic equations.

A simple model is proposed for the dynamical effects of a strongly coupled plasma on the center-of-mass and internal coordinates of an ion. The ion is coupled to the plasma through monopole and dipole interactions. The radiative and transport properties of the ion are intimately related since both are governed by the electric microfield at the ion. A unified description of both types of properties is obtained by a formulation focused on the dynamics of the electric microfield. The velocity autocorrelation function, self-structure factor, and electric field correlation function are all in good agreement with computer simulation results, even for strongly coupled plasmas. The effects of perturbing ion motion on Lyman-α and Lyman-β spectral line profiles are calculated. Again, good agreement with computer-simulation results is obtained.

Spectral line shapes of 3p-4d, 3d-4f, 4d-5f, and 4f-5g transitions in the lithiumlike ions C iv and N v have been measured in a gas-liner pinch discharge at a density of 7.7×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$. The full widths at half maximum are larger than theoretical values obtained by the impact approximation by factors between 3 and 4 and smaller than theoretical full widths at half maximum calculated in the quasistatic, linear Stark effect approximation by factors between 1.2 and 3.

Accurate neutron-diffraction data are presented for krypton at three densities along a supercritical (T=220 K) isotherm and at three densities in the liquid state along a subcritical (T=200 K) isotherm. The density dependence of the Fourier transform of the total correlation function, H(κ), differs significantly from the one for dense liquid rare gases determined from recent neutron scattering data. Comparisons with modified-hypernetted-chain and molecular-dynamics calculations suggest that the present data cannot be described adequately with a reliable pair potential and an (effective) Axilrod-Teller three-body potential.

Coarsenings of percolated binary fluids are discussed. Here we focus on the nondissipative or turbulent coarsening where the dissipation term is neglected. The energy dissipation is then done by the energy transfer by turbulent eddies. The energy decay time by turbulence is of the order of the coarsening time. Then droplet growth law R∝$t^{2/3}$, which was predicted previously only by the energy transfer from surface tension to the kinetic energy, becomes valid. When the droplet becomes large, the convective motion becomes effective and the turbulent growth law is given by R∝$t^2$, if the two phases have different mass densities. This last growth law only depends on the fact that the fluid motion is nondissipative.

The intensity autocorrelation function of laser light quasielastically scattered at the growing crystal-melt interface of cyclohexanol was found to fit the single-exponential form previously found with ice and salol, indicating diffusional scattering. The diffusion constant D was found to vary in the range (0.2–0.9)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^2$/sec. Scattering was observed to persist for times on the order of 6 h after growth was stopped. A similar result was found in salol, but the possible interpretations are shown to differ fundamentally for these two materials.

The highly sensitive technique of infrared ion spectroscopy using frequency-tunable diode lasers has been introduced to study radial distribution of molecular ions in the positive column of dc glow discharges. Compared with previous techniques of plasma diagnostics, this method has the advantage that it is in situ and nonintrusive, has a high spatial resolution, and is sensitive to quantum states and velocities of molecular ions. ${\mathrm{ArH}}^{+}$ in Ar or He discharge and ${\mathrm{H}}_3$${\mathrm{}}^{+}$ in an ${\mathrm{H}}_2$ discharge have been used because of the strong infrared absorption and relative simplicity of the plasma chemistry. Our observations show that, while under certain discharge conditions where the radial distribution of molecular ions has the form of the zeroth-order Bessel function $J_0$(√a/D r) predicted by Schottky, it deviates markedly from the Schottky form in most plasma conditions. In particular, for ${\mathrm{ArH}}^{+}$ in an Ar plasma under high-current (1.25-A), high-pressure (10-torr) conditions, a large center depletion of the ion is noticed in the observed radial intensity variation of the absorption line. The observed intensity variation has been converted to radial concentration using vibrational and kinetic temperatures determined from relative intensities and widths of spectral lines. The result shows a large center depletion in molecular-ion concentration. Possible causes of such an effect are discussed. The variation of molecular-ion density at the center of the positive column as a function of discharge current has also been measured for ${\mathrm{ArH}}^{+}$ and ${\mathrm{H}}_3$${\mathrm{}}^{+}$.

The role played by the short-ranged repulsive forces in the formation of the liquid phase is investigated in a model system of interacting hard spheres. We find that the fluid undergoes critical condensation up to the limit of vanishing attractive interactions. The asymptotic value of the critical density predicted by the theory consistently falls within the range of fluid stability. Correspondingly, at nearly the same density, hard spheres manifest a change of structural behavior which is interpreted as a remnant of the thermodynamic transition from a gaslike to a liquidlike packing regime.

A percussion on particles moving in a uniform magnetic field induces a distribution of charges in a plasma. The accrued charge tensor $q_{\mathrm{ik}}$(x,t), which is the electric charge that has passed from t=0 to t through the unit area normal to $x_i$ due to a percussion of unit strength exerted in the $x_k$ direction at x=0 and t=0, is computed. The tensor $q_{\mathrm{ik}}$ is equivalent to the space-time polarization response of plasma electrodynamics. In this derivation, neither the Vlasov equation nor Fourier-Laplace transforms are employed. As an application, a priori bounds (i.e., independent of the distribution functions and of Laplace transforms) for the growth in time of plane-wave modes of a magnetized plasma are obtained by an operational method. The connection of the impulsion with statistical theoretical concepts is also noted. The fluctuation-dissipation theorem is given in a classical-physics version and it is found that the correlator of microscopic currents for noninteracting particles 〈$j_i$$j_k$${〉}_{\mathrm{x}}$,${\mathit{t}}^0$ of a nonequilibrium plasma is related to $q_{\mathrm{ik}}$ through (∂/∂t)$q_{\mathrm{ik}}$ =(δ/δE)〈$j_i$$j_k$${〉}_{\mathrm{x}}$,${\mathit{t}}^0$.

We present an analytic approach to the Saffman-Taylor problem of predicting the width of a viscous finger in a Hele-Shaw cell. Our first purpose is to provide a systematic description of the way in which the singular perturbation introduced by capillary forces leads to a solvability mechanism for pattern selection. We then show how recent experimental observations by Couder e al. may be interpreted in terms suggested by this mechanism. In particular, we show that the remarkable changes in pattern selection induced by bubbles trapped at the tips of fingers can be explained by assuming that the perturbation caused by a bubble is effectively equivalent to a positive opening angle at the tip.