The dielectronic recombination (DR) rate coefficients are calculated in the nonoverlapping resonance approximation for the target ions ${\mathrm{O}}^{5+}$, ${\mathrm{Ar}}^{15+}$, ${\mathrm{Fe}}^{23+}$, and ${\mathrm{Mo}}^{39+}$ at several electron temperatures for the initial state $1s^{2}2s$. The autoionizing and radiative transition probabilities are computed with single-configuration, nonrelativistic Hartree-Fock wave functions and $\mathrm{LS}$ coupling. All possible Rydberg autoionizing states and their cascades are included. The relative contributions to the total DR rate of the $1s$, $2s\left(\Delta n\ne 0\right)$, and $2s(\Delta n=0;2s\to 2p)$ transitions are examined for each ion. We find that the main contribution to the DR rate is from $2s$-electron excitation (both $\Delta n\ne 0$ and $\Delta n=0\mathrm{}$ processes), although the contribution from $1s$ excitation is found to be as large as 40% of the total rate at high temperatures. Finally, the effect of configuration mixing is examined for a group of dominant states and the effect on the overall rate is estimated.

A computer-controlled, frequency-doubled, pulsed dye laser has been used in conjunction with a sensitive and linear photodetection scheme to measure the two-photon absorption profiles of the ground to $6p{\left[\frac{1}{2}\right]}_0$, $6p{\left[\frac{3}{2}\right]}_2$, and $6p{\left[\frac{5}{2}\right]}_2$ two-photon transitions in xenon over a pressure range of a few Torr to 10 000 Torr. Absolute two-photon coefficients are reported. Line-shape measurements of the shift and width of the Lorentzian core allow the deduction of the long-range dispersion terms of the Xe-${\mathrm{Xe}}^{*}$ interaction potentials. An analysis of the line wings under the quasistatic approximation has permitted the extraction of the difference potentials for $3.75\le R\le 8.0$ Å. These short-and long-range difference potentials have been combined and used in an Anderson-Talman phase-shift calculation to reconstruct the absorption profiles. Measurements of the fluorescence following selective laser excitation have been taken and branching fractions for collisional excitation to other members of the $6p$ manifold at a xenon pressure of 100 Torr are reported.

We show that a sizable electric dipole moment can be induced between the ${}_{}{}^3{}_{}{}^{}\Sigma _g^{-}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ states of ${\mathrm{O}}_2$ when oxygen is placed in an environment of particles with spin ½.

It is observed that when an intense, nearly resonant laser beam propagates through a dilute ($N<\mathrm{}5\mathrm{}\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$) vapor of sodium atoms, a four-wave-mixing process occurs, leading to the generation of strong, coherent radiation in the forward direction at frequencies symmetrically detuned from that of the exciting laser by the generalized Rabi frequency. This phenomenon is explained as resulting from a nearly phase-matched mixing process utilizing the nonlinear response of the sodium atom. Our analysis is based on a solution of the density-matrix equations of motion that includes the effect of level shifts induced by the ac Stark effect, which can be as great as 10 Å for our experimental conditions, and which leads to gain due to the stimulated three-photon effect at one Rabi sideband and to strong coupling due to a parametric mixing process between radiation at the two sideband frequencies. It is also observed that at larger sodium densities ($N\gtrsim 5\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$), self-focusing of the laser beam can occur, leading to several complicating effects. We find experimentally that the on-resonance Rabi frequency $\Omega$ within a self-trapped filament lies preferentially within the range from 1 to 3 times the laser detuning from resonance $\Delta$ and we explain this result as a consequence of strong saturation of the refractive index that occurs for $\Omega \gtrsim \Delta$. Four-wave mixing is found to occur within these self-trapped filaments. The high-frequency sideband thus generated is trapped within the filament, whereas the lower-frequency sideband is ejected as a consequence of Snell's law and forms a cone surrounding the transmitted laser beam.

Continuous-wave lasing without the use of any feedback mirrors is observed when atomic cesium is optically pumped to its second excited resonance state. Resonant enhancement of the lasing intensity is observed at certain magnetic fields when the atoms are pumped by multimode laser light. The resonances, with widths of only a few gauss, are shown to be due to frequency crossings in the peak gains of certain velocity groups of excited atoms.

The transient behavior of an optically pumped, monomode, far-infrared laser is investigated with the use of on-off switching of the pump power. Various regimes of the onset of laser action are observed and described with the use of a two-level model for the lasing medium. At low pressures there is a possibility of undamped oscillation for the output power, which is assigned to a competition between two fields. The transients observed as the pump power is switched off are explained with the use of a three-level model.

For the two-dimensional model of dispersive optical bistability put forward by Graham and Schenzle [Phys. Rev. A 23, 1302 (1981)] the activation rates of the metastable states at low noise are evaluated explicitly. The rates are calculated in terms of the mean first-passage time of a two-variable Fokker-Planck equation which does not obey detailed balance and which has a drift field not expressable as the gradient of the corresponding nonequilibrium potential. The forward rate, describing the transition from the state with low transmission to the state with high transmission, is exponentially decreased with increasing detuning ${\delta }^2$, whereas the backward rate is exponentially enhanced with increasing ${\delta }^2$. The prefactor of the rate exhibits a complicated dependence on the detuning parameter which for the absorptive case with zero detuning, $\delta =0\mathrm{}$, reduces to the familiar Kramers result of a Fokker-Planck system with a drift field derivable from a potential.

A generalized Fokker-Planck equation is derived for a system undergoing optical bistability when the dominant source of fluctuations is due to fluctuations in the incident field rather than spontaneous emission. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. Both amplitude and phase fluctuations are included on the incident laser field. The effect of fluctuations of the incident laser on optical bistability are different for amplitude and phase fluctuations and are different for absorptive and dispersive optical bistability. The combination of incident laser phase fluctuations and dispersive optical bistability leads to large amplitude fluctuations near the turning points of the optical bistability curve and causes the system to make a transition from one branch of the optical bistability curve to the other before reaching the mean-field turning points. We take the high-$Q$ cavity limit of our generalized Fokker-Planck equation, solve the linearized equations, and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters. The magnitude of incident laser fluctuations are typically orders of magnitude larger than fluctuations due to spontaneous emission and are therefore important for practical applications of optical bistability devices.

A class of nonlinear integro-differential evolution problems arising in space-independent particletransport theory is studied for the case of general speed dependence of the collision frequencies. A decomposition of the high nonlinearity associated with this class of problems, and a classification of the relevant solution for the distribution function, are attempted via a systematic reference to the continuity equation for the total density of the particles considered, and to other additional algorithms. Different cases of plausible behaviors for the cross sections are then examined. Some generalizations of the continuity equation so obtained are, finally, discussed with comparison also made to the simple form holding in the case of $\frac{1}{v}$ cross sections.

The relativistic motion of an electron is calculated in the combined fields of the longitudinal magnetic wiggler field $[B_0+B_{w}sin(k_{0}z\left)\right]{\hat{e}}_z$ and constant-amplitude, circularly polarized primary and secondary electromagnetic waves propagating in the $z$ direction. It is shown that the presence of the secondary electromagnetic wave can detrap electrons near the separatrix of the primary wave or near the bottom of the primary-wave potential well. The results obtained are also applicable to the electron cyclotron maser (gyrotron) in the limit $B_w=0\mathrm{}$ and $k_0=0\mathrm{}$.

In most treatments Brownian motion is considered either in position or in velocity space. While the description of Brownian motion as a Markov process via a master equation in phase space can, in principle, deal with the full problem, assumptions are usually introduced which lead to the formulation of the generalized Fokker-Planck equation. In the following we want to show how, in the field-free one-dimensional case, the transport equation for a time-dependent conditional average of an arbitrary physical quantity (depending on position and velocity coordinates) of a tagged particle in phase space can be derived and solved successively if the time- and position-independent moments of the transition probability can be expanded in terms of a parameter ${\Omega }^{-1\mathrm{}}$. The transport equation can then be transformed into a set of $l$ linear partial differential equations, whose solutions provide the $l\mathrm{th}$ approximation in the expansion parameter ${\Omega }^{-1\mathrm{}}$ to the full solution of the transport equation. The system of linear partial differential equations is closed in the sense that the solution of the $l\mathrm{th}$ partial differential equation is determined by the solutions of the $l-1\mathrm{}$ partial differential equations. It turns out that the $l=0\mathrm{}$ partial differential equation describes the macroscopic (nonfluctuating) motion of the tagged particle. It is discussed in which sense a bivariate Gaussian distribution describes the full Markov process and how the full phase-space treatment provides more insight into Brownian motion. It is shown how the special cases described by the Langevin equation and the Fokker-Planck equation are contained in the new method presented.

Ferromagnetic resonance in a polished 0.047-cm-radius sphere of gallium-doped yttrium iron garnet is studied at 1.3 GHz in a magnetic field of 460 G. A second-order Suhl instability is observed, owing to the nonlinear coupling of the precessing uniform magnetization with spin waves. This is detected by the onset of auto-oscillations of the magnetization. One of these modes with frequency ≈16 kHz corresponds to the lowest spherical dimensional resonance of a packet of spin waves of small wave vector and long lifetime (≈ ${10}^3$ cycles). From real-time signals, spectral analysis, and return maps this mode is found to display chaotic dynamics as the driving rf field is increased: thresholds for the onset of period-doubling bifurcations, chaos, and periodic windows. Some observed return maps bear resemblance to the two-dimensional area-preserving quadratic map of Hénon. The system has several attractors and displays "solid-state turbulence," analogous to that in fluids.

The quantum kicked rotator, the classical limit of which is described by the standard map, is considered. Particular attention is devoted to a study of the effect of finite quantum wavelength on the detailed structure of phase space which appears in the classical limit. In the classical case, for large values of the nonlinearity parameter, most of the trajectories are ergodic. However, in addition to these ergodic trajectories, there can be small integrable regions of phase space, known as accelerator modes, which dominate the long-time evolution of the expected value of the particle energy. In this paper it is shown that this behavior is modified in the quantum case for small but finite values of the wavelength (i.e., Planck's constant). A simple model is presented to explain this modification. Based on our results, it is speculated that certain problems in the application of statistical concepts to intrinsically stochastic problems of classical mechanics may, in some cases, be mitigated by quantum effects.

The shear viscosity of the system polystyrene-cyclohexane was measured along the isochores near the critical concentration. The value of the critical exponent for the shear viscosity (${\phi }_{\eta }=0.029\mathrm{}\pm 0.003$) is obtained by analyzing the results from the viewpoint of multiplicative renormalization of transport coefficients. In addition, it is shown that the shear viscosity satisfies scaling-law relations and the pseudospinodal generalization previously established for fluids and binary mixtures.

Given some functional $F\left(T\right)\mathrm{}$ of interest in a heat-transfer problem, with $T$ the true temperature, one often introduces a fictitious "alias" temperature $\theta$ and an associated functional $F(T,\theta )$. A variational principle (VP) for $F(T,\theta )$ provides estimates of $F\left(T\right)\mathrm{}$ and of $T$. Such VP's have been derived on the basis of different physical principles and by means of different mathematical procedures. The unified formulation of the construction of VP's, used previously to derive VP's in a wide range of problems, can also be used in the present context. One introduces one Lagrange multiplier—which can be a constant, a function, an operator, etc.—for each of the constraints necessary to define $T$. While a VP $F_v(T_{\mathrm{tr}},\theta )$ for a functional $F(T,\theta )$, with $T_{\mathrm{tr}}$ a trial function, can provide a systematic method for an estimation $T_{\mathrm{est}}(\overrightarrow{\mathrm{r}},t)$ of the temperature distribution $T(\overrightarrow{\mathrm{r}},t)$ at a $\overrightarrow{\mathrm{r}}$ point at the time $t$, it is only the estimate $F_v(T_{\mathrm{tr}},\theta )$ of $F(T,\theta )$ which is stationary. The estimate $T_{\mathrm{est}}$ is not stationary; it contains first-order errors. Our main interest is in the development of a VP for $T$. Consideration of $F\left(T\right)=T$—we are no longer concerned with alias temperatures—provides a VP for $T(\overrightarrow{\mathrm{r}},t)$ itself. $T(\overrightarrow{\mathrm{r}},t)$ can be defined as the solution of linear or nonlinear differential equations, which can be homogeneous or inhomogeneous, and subject to a variety of boundary conditions. An almost identical procedure will provide a VP for the solution of any other equalization process such as the concentration $\Gamma (\overrightarrow{\mathrm{r}},t)$ in a diffusion process. We also derive a VP for the temperature $T\left(r\right)\mathrm{}$ and density $\rho \mathrm{}\left(r\right)\mathrm{}$, under specified quasiequilibrium conditions, of the coupled differential equations which characterize some stars. In addition, we consider variational identities. [It has often been stated, incorrectly, that one cannot obtain a VP for $T(\overrightarrow{\mathrm{r}},t)$.]

A new approach to the partial response functions in multicomponent plasmas is introduced. Central to the approach is that the density response function responding to the total (plasma plus external) field and a newly introduced dielectric matrix in species space are regarded as the primary quantities. A considerable simplification is achieved this way. Correlational terms to $O\left(\gamma \right)$ and pair-correlation functions both for ion-electron and binary-ion-mixture plasmas are calculated. Finally, the partial response functions in the mean-field-theory approximation are analyzed and it is shown that the consistency requirement based on the required symmetry of the response function is not always satisfied.

Large-time asymptotic solutions of the Smoluchowski equations for rapid coagulation are displayed for two common forms of the reaction kernel, namely, $R_{\mathrm{ij}}=i^{\omega }{j}^{\omega }$ and $R_{\mathrm{ij}}=i^{\omega }+j^{\omega }$. If no singularity occurs at finite time, it is shown that indices similar to $\tau$ and $\sigma$ in percolation can be defined: The concentrations approach a power-law behavior with an exponential correction the importance of which diminishes as a given power of time.

By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to $d=4\mathrm{}$ to study the crossover to classical behavior. Up to a crossover dimension $d\simeq 3.4$, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At $d\simeq 3.4$, both fixed points merge, representing in this way the crossover to classical behavior. At $d>\mathrm{}3.4\mathrm{}$, indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.

A pseudoclassical integral-equation method for obtaining the equation of state, pair-distribution functions, and static structure factors for partially ionized plasmas is presented. The electron-ion charge distribution is separated into a localized, quantum-mechanical part and a delocalized, nearly classical part. The Planck-Larkin method is used to separate the electron distribution. Localized-electron distributions are obtained from solutions of the Schrödinger equation. Distribution functions for ions and free electrons, including weakly bound electrons, are obtained from solutions to the classical hypernetted-chain (HNC) integral equation. Pseudopotentials that have two-body quantum mechanics built in, but which preclude strong bound states, are used as input to the HNC. The results are applied to H and Ar plasmas.

The Baranger-Mozer formalism for the computation of low-frequency thermal electric microfield distributions is extended to dense and hot binary ionic mixture relevant to inertial confinement fusion (ICF). The corresponding low-frequency microfield distribution of the thermal electric field, $H\left(\beta \right)$, reproduce the Tighe-Hooper results within 0.5%. However, the numerical procedures are more straightforward and shorter. We pay special attention to proportion effects in various ${\mathrm{Ar}}^{17+}$-${\mathrm{H}}^{+}$ and ${\mathrm{Ne}}^{9+}$-${\mathrm{H}}^{+}$ mixtures. Particular emphasis is also given to analytic asymptotic distributions valid for $\beta \ge 5$. Extensive numerical results are given in tables and figures.