Measurements of resonant, two-step excitation of sodium in the presence of very-low-pressure buffer gases (He, Ar, Xe, and ${\mathrm{N}}_2$) are reported. These data are analyzed to isolate the effects of line broadening and velocity-changing (VC) collisions in the single-collision limit. Velocity dependence of the several line broadenings involved is obtained from this data analysis. The inelastic VC kernels are also obtained as a function of initial velocity.

Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming $C_6$ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small Δ$v_z$ collisions and a Keilson-Storer kernel for large Δ$v_z$ collisions is used. It is also demonstrated how the inelastic (3$P_{3/2}$-3$P_{1/2}$) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.

A classical analysis of the radiation reaction associated with a rotating charge distribution is carried out. This analysis is analogous to Lorentz’s classic description of radiation reaction for a charge in translational motion. As in the Lorentz analysis, reaction fields are found that are independent of the structural details of the charge distribution. In addition, if it is also assumed that the distribution’s magnetic moment M does not go to zero as the charge volume goes to zero, then some of the reaction fields also remain constant in that limit. For example, it is found that the charge distribution experiences a spatially uniform magnetic field of the form (2/3$c^3$)$d^3$M/${\mathrm{dt}}^3$, which is formally similar to the Lorentz’s radiation reaction electric field which is expressed in terms of the system’s electric dipole moment d as (2/3$c^3$)$d^3$d/${\mathrm{dt}}^3$. However, the two fields have fundamentally different effects since a magnetic field can do no work on the charge distribution.

Expressions are found for the electric fields that react back on the charge distribution to produce the self-torques necessary to conserve energy during magnetic dipole and electric quadrupole radiation. The analysis is then specialized to study the motion of a rigid, spinning, spherically symmetric charge distribution. A nonlinear equation of motion is found that describes the motion of the system, in an externally applied, constant magnetic field for all orders of the expansion parameter a/c, where a is the radius of the distribution. An approximate solution of this equation is found that describes the ‘‘spinning’’ charge precessing in the external magnetic field and spontaneously emitting magnetic dipole radiation. The magnitude of the magnetic moment and angular velocity of the ‘‘spin’’ rotation remain constant while the ‘‘spin’’ axis rotates to a position parallel to the magnetic field. The time dependence of this rotation is expressed in terms of a hyperbolic tangent. The power radiated varies as the square of a hyperbolic secant. In addition, the reaction field causes a small time-dependent shift in the frequency of radiation away from the Larmor frequency. Finally, a radiation reaction field is incorporated into the phenomenological Bloch equations of magnetic resonance to include the effects of magnetic dipole radiation.

Many-body perturbation theory has been used to calculate the photoionization cross sections of the argon atom for the production of singly and doubly charged ions by photons of energy from 100 to 290 eV. Effects of correlations involving 2p excitations on both single- and double-ionization cross sections are included. Effects of relaxation and polarization on the total cross section above the 2p threshold are also calculated. The results of our calculations are compared with experiment and other calculations.

The Coster-Kronig transition probabilities $f_{\mathrm{ij}}$ for shifting a vacancy from the $L_i$ to the $L_j$ subshell of Ag have been measured by differential photoionization of the subshells with synchrotron radiation by observing the intensity of the ensuing $L_j$-$M_4$,5${\mathrm{M}}_4$,5 Auger transitions. In the course of the analysis, spectator satellites in these Auger spectra were identified. The following Ag Coster-Kronig yields were determined: $f_{23}$=0.16±0.03, $f_{12}$=0.044±0.004, and $f_{13}$=0.61±0.05. While $f_{23}$ agrees very well with relativistic independent-particle calculations by Chen et al. [Phys. Rev. A 24, 117 (1981)], $f_{12}$ and $f_{13}$ fall below predictions by 35% and 18%, respectively, in qualitative accord with expected many-body effects.

A new method for calculating Auger decay rates in molecules is proposed and tested. Essential features are (1) construction of the continuum orbital via solution of the Lippmann-Schwinger equation with a projected potential, (2) matching in the asymptotic region of the Lippmann-Schwinger wave function with the eigenfunctions of the long-range Hamiltonian, and (3) complete evaluation of the Auger matrix elements between Hartree-Fock wave functions for the initial and final states. The method is tested on the KLL Auger spectrum of atomic Ne and then used to predict Auger decay rates for the LiF molecule ionized in its deepest shell.

Nonclassical fields with coherent components generated in a large number of optical processes including losses can be characterized by a Gaussian Wigner function centered around the mean value of the field. The photon-number distributions for such fields are calculated and the numerical results are presented for a range of parameters. As a special case we give the number distributions for photons produced in down-conversion problems. We also give the analytical expression for the photoelectron distributions.

This paper considers the ‘‘positive-P’’ description of nonlinear optical damping where one-photon and two-photon loss mechanisms are allowed. An exact solution of the corresponding stochastic differential equations is presented that graphically shows the breakdown of the positive-P representation found in earlier numerical-simulation work. The problem of ‘‘spiking’’ in simulations of nonlinear optical processes is then addressed, using the nonlinear damping process as an example. It is pointed out that although ‘‘spiking’’ can be exascerbated at high levels of quantum noise by numerical inaccuracy, the tendency to spike is in fact an analytic property of the stochastic variables.

Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell’s theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus’s law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.

The effect of velocity-changing collisions in an extended-pulse photon echo is studied. In an extended-pulse photon echo, the second excitation pulse has a duration comparable with the relaxation time of an atomic system. We present an analytic solution of the quantum-mechanical transport equation in the perturbation-theory limit and apply it to the extended-pulse photon echo. It is found that the decay rate of the echo signal due to velocity-changing collisions is significantly modified by the variation of the second pulse’s duration. The results are compared with those of conventional theories of two- and three-pulse echoes using temporally narrow excitation pulses. A physical interpretation of the results is given using both time- and frequency-domain arguments.

The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.

The structure factor of gallium has been measured by neutron scattering at temperatures 326 and 959 K and densities 0.0525 and 0.0490 at./A${̊}^3$ (6.08 and 5.674 g/${\mathrm{cm}}^3$). The domain of measured wave vectors ranges from 0.26 to 16.2 A${̊}^{\mathrm{-}1}$. The precision of the experiments allowed us the determination of an effective pair potential between the gallium atoms at these two thermodynamic states.

We discuss the low-frequency, long-wavelength behavior of systems close to thermodynamic equilibrium which form spatially varying patterns due to external constraints or fields. Among the systems discussed are the buckling in plates, the ‘‘dimple’’ instability of electrons at ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ interfaces, and the Rosensweig instability in ferrofluids. We point out that the ‘‘phase’’ in these systems can propagate; i.e., the dynamic equation for the slow variable is second order in time.

This study illustrates the interest of continuum spectra resolved in angle and polarization for investigating the anisotropy of a plasma. After discussing the validity of two types of relatively simple atomic bremsstrahlung cross sections, we establish easily usable expressions for the continuum emissivity coefficients (emission due to bremsstrahlung and direct radiative recombination) appropriate for electron distributions of a plasma with toroidal symmetry. In the example of a tokamak plasma, the distribution functions for the superthermal electrons were obtained from a Monte Carlo code. The simulated and experimental spectra (measured only in one direction of observation and with no polarization resolution) are in good agreement. The theoretical evaluations show the interest of more detailed measurements. The predicted dependence of the intensity of radiation on the direction of observation and the predicted polarization are large, and they would be a good means to probe the evaluation of the electron distributions in detail and, more generally, to diagnose the anisotropy of the free electrons in plasmas.

In this paper we apply the transient-time-correlation function (TTCF) method to the calculation of the nonlinear shear viscosity of the two-dimensional soft-disk fluid. At low reduced strain rates ${(10\mathrm{}}^{\mathrm{-}8}$<γ${<10\mathrm{}}^{\mathrm{-}2}$), the results are bounded by ‖$P_{\mathrm{xy}}$+η(0)γ‖∼${\eta }_2$${\gamma }^2$ and ‖p‖∼$p_2$${\gamma }^2$. For measurements of the shear stress at low strain rates, the TTCF method is clearly superior to the widely used subtraction technique. The differential TTCF method for calculating the intrinsically nonlinear response suffers, like the subtraction technique, from an exponential growth of noise.

An attempt is made to develop the picture of an interface near the critical temperature as an intrinsic Fisk-Widom interface broadened by capillary waves. We propose a method for determining the free parameters appearing in the capillary-wave theory by requiring that the capillary waves smoothly renormalize the surface tension from the bare to the experimental value. We evaluate the effect of the capillary waves on the width of the interface and make a comparison with experimental reflectivity measurements obtained by Wu and Webb [Phys. Rev. A 8, 2065 (1973)] for ${\mathrm{SF}}_6$ and also with the renormalization results of Jasnow and Rudnick [Phys. Rev. Lett. 41, 698 (1978)].

The electrons in the cathode-fall (CF) region of a helium dc glow discharge have been modeled at the kinetic level with a self-consistent electric field using a ‘‘convective-scheme’’ (CS) (propagator or Green’s-function) solution method. The CS is both straightforward to implement and numerically efficient. CS electron calculations using one spatial and two velocity variables are shown to match Monte Carlo simulations of swarms in uniform E/N and in the CF. The CS predictions are also shown to match experimental swarm results. A self-consistent CF solution is obtained through a slow relaxation of the electric field to that indicated by Poisson’s equation. The electric field configuration as predicted by the CS agrees well with optogalvanic measurements. The discussion emphasizes both the physical nature of, and the difficulties associated with, a self-consistent-field calculation.

In an earlier paper, we developed a general physical picture for the linear-marginal-stability mechanism governing the dynamics of front propagation into linearly unstable states. The main conclusion from this approach and the expressions for the resulting front velocity are similar to those obtained along different lines for the space-time evolution of instabilities in plasma physics and fluid dynamics with the so-called pinch-point analysis (a special type of saddle-point analysis). However, as stressed by Ben-Jacob et al. [Physica 14D, 348 (1985)], it is known from the work of Aronson and Weinberger [in Partial Differential Equations and Related Topics, edited by J. A. Goldstein (Springer, Heidelberg, 1975); Adv. Math. 30, 33 (1978)] on a class of simple model equations that exceptions can occur to the linear-marginal-stability velocity selection. In this paper, we generalize these observations and incorporate such exceptions into our general picture of front propagation into unstable states. We show that a breakdown of linear marginal stability occurs if the linear-marginal-stability front profile becomes unstable against a particular nonlinear ‘‘invasion mode.’’

If this happens, a larger front speed is selected at a point at which the front profile is now marginally stable against this nonlinear invasion mode. We therefore refer to this as the nonlinear-marginal-stability mechanism. (Ben-Jacob et al. call it case-II marginal stability.) We present the results of detailed numerical studies that support our identification of the nonlinear-marginal-stability mechanism, and present the first examples of it for fronts in pattern-forming systems. In the neighborhood of a transition from linear to nonlinear marginal stability, the wavelength of the pattern generated by the front is only weakly dependent on the nonlinearities. We also analyze front propagation properties close to the threshold for instability at a pitchfork bifurcation. We conclude that linear marginal stability generally holds near a continuous transition (corresponding to a supercritical or forward bifurcation point), while front propagation close to a first-order transition (corresponding to a subcritical or inverted-bifurcation point) is generally governed by nonlinear marginal stability. These results are of importance for recent applications of the various approaches in fluid dynamics and other fields.

Finally, we derive an expression for the rate of convergence of the front velocity to its asymptotic value. For the class of equations studied by Aronson and Weinberger, our expression reduces to a rigorous result by Bramson [Mem. Am. Math. Soc. 285, 1 (1983)], but it differs from the one often quoted in the pinch-point or saddle-point analysis. We argue that the latter one is only valid in a limited region of space, and show how to extend the usual analysis to arrive at our result. Several experimental systems to which our results are relevant are discussed.

For several liquid and fluid states of the Lennard-Jones system, the shear viscosity ${\eta }_s$ and the thermal conductivity λ were calculated with the Rice-Allnatt (RA) theory and compared with molecular-dynamics (MD) data. The pair potential was split as Weeks, Chandler, and Andersen proposed [J. Chem. Phys. 54, 5237 (1971)], the pair correlation functions were generated by the perturbation method using the Baxter technique, and the friction coefficient was obtained from MD computations with use of the Green-Kubo relation. Though sufficient agreement with MD results occurred for a certain small region of states, the RA transport coefficients generally deviated largely from the MD data. The failure of the RA theory cannot be ascribed to the uncertainty in the soft part of the friction coefficient, ${\zeta }_s$, necessary for the kinetic equations. We proved this for states where the product, λ${\eta }_s$, is only negligibly dependent on ${\zeta }_s$.

A Monte Carlo model is used to simulate the morphological evolution of crystals growing under the influence of a uniform drift in the nutrient phase. The model combines nutrient transport (via a biased random walk) with anisotropic surface attachment kinetics and surface diffusion. It is found that the crystal morphology closely depends upon the imposed drift, growth temperature (or bond strength), and supersaturation. Facets facing the drift direction exhibit enhanced morphological stability as compared with the no-drift situation.