We study the semiclassical mean-field theory of absorptive optical bistability in the limit of a fully developed hysteresis cycle, i.e., in the limit of large values of the bistability parameter $C$. We show by multiple time-scale perturbation analysis that it is possible to describe the transition between the two stable branches by simple equations. Near the low-transmission branch, the behavior of the system is governed by an equation for the atomic population, whereas, near the high-transmission branch, it is an equation for the field amplitude which determines the long-time evolution of the system. We then present an analytic study, completed by numerical results whenever necessary, of the time-dependent response of the system when the input field is swept across the bistable region. We study the influence of the initial conditions, the sweeping velocity, and the ratio of the atomic relaxation times on the dynamical hysteresis as well as its relation with the stationary hysteresis.

Starting from a Hamiltonian which describes the interaction of the many-electron system of a crystal with the quantized light field, we derive nonlinear coupled equations of motion for the light-field amplitude, the electron-hole-pair amplitude, and the inversion. These equations yield the basis for the investigation of space-dependent nonlinear interaction effects between light and electrons in direct band-to-band transitions. With the aid of these equations we investigate the saturation behavior of direct band-to-band transitions for an incident monochromatic electromagnetic plane wave. We determine the nonlinear absorption coefficient and nonlinear refractive index. We compute the nonlinear transmissivity taking into account the boundary conditions at the end faces of the crystal and discuss the effect of optical bistability.

Interference effects produced by independent quantum sources are investigated, when the state of the field is not describable as a simple mixture of coherent states. The results of classical and quantum-mechanical calculations are compared. Whereas correlation effects are predicted both classically and quantum mechanically when the sources have random phases, there are important differences when the number of atoms is small. In particular, when each source consists of just one atom, the joint probability of detecting two photons at two different points in the receiving plane is found to vanish when the distance between them is an odd number of half fringes. Finally it is shown that when the number of atoms of each source is subject to Poisson fluctuations, one recovers the solution given by classical optics for thermal light, no matter how weak the sources may be on the average.

The general kinetic equation for the charge-charge structure factor of a fully ionized strongly coupled hydrogen plasma is solved in three distinct collision approximations. The equilibrium correlation functions necessary to these solutions are provided by solution of the hypernetted-chain integral equation in which an effective pair potential has been used to take into account short-range quantum effects. The results are compared with molecular-dynamics simulations of the plasma using the effective pair potential and with a hierarchical approach involving known sum rules.

It is shown how a one-dimensional transport equation (derived from a master equation) for a time-dependent conditional average of an arbitrary function can be solved successively, if the moments of the transition probability can be expanded in a series of a special parameter. The transport equation for the time-dependent conditional average value can be transformed into a set of $l$ linear partial differential equations of first order for the $l\mathrm{th}$ approximation of the conditional average value. The system of equations is closed in the sense that the $l\mathrm{th}$ partial differential equation is determined by the solutions of the $l-1\mathrm{}$ partial differential equations. It is shown how the results obtained compare with the linear noise approximation. Two examples are chosen to illustrate the way to use the method. One is the classical example of the diffusion of a Brownian particle, the other is Alkemade's diode.

High-energy C${\mathrm{O}}_2$-laser radiation has been used to implode gas-filled spherical targets to very high densities (${10}^{23}<n_e<{10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$) and temperatures (∼800 eV). The imploded gas was composed primarily of DT with a small amount of argon seed. The detailed observation of radiation from the argon was a primary diagnostic of the imploded-plasma conditions. An extensive analysis of the emitted argon spectrum provides a rich source of information on plasma parameters. In most cases one could not assume local-thermodynamic-equilibrium conditions. A very detailed collisional-radiative model was constructed in order to analyze the spectrum. In view of the complexity of the calculations that had to be performed and the care needed in data acquisition and processing, the agreement between theory and experiment was very good.

New frequency-moment sum rules are formulated for the purpose of assessing the behavior of two-dimensional classical electron liquids at high frequencies [$\omega \gg {\omega }_p\mathrm{}\left(k\right)\mathrm{}$]. For nonzero coupling strength (characterized by $\gamma$), the convergence of our new fifth-frequency-moment rule $〈{\omega }^5〉$ is guaranteed at short range. However, in the Vlasov ($\gamma =0\mathrm{}$) limit, $〈{\omega }^5〉$ exhibits marked $\frac{1}{\gamma }$ and $\ln \gamma$ divergences. The ensuing breakdown in the high-frequency structure of the dielectric response function leads to the conclusion that the Vlasov limit is unphysical for two-dimensional classical electron liquids in the high-frequency domain. Our theory complements the current low-frequency [$\omega \cong {\omega }_p\mathrm{}\left(k\right)\mathrm{}$] theories, all of which reinforce the notion that the reduced dimensionality of surface plasmas considerably enhances short-range correlation and dynamic collisional effects.

The microscopic model of Ford, Kac, and Mazur for the interaction of an oscillator with a thermal reservoir is considered within the framework of stochastic quantization. The process executed by the Brownian particle is derived exactly and it is analyzed in detail. The phenomenological equations for the dynamics of the quantum oscillator in the equilibrium state, which we have previously derived, are recovered as the weak coupling limit of the exact theory.

The two-dimensional flow of a collision-dominated hydrogen scrape-off plasma in an axisymmetric tokamak is examined. This flow is described by a set of equations which contain the dominant terms in a maximal ordering appropriate to high-density experimental divertors and reactor scrape-off plasmas. Comparison of the theory to estimates of scrape-off parameters in the Doublet III expanded boundary plasmas suggests that analysis of classical and neoclassical processes alone may be sufficient to predict plasma transport in high-density scrape-off plasmas of practical importance.

The effects of a moving medium on the phase of a massive particle are studied theoretically. The discussion explains a recently published Fizeau-type neutron-interferometer experiment. It is shown explicitly that the physics of this experiment can be described either as a manifestation of a time-dependent potential in the Schrödinger equation or as a verification of the Galilean-transformation properties of Schrödinger waves. An intriguing consequence of these considerations is that for most materials no Fizeau phase shift occurs if the boundaries of the moving medium are at rest. However, we point out that such would not be the case in an experiment involving a medium whose potential is velocity dependent.

The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms ($n=10, 15, \mathrm{and} 20$) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number $m$. The origin of this tendency is discussed.

Absolute cross sections for the excitation of optically emitting states in collisions of ${\mathrm{He}}^{+}$, ${\mathrm{Ne}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, ${\mathrm{B}}^{+}$, ${\mathrm{He}}^{2+}$, ${\mathrm{Ne}}^{2+}$, and ${\mathrm{Ar}}^{2+}$ with oxygen molecules are measured, the energy range of the ion being 1-1800 eV (laboratory frame) for singly charged and 1-3600 eV for doubly charged ions. Seven important processes can be distinguished: charge-exchange excitation of ${\mathrm{O}}_2^{+}$ bands, O I, O II, $X$ i, and $X$ ii lines ($X^{+}$,$X^{2+}$ being the primary ion), direct excitation of $X$ ii, and double-charge-exchange excitations. The energy dependences of the excitation cross sections are remarkably different for different processes but similar for one process with different ions. They are given in a few examples. The sum total of all cross sections together for excitations which lead to light emission is on the order of a few ${\mathrm{\AA }}^2$ at 1000-eV energy (c.m. frame). The results are of interest for surface investigations, plasma diagnostics, and laser work.

Translation-energy spectra of charge-state-changed projectile ions scattered in the forward direction in collisions of ${\mathrm{C}}^{q+} \mathrm{}(q=5,4\mathrm{})\mathrm{}$, ${\mathrm{N}}^{q+} \mathrm{}(q=6,5\mathrm{})\mathrm{}$, and ${\mathrm{O}}^{q+} \mathrm{}(q=6\mathrm{})\mathrm{}$ ions with He atoms have been measured at collision energies of $q$ and $2q$ keV. All the product peaks observed in the spectra come from exothermic electron-capture processes. From the measured energy gains of the product ($q-1\mathrm{}$)—charge-state ions, it has been found that an electron is captured selectively into a single shell with a particular principal quantum number $n=2\mathrm{}$ for the incident ${\mathrm{C}}^{4+}$ ion and $n=3\mathrm{}$ for the incident ${\mathrm{C}}^{5+}$, ${\mathrm{N}}^{5+}$, ${\mathrm{N}}^{6+}$, and ${\mathrm{O}}^{6+}$ ions. This fact is in accord with the prediction of the one-electron classical theory. It has also been revealed that there is good similarity among the energy-spectral patterns obtained for the ions having the same charge $+q$, irrespective of ionic species; such a similarity results from the similarity among diabatic potential curves for the collision systems of the $q$—charge-state ions and He. In the case of ${\mathrm{C}}^{4+}$+He collision, the two-electron—capture process into the ground state of ${\mathrm{C}}^{2+}$ occurs more efficiently than the one-electron—capture process at the low energies studied.

The theory of the random walk on a sphere is derived by elementary methods and by specializing the general theory of random walks on group ($G$) spaces. The result is applied to find the angular distribution in multiple elastic scattering after $N$ steps. The case of electron scattering from a screened Coulomb potential is done in detail. Formulas which are exact in principle and asymptotic in practice are found, giving the distribution with many-place accuracy at all angles for $N\ge 20$. Methods for generating a random variable with this distribution are also given.

An electrostatic ion trap is used to trap ${\mathrm{Ne}}^{q+} \left(1\mathrm{}\le q\le 10\right)$ ions created by a fast xenon beam passing through neon gas. Decay of a given charge state during the trapping time is due to electron-capture collisions with the ambient gas. Measurement of the decay constant versus density yields a rate constant, from which an effective cross section is derived. ${\mathrm{Ne}}^{q+} + \mathrm{Ne} \mathrm{}(q=3-10\mathrm{})\mathrm{}$ and ${\mathrm{Ne}}^{q+}+\mathrm{Xe} \mathrm{}(q=6-10\mathrm{})\mathrm{}$ collisions have been studied at mean collision energies in the range 1.0-70.0 eV. Marked oscillation of the effective capture cross sections with charge at fixed mean collision energies is observed. A strong velocity dependence of the effective cross section (rising as the velocity decreases) is observed for several collision pairs.

Differential (in angle) electron scattering experiments on laser-excited ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ ${}_{}{}^1{}_{}{}^{}P$ were carried out at 30- and 100-eV impact energies. The laser light was linearly polarized and located in the scattering plane. The superelastic scattering signal was measured as a function of polarization direction of the laser light with respect to the scattering plane. It was found at low electron scattering angles that the superelastic scattering signal was asymmetric to reflection of the polarization vector with respect to the scattering plane. This is in contradiction with theoretical predictions. An attempt was made to pinpoint the reason for this observation, and a detailed investigation of the influence of experimental conditions on the superelastic scattering was undertaken. No explanation for the asymmetry has as yet been found.

Total cross sections for Si $L$ and Ar $L$ Auger-electron production were measured in collisions of 35-500-keV ${\mathrm{Si}}^{+}$ ions incident on Ar atoms, and absolute cross sections for $L$-shell vacancy production were deduced. The experimental results are discussed in terms of the molecular-orbital model of atomic collisions. It is found that electron promotion via the $4f\sigma$ molecular orbital is the dominant mechanism for Si $L$-shell vacancy production. Excitation of $3d\pi$ and $3d\sigma$ electrons via $3d\delta -3d\pi -3d\sigma$ rotational coupling at small internuclear distances is treated explicitly. The calculated cross section for $3d\sigma$ excitation is found to reproduce the experimental cross section for Ar $L$-shell excitation in the range of collision energies up to 200 keV. $L-L$ vacancy-sharing processes at large internuclear distances are discussed as possible mechanisms for the observed rise of the Ar $L$ cross section beyond this energy.

An effective optical potential approach is applied to the scattering of electrons by ${\mathrm{H}}_2^{+}$ within the linear algebraic prescription. Widths and positions of the lowest few ${}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ resonances appearing in the elastic-scattering channel are calculated and compared with the results of other methods.

The polarization potential for electron-neon scattering is calculated from a dispersion relation relating the real and imaginary parts of the optical potential. The input to the calculation is the absorption potential of Green, Rio, and Ueda. The polarization and absorption potentials, along with a Hartree-Fock static potential and an exchange potential calculated by the semiclassical exchange approximation, are used to predict integral and differential cross sections for elastic scattering at impact energies 30-3000 eV. The results are compared to those obtained with Hartree-Fock adiabatic polarization and in the static-exchange-plus-absorption approximation. The dispersion-relation polarization potential is more successful than either of these models in reproducing the energy dependence of the integral and small-angle differential cross sections over the whole energy range. At 50 eV and higher the calculated values of the large-angle differential cross sections are also reasonably accurate.

Absolute cross sections for the emission of Balmer-$\alpha$ and Balmer-$\beta$ radiations resulting from H + He and H + ${\mathrm{H}}_2$ collisions are reported for hydrogen-atom energies between about 50 eV and 2.5 keV. The polarizations of the emitted radiations are also reported. For hydrogen-atom energies above 200 eV, the contributions to these radiations from decay of the relatively long-lived $3s$ and $4s$ excited states of the projectile atoms are resolved. The results of the measurements are compared with other available data for these reactions, as well as with data for H impact on other target species.