This paper presents a study of angle- and spin-resolved photoelectron spectroscopy in a randomly oriented nonlinear molecule in the nonrelativistic, electric dipole approximation. The theory formulated in the preceding paper has been used along with the methods of the extended point (or spin-double) group to develop, perhaps in their simplest possible forms, the expressions for the five parameters needed to specify the angular distribution of spin-polarized electrons ejected in photoionization by unpolarized, or by linearly or circularly polarized light in the $a_1$ orbital of a $T_d$ molecule. The polarization of the photoelectrons in this case is due directly to the spin-orbit interaction in molecular continua. Such angle- and spin-resolved studies will therefore provide more stringent tests of theoretical models, probes of photoionization dynamics, and a measure of the influence of the spin-orbit interaction on the continuum part of the spectrum.

The procedure adopted and the formulation presented here set a methodology and a framework for the analysis of measurements and calculations of spin-resolved spectra in nonlinear systems in general and $T_d$ molecules in particular. The specific examples treated in this paper are those of photoionization in the respective 4$a_1^2$, 6$a_1^2$, and 7$a_1^2$ orbitals of unoriented ${\mathrm{CF}}_4$, ${\mathrm{CCl}}_4$, and ${\mathrm{SiCl}}_4$ molecular targets. Without any dynamical calculations, and by use instead of the experimentally measured values of the angular asymmetry (β¯) as a function of the photon wavelength, the variations in ξ¯, δ¯-γ¯, and 2γ¯+δ¯ with respect to the energy of the incident radiation and to the phases involved have been studied in detail. These three quantities (where γ¯, δ¯, and ξ¯ are the spin parameters) determine the degree of spin polarization of photoelectrons in various experimental configurations. While δ¯-γ¯ is found to be independent of phase, both ξ¯ and 2γ¯+δ¯ depend very strongly upon it. The phase, in turn, is influenced by the spin-orbit interaction. This study has helped also in analyzing and revealing the nature of the Cooper minima observed in ${\mathrm{CCl}}_4$(6${\mathrm{a}}_1^2$${)}^{\mathrm{-}1}$ and ${\mathrm{SiCl}}_4$(7${\mathrm{a}}_1^2$${)}^{\mathrm{-}1}$ spectra and in predicting the values of the spin parameters γ¯, δ¯, and ξ¯ in the corresponding energy regions.

We have obtained for Rydberg systems a Stark density-of-states matrix deduced from the multichannel-quantum-defect theory that has been defined in operator form. Some general properties of this matrix are discussed. We also study the electric-field effect upon autoionization processes. Numerical calculations are performed for a simple two-channel system, one corresponding to an open, i.e., above zero-field ionization limit, and the other to a closed channel.

We extend the quantum theory of multiwave mixing developed in previous papers in this series to include side-mode saturation. Specifically, the earlier papers calculate the absorption and resonance-fluorescence coefficients to second order in the weak-field interaction for an arbitrarily intense pump field. This paper extends those calculations to fourth order in the weak-field interaction. We find significant differences in the amplified resonance fluorescence spectra given by the second- and fourth-order treatments, particularly as the side mode approaches the laser threshold. In particular, while the second-order spectra diverge at this threshold, the fourth-order spectra remain finite. Although fourth- and higher-order theories are very desirable for applications to larger fields and optical instabilities, the present analysis reveals that their calculation is very complex. This fact poses an important limitation to the generalization of the theory to still higher-order accuracies.

A formalism that is based on projection operators is employed to obtain a general recipe for constructing matrix elements of the transition or T operator for electron-ion photorecombination processes in model systems featuring a limited number of discrete states and continua. The projection-operator formalism allows for a natural separation of the total transition operator into a direct, or radiative recombination, contribution and a resonance, or dielectronic recombination contribution. Implementation of the general recipe is discussed, and expressions for matrix elements of needed propagators in the combined Hilbert space of electron and photon continua are derived for model systems in which one makes the pole approximation on the photon continua, but not on the electron continua. The simplifications that occur when the pole approximation is made on all continua are presented. Finally, the recipe is employed to describe photorecombination for two model systems that feature an isolated autoionizing state. One model includes an arbitrary number of possible final-state photon continua, and the second model includes an arbitrary number of possible final-state electron continua. For the former model, it is shown how the various terms entering into the expression for the recombination transition amplitude can be obtained from a perturbation series and interpreted in terms of Feynman-like diagrams.

We present recent experimental and theoretical results on the behavior of two-, three-, and four-ion crystals close to the Mathieu instability. In particular, we show that the crystals are stable until the Mathieu instability is reached, i.e., for the parameter space investigated, there is no ‘‘melting’’ of the crystals. Laser and rf heating are studied in detail. A simple model of chaotic rf heating as well as a classification of the ion dynamics into four characteristic regimes are presented.

In the femtosecond pump-probe pulse experiments, the pump pulse with duration comparable to or shorter than a typical vibrational period creates a nonstationary wave pocket. In this paper, we use the density-matrix method to treat the dynamic behavior of the system (embedded in a heat bath) in the femtosecond pump-probe pulse experiment. The expression for the coherence of the system due to the pumping laser is derived, and the generalized master equations for the dynamical behavior of the system after the pumping pulse is over are also obtained. Some numerical calculations are performed for a two-level system to demonstrate the time-dependent behaviors of memory kernel, rate constant, and population.

In single-mode laser systems with an injected signal, we find a codimension-three bifurcation point at Δ=-θ=(2C${\mathrm{-}1)}^{1/2}$ when C>(1/2. In the vicinity of the bifurcation point, the initial five-dimensional coupled differential equations are reduced to two-dimensional ones by adiabatic elimination. The dynamics about the critical point is analyzed. Based on the revealed critical point, a parameter region where a full hysteresis loop exists can be predicted. This optical-bistability system can be operated by a rather small signal.

This paper is the first part of a two-part study on the quantum nonlinear Schrödinger equation [the second paper follows: Lai and Haus, Phys. Rev. A 39, 854 (1989)]. The quantum nonlinear Schrödinger equation is solved analytically and is shown to have bound-state solutions. These bound-state solutions are closely related to the soliton phenomenon. This fact has not been pursued in the literature. In this paper we use the time-dependent Hartree approximation to construct approximate bound states and then superimpose these bound states to construct soliton states. This construction enables us to study the quantum effects of soliton propagation and soliton collisions.

In the preceding paper [paper I of a two-part study; Lai and Haus, Phys. Rev. A 40, 844 (1989)] we have used the time-dependent Hartree approximation to solve the quantum nonlinear Schrödinger equation. In the present paper, the eigenstates of the Hamiltonian are constructed exactly by Bethe’s ansatz method and are superimposed to construct exact soliton states. Both fundamental and higher-order soliton states are constructed and their mean fields are calculated. The quantum effects of soliton propagation and soliton collisions are studied in the framework of this construction. It is shown that a soliton experiences dispersion as well as phase spreading. The magnitude of this dispersion is estimated and is shown to be very small when the average photon number of the soliton is much larger than unity. The phase and position shifts due to a collision and the uncertainty of these shifts are also calculated.

A source of white light (i.e., with a flat spectrum) can separate the components of a gas mixture. This effect, which may have applications in stellar atmospheres, is due to light-induced drift which appears when absorption lines form in the intensity spectrum of the propagating light. We theoretically discuss the effect in its simplest form: white light shining into a gas containing two optically absorbing species and a buffer gas. Transport equations are presented, assuming two-level atoms and ignoring stimulated emission. Several limiting cases are discussed analytically. A numerical solution is also presented and used to estimate the ranges of validity of the analytical solutions.

We analyze the operation of a free-electron laser in an open periodic structure. When operated as an amplifier, it is shown that exponential gain can develop in such a device. An analytic expression for this gain is presented, and it is shown that this gain decays exponentially with the beam height above the grating; the gain dependence on the beam thickness is also analyzed. As the energy extraction rate is much higher in an exponential gain regime, we also investigate the operation of an oscillator based on the same concept. In this case, the Smith-Purcell radiation ‘‘provides the startup’’ through a feedback system. The latter consists of several mirrors, which are placed in such a way that (1) only a wave with the desired frequency develops and, at the same time, (2) small deviations in the wave parameters due to the wave-beam interaction do not cause deflection of the wave from the feedback loop. The minimal current needed to sustain oscillations is given in an analytical form. Numerical calculations show that this current is more than three orders of magnitude lower than that necessary for an oscillator which operates in an algebraic gain regime.

This paper derives in detail the Madey-theorem derivation for the gyrotron, the cyclotron autoresonance maser (CARM), and the nonwiggler free-electron laser with traveling-wave mode or standing-wave mode. The results show that CARM’s and nonwiggler free-electron lasers may have higher conversion efficiency of electron-beam kinetic energy than ordinary gyrotrons.

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

We point out in this paper the possibility of demonstrating the Einstein-Podolsky-Rosen paradox via quadrature phase measurements performed on the two output beams of a nondegenerate parametric amplifier. A technique that might be used to demonstrate the paradox has already been partly developed experimentally.

The neon liquid-vapor interface was studied at the triple point by path-integral Monte Carlo simulation with a view to determining the magnitude of quantum effects. Comparison is made between classical and quantum descriptions. The quantum interface is found to be approximately one quarter of an interatomic spacing wider than the classical counterpart. The surface tension is 20% lower than that obtained classically. Kinetic energy density profiles through the interface show anisotropy between the x and z directions. Marked differences are also found between the zero-pressure densities of the quantum and classical bulk liquid phases.

The two-dimensional Coulomb gas is studied in a particular case where the positive charges (or ‘‘ions’’) are smeared over disks of radius σ, and held fixed on the sites of a triangular lattice, while the opposite point charges (the ‘‘electrons’’) move freely in the periodic field of the ions. At low temperatures and densities, the resulting ‘‘Thomson atoms’’ form a dielectric phase. The complete phase diagram of the model in the density-temperature plane is mapped out by a combination of harmonic lattice dynamics and molecular-dynamics simulations. At sufficiently low densities the model undergoes, at high temperatures, a Kosterlitz-Thouless transition to a plasma phase. The phase diagram is considerably more complex at high densities, where the low-temperature dielectric phase undergoes an infinite succession of first- and second-order transitions between paraelectric and ferroelectric phases, while the Kosterlitz-Thouless transition crosses over to a first-order melting transition, as shown by a variety of static and dynamic diagnostics.

The Reynolds-number dependence is calculated for the shear stress, normal stress difference, velocity, effective viscosity, and effective normal stress coefficient by using the generalized hydrodynamic equations in the case of cylindrical Couette flow of a Lennard-Jones gas. The drag coefficient is shown to decrease more rapidly than the inverse Reynolds number and rapidly vanish on passing a critical Reynolds number. The shear stress and normal stress difference also vanish beyond the critical Reynolds number, and there is a region in space where the effective shear viscosity and normal stress coefficients become so small that the fluid behaves like an almost inviscid fluid in the region. These numerical results indicate that the generalized hydrodynamic equations tend to the Euler equations in the limit of sufficiently large Reynolds number at a rate faster than that for the Navier-Stokes equation and that the fluid is almost inviscid in some parts where the velocity changes steeply, and viscous in the rest.

The Landau-Zener model with rotational and degenerate Stark-effect coupling has been employed to calculate electron transfer in ${\mathrm{C}}^{6+}$+H collisions for relative velocities between 0.5 and 50×${10}^7$ cm/s. The total cross section for capture to n=4 levels of ${\mathrm{C}}^{5+}$ and the distributions over angular momentum sublevels are obtained. The results are compared to other calculations and available experimental data.

Conditions for the existence of an inversely (distance${)}^{1/2}$-dependent far field along the direction of the external magnetic field in a cold magnetoplasma are studied and applied to classify the plasma parameter domains in the Clemmow-Mullaly-Allis diagram. Such an axially enhanced far-field flux from a dipole source is then evaluated explicitly and found to be confined within a finite cross-sectional area in most cases. Origin of the axial enhancement is explained and its relevance to energy conservation is discussed; in particular, the divergent radiation flux lines are described by z/$r_{\perp }^2$=const, where z and $r_{\perp }$ are, respectively, the axial and the transverse coordinates. Attention is also drawn to the existence of an enhanced electric far field oscillating parallel to the magnetic field and at frequencies below the plasma frequency.

A lattice-gas automaton is a variant of a cellular automaton. Its cellular universe is a regular triangular lattice, and particles reside on the lattice nodes. The time evolution of this discrete dynamical system of particles proceeds in two alternating phases: collision and propagation. Such a model, though very simple and deterministic, is capable of producing very complex behaviors. A boundary layer develops whenever a real, viscous fluid flows along a solid boundary. We simulate boundary-layer and related problems in the incompressible limit of fluid dynamics using a lattice-gas automaton. Our lattice-gas automaton simulations show that viscosity effects on Couette flows (flows between parallel plates), Stokes flows, and Blasius flows (flows across a plate) give results as predicted by the Navier-Stokes equations. By considering different geometries and by carefully varying the gas properties, we obtain in particular the time-dependent velocity profiles, which are in good agreement with theoretical predictions. These inferences may be viewed as further support for the internal consistency of the lattice-gas approach, and they also substantiate the belief that the lattice-gas automaton can be a useful, viable tool for simulating fluid dynamics.