The positronium formation processes in the ground and excited n=2 levels have been investigated in $e^{+}$-H atom collision using the Glauber eikonal approximation. Both the differential and total formation cross sections have been studied in the intermediate- and high-energy regime. Present eikonal results are found to differ appreciably from the corresponding first-order Born values even at very high energies. The total-cross-section results have been compared with other existing theoretical values as well as with the corresponding Born cross sections.

Target-atom excitations in the collisions of ${\mathrm{He}}^{2+}$ ions with Na atoms in the energy range 60–280 keV have been studied by optical measurements for the first time. The emission cross section of the NaI $D_1$,2 line was deduced from the experimental measurements. The agreement between the experimental results and the theoretical Na(3p) excitation cross sections of Shingal, Noble, and Bransden [J. Phys. B 19, 793 (1987)] is good within the experimental error.

A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization (2PI) of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed. The rapid energy variation of such amplitudes is extracted in terms of elementary functions of energy and a set of MQDT parameters, which are ‘‘smooth’’ functions of energy. As an example, results of numerical computations of MQDT parameters for 2PI of atomic hydrogen (1s, 2s, and 3s) by circularly polarized light are presented. MQDT parameters for the many-channel case are derived, and an analysis of their energy dependence across Rydberg thresholds is given. The two-channel case is analyzed using phase-shifted Coulomb functions, and simple analytic formulas are given for the energy dependence of the amplitude as a function of a small set of physical parameters.

High-resolution measurements of the hyperfine structures and isotope shifts are reported for Kr i n=5,6,7 4$p^5$ns Rydberg levels, obtained using an extreme-ultraviolet laser with a bandwidth of 210 MHz in a resonant two-photon-ionization scheme. Use of known ${\mathrm{I}}_2$ frequencies yields an improved absolute calibration of the Kr energy levels by more than one order of magnitude. The nuclear quadrupole hyperfine structure indicates that the 4$p^5$6s and 4$p^5$7s states are described by a pure jj-coupling scheme, whereas the 4$p^5$5s states depart from a pure jj-coupling scheme by 0.37(6)%. The magnetic hyperfine structure shows that the 4$p^5$ns states are mixed with 4$p^5$n’d states. The isotope shifts can be described as pure mass effects within the precision of our experiment. For the 4$p^5$6s and 4$p^5$7s states, lifetimes were determined that differ markedly from theoretical literature values.

The 3s ${}_{}{}^5{}_{}{}^{}–$3p ${}_{}{}^5{}_{}{}^{}D$° Oiii transitions have been studied in the spectrum of a foil-excited oxygen beam. Radiative lifetimes of the 3$p^5$D${°}_0$,1,2,3,4 energy levels have been measured using the techniques of beam-foil spectroscopy. The measured decay curves were analyzed by means of a curve-fitting technique and the arbitrarily normalized decay curve method, which corrects for cascading in a very detailed way. Accurate results were thereby obtained which show that good agreement exists between experimental and theoretical values.

The dynamical interaction of an oscillator with squeezed radiation inside a cavity is considered. Exact solution of the dynamical equation is presented using the Wigner function for the combined system of the atomic oscillator and the squeezed radiation. This solution enables us to study (i) relaxation of the oscillator for arbitrary bandwidth of the squeezed radiation, and (ii) effects of squeezed radiation on vacuum-field Rabi splittings. Explicit results for fluctuation spectra and the oscillator polarizabilities are given. New resonances in the fluctuation spectra appear as the radiation in the cavity becomes more and more squeezed. Strong narrowing of the vacuum-field Rabi splitting due to squeezed radiation is predicted. Very large enhancement of the oscillator polarizability at Rabi side peaks is also predicted. The modification of the cavity output due to the atomic oscillator is discussed.

A quantum theory of the propagation of a single-mode resonant field through a Kerr-like medium is given. Numerical studies show the existence of the quantum collapses and revivals in the otherwise periodic exchange of energy between the field and the atomic oscillator. Approximate analytical methods are developed to explain the numerical results for the case of weak nonlinearity of the Kerr medium. For large nonlinearity, the correspondence with the Jaynes-Cummings model is discussed.

We consider the problem of coherent population trapping in a model quantum system consisting of two (and briefly three) coupled continua of energy levels. While an earlier study [Z. Deng and J. H. Eberly, Phys. Rev. A 34, 2492 (1986)] has demonstrated population trapping in a closely related system, it has done so only for the case of a broad featureless continuum. We will demonstrate, on the other hand, that the time evolution of the continuum is qualitatively very different when different types of continua are allowed, and that population trapping is not likely to occur except in the broad featureless continuum. We do show, however, that in some cases other counterintuitive results surface.

Classical linear transformations in coordinate-momentum phase space are mapped to unitary quantum-mechanical operators in Hilbert space to produce a generalization of squeeze operators. The classical to quantum transition is manifestly apparent in the derivation. The unitary operators are evaluated in the coherent-state representation using the ‘‘integration within ordered products’’ technique in the one- and two-mode cases. Application of these operators results in a new generalization of coherent states.

The total noise of a field state is a measure of the fluctuations of the field amplitude. It is a minimum for coherent states. As the behavior of a state becomes more nonclassical, its total noise increases. This is shown first for several specific types of nonclassical states, among them squeezed and sub-Poissonian states. These results are generalized by using nonclassical distance to measure how nonclassical a field state is. A lower bound for the total noise is derived that is an increasing function of nonclassical distance. From it one can conclude that highly nonclassical states have large amplitude fluctuations.

We have measured absolutely the intensity-dependent change in the state of elliptical polarization of a well-characterized 1-ns laser beam propagating in 68 m of air, at intensities ranging from 0.5 to 1.5 GW/${\mathrm{cm}}^2$. From the data we deduce a value for the nonlinear susceptibility coefficient $c_{1221}$(-ω,ω,ω,-ω) for air at 20 °C and 1.053 μm of (20±5)×${10}^{\mathrm{-}19}$ esu, corresponding to a nonlinear index $n_2$=1.0×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^3$ ${\mathrm{erg}}^{\mathrm{-}1}$. This value is consistent with the value inferred from low-power Kerr and harmonic-generation measurements in ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$, but it is approximately one half of a previously reported experimental value for air. We also replaced 58 m of the air path with argon gas at 1 atm pressure and verified that a substantial reduction in nonlinear beam refraction can thereby be achieved.

Time correlations in the fluorescence of a multilevel atom are studied in terms of the quantum statistics which describe the emission of the next photon. The next photon equations are substantially simpler than the a photon equations (or so-called optical Bloch equations) yet they contain phase information lost in the averaging procedure that yields the a photon equations. Employing the next photon equations we present a quantum formalism in which the time development of the wave function of the atom is dramatically modified by the observation of a dark period. This ‘‘collapse’’ of the quantum state due to measurements with a null result (such as the failure to record events in a photodetector) is the cause of intermittent atomic fluorescence even when the exciting field is arbitrarily coherent. The next photon and a photon formalisms are contrasted and applied to photon antibunching. The phenomenon of photon bunching which characterizes sideband correlations is also calculated. Observable effects particular to the coherent intermittency are emphasized.

A model of free convection is developed for the case of pure water contained in a cylindric reservoir submitted to arbitrary boundary conditions. In the temperature region where water has a density maximum a quadratic ρ(T) function is assumed and the asymptotic solution is found as a sample calculation. Discontinuities in the T(z,t) behavior observed experimentally are fully explained in terms of a function that includes the small coefficient of the quadratic term of ρ(T) in the denominator with dramatic effects in the vicinity of the density maximum.

The non-Newtonian viscosity of a dilute gas of hard spheres under uniform shear flow is obtained by means of a Boltzmann–Monte Carlo simulation method. The influence of initial conditions is analyzed. The results are compared with exact solutions of the Boltzmann and the Bhatnagar-Gross-Krook equations. The agreement is shown to be fairly good over a wide range of shear rates.

We study cellular structures moving at constant velocity, in a symmetric model of directional solidification. This is done by employing Newton’s method to solve a discretized version of the integro-differential equation for the solid-liquid boundary. Our results indicate that there is a continuous band of allowed wavelengths and that there is a generic fold in the solution diagram. This fold provides a maximum allowed wavelength for any given velocity. Also, we argue that the mechanism of microscopic solvability serves to fix the tip shape at fixed wavelength. The implications of our results for wavelength and shape selection are briefly discussed.

The Burgers equation is the simplest nonlinear generalization of the diffusion equation. We present a detailed dynamical renormalization-group analysis of this equation subject to random noise. The noise itself can be the product of another stochastic process and is hence allowed to have correlations in space and/or time. In dimensions higher than a critical $d_c$ weak and strong noise lead to different scaling exponents, while for d<$d_c$ any amount of noise is relevant resulting in strong-coupling behavior. In the absence of temporal correlations we find two regimes for d<$d_c$: either the hydrodynamic behavior is determined by white noise and correlations are unimportant, or correlations dominate and the resulting scaling exponents can be obtained exactly. With temporal correlations present, the hydrodynamic behavior is much more complex, as renormalization predicts a complicated dependence of the effective noise spectrum on frequency in certain regimes. The relevance of these results to two interesting problems is discussed. One is the anomalous transverse fluctuations of a directed polymer in a random medium, and the other is a description of a growing interface. Various recent numerical simulations are reviewed in the light of these results. For example, we show that an exponent identity observed in all simulations so far follows simply from the Galilean invariance of the equation in the absence of temporal correlations.

A new theory for turbulent acceleration of plasma particles is applied to the beam-plasma interaction problem. This theory modifies the particle distributions, obtained from the test-particle analysis, in order to satisfy the conservation laws. The particle distribution obtained from the theory is found to be in agreement with the result of a numerical experiment.

The structure of the strongly coupled uniform one-component plasma (OCP) in two and three dimensions and the density profile of a three-dimensional OCP near a hard wall are calculated by the ‘‘Onsager-molecule’’ approach. We demonstrate that the structure of a strongly coupled plasma can be calculated very accurately (nearly within the simulation uncertainty) by employing only the leading term in the strong-coupling expansion of the bridge function.

We investigate theoretically the low-frequency noise arising in layers of fluid of large horizontal extent subjected to the Rayleigh-Bénard instability. Two models built on the phase-diffusion equation are investigated. In the first the phase of the rolls obeys a diffusion equation with a white-noise forcing. This corresponds to local agitation that does not result in nucleation or annihilation of rolls. It produces an $f^{\mathrm{-}1}$ noise for two-dimensional patterns and an $f^{\mathrm{-}3/2}$ noise in the one-dimensional case. The $f^{\mathrm{-}1}$ noise can be identified with noise observed in convective patterns very close to threshold. In the second model, roll patterns where a single dislocation performs a Brownian motion are investigated. It is shown that the corresponding stochastic phase equation can be solved for an infinite domain. The result is an $f^{\mathrm{-}2}$ noise, in agreement with recent experimental observations by Croquette, Le Gal, and Pocheau [Phys. Scr. T13, 135 (1986)]. The theoretical result is also valid for an arbitrary number of dislocations performing independent random walks.

A mean-field theory of (probabilistic) cellular automata is developed and used to select a typical local rule whose mean-field analysis predicts first-order phase transitions. The corresponding automaton is then studied numerically on regular lattices for space dimensions d between 1 and 4. At odds with usual beliefs on two-state automata with one absorbing phase, first-order transitions are indeed exhibited as soon as d>1, with closer quantitative agreement with mean-field predictions for high space dimensions. For d=1, the transition is continuous, but with critical exponents different from those of directed percolation.