Excitation coefficients for production of 1$s_5$ and 1$s_4$ levels (Paschen notation) of neon in collisions with low-energy electrons have been measured using a drift-tube technique combined with laser absorption and laser-induced fluorescence techniques. The absorption and fluorescence signals have been analyzed using coupled rate equations which include the effects of population mixing among these levels in collisions with neon atoms. The excitation coefficients for the metastable and resonance levels ${\alpha }_M$/N and ${\alpha }_R$/N have been obtained as functions of the electric field to gas density ratio E/N. The measured values of ${\alpha }_M$/N vary from 1.3×${10}^{\mathrm{-}24}$ ${\mathrm{m}}^2$ at E/N=1.6×${10}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$ to 6.5×${10}^{\mathrm{-}22}$ ${\mathrm{m}}^2$ at 3.0×${10}^{\mathrm{-}19}$ V ${\mathrm{m}}^2$. The values of ${\alpha }_R$/N are comparable in the experimental E/N range. The experimental excitation coefficients are in agreement with values calculated from a Boltzmann analysis using a recommended set of electron excitation cross sections derived from published experimental electron beam data.

An analytic series solution to the Schrödinger equation with the Morse potential has been obtained. In the present solution the Morse potential itself is also expanded in a series about the origin. For application to the problem of the density dependence of muon-catalyzed d-t fusion, the effective two-body molecular problem is also formulated in terms of the superimposed potential field inside a liquid cell due to nearest-neighbor molecules (atoms). In this approach, more detailed studies can be carried out of the density effect on the various matrix elements needed in the calculations of the rates of μ-meson d-t fusion.

We discuss Berry’s phase rotation for electromagnetic radiation propagating in an optical fiber as a classical effect. We show that the evolution of the polarization vector is determined by a connection on the tangent bundle of the two-dimensional sphere. We use a topological argument to show that there exists only one rotationally invariant connection on the tangent bundle of the two sphere. The arguments apply to any classical transverse wave: for example, transverse vibrations propagating in a bent solid rod. The analogous effect in quantum electrodynamics, namely, Berry’s phase for a single photon propagating in an optical fiber, is a simple consequence of the classical effect described. We argue that this should be viewed as a classical, rather than a quantum, effect. We also comment on recent related work of Haldane and of Berry.

A detailed exposition on the origin and buildup of polarization in high-energy electron storage rings is presented. Fundamental, but not clearly understood, theoretical results are rederived and clarified (Ya. S. Derbenev and A. M. Kondratenko, Zh. Eksp. Teor. Fiz. 64, 1918 (1973) [Sov. Phys.—JETP 37, 968 (1973)]). It is explained how to diagonalize the Hamiltonian of a storage ring, in particular the spin-dependent terms, to the first order in Planck’s constant. Relevant perturbations, their time scales, and the various ensemble averages, are elucidated: the use of statistical concepts is shown to be essential to the calculation. Semiclassical techniques are used to derive, and extend to first order in g-2, the equilibrium degree of polarization (the Derbenev-Kondratenko formula). In so doing, some aspects of the polarization mechanism not previously recognized are uncovered. Because Derbenev and Kondratenko use a different mathematical approach, a proof is given of the equivalence between their formalism and the one used here.

A new algorithm is presented to evaluate the equilibrium degree of polarization in a high-energy electron storage ring (the Derbenev-Kondratenko formula). The algorithm includes all modes of orbital motion, to arbitrary orders in principle, thus facilitating the calculation of so-called ‘‘spin resonances,’’ especially higher-order resonances. The algorithm is applicable to storage rings of arbitrary geometry and energy, and, in particular, is able to deal with overlapping resonances. Precautions are described to ensure stability of the algorithm. In the approximation of linear orbital dynamics, a computer program has been written to implement this algorithm, and sample results are presented.

We study the correlation between modulations in the photoabsorption cross sections of diamagnetic Rydberg atoms and classical periodic orbits in a completely chaotic regime. Extensive quantum-mechanical calculations of photoabsorption cross sections and classical calculations of periodic trajectories are presented. In accordance with the scaling property of the classical Hamiltonian, the photoabsorption cross sections are studied for fixed values of the scaled energy ɛ=E/${\gamma }^{2/3}$ (γ is the magnetic field strength parameter) as a function of ${\gamma }^{\mathrm{-}1/3}$. The modulations of the photoabsorption cross sections appear as prominent peaks in the Fourier-transformed cross sections and can be related to periodic classical orbits. The positions of the peaks are given quantitatively by the scaled action along the periodic orbits and the relative strengths of the peaks can be understood qualitatively by considering the geometry of the orbits and the transition involved and the stability of the classical orbits. The one-to-one correspondence between peaks in the Fourier-transformed cross sections and classical periodic orbits applies not only to the traditional quasi-Landau modulation associated with the classical orbit in the plane perpendicular to the field, but also to a large number of further modulations corresponding to topologically different series of periodic orbits. In the completely irregular region around the zero-field threshold, the unstable periodic classical orbits and the observable peaks in the modulated cross sections cannot in general be related to individual eigenstates of the quantum system.

A rigorous theory of the stochastic field-induced resonances in four-wave mixing with cross-correlated pump and probe fields is developed. The behavior of the extra resonance for a range of fluctuation and collisional parameters is discussed. Our results differ significantly from those obtained from a decorrelated theory.

We present an analysis of a free-electron laser within a three-dimensional model, in which the finite transverse dimensions of the electron beam are taken into account together with the confinement of the electromagnetic modes by a guiding structure. The analysis is based on the expansion of the beam’s self-potential into an infinite set of modes that interact simultaneously with the wiggler and signal fields. Explicit gain-dispersion equations are developed for several cases including a waveguide tube completely filled by an electron beam of uniform density, and a uniform-density electron beam partially filling a waveguide (or in free space). This is carried out in both the magnetized beam limit and the general case which includes surface currents. The results bear significant effect on free-electron-laser gain operating parameters in the collective regimes and on the threshold of absolute instability oscillation.

Measurements are reported of the cross sections for collisional destruction (single- and double-electron loss) of ${\mathrm{H}}^{\mathrm{-}}$ and for its formation through single- and double-electron capture by H and ${\mathrm{H}}^{+}$, respectively. Three different targets were employed (He, Ne, and Ar) and the velocity (in a.u.) of the projectiles was 2.4≤v≤12.6 for ${\mathrm{H}}^{+}$ and 4<v<9 for H and ${\mathrm{H}}^{\mathrm{-}}$. The charge states emerging from the target were simultaneously detected and the data were analyzed by the growth rate and attenuation methods from which individual cross sections could be deduced. Special attention was paid to the double-capture process in Ar where a very pronounced shell effect was firmly established on experimental grounds and was successfully described by theoretical estimates based on independent-electron probabilities of capture and simple scaling rules. Difficulties for obtaining an overall description of the cross sections for either destruction or formation of ${\mathrm{H}}^{\mathrm{-}}$ based on simple models are discussed.

We address theoretically the effects of a large laser intensity on the phenomenon of light-induced drift. The velocity selectivity of the atom-field interaction decreases due to saturation broadening and this leads to a maximum of the drift velocity as a function of the laser intensity. Analytical expressions for the drift velocity are derived in the case of two-level atoms, assuming a strong collision model. Consequences of this high-field effect are discussed for various manifestations of light-induced drift such as propagation of a soliton in an infinitely long cell, described by the Burgers equation, and collisions of such solitons. The analogy with hydrodynamic shock waves, described by the same Burgers equation, is fruitfully explored. We also address high-field effects on the density distribution produced by light-induced drift in a finite cell. In all these manifestations of light-induced drift the cases of high field and low field show qualitatively different behaviors which are of a complementary nature.

The dependence of the optical Autler-Townes effect on laser field phase fluctuations describable by a two-dimensional Markovian process (phase-diffusion model with a non-Lorentzian line shape) is investigated experimentally in atomic sodium. An intense cw laser tuned to near resonance with the ${3\mathrm{S}}_{1/2}$(F=2,${\mathrm{M}}_{\mathrm{F}}$=2)→${3\mathrm{P}}_{3/2}$(F=3,${\mathrm{M}}_{\mathrm{F}}$=3) transition was frequency modulated to generate phase fluctuations with the desired characteristics. A weak probe laser coupling to the 4$D_{5/2}$(F=4, $M_F$=4) state was used to obtain the double-peaked optical Autler-Townes absorption profiles in order to investigate their dependencies on band shape, bandwidth, intensity, and detuning of the intense fluctuating laser field. Reversals of the peak-height asymmetry and reversion to normal asymmetry with increased detuning were observed and measured. Quantitative studies of the spectral widths and splittings of the peaks are also reported. Measured absorption profiles are in excellent agreement with calculations based on previous theoretical work.

The problem of the intrinsic linewidth of a free-electron laser is analyzed. As opposed to the traditional Schawlow-Townes linewidth in atomic lasers, which is a quantum-mechanical result, the free-electron-laser linewidth is classical, that is, independent of ħ. The theory of the ultimate linewidth of a free-electron laser is developed here, using the master Fokker-Planck approach with the advantage, over previous work, that it does not make use of any ansatz.

A new method for detecting a squeezed state by coincidence counting or cross correlation of the signals from two photodetectors is proposed. The two light beams falling on the two detectors are obtained from the two outputs of a homodyne beam splitter, whose inputs are the squeezed light and the local oscillator beam. With fast detectors the squeezing gives rise to excess photon coincidence counts. When a spectral analysis of the photoelectric currents is made, squeezing shows up as a positive cross correlation between the two signals, whereas unsqueezed light always produces negative correlations. Although the technique does not always cause the effects of local oscillator fluctuations to cancel out, as does the method of Yuen and Chan [Opt. Lett. B8R, 177 (1983)], they cancel in special cases, and the method has the advantage of being largely unaffected by detector after-pulsing. A simple combination of autocorrelation and cross-correlation measurements yields the degree of squeezing.

The induced-resonance electron-cyclotron maser operates at Doppler-upshifted frequencies ω≃${\gamma }^2$${\Omega }_0$, with γ the relativistic factor and ${\Omega }_0$=${\mathrm{eB}}_0$/γmc. In addition, the mechanism is insensitive to the beam thermal spreads when the index of refraction n=$k_z$c/ω is properly adjusted. A set of simplified equations, describing the electron dynamics near the axis of the configuration, is derived in the limit of small Larmor radius. The linear efficiency is derived for radiation having a Gaussian profile and propagating at an angle α relative to a constant external magnetic field. The start-up current for operation in the submillimeter regime is well within the capabilities of today’s long-pulse relativistic electron beams.

The effect of degradation of the coherence of the pump beam by a random phase screen on the conversion efficiency in the second-harmonic generation process is considered. It is shown that, under suitable conditions, the conversion efficiency can be increased significantly.

The double-slab waveguide configuration for a Čerenkov free-electron laser is discussed. It is shown that it may allow higher emission brightness with respect to the single-slab configuration.

We investigate the effects of liquid structure on the transport properties of dense fluids, using nonlinear fluctuating hydrodynamics. The longitudinal and shear viscosities for a Lennard-Jones system at different temperatures and pressures are computed. We find a rounded version of the transition to a glassy phase. Agreement of our results with computer simulation data is good. We also find qualitative agreement between our results and real experiments.

Onsager’s symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

The molecular dynamics of water in an anisotropic environment are investigated with autocorrelation and cross-correlation functions in the laboratory and moving frames of reference. The anisotropy is generated by an uniaxial electric field which destroys the invariance of the Hamiltonian to symmetry operations in the laboratory frame of reference, thus making possible the appearance of new time correlations in this frame. The effect of the electric field is recorded systematically in terms of the symmetry of cross-correlation tensors and the anisotropy induced in autocorrelation functions. The field-induced anisotropy in the diagonal elements of the center-of-mass velocity autocorrelation function suggests a new experimental method of detecting directly the effect of rotation-translation coupling on the single-molecule level.

We study the free-boundary problem of the steady growth of a solid into its undercooled melt, allowing the thermal diffusion coefficient to have an arbitrary temperature dependence. By developing a novel approach to the Ivantsov method, we show that needle-crystal solutions can be found in two and three dimensions. The calculation establishes that the only steadily advancing, shape-preserving solidification fronts the method can produce, for linear or nonlinear diffusion, are parabolas in two dimensions and elliptic (or circular) paraboloids in three dimensions. We discuss the limitations on the Ivantsov method, pointing out that it is only capable of finding families of solutions of the problem, whose members are related by a rescaling of space and time. We show explicitly that including a heat-loss term in the equations causes the method to fail, and argue that any term which introduces a length scale into the problem will, in general, do likewise.