Auger-electron spectrum of Cs in the 15-75-eV energy region following 20 keV electron impact is presented. The most intensive structures in the spectra are analyzed by comparing their energies with the calculated energies of the Auger transitions applying a multiconfiguration Dirac-Fock method. Also the free-atom binding energies $E_B\left(N_5\right)=\mathrm{82.79.}\mathrm{}\pm 0.10$ eV and $E_b\left(N_4\right)=85.07\mathrm{}\pm 0.10$ eV are obtained with the aid of optical double-hole final-state energy levels.

This is an extension of a recently developed quantal theory of laser-induced Penning and associative ionization. Its purpose is to construct cross-section formulas which are specific to a semiclassical description of the heavy-particle motions. The photoionization transition amplitudes occurring in these formulas involve electric dipole matrix elements which connect the initial electronic state of two colliding atoms to the final, ionized state. Which matrix elements appear in the cross-section formulas is dependent upon how the state of the ejected photoelectron has been specified. In our previous theory this specification included both the energy and momentum (direction of motion) of the photoelectron. Here we include the cross-section formulas and collision theory which are appropriate when the direction of motion of the photoelectron is left unspecified.

The vibrational dipole transition moment integrals are calculated for the individual $v^{\prime }$, $v^{\prime \prime }$ bands of the $E$,$F{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, $G$,$K{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, $H$,$\overline{H}{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}-B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $B^{\prime }{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $C{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ systems on the basis of the $R$-dependent ab initio electronic transition dipole moments of Wolniewicz and Dressler. Nonadiabatic effects are included for the transition probabilities and lifetimes by the representation of the nonadiabatic wave functions of all bound vibrational ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{} \mathrm{}(J=0\mathrm{})\mathrm{}$ levels in the adiabatic basis of the $E$,$F$, $G$,$K$, and $H$,$\overline{H}$ electronic states. Wherever possible the calculated lifetimes are compared with experimental results.

An absorption spectrum of neutral cesium between the $5p^5\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)6s$ and $5p^5\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)6s$ thresholds was observed in the range of 650-700 Å with the National Bureau of Standards 10.7-m grazing-incidence spectrograph. Rydberg series $5p^{5}6sns$ and $5p^{5}6snd$ approaching both upper threshold states $\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)6s$, $J=0,1\mathrm{}$ were identified on the basis of quantum-defect comparisons and Hartree-Fock term energies. Distinctive $\mathrm{nd}$ line shapes are compared with those of neutral xenon.

One-photon free-free absorption cross sections are evaluated by means of an integral relationship involving electron-atom off-shell scattering amplitudes. Off-shell effects are explicitly calculated and compared to various on-shell approximations. This calculation shows that off-shell effects become small with increasing energy as expected. One of the on-shell approximations agrees with the exact result over the entire energy range under consideration to within a few percent. The only integrals which appear in the calculations are absolutely convergent in contrast to methods used in previous calculations.

Relativistic Dirac-Slater calculations of the photoionization of the $6p$ subshell in elements in the range $82\le Z\le 100$ have been performed, examining cross sections, branching ratios, and angular distributions. The zero (Cooper minimum) which appears in the $6p\to \epsilon d$ nonrelativistic matrix element is split into three relativistically, for the matrix elements $6p_{\frac{3}{2}}\to \epsilon d_{\frac{3}{2}}$, $6p_{\frac{3}{2}}\to \epsilon d_{\frac{5}{2}}$, and $6p_{\frac{1}{2}}\to \epsilon d_{\frac{3}{2}}$. The outstanding feature of our results is the huge energy splitting between these minima, more than an order of magnitude larger than the discrete $6p_{\frac{3}{2}}-6p_{\frac{1}{2}}$ splitting. The origin of this phenomenon is discussed along with its consequences for angular distributions and branching ratios.

Analytic expressions for electron orbits in a longitudinal magnetic wiggler field of the form $\overrightarrow{\mathrm{B}}=B_0[1+\epsilon cos(k_{0}z\left)\right(1+\frac{k_0^2{r}^2}{4}\left)\right]{\overrightarrow{\mathrm{e}}}_z+\epsilon B_{0}sin\left(k_{0}z\right)\left(\frac{r{k}_0}{2}\right){\overrightarrow{\mathrm{e}}}_r$ are derived by asymptotic techniques valid for more general wiggler- and guide-field configurations. The implications of the orbit results for this particular configuration on free-electron-laser gain are discussed in detail.

A method for producing electronic-state coherences using either collisionally-aided radiative excitation (or "optical collision") or laser-induced collisional energy transfer (or "radiative collision") is proposed. Two atoms, $A$ and $A^{\prime }$, collide in the presence of two pulsed-laser fields having frequencies $\Omega$ and ${\Omega }_1$. It is shown that by choosing ${\Omega }_1\pm \Omega$ such that an energy-conserving transition can occur in the composite $A{A}^{\prime }$ system, one can create an electronic-state coherence in the $A$ or $A^{\prime }$ atoms. The coherence can be produced between states of the same or of opposite parity; if it is between states of opposite parity, coherent emission at frequency ${\Omega }_1\pm \Omega$ may be generated. The relationship of this work to theories of "pressure-induced extra resonances" in four-wave mixing is discussed.

A systematic study of the temporal evolution and of the power spectrum of the output intensity produced by a hybrid bistable system with a delay in the feedback loop has shown that self-pulsing and chaotic oscillations are the result of the nonlinear coupling among an infinite number of modes of the linearized system. The main qualitative differences observed both experimentally and in computer simulations between short- and long-delay-time regimes are caused by the emergence of progressively more unstable modes as the delay of the feedback is made larger. The fairly abrupt changes in the temporal patterns, which in earlier numerical studies have been interpreted as periodicity windows are, instead, the result of frequency locking among a large number of modes of the system. From this work we conclude that the short- and long-delay-time regimes do not differ fundamentally from one another, and can easily be described in terms of a common analysis.

A helium-neon laser at 3.39 μm has been operated under cavity and discharge conditions permitting three modes to simultaneously oscillate for some regions of cavity tuning. Both mode-locked and -unlocked regions have been found. For unlocked three-mode operation, the laser output may include a secondary beat frequency. As the cavity length is tuned to the mode-locked region, this secondary beat frequency approaches zero and displays critical fluctuations at the transition to mode-locked operation. As the discharge current is increased, for fixed cavity length, the peaks in the power spectrum representing the secondary beat and its harmonics undergo a 100-fold broadening enroute to a broad chaotic spectrum before the laser reaches a mode-locked, low-noise configuration. This appears to be the onset of a deterministically chaotic behavior of the coupled modes that is distinct from the critical fluctuations. Details of cavity tuning and current variation on the laser output, including hysterisis effects, are reported here.

The scalar wave equation is analyzed in the relativistic front form, appropriate for paraxial-wave optics. The group-theoretical basis for this treatment is uncovered. The formal similarity of the propagation of paraxial beams through optical systems to the quantum mechanics of particles in two dimensions subject to harmonic impulses, and the role of the metaplectic group of Bacry and Cadilhac, are both traced back to the structure of the Poincaré group. Light rays are defined in this context as in statistical-wave optics, and the laws for their free propagation as well as transmission through lenses are derived.

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Three-dimensional theory of the initiation of superfluorescence from a spherical medium with a radius much larger than the optical wavelength is developed. Time evolution of the average intensity of the superfluorescence pulse from its initial spontaneous stage to the exponential-growth limit is found. It is shown that light propagates along rays, governed by laws of geometrical optics. Amplification of light along each ray is the same as determined from the conventional one-dimensional theory. It is proved that although the average intensity is isotropic, each pulse is strongly directional.

The dynamics of solidification are investigated at the ice-water interface by means of Rayleigh-Brillouin spectroscopy. If a critical growth velocity is exceeded, Rayleigh scattering occurs in a layer which has a thickness between 1.4 and 6 μm and a density between water and ice, close to that of water. At constant intensity the width $\Gamma$ of the central line is proportional to the square of the scattering vector $\overrightarrow{\mathrm{k}}$, $\Gamma =D_i{k}^2$, independent of the orientation of $\overrightarrow{\mathrm{k}}$ relative to the interface. The measured diffusion constants $D_i$ are in the range $1.4\times {10}^{-8\mathrm{}}<D_i<5.7\mathrm{}\times {10}^{-8\mathrm{}}$ ${\mathrm{cm}}^2$ ${\mathrm{s}}^{-1\mathrm{}}$ and isotropic in space. The intensity of the scattered light depends on the heat flow from the liquid into the solid and on the growth velocity. The linewidth of the scattered light decreases with increasing scattering intensity, and vice versa. We interpret $D_i$ as an effective thermal diffusion constant that describes the transport of heat involving fluctuations of order and disorder in the layer (Frenkel's "structure diffusion"). The increase of the total scattering intensity corresponds to an increase of the isothermal compressibility by a factor of 700 as compared to water.

The dielectronic satellite lines from the $n=2\mathrm{}$ doubly excited levels of lithiumlike and heliumlike ions have been studied theoretically in dense-plasma environments. A comprehensive level structure including ground, singly excited, and doubly excited levels was included in a collisional-radiative equilibrium model to calculate level populations and the satellite intensities self-consistently for carbon, aluminum, and argon plasmas. The effects of inner-shell excitation rates (calculated via the distorted-wave approximation with configuration mixing) and collisional ionization and recombination of the doubly excited levels are included in the model and their effects on the satellite intensities assessed. The well-known heliumlike intercombination-to-resonance line ratio, used in density determinations, is shown to be strongly affected by blended satellite lines at high density, causing significant error in the measured density when their intensities are not accounted for.

We consider the action of a heat bath on one particle of a pair of spin-$\frac{1}{2}$ particles in a singlet state. The related relaxation effects are described by the Pauli master equation. We show that the density matrix of the two-particle system tends toward a product. The interpretation of this result is, however, complicated by the nonuniqueness of the decomposition of a given density matrix into pure states. To circumvent this difficulty we study separately the terms describing the fluctuations and the friction. The first one does not modify the correlations, although it screens them but the second one separates the systems. The action of a fluctuating magnetic field on one particle of a correlated pair is also investigated.

When an aggregate grows by the irreversible attachment of diffusing particles, only a small fraction of the $N$ aggregated particles will collect new particles. These constitute the growing interface. We study the properties of this interface by computer simulation and analytical estimates. The mass $N_i$ of the interface grows as $N$ and to the 0.6th power in two dimensions and as $N$ to the 0.74th power in three dimensions. Several other masses characteristic of the interface are found to scale as the same power of $N$. We argue that these powers represent a critical exponent $\delta$ independent of the Hausdorff dimension.

The one-component plasma structure factor $S(q,\Gamma )$ has been computed with a hypernetted-chain equation modified by the hard-sphere bridge function. The structure factor is tabulated for reduced wave number $0.1\le q\le 25.0$ and Coulomb coupling parameter $0.1\le \Gamma \le 180$. The hypernetted-chain results are in excellent agreement with Monte Carlo calculations. This table should be useful for calculations on dense plasmas and liquid metals.

A theoretical analysis based on the method of system-size expansion of the master equation is carried out for a generalized nonlinear stochastic model with cubic interactions. The resulting Fokker-Planck equation enables us to derive the relevant probability distributions in the critical region as well as away from it; in the former case, the distribution turns out to be non-Gaussian and is dominated by fluctuations which are non-negligible. The onset of a first-order phase transition in the system is investigated in some detail. In particular, a Maxwell-type "theorem of equal areas" is discovered which might hold for a much wider class of systems with cubic interactions.

A path-integral solution is derived for processes described by nonlinear Fokker-Planck equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is shown to give accurate results.