A formalism is developed for the study of autoionizing states under the influence of strong lasers. It is cast in both a semiclassical as well as a fully quantum-mechanical form. A set of integrodifferential equations is derived and solutions are obtained for certain special cases. It is demonstrated that the strong field causes significant distortion of the line profile and that new effects appear in double optical resonance when autoionizing states are involved.

Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.

All effective Hamiltonians fulfilling three very general conditions are derived. It is shown that they all stem both from a transformation operator implicitly defined by a nonlinear equation, and an arbitrary "diagonal" and nonsingular operator. The canonical case is discussed, as well as the particular restrictions that lead to the previous schemes of Bloch, des Cloizeaux, and Jørgensen.

We present an analysis of four-wave parametric amplification resulting from the nonlinear response of a two-level atomic system. The atomic dipole moment induced by weak optical fields at frequencies ${\omega }_3$ and ${\omega }_4$ in the presence of an optical field of arbitrary intensity at frequency ${\omega }_1$, where ${\omega }_3+{\omega }_4=2\mathrm{}{\omega }_1$, is obtained by solving the density-matrix equations of motion with phenomenological damping constants. The resulting nonlinear polarization can induce loss or three-photon gain in either weak wave and can act to parametrically couple these waves. The spatial evolution of the weak-field amplitudes is obtained by finding approximate solutions to the Helmholtz wave equations using the nonlinear polarization for the source terms. These solutions predict large gain for either or both of the weak waves under experimentally attainable conditions. Depending on the circumstance, this gain can be attributed solely to the three-photon gain, solely to the parametric coupling, or to an interplay between these effects. In addition, the solutions show an enhancement in the gain when $|{\omega }_3-{\omega }_1\mathrm{}|=|\mathrm{}{\omega }_4-{\omega }_1|={\Omega }^{\prime }$, where ${\Omega }^{\prime }$ is the generalized Rabi frequency associated with the driving of the atoms by the wave at frequency ${\omega }_1$.

The hypernetted chain equation is solved numerically near its critical point and the compressibility is found to deviate from power-law behavior. This failure can be traced to the asymptotic form of the bridge function, an analysis of which is given. A comparison is also made with the analytic behavior of the Percus-Yevick equation and suggestions for improved integral equations are discussed.

Electron-impact ionization-rate coefficients are obtained for lithiumlike, heliumlike, and hydrogenlike ions by the plasma spectroscopy method. The plasma is produced in a 140-kJ large-bore theta pinch, and electron density and temperature are determined by 90° Thomson scattering. The basic requirements of the evaluation technique employed are briefly discussed and the results are compared with other measurements and theoretical calculations.

This study is devoted to the broadening of hydrogenic x-ray lines emitted by plasmas produced by laser impact or implosion. In addition to the traditional broadening processes due to high- and low-frequency components of the electric microfield, we have examined the influence of the self-generated magnetic field $\overrightarrow{\mathrm{B}}$ correlated with the Doppler effect by the motional electric field ${\overrightarrow{\mathrm{E}}}_m={\overrightarrow{\mathrm{V}}}_E\times \frac{\overrightarrow{\mathrm{B}}}{c}$. For the interaction between plasma electrons and radiating ions with high charge number $Z_E$, fully quantum-mechanical results [Phys. Rev. A 19, 2421 (1979)] have been used to include all multipole orders of the Coulomb interaction. An analytical treatment of the combined effect of the ion microfield and the self-generated magnetic field shows clearly that the latter is quite important. Its influence consists principally in giving the line profiles a sensitive dependence on polarization and the observation direction $\overrightarrow{\mathrm{k}}$. In case of the C VI resonance line emitted from a plasma corresponding to the critical density in glass laser experiments and a magnetic field of about 10 MG, the profiles are considerably broader than those deduced from only the particle fields. In addition, the profiles observed parallel to the magnetic field ($\frac{\overrightarrow{\mathrm{k}}}{\frac{}{\overrightarrow{\mathrm{B}}}}$) may show a central dip which cannot be ignored in a quantitative study of the line absorption properties.

Measurements are reported for the total charge-changing cross sections ${\sigma }_{-0\mathrm{}}$ for 1-25-keV ${\mathrm{H}}^{-}$ ions incident on a Na vapor target and ${\sigma }_{-+}$ for 7.5-25-keV ${\mathrm{H}}^{-}$ ions incident on a Na vapor target. The cross section ${\sigma }_{-0\mathrm{}}$ is 4.2 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 1 keV and falls monotonically to 1.5 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 25 keV. The cross section ${\sigma }_{-+}$ is 9 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 7.5 keV and rises to 4.0 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 25 keV.

For a better understanding of the high-frequency waves observed during active experiments of electron-beam injection into the ionospheric plasma, we do a complete investigation of the electrostatic-beam-plasma instabilities that do occur in such a situation. The electron beam is cold, it is aligned with the vacuum magnetic field, and has a finite radius; the background plasma is cold and homogeneous. We study both analytically and numerically the dispersion equation of the different branches and follow the dependence of the temporal and spatial growth rates with the beam and plasma parameters. Simultaneously we investigate the different types of instabilities (radiated or confined to the beam) in the various frequency ranges which are of interest. We give an analytical criterion for the convective or absolute character of these instabilities, taking into account the two-dimensional wave propagation along and across the vacuum magnetic field.

The transformation on heating of an ordinary (helical) cholesteric liquid crystal (CHOL) into the isotropic phase (ISO) often occurs via a number of intermediate "blue" phases. We find the following scheme of phase transitions in cholesteryl nonanoate: $\mathrm{CHOL}\underset{91.35}{\to }\mathrm{BPI}\underset{91.76}{\to }\mathrm{BPII}\underset{91.84}{\to }\mathrm{BPIII}\underset{91.95}{\to }\mathrm{ISO}$. Here BPI, BPII, and BPIII indicate three distinct, thermodynamically stable phases; transition temperatures are in °C. From observations of supercooling and coexistence, we conclude that all these transformations are first order, except possibly the BPIII→ISO, the character of which remains in doubt. A similar behavior is found in cholesteryl myristate and in a mixture of cholesteryl nonanoate and cholesteryl chloride. A few observations having a bearing on the structure of the blue phases are reported.

In this paper we have utilized resummation methods to eliminate the divergent behavior of truncated moment expansions of the velocity-autocorrelation function. We have demonstrated the equivalence between these resummation methods and Padé approximants. We have utilized the second row of the Padé table to simulate the well-known cage effect to obtain the negative dip in the correlation function. Finally, we have shown that these approximants have the correct time parity and yield a good value for the diffusion coefficient.

Experimental data are presented for the absolute cross section for atomic-field bremsstrahlung produced by 50-, 100-, and 140-keV electron bombardment of thin targets of aluminum, copper, silver, and gold at photon angles of 30°, 45°, 60°, 90°, and 135°. The data are compared with the theory of Pratt et al. and generally found to be in very good agreement, although there are some small discrepancies between theory and experiment.

It has been suggested previously by the author that the correlation length $\xi$ can be calculated from the Gaussian curvature in a Riemannian geometric model of thermodynamics. In the present paper, this hypothesis is tested for the one-dimensional Ising model. It is found that for ferromagnetic interactions ($J>\mathrm{}0\mathrm{}$) the thermodynamic ${\xi }_G$ is in excellent agreement with the correlation length $\xi$ which gives the range of the exponentially decaying spin-spin correlation function $G\left(r\right)\mathrm{}$; ${\xi }_G$ and $\xi$ are never found to deviate by more than one lattice site. If $J=0\mathrm{}$, there is no curvature, in accordance with expectations that curvature be a measure of interactions. If $J<\mathrm{}0\mathrm{}$, ${\xi }_G$ does not give the range of the envelope of the oscillatory $G\left(r\right)\mathrm{}$, and hence, does not agree with usual definitions of the correlation length; however, ${\xi }_G$ can be interpreted satisfactorily as giving the average length, due to interactions, of clusters of aligned spins. The results in this paper support the contention that thermodynamics in general contains more information than had previously been thought.

We study the effects of an external field on the isotropic-nematic transition in liquid-crystalline substances. The theoretical technique employed is called the "orientationally averaged pair correlations" approximation. It takes into detailed account spatial correlations between the molecules while treating orientational order in a mean-field-like manner. The results obtained for MBBA ($4-\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{e}-4\prime -n-\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}$) are compared to those of the Maier-Saupe theory and the Landau-de Gennes theory. We determine the paranematic-nematic coexistence curve, the temperature-external field phase diagram, the Cotton-Mouton coefficient, the maximum supercooling temperature, critical exponents, and the relation between the transition temperature and the electric field in laser-induced isotropic-nematic transitions. These results are compared to experimental data. Their implications are discussed.

The coverage of a two-dimensional surface by the random sequential adsorption of hard disks is shown to approach the "jamming limit" with time as $t^{-\frac{1}{2}}$ (or $t^{-\frac{1}{d}}$ for general dimension $d$), confirming a conjecture by Feder. The same argument predicts a logarithmic divergence of the two-particle correlation function at contact, confirming a second conjecture by Feder. The effects of placing squares on the surface instead of disks, and the consequences of these results for future numerical work on related problems are discussed.

The Boltzmann equation for a spatially uniform system of Maxwellian molecules is transformed into an energy-space equation, in the same form as many model Boltzmann equations that have been discussed.

The normal modes of stationary vortex patterns in two dimensions are studied for arbitrary dissipation in both the unbounded and circle-bounded cases. All eigenvectors are given for the ground-state patterns of $N=2\mathrm{}$ through 12 vortices and $N=19\mathrm{}$; all frequencies are given for $N=2\mathrm{}$ through 20. The complete eigenfrequency spectrum of single-ring patterns is given for all $N$. The integrals of unbounded motion are generalized to include dissipation. It is shown that angular momentum is strictly confined to the breathing mode of all unbounded patterns and of all bounded, single-ring patterns. Comparisons are made with infinite-vortex lattice modes, with a continuum model, and with earlier predictions of pattern stability and mode frequencies.

A direct measurement of the ion-to-neutral-atom density ratio has been made in a rapidly expanding ablation plasma by means of laser selective-excitation spectroscopy. Evidence of an ionization freeze out at a degree of ionization of about 0.1% is presented.

Second- and third-order corrections in the plasma parameter $\Lambda$ to the equilibrium pair correlations are systematically included in the Baranger-Mozer scheme for the computation of the high- and low-frequency components of the static microfield distribution in a dense plasma. Both neutral-point and once-charged-point cases are treated. Numerical data are given for $0.8\le v\le 1.4$. Asymptotic and compact expressions valid for $\beta \ge 8$ are also presented. The ${\Lambda }^n$ corrections are mostly significant near the peak values of $H\left(\beta \right)$. The case of multiply stripped ions is planned to be considered in another work.

A general expression for the energy loss per unit length of a relativistic cluster of particles is derived. The collective nature of the energy loss is examined using a classical dielectric description of the medium to which the particles lose energy in distant collisions. A special case, in which the particles in the cluster are assumed to have equal velocities, is also given using an extension of Fermi's method for deriving the density effect. In the nonrelativistic limit of the general result, new expressions for collective energy loss are obtained for clusters of particles moving with different velocities, as well as for particles having identical velocities. The simple dielectric function used in the nonrelativistic results can represent the frequency-dependent response function for a gas, a solid, or a plasma medium.