Examples of a Cooper minimum inside the range of a shape-resonance maximum of a photoionization cross section have been found in numerical calculations within a single-electron model in a relativistic Hartree-Fock-Slater potential. In these model calculations for the photoionization of tin and uranium we find relatively broad shape resonances in all the $d$ and $f$ subshells. In addition a Cooper minimum occurs in the outer subshells of these high-angular-momentum states within the region of the shape-resonance maximum. We examine the matrix elements for these subshells and the resulting cross sections and angular distributions.

An examination of the Rayleigh-Bénard convection experiment shows that the defining features of long-range order and spontaneous symmetry breaking, as they occur in equilibrium transitions, are also observed far from equilibrium. The broken symmetry is not, as has been suggested, translational invariance, but rather a discrete symmetry under velocity reversal. Some experimental consequences of these observations are outlined.

A simple and efficient method avoiding charge-state contamination problems is described to measure the lifetime of the metastable $2s_{\frac{1}{2}}$ level in hydrogenlike ions. Applying the method to the phosphorus ion, we obtain the lifetime in good agreement with the theoretical prediction.

Weyl's theory for a singular second-order differential equation and the complex scaling method of Balslev and Combes are combined to obtain a stable method for describing the continuous spectrum. The method obtained can be viewed as an extension of the Siegert method. The theory is applied to a model potential earlier used by Moiseyev et al.

One can define an effective dissipation for highly iterated two-dimensional maps or recursion relations. The convergence rate ${\delta }_{\mathrm{eff}}$ of the sequence of period-doubling bifurcations is shown to depend in a universal way on this effective dissipation in the limit of long $2^n$ cycles. These conclusions are based on both a renormalization argument and numerical calculations. The paper concludes with a brief discussion of the implications for physical systems.

A theory of critical ultrasonic attenuation in binary liquids based on the frequency-dependent specific heat is presented. Excellent agreement with experiment, without any adjustable parameters, is found for the frequency dependence of the consolute point attenuation and for the temperature dependence away from the consolute point. The latter is exhibited for two different mixtures at several different frequencies.

Strong interference effects have been found in the electric-field-induced autoionization signal of an isolated, doubly excited bound state in Ba. These interferences arise from interaction with narrow, long-living Stark resonances, which exist degenerately with a quasicontinuum of rapidly ionizing Stark states in the neighboring channel. By comparison with a theoretical model we conclude that the configuration interaction is energy dependent and increases by about a factor of 2 in the center of each Stark resonance.

We investigate the photon statistics of light whose intensity fluctuations are due to shot noise, such as occurs in certain kinds of luminescence involving multiplied-Poisson processes. The degrees of freedom and degeneracy parameters are obtained and contrasted with those for thermal light. The excess count variance for shot-noise light exhibits particle-like fluctuations and is maximized for large counting times. Radioluminescence photons produced in glass obey the Neyman type-$A$ counting distribution predicted by the theory.

By self-consistently calculating x-ray spectra from first principles, we have delineated the relationships between the spectrum and the state of compression and heating of a neon plasma in detail. A collisional-radiative model including Stark line profiles is used to determine the highly ionized high-density states of neon. One of our calculated spectra reproduces remarkably well an experimental spectrum obtained from laser implosion by Yaakobi et al. and indicates compression conditions significantly different from those obtained assuming the validity of local thermodynamic equilibrium. Implications of our calculations for spectroscopic diagnoses of fusion plasmas are discussed.

Quantitative results for the correlation functions for the Lorentz model of overlapping hard spheres are worked out and discussed within the recently proposed theory of diffusion and localization of a classical particle moving in a random static field. The applicability of the theory to the diffusion phase is established by a successful comparison of the diffusivity as a function of density and the velocity-autocorrelation function as a function of time for various densities, with the computer simulation results of Bruin. Specific predictions of the localization length as a function of density, of a nonmonotonic density dependence of the effective power-law exponent of the long-time tail of the velocity correlations, and of an oscillatory wave-number dependence of the normalized width of van Hove's scattering function are presented.

Monte Carlo calculations of the thermodynamic properties of a pseudopotential metal fluid, approximating lithium, were carried out over a wide range of temperatures and densities. The calculations were compared with the predictions of variational perturbation theories employing the hard sphere, soft sphere, and the one component plasma (OCP) as reference systems. The OCP predictions are in better agreement with Monte Carlo pressures, but are comparable for energies. The OCP reference system has the lower Helmholtz free energy at all points studied.

A group of nonthermal ions (> 10 keV/$Z$) have been measured from an expanding plasma generated by the irradiation of a 50-psec, 1.06-μm Nd:glass laser on glass microballoons. The effect of prepulse radiation on nonthermal-ion behavior has been investigated for various prepulse-main-pulse timing and amplitude. The measured asymptotic ion density distribution is consistent with an isothermal expansion of the plasma. The hot-electron temperature deduced from these measurements varies as ${\left(I{\lambda }^2\right)}^{0.32}$. Large-amplitude, high-frequency modulations have been observed in the ion density distribution. Nonthermal ions of energy up to $50k{T}_e$ have been detected.

A periodic function for the charge density of a Coulomb system, with uniform background, is constructed using Debye's equation for an unphysical imaginary plasma parameter. In order to explore the feasibility of a molecular-field approach for a crystal we study the one-dimensional case with techniques akin to "instanton techniques" which will be described in the text.

The behavior of an extra roll extending into an otherwise regular convection pattern is studied as a function of Rayleigh number, Prandtl number, $P$, and wavelength, by means of a fully resolved numerical simulation of the Boussinesq equations with free-slip boundary conditions. For reduced Rayleigh numbers of order one or less and $P\gtrsim 40$, numerical simulations of the lowest-order amplitude equations reproduce the Boussinesq results semiquantitatively. In particular, we find that when this class of defects is stable, they move with constant velocity $v$, parallel to the roll axis and give rise to a slow modulation of the roll pattern of the form $f(x,y-vt)\mathrm{}$. Both $f$ and $v$ have been calculated analytically within a linearized theory. The envelope function $f$ depends in an essential way on $v$ such that the limit $v\to 0$ cannot be sensibly taken.

Equilibrium polymerization of a monomer to long-chain polymers can be usefully described by the $n\to 0$ limit of the $n$-vector model of magnetism in a small magnetic field. In the molecular-field approximation, the $n\to 0$ vector model becomes identical to the earlier Tobolsky-Eisenberg theory of equilibrium polymerization. An error in an earlier analysis of the $n\to 0$ vector model is corrected and the consequences for polymerization and polymer solutions are discussed. A curiosity of the $n\to 0$ vector model—that its free energy does not everywhere satisfy the usual convexity requirements of thermodynamic stability—is also discussed. In an appendix the $n\to 0$ limit of the cubic discrete $n$-vector model (Hillhorst model) is also shown to be equivalent in mean field to the Tobolsky-Eisenberg theory of equilibrium polymerization.

A single plasma moving along a curved trajectory is electromagnetically unstable; the radiation fields excite a bunching instability. We show that the presence of metal surfaces near the beam may quench the instability. Our calculations apply to realistic physical situations: laboratory relativistic beams rotating in a vacuum bounded by metallic walls.

A detailed study of the effect of temperature on electron mobility in low-density nitrogen gas has revealed a Ramsauer-Townsend minimum in the scattering cross section at 1.7×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ and 15±2 meV. The cross sections at $\epsilon <0.010\mathrm{}$ eV are much larger than those previously reported. Energy gained by the electrons from the field is imparted to the molecules mainly through inelastic collisions, down to mean energies of a few meV. With increasing gas density the temperature coefficient ${\theta }_{n,T}={\left(\frac{\partial log\left(\mu n\right)}{\partial logT}\right)}_{n,T}$ near the vapor-liquid coexistence curve increases from -0.6 at the low-density limit and 80 K to zero at $\frac{n}{n_c}\ge 0.5$ and $\frac{T}{T_c}>0.97\mathrm{}$. While $\frac{n}{n_c}$ increases from 0.5 to 1.0 along the coexistence curve, the density-normalized mobility $\mu n$ decreases from 14 to 1.0 (${10}^{22}$ molecule/cm Vs) and the electric-field effect $\frac{d\mu }{\mathrm{dE}}$ changes sign from negative to positive. This behavior at high densities is attributed to electron capture, $e^{-}+{\mathrm{N}}_2\rightleftharpoons {\mathrm{N}}_2{\rightleftharpoons }^{-\mathrm{N}2}{\left({\mathrm{N}}_2\right)}_2{\rightleftharpoons }^{-\mathrm{N}2}$ and so on. The capture coefficient ${\nu }_a$ decreases with increasing electron energy.