The ground-state energy of the helium atom in a plasma is calculated by the variational method with the static screened Coulomb potential as the interparticle potential. This is used to calculate the ionization energy of the helium atom as a function of the screening parameter. The critical value of the screening parameter at which the ionization energy becomes zero is also estimated.

We consider here a dilute hot plasma which is homogeneous and in equilibrium in the framework of classical relativistic statistical mechanics as formulated recently by the authors. No external fields are present. The two-particle distribution function of the plasma is calculated for any temperature. This distribution will be physically significant, as long as the creation of pairs can be neglected. Several limits which apply at low or high temperatures are discussed. Comparison with previous work from several authors is made.

The structures of the blue phases are investigated in the homologous series of cholesteryl $n$-alkanoates by the examination of Bragg reflections. Through the use of the selection rules developed by Hornreich and Shtrikman, evidence is presented for the first time for the existence of a body-centered-cubic structure of $O^5$ symmetry. The first direct demonstration by this technique for the existence of simple cubic structures is also given.

We argue that the basic mechanism stabilizing the blue phases is the appearance of double cholesteric twist. The free-energy cost of the disclination lattice that inevitably accompanies double twist becomes small near the clearing point. We use the director picture and the Oseen-Frank equations in a computer calculation of the free energy for three specific models, with $O^5$, $O^2$, and $O^8$ symmetry. Disclinations are treated as having an isotropic core. Comparison of the results of the computation with a number of experimental quantities is given. In a final section, a mean-field theory of disclinations is presented. It is argued there that the biaxiality, which is a characteristic of Landau theories of the blue phase, can be considered as an "escape" of the core of the disclination, forced by the implicit requirement of analyticity.

We present a simple approximation for the velocity autocorrelation function of a tagged charged particle immersed in a liquid of charged particles. Application to a classical one-component plasma and a simple molten salt manifests the importance of the coupling between single-particle motion and charge-density excitations in both systems. The theory is also applied to molten sodium chloride with the result $\frac{D_{{\mathrm{Na}}^{+}}}{D_{{\mathrm{Cl}}^{-}}}=1.5\mathrm{}$ for the diffusion coefficients of ${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{-}$ ions.

The long-time behavior of two classical systems consisting of two and three particles with nonlinear interactions is investigated both numerically and analytically. The two systems exhibit quasiperiodic and ergodic motions at arbitrarily high total energy. The equipartition of energy is thus violated. The Lyapunov stability of the quasiperiodic motions is investigated. As expected, the number of quasiperiodic motions is infinite.

Liquid lead at 1173 K has been studied by the thermal neutron scattering technique. The symmetrized scattering function is obtained at constant momentum transfers from 1.8 to 7.1 ${\mathrm{\AA }}^{-1\mathrm{}}$. The highest observable energy transfer is 8 meV for the lowest momentum transfers and 28 meV for the highest. The measurement is corrected for experimental effects and special care has been given to the multiple-scattering corrections and subtraction of the container background. The first two even moments of the scattering function are determined and compared to an independent diffraction measurement and theoretical values, respectively. The full width at half maximum of the symmetrized scattering function is determined up to the ideal gas limit and compared with the corresponding quantity obtained at a lower temperature.

Dissipative structures in charged-fluid layer systems have been investigated by computer simulations. In a supercritical condition the system takes a convective state. It was found that the steady convective states were highly degenerate and one of the states gave the maximum charge transport. Relative stabilities of such metastable states were examined by disturbing each state. These investigations revealed that the most stable convective state corresponded to the state of maximum charge transport within the computational error, supporting the maximum-entropy-production hypothesis for a multi-stable-state system.

The equation of motion for the slow time dependence of convective rolls due to long-wavelength inhomogeneities is shown to have a singular dependence on the wave vector of the disturbance. Consequences for the skew varicose instability and the wave-number selection principle in textures of curved rolls suggested by Pomeau and Manneville are discussed.

An oversimplified mathematical model that contains some of the basic features of the mode-selection problem in dendritic solidification is developed and investigated both analytically and numerically. We find that there exists a unique side-branching state of this system in which the dendrite tip is performing small oscillations about its point of marginal stability, and we argue that this state is the natural operating mode of our model. We also argue that external noise will always tend to drive the system into this state, but that purely thermal fluctuations are much too small to provide the mode-selection mechanism that is seen experimentally.

The observed correlation functions $g\left(r\right)\mathrm{}$ on liquid Rb and Cs have been compared with theoretical correlation functions which were calculated by means of three-dimensional convolution polynoms. These are given in terms of paracrystalline distorted body-centered tetragonal lattices with $\frac{c}{a}=1.23\mathrm{}$. The lattice types of fcc and bcc can be excluded. The present method provides detailed statistical information about the short-range atomic arrangement in the liquid state. From the macroscopic density of the liquids and the nearest-neighbor average distance it can be concluded that about 4-7% of the atoms lie on interstices.

The exact solution to Maxwell's equations in a cholesteric planar texture is described and an algorithm for computing it is given. This algorithm makes use of a matrix continued fraction which converges so rapidly that the solution is, for practical purposes, in closed form. The solutions thus found can be used to describe scattering from dielectric inhomogeneities in a cholesteric in Born approximation, taking exact account of the cholesteric medium in which the scattering takes place. The general expression for the $S$ matrix in the Born approximation is given. The consequences for scattering from slowly varying order-parameter fluctuations are worked out in detail and several features are noted which depend in an essential way on the form of the exact cholesteric modes. These features include: (1) the scattered amplitude goes to zero in the forward direction, (2) there is a kind of anomalous diffraction for wavelengths near the pitch length, and (3) the scattered light may show complex spatial structure, even if the scatterer is essentially structureless, due to a kind of spatial beating of the cholesteric modes.

In this report the order-$\alpha$ correction to the lowest-order orthopositronium decay rate due to the two outer-vertex graphs is obtained in analytic form.

The concept of correlation between two parts of the total Hamiltonian is used to obtain information about the eigenfunction of a total Hamiltonian. Using a solvable model it is shown that the present formulation gives an energetically good wave function.

A theoretical treatment of the fluctuations in the ionization yield in finite regions of a medium under electron irradiation is presented, and its salient features are discussed vis-à-vis the existing theory for the completely space-independent case. It is shown that unlike in the latter situation, the integral equations for the moments of the probability distribution are not adjoint to the integral equation for the flux, though their corresponding integro-differential forms are. For a uniformly distributed source, the Spencer-Fano equation again turns out to be adjoint to the integral equations for the moments; however, in contrast to the space-independent case, a knowledge of the degradation spectra is not sufficient to determine the moments in this case. Finally, to characterize the fluctuations in any volume $v$, a volume-dependent Fano factor is introduced. The theory indicates that this factor should initially increase with $v$ from a value of 1 for small $v$, pass through a maximum, and then approach the conventional Fano factor, which, as is well known, is generally much less than unity.

The recent work of Anholt on $K$-vacancy production by relativistic projectiles has been applied to calculate the stopping power of the $K$ electrons. The results show that for protons of energy ∼${10}^3$ GeV and heavy target elements, the relativistic contributions to the stopping power amount to several times the results due to the longitudinal terms obtained from Walske's work.

Auger and x-ray emission rates have been computed relativistically for the $1s2s2p$ configuration of three-electron ions with $6<~Z<~10$. Results are compared with earlier calculations and with experiment.

The effect of a general additive symmetry on level density in finite spaces is investigated. It is found that with the introduction of symmetry, the level density moves closer towards a Gaussian distribution.

It is shown that short-wavelength Langmuir waves can parametrically excite electromagnetic radiation near the electron-plasma frequency. The theory presents a possible explanation of the electromagnetic waves observed in a recent experiment of Whelan and Stenzel [Phys. Rev. Lett. 47, 95 (1981)].

We show that dissociation-recombination equilibria are strongly affected by critical phenomena. The concentration of monomers can increase with infinite slope (determined by critical indices) upon cooling towards $T_c$, in agreement with experiments.