Percolation is often used as a model for critical behavior of the sol-gel transition. A three-dimensional kinetic model for gelation, similar to that of Manneville and de Seze, is investigated with a Monte Carlo method. By looking at the ratios of the critical amplitudes of the "susceptibility" (weight-average degree of polymerization) below and above the percolation threshold, clear evidence is found that this model is neither in the universality class of standard percolation nor in that of classical (Flory-Stockmayer) theory.

The size dependence of slow relaxation processes in the infinite-range Ising spin-glass is investigated by computer simulation. Below the transition temperature, relaxation of variables which do not change sign under inversion of the spins is complete by a time $\tau$, where ln $\tau \propto N^{\frac{1}{4}}$ and so diverges as $N$, the number of spins, tends to infinity. The "ergodic time" ${\tau }_{\mathrm{eg}}$ satisfies ln ${\tau }_{\mathrm{eg}}\propto N^{\frac{1}{2}}$. These results are consistent with a physical picture where barriers between free-energy minima in phase space have a height proportional to the square root of the number of spins to be flipped.

It is shown, from microscopic considerations based on the Fokker-Planck equation, that the boundary condition (used in conjunction with the diffusion equation) in which the particle density is set to zero on a perfectly absorbing surface is untenable, and, for the first time, the boundary condition for any plane (partially or perfectly) absorbing surface is derived.

Multiple-particle, $\gamma$-ray coincidence techniques have been used to study neutron-deficient isotopes near $N=Z=40\mathrm{}$. Results are presented for ${}_{}{}^{77-80}{}_{}{}^{}\mathrm{Sr}$. Levels in ${}_{}{}^{78}{}_{}{}^{}\mathrm{Sr}$ were seen to $J=10\mathrm{}$ with $E\left(2^{+}\right)=278\mathrm{}$ keV and $T_{\frac{1}{2}}=155\mathrm{}\pm 19$ ps. The results suggest that this region contains some of the most deformed nuclei known, with quadrupole deformations ${\epsilon }_2\approx 0.4$. These data resolve conflicting theoretical predictions of nuclear shapes and emphasize the important contribution of hexadecapole deformation in determining the most stable shape.

The analyzing power $A_y\left(\theta \right)$ for scattering of neutrons from deuterons at 10 MeV for 30° to 145° (c.m.) was measured to an accuracy better than ± 0.005. The results are compared to published $p-d$ data at 10 MeV, and convincing differences are noted for the first time. These differences provide a sensitive test both of calculations for the three-nucleon system and, more importantly, of the fundamental nucleon-nucleon interaction.

A new fast-beam microwave optical detection technique which uses a specially designed interaction region to observe resonances with both polarizations of the microwave field and both polarizations of the emitted light has been developed to study charge-exchange collisions in greater detail. The first measurements of the partial cross sections for capture into each of the $L$ and $M_L$ states in the $n=3\mathrm{}$ manifold for protons incident on a nitrogen target are reported.

The measured total electron-capture cross sections per number of carbon atoms in ${\mathrm{C}}_m{\mathrm{H}}_n$ ($m=1, 2, 3, 4$), $\frac{{\sigma }_c}{m}$, decrease with increasing $m$. This decrease is largest at the lowest velocities of 0.8-3 MeV ${}_1{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$ ions, and diminishes in the limit of high velocities where the strict additivity of atomic cross sections in a molecular target is approached. The breakdown of the additivity rule in the present data is primarily attributed to, and accounted for in terms of, intramolecular electron loss processes.

It is found through theory and magnetohydrodynamic particle simulation that fast magnetic-field-line reconnection may consist of more than one stage. After the Sweet-Parker phase is established for an Alvén time, a faster "second phase" of reconnection takes over if the plasma is compressible: The reconnected flux varies as $\psi ={\psi }_0{t}^{\frac{{\rho }_i}{{\rho }_e}}$, where ${\rho }_e$ and ${\rho }_i$ refer to the plasma densities outside and inside of the current channel.

Plasma heating by near-perpendicular injection of up to 7.2 MW of neutral-beam power has been studied in the PDX tokamak. Collisionless plasmas with centrla ion temperatures up to 6 keV have been obtained. The total plasma energy, which is dominated by contributions from beam and thermal ions, rises linearly with increasing beam power. The ion heating efficiency in PDX is comparable to the measured in the Princeton Large Torus with tangential injection.

Characteristic x-ray spectra of plasma impurity ions have been measured in the region $\lambda =4.3-5.1\mathrm{}$ Å. The observation of strong principal $n=2\mathrm{}$ to $n=1\mathrm{}$ x-ray lines for H-like sulfur and for He-like sulfur and chlorine in the density range (1-6) × ${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$ is reported. Dielectric recombination and inner-shell excitation satellite lines are weak. The results, which are of interest for both atomic physics and plasma diagnostic applications, are compared with atomic calculations of line spectra and transition rates.

It is argued that an array of potential barriers modulated in position and strength in a manner incommensurate with the barrier spacing can be replaced by a $\delta$-function Kronig-Penny model. With this equivalence it is shown, with use of renormalization-group arguments as well as known results from other calculations, that this model possesses both localized and extended states separated by mobility edges.

This paper reports consideration of the Hamiltonian for tight binding in one dimension with off-diagonal disorder of two forms, corresponding to Dyson's types I and II. The density of states and localization function at the center of the band are found by perturbation theory and a scaling argument. The distinction between the two types of disorder is clearly drawn, and new singularities in the Green's function pertinent to the problem of random classical diffusion are predicted.

Starting from a microscopic description of the interaction of a helium atom with a metal surface, a simple approximate result is derived which shows that the lateral corrugation of the repulsive potential decreases exponentially with distance $z$ from the surface. For Cu(110) this theory leads to an interaction potential that reproduces all the observed bound states and gives a quantitative fit of recent helium diffraction data taken at various incident energies and angles.

The chemisorption of CO on Ti(0001) is treated with a many-electron configuration-interaction theory for adsorbate-surface interactions. When perpendicular, threefold, atopatom and bridge adsorption sites are compared with CO adsorption parallel to the surface, CO parallel with C and O stretched toward adjacent threefold sites is the more stable (60 kcal/mole exothermic). A distinctive upward shift of CO energy levels occurs for stretched and dissociated CO adsorption as a result of increased electron transfer from the lattice. Binding-energy contributions are discussed.

With use of radiative detection, NMR was performed on "brute-force"-oriented ${}_{}{}^{111}{}_{}{}^{}\mathrm{In}$ implanted in copper by use of an electromagnetic isotope separator. A sharp resonance line was detected, in contrast with hyperfine-enhanced NMR on oriented nuclei. The deduced Knight shift of In in Cu is 0.65(11)%.

Experiments on the Belousov-Zhabotinskii reaction in a stirred flow reactor reveal behavior that is strikingly similar to that generated by one-dimensional maps with a single extremum. In particular, a period-doubling sequence is observed that leads to a regime containing both chaotic and periodic states. Within the experimental resolution the ordering of the periodic states is in accord with the theory of one-dimensional maps.

It is shown rigorously that the one-dimensional Ising model with long-range antiferromagnetic interactions exhibits a complete devil's staircase.

The equivalence between a six-dimensional stochastic classical scalar field theory and the corresponding four-dimensional quantum field theory has been shown to stem from a hidden supersymmetry of the former. This has led to a formulation of the quantum theory in an eight-dimensional superspace with six commuting and two anticommuting coordinates. This formalism is generalized to include gauge and fermionic field theories.

The $\mathrm{np}$ total cross section has been measured from 40 to 770 MeV with good statistical precision and better than 1% energy resolution. No evidence is seen for narrow resonances with areas greater than 5 mb MeV or for the $I=0\mathrm{}$, ${}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}$ state reported by other authors. From 200 to 700 MeV the present results are as much as 6% lower than previous data.

From a partial-wave analysis of the $K\overline{K}\pi$ system in the decay $\frac{J}{\psi }\to \gamma K^{+}{K}^{-}{\pi }^0$, it is determined that the quantum numbers of the $K\overline{K}\pi$ resonance at 1440 MeV, previously identified as the $E\left(1420\right)\mathrm{}$, are $J^{\mathrm{PC}}=0^{-+}$. This new particle has been named the $\iota$.