It is shown that the three-cocycle arises when a representation of a transformation group is nonassociative, so that the Jacobi identity fails. A physical setting is given: When the translation group in the presence of a magnetic monopole is represented by gauge-invariant operators, a (trivial) three-cocycle occurs. Insisting that finite translations be associative leads to Dirac's monopole quantization condition. Attention is called to the possible relevance of three-cocycles in the quark model's U(6) ⊗ U(6) algebra.

We formulate the Ising model with competing interactions on a Cayley tree, in the infinite-coordination limit, as a two-dimensional nonlinear mapping. The phase diagram displays a Lifshitz point and many modulated phases. We perform calculations to show the existence of a complete devil's staircase at low temperatures. Also, we give strong numerical evidence for the existence of chaotic phases associated with strange attractors.

The analysis of the phase structure of the SO(3)=SU(2)/Z(2) lattice gauge theory in different space-time dimensionalities is presented. With use of Monte Carlo simulations the absence of phase transitions is shown for both $d=2\mathrm{}$ and $d=3\mathrm{}$. In the five-dimensional case I observe the persistence of the first-order phase transition previously seen at $d=4\mathrm{}$. A monopole condensation mechanism is suggests as responsible for this transition.

Parity nonconservation has been studied in elastic $p\alpha$ scattering at 46 MeV with longitudinally polarized protons. The longitudinal analyzing power averaged over the range of laboratory scattering angles of roughly 30° to 60° is found to be $A_z=(-3.3\mathrm{}\pm 0.9)\times {10}^{-7\mathrm{}}$. This result and measurements in other light nuclear systems are used to determine weak meson-nucleon coupling constants.

This paper reports the first demonstration of nuclear orientation of radioactive xenon atoms by spin exchange with polarized rubidium atoms. The nuclear tensor alignment, as measured by gamma-ray anisotropy, is about 30% of the maximum possible. The magnetic dipole moments for ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$ have also been measured by NMR spectroscopy. The methods developed here have possibilities for wide applications to nuclear and atomic studies of other radioactive rare-gas atoms.

Fission-fragment angular distributions in a number of heavy-ion-induced fusion reactions are explained on the basis that for composite systems with fission barrier heights comparable to their intrinsic temperatures, a fraction of the fission events take place before the fused system equilibrates fully in the $K$ degree of freedom. A value of about 8×${10}^{-21\mathrm{}}$ s is deduced for the characteristic time for $K$ equilibration.

Auger satellites have been measured to determine the probability of $M$-shell excitation accompanying $K$-shell photoionization of Ar, as a function of photon energy. The theoretically predicted difference between the dependence of shakeup and shakeoff probabilities on the photon energy near threshold is demonstrated for the first time. Results are critically compared with calculations.

Hanle resonances for coherent four-wave mixing in the ground state of Na are reported whose intensity increases and whose linewidth decreases with increasing inert buffer gas pressure. In 10-mTorr Na vapor with 4 atm of argon, resonances of less than 35 mG full width at half maximum are observed. The high resolution permits direct observation of the fundamental homogeneous broadening mechanisms for the Zeeman coherences responsible for four-wave mixing.

Experiments using 1.5 kJ of 0.26-μm wavelength light to irradiate thin "burn-through" targets show less stimulated Raman scattering (SRS) than similar experiments at 0.53 μm. The SRS from high-$Z$ (Au) targets is 3 orders of magnitude less than SRS from low-$Z$ (CH) targets irradiated at similar intensities. These results are the first direct observation of collisional damping of the Raman instability in high-$Z$ targets as predicted by theory and simulations.

Inelastic neutron-scattering measurements of the torsional levels of C${\mathrm{H}}_3$N${\mathrm{O}}_2$ and C${\mathrm{D}}_3$N${\mathrm{O}}_2$ are presented as functions of pressure and temperature. In contrast to all previously observed pressure dependence of hindered rotors, the ground-state tunnel splitting increases and the energies of the bound torsional levels decrease with pressure. A potential which reproduces these anomalous effects is found and the source of the anomaly explained.

Metallic-glass formation by solid-state reactions has been observed in multilayer Zr-Co diffusion couples and studied by cross-sectional transmission electron microscopy. Planar growth of a Corich amorphous phase proceeds from each interface of the unreacted sample, thus consuming the Co layers at a higher rate. Further annealing results eventually in a reaction of the Co-rich glassy phase with remaining Zr. Because of the high diffusivity of the Co in the amorphous phase, Kirkendall voids are formed during this homogenizing process and are lined up with the periodicity of the original layered structure.

We report the first observation of long-range order in a semiconductor III-V ternary alloy. ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ thin crystals grown by metal-organic chemical vapor deposition or molecular-beam epitaxy have Ga atoms preferentially occupying the 0,0,0 and ½,½,0 sites and Al atoms the ½,0,½ and 0,½,½ sites in each unit cell. Our results indicate that this ordered structure is the equilibrium state of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$.

I show that the observed large rotation-induced mutual friction in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ close to $T_c$ implies a reactive interaction between the normal fluid and a vortex, similar to a Magnus force. In the $A$ phase the absence of a singular vortex core enables a purely hydrodynamic description of this interaction to be given, and I argue from hydrodynamics that the experimental observations require the existence of an intrinsic angular-momentum density of order $\left(\frac{{\rho }_s\hslash }{2m}\right)\hat{1}$.

We present new exact results for the checkerboard $q$-state Potts model with a magnetic field. An exact expression for the partition function is given on some disorder varieties. We argue that the partition function exhibits, even in the presence of a magnetic field, an unexpected $S_4$ symmetry. A universal and exact expression for the magnetization discontinuity at the first-order phasetransition point ($q>\mathrm{}4\mathrm{}$) is proposed. This expression is shown to depend only on $q$ and to be independent of the coupling constants.

Intraionic spin-orbit-split multiplet levels have been observed by electronic Raman scattering in the intermediate-valence compound Eu${\mathrm{Pd}}_2$${\mathrm{Si}}_2$. From the temperature dependence of the Raman peak positions and widths the interconfigurational excitation energy $E_x$ and an upper limit of the interconfigurational mixing width $T_f$, respectively, have been obtained. This is the first spectroscopic support for the underlying assumptions of the ionic interconfigurational fluctuation model that has been proposed to describe intermediate valence.

The density of states at a Ti${\mathrm{O}}_2$-electrolyte interface is measured by a photoelectrochemical technique. The Schottky barrier height for various redox couples is also obtained for the surface containing this measured density. Good agreement is obtained between the band bending calculated from the interface density of states and the measured band bending as a function of the electrolyte redox Fermi potential.

We have determined that the initial photoluminescence decay in $a$-Si: H (at emission energies > 1.5 eV) follows an algebraic form $t^{-\alpha }$, for $50 \mathrm{psec}<t<\mathrm{}3\mathrm{} \mathrm{nsec}$, with $\alpha \mathrm{}\left(T\right)={\alpha }_0+\beta T$. These results are interpreted with a comprehensive model of nonradiative relaxation through electron band-tail thermalization. From our data we find a maximum hopping rate of 3 × ${10}^{13}$ ${\sec }^{-1\mathrm{}}$, an effective energy width of 20 meV for single-hop relaxation in the band tail, and that electrons have relaxed 50 meV from the conduction-band edge within 50 psec of excitation.

We have observed completely $p$-polarized light emission from smooth $\mathrm{A}\mathrm{l}-\mathrm{A}\mathrm{l}{\mathrm{O}}_x-\mathrm{A}\mathrm{u}$ tunnel junctions placed on a prism coupler. The angle and polarization dependence demonstrate unambiguously that the emitted light is radiated by the fast-mode surface plasmon polariton. The emission spectra suggest that the dominant process for the excitation of the fast mode is through conversion of the slow mode to the fast mode mediated by residual roughness on the junction surface.

Improvements in neutron spectroscopy have made possible measurements of the spin-wave spectra for nickel over much of the zone for the [111] and [100] directions. Broadening of the spin-wave excitations has been directly observed for the [111] direction and the nature of the optical spin wave has been further characterized for the [100] direction. Comparison of the measured results is made with recent theoretical calculations.

A unified view of the mixed-valence system of Ce impurities in a metal results from a comprehensive calculation of its properties. The peak position $T_0$ of the Kondo resonance in the photoemission spectrum sets the scale for the universal functions describing the specific heat, susceptibility, resistivity, thermopower, thermal conductivity, and neutron-scattering function. Deviations from universality arise when $T_0$ becomes comparable to the hybridization width $\Gamma$ or the spin-orbit splitting $\Delta$.