It is shown that certain types of position-space, or "cell," renormalization-group transformations from an Ising-model object Hamiltonian onto another Ising-model image Hamiltonian are well defined and smooth in the thermodynamic limit, provided the object Hamiltonian has a large enough magnetic field. In certain other cases there is evidence (though not a rigorous proof) that no thermodynamic limit exists, or, if it exists, the transformation is not smooth.

We examine the effect of an assumed variation in Planck's constant $\hslash$ on the element abundances produced by nucleosynthesis in the standard hot big-bang model of the universe. In order to be consistent with current estimates of the primordial helium and deuterium abundances, we find that at the epoch of nucleosynthesis (a red shift $z\approx {10}^8-{10}^{10}$, $t\approx {10}^{-1\mathrm{}}-{10}^3$ sec after the initial event), $0.2\lesssim \frac{{\hslash }_{\mathrm{nucleosynthesis}}}{{\hslash }_{\mathrm{present}}}\lesssim 3$. This result supports the applicability of the local laws of physics to the earliest epoch of the universe examined to date.

Proton-proton elastic scattering at 400 GeV/c has been measured in the region $5.4<-t<\mathrm{}14.4\mathrm{}$ Ge${\mathrm{V}}^2$ with no sign of a second dip or "break." If the data are fitted by $\exp \mathrm{}\left(\mathrm{At}\right)\mathrm{}$, the slope $A$ decreases from 1.5±0.1 to 0.7±0.2 Ge${\mathrm{V}}^{-2\mathrm{}}$ over the range. At fixed $t$ the 400-GeV/c cross sections are about 0.6 times those at 200 GeV/c in this $t$ range. At fixed ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=15\mathrm{}°$, $\frac{d\sigma }{\mathrm{dt}}\propto s^{-n}$ where $n=9.7\mathrm{}\pm 0.3$.

The difference between the Schrödinger and Klein-Gordon wave functions is calculated for 100-200-MeV pions. The same optical-model potential is used in each case. The differences in the distorted waves so calculated are shown to be significant even though the elastic scattering phase shifts are nearly identical.

Measurement of the spin-flip probability in the reaction ${}_{}{}^{10}{}_{}{}^{}\mathrm{O}(p_{\mathrm{pol}}, {p_{\mathrm{pol}}}^{\prime }){}_{}{}^{16}{}_{}{}^{}\mathrm{O}(2^{-}, 8.88 \mathrm{MeV})$ at $E_p=40\mathrm{}$ MeV yields values that are significantly smaller than those predicted by microscopic distorted-wave Born-approximation calculations. This is interpreted as direct evidence for the dominance of multistep processes in this reaction. Analysis of the data in terms of the spin-flip cross section (spin-flip probability times the differential cross section) yields an isoscalar $M2\mathrm{}$ strength for the $2^{-}$ which is significantly smaller than that predicted by random-phase-approximation wave functions.

The spins and parties of the five reported $l=0\mathrm{}$, $J^{\pi }={\frac{1}{2}}^{+}$ substructures nested within the bróad $l=0\mathrm{}$ analog resonance in ${}_{}{}^{71}{}_{}{}^{}\mathrm{As}$ at $E_p=5.05\mathrm{}$ MeV have been measured. Three of the five substructures were determined as having $J^{\pi }$ different from ${\mathrm{½}}^{+}$, casting doubt on the interpretation of this resonance as an example of intermediate structure.

We have developed a new method for determining state-resolved differential cross sections in inelastic collisions. A single-frequency laser provides level-specific detection of scattered atoms, while the Doppler shift of the same laser provides a completely non-mechanical angular selectivity in the detection. We have used this technique to make the first measurement of an alkali fine-structure transfer cross section in which both the scattering angle and final state are determined.

Very narrow saturated double-quantum transitions ($2{}_{}{}^2{}_{}{}^{}S-3\mathrm{}{}_{}{}^2{}_{}{}^{}S, 3{}_{}{}^2{}_{}{}^{}D$) have been observed for atomic H in a He-${\mathrm{H}}_2$ dc discharge using rf and a cw dye laser. The H $3P_{\frac{3}{2}}-3\mathrm{}{D}_{\frac{3}{2}}$ Lamb shift has been measured directly by comparing single- and double-quantum saturation signals to be - 5.5(0.9) MHz, confirming that $3D_{\frac{3}{2}}$ lies lower than the $3P_{\frac{3}{2}}$ state. Further applications of the method are discussed.

A classical theory gives excellent agreement with the Bayfield-Koch experiment on microwave ionization of Rydberg hydrogen atoms. The time dependence of excitation and ionization is presented, and classical trajectories are divided into four significant categories. The results suggest that nonresonant laser ionization of atoms in states of low quantum number can also take place as a result of extremely high-order processes with large numbers of intermediate states of excitation.

We have observed a chaotic response to a small periodic thermal perturbation in time-dependent Rayleigh-Bénard convection. The induced noise shows a threshold in the driving amplitude, and occurs when the driving frequency nearly equals the frequency difference between two spontaneous oscillatory modes. The behavior for time-independent boundary conditions is qualitatively similar to that of a fourteen-mode model recently studied by Curry.

Experimental investigations of strong turbulence in low-$\beta$ plasmas are reported. The measurements were carried out in a rotating plasma column produced by surface ionization. The turbulence is excited by instabilities associated with the radial gradients of the plasma column. Measured variations of spectral structure and spectral coefficients agree with recent theoretical predictions.

The relative orientation between solid argon monolayers and the basal plane of graphite single-crystal substrates has been measured as a function of mean overlayer interatomic spacing $d$ by low-energy electron diffraction for $32 \mathrm{K}\lesssim T\lesssim 52 \mathrm{K}$. For $3.82 \AA \lesssim d\lesssim 3.95 \AA$, the measured orientation varies with $d$ as quantitatively predicted by Novaco and McTague because of periodic static distortions of the argon monolayers by lateral argon-graphite forces. The relevance of these results to Villain's calculations is discussed.

The experimental observation phonons localized to step edges on platinum $6\left(111\right)\mathrm{}\times \left(11\mathrm{}\overline{1}\right)$ surfaces is reported. Their frequency is above the maximum frequency of the bulk phonon spectrum.

We present the results of a detailed x-ray scattering study of submonolayer krypton films physisorbed onto basal-plane surfaces of exfoliated $\mathrm{ZYX}$ graphite. Results illustrate that x-ray scattering may provide precise structural information about the solid and liquid phases of adsorbed films. For near-monolayer coverages, melting of the commensurate kypton solid appears to be a second-order transition with a critical exponent $\beta$ consistent with a Potts lattice-gas model of the melting process.

Using a molecular-dynamics technique, we studied the excitation spectrum of an Ising-like lattice-dynamic model in four space dimensions. We found a central peak close to the transition temperature which does not evolve from the damped soft mode. Our results reveal that the overdamped-soft-mode picture and current interpretations of renormalization-group results for dynamic properties should be revised. They also provide testable predictions for Ising-like dipolar systems.

Textures of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ confined to 2-μm-diam cyclinders contain singular regions. We have observed and characterized at least two such textures with an external magnetic field parallel and perpendicular to the cylinders. We also found an unexpected effect of the cylinders on the transition from the $A$ to the $B$ phase.

Brillouin scattering from thermal surface phonons has been observed in thin films deposited on semi-infinite media. The velocity of Rayleigh and Sezawa waves was measured and interpreted in terms of the film elastic constants. Surface phonon attenuations were also measured and it was found that the lifetimes of surface and bulk phonons of the same wave vector are comparable in the glass studied.

The dynamic structure factor, $S(Q, \omega )$, for superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at finite temperatures is described as the sum of two components: a "superfluid" component with a shape characteristic of $S(Q, \omega )$ at $T=0\mathrm{}$ and a weight $\frac{{\rho }_s}{\rho }$, and a "normal-fluid" component with a shape characteristic of $S(Q, \omega )$ for nonsuperfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and a weight $\frac{{\rho }_n}{\rho }$.

An $S=\frac{1}{2}$ EPR spectrum is observed in electron-irradiated GaP: Zn with an isotropic $g=2.0130\mathrm{}\pm 0.0015$ and resolved ligand hyperfine splitting from four equivalent $I=\frac{1}{2}$ neighbors. This spectrum is assigned to the isolated Ga vacancy. A molecular-orbital model for ${V_{\mathrm{Ga}}}^{--}$ is consistent with the experimental data. Analysis of the hyperfine parameters reveals some lattice relaxation although the full $T_d$ symmetry is maintained.

By heating the droplet cloud in Ge with infrared radiation, we increase the low-frequency phonon emission rate of the droplets. By measuring the resulting velocity increase, we give convincing evidence that this "phonon wind," powered by Auger decay, is the cause of droplet motion, as originally proposed by Keldysh.