We give the first nonlinear solution of renormalization-group equations. This solution, based on the differential generator of Wegner and Houghton, exhibits an explicit mixing of (or crossover between) critical and mean-field behavior. The solution is given for all values of the spin dimension $n$ and to first order in $\epsilon \equiv 4-d$, where $d$ is the lattice dimensionality.

From measurements of resonance-fluorescence cross section, angular distribution, and polarization, the 4843-keV level of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been shown to have a $1^{+}$ character and a width of 5.1 ± 0.8 eV with all of the decays to the ground state. As the probable lower member of the giant $M1\mathrm{}$ excitation, this state is at a significantly lower energy and has a decay strength which is an order of magnitude larger than the predictions of simple shell-model calculations.

Angular distributions of cross sections and vector analyzing powers were measured in the reactions ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(d,t)\mathrm{}{}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ at 30 MeV. The vector analyzing powers show a strong $j$ dependence in both reactions. The distorted-wave Born approximation provides qualitative fits to the data for several transitions in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.

We report here additional positive results of a search for muonless neutrino- and anti-neutrino-induced events using an enriched antineutrino beam and a muon identifier of relatively high geometric detection efficiency. The ratio of muonless to muon event rates is observed to be $R=0.20\mathrm{}\pm 0.05$. We observe no background derived from ordinary neutrino or antineutrino interactions that is capable of explaining the muonless signal.

Relative rates for deep inelastic neutrino and antineutrino scattering without a finalstate muon have been measured. For neutrinos the result is $R^{\nu }=\frac{\sigma ({\nu }_{\mu }+\mathrm{nucleon}\to {\nu }_{\mu }+\mathrm{hadrons})}{\sigma ({\nu }_{\mu }+\mathrm{nucleon}\to {\mu }^{-}+\mathrm{hadrons})}=0.11\mathrm{}\pm 0.05$. The corresponding ratio for antineutrinos is $R^{\overline{\nu }}=0.32\mathrm{}\pm 0.09$.

By following 280.11 m of track length of 15.8-GeV/c negative muons in nuclear emulsion, twenty direct electron pairs were observed. For these pairs we have analyzed (i) the total energy distribution, (ii) the energy partition between the two members, (iii) the angular divergence, (iv) the transverse momentum distribution, and (v) the invariant mass of the electron pairs. The experimental results are compared with the present theories.

Cross sections and density-matrix elements for ${\pi }^{-}p\to \varphi n$ have been measured for - $-t\lesssim 1.5$ ${\mathrm{GeV}}^2$ at 3, 4, 5, and 6 GeV/c, using the Argonne effective-mass spectrometer to observe the decay $\varphi \mathrm{}\left(1019\right)\mathrm{}\to K^{+}{K}^{-}$. This is the first observation of the reaction in this energy range. The remarkably flat differential cross section at 4 GeV/c and the strong energy dependence suggest a production mechanism not normally seen at these energies. Data on $K^{-}p\to \varphi \Lambda$ and $K^{-}p\to \varphi {\Sigma }^0$ from the same experiment are also presented.

A class of relativistic-field-theoretic models of permanently bound quarks are shown to exhibit new and unconventional properties. They display crossing symmetry, but their Green's functions have an infinite array of singularities in momentum space and are singular everywhere in coordinate space. Nevertheless, these models are consistent quantum field theories that describe a system of interacting bound states which can decay into one another but not into quarks.

I consider the average displacement from its near neighbors of a parton in a hadron string after absorbing a highly virtual photon. It is found that for $Q^2\gtrsim 60$ ${\mathrm{GeV}}^2$, the struck parton would find itself separated from its near neighbors by a distance greater than the average internucleon spacing in a nuclear matter. I discuss the consequences of this result vis à vis deep inelastic scattering of leptons from complex nuclei.

We propose that extended lepton structure with size $\sim G_F^{}{}_{}{}^{\frac{1}{2}}$ leads to diffractive lepton scattering with constant $\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})\sim 2\pi G_F$. We predict that diffractive contributions to single-particle inclusive hadron distributions in $e^{+}{e}^{-}$ collisions are the same as in analogous hadron collisions, and are negligible for $e^{+}{e}^{-}\to e^{+}{e}^{-}$, $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, $e^{+}{e}^{-}\to e^{+}{e}^{-}+\mathrm{hadrons}$, and $\mathrm{eN}\to \mathrm{eX}$ at present energies.

Zeeman quantum beats have been observed in the fluorescent emission from individual rotational levels of the $B{}_{}{}^3{}_{}{}^{}\Pi _{0\mathrm{u}}^{}{}_{}{}^{+}$ state of ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}_2^{}{}_{}{}^{}$ after excitation by a short resonant dye-laser pulse. The derived Landé factors $g_J$ and $g_1$ (chemical shift) are compared with the spinrotation hyperfine coupling constants.

We have determined a new Rydberg value, $R_{\infty }=109737.3143\mathrm{}\left(10\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, with an order of magnitude improvement in precision, by measuring the absolute wavelengths of resolved fine-structure components of the Balmer $\alpha$ line in hydrogen and deuterium, excited in a dc gas discharge. Doppler broadening was eliminated by saturation spectroscopy with a pulsed dye laser. An iodine-stabilized He-Ne laser was the wavelength standard. Possible sources of systematic errors have been carefully investigated.

A new technique, cascade anticrossing spectroscopy, has been developed to determine the effective values of $〈r^{-3\mathrm{}}〉$ for the spin-dipole, orbital, contact, and quadrupole hyperfine interaction terms for the $4{}_{}{}^2{}_{}{}^{}D$ state of Rb. They are, in units of ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$, ${〈r^{-3\mathrm{}}〉}_d=-0.36\mathrm{}\left(8\right)\mathrm{}$, ${〈r^{-3\mathrm{}}〉}_l=+0.20\mathrm{}\left(2\right)\mathrm{}$, ${〈r^{-3\mathrm{}}〉}_c=-4.3\mathrm{}\left(1\right)\mathrm{}$, and ${〈r^{-3\mathrm{}}〉}_q=+0.79\mathrm{}\left(66\right)\mathrm{}$, respectively. The negative value of ${〈r^{-3\mathrm{}}〉}_d$ and the unexpectedly large value of ${〈r^{-3\mathrm{}}〉}_c$ are surprising. The fine-structure splitting has been measured to be - 13 360.9(8) MHz.

The specific heat of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ has been measured between 1 and 25 mK. The results indicate that the ordering of the nuclear spins takes place at a lower temperature than was anticipated theoretically, and with an unexpected temperature dependence.

Superfluid persistent currents have been studied in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed on a porous Vycor glass substrate at temperatures down to 150 mK. Stable superflow was observed in films as thin as 2.4 atomic layers at the lowest temperatures. Critical-velocity and superfluid-mass data were obtained as a function of film thickness. These data indicate that on a Vycor substrate superflow is only possible for films greater than 2 atomic layers in thickness and, further, that only the coverage above the first two layers contributes to the superflow.

A scaling theory is introduced for bicritical points, such as antiferromagnetic spinflop points (with analogies to the upper $\lambda$ point in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$), where two distinct critical lines meet. Experimentally testable predictions follow from renormalization-group calculations which indicate that the bicritical exponents should be Heisenberg like for systems with $n\le 3$ components; the crossover exponent $\phi (\simeq 1.25 \mathrm{for} n=3)$ is directly observable. For $n>\mathrm{}3\mathrm{}$ an intermediate ("supersolid") low-temperature phase may appear, the bicritical point then becoming tetracritical.

For the first time a critical slowing down of orientational fluctuations on approaching the order-disorder transition of a plastic crystal has been detected. The observed inverse relaxation rates ${\Gamma }^{-1\mathrm{}}$ in solid ${\mathrm{CD}}_4$ range from ${10}^{-11\mathrm{}}$ sec (11° above $T_0=27\mathrm{}$ K) to 2.5×${10}^{-10\mathrm{}}$ sec (close to $T_0$). The temperature dependence of $\Gamma$ can be fitted by a power law with an exponent $\rho =1.13\mathrm{}\pm 0.13$. For the $q$ dependence of $\Gamma$ an exponent $z=1.90\mathrm{}\pm 0.14$ is found close to $T_0$.

In optically excited Ge at $T=1.5\mathrm{} \mathrm{to} 4$ K, we observe a series of new microwave resonances at 3 to 20 kOe for $\nu =25\mathrm{}$ GHz. The resonant fields increase markedly with light intensity and are strongly correlated with the 709-meV electron-hole drop luminescence. We interpret the new lines as magnetoplasma dimensional resonances of single drops of ∼ 1 mm diam. We use magnetoplasma dimensional resonance as a direct probe of drop size and kinetics.

The transverse magnetoresistance effect of (100) $n$-channel silicon inversion layers was measured at low temperatures. Negative and/or positive effects have been obtained depending on surface-state density.

EPR and magnetic-susceptibility studies of TTF-TCNQ indicate that in the temperature region $T\gtrsim 60°$ K this compound consists of a metallic ${\mathrm{}\left(\mathrm{TTF}\right)\mathrm{}}^{+}$ chain and a ${\mathrm{}\left(\mathrm{TCNQ}\right)\mathrm{}}^{-}$ chain with localized spins. The metal-insulator transition at ∼ 60°K is accompanied by a strong interchain interaction.