The critical behavior of the gelation of polymers is studied as a kinetic process in which only surface interactions between polymers are assumed. It is found that gelation occurs when the exponent $\omega$, which characterizes the effective surface area, is greater than ½, and that the exponent $\tau$, which characterizes the size distribution at the gel point, is related to $\omega$ by $\tau =\omega +\frac{3}{2}$.

The Brownian motion of a general classical anharmonic oscillator is studied in the lowviscosity limit for a general non-Markoffian interaction with a heat bath. Memory effects are shown to have a profound influence on the rate of energy accumulation and relaxation.

The rotational quantum mechanics of a new analytic model for a hindered rotor is presented, and rotational-state distributions of the hindered rotor are given in terms of unhindered rotor states.

The production of the charmed meson state $D^{*+}$ has been observed in $e^{+}{e}^{-}$ annihilation at 29 GeV. The fragmentation function for charmed quarks appears to be peaked about $z=0.5\mathrm{}$.

Spectra of $\gamma$ rays associated with deep-inelastic products from the 1150-MeV ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ + ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ reaction have been measured. The yield of 10-20-MeV $\gamma$ rays initially increases rapidly with the excitation energy of the products and then more slowly for excitation energies in excess of 120 MeV. Statistical-model calculations with ground-state values of the giant dipole strength function fail to reproduce the shape of the measured $\gamma$-ray spectra. This suggests a dependence of the giant dipole strength function on excitation energy.

Doppler-shift attenuation measurements have yielded lifetimes of $\tau =254\mathrm{}\pm 23$ fs for the $2_1^{+}$, 2211-keV level and $\tau =169\mathrm{}\pm 21$ fs for the $2_2^{+}$, 3403-keV level in ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$. In conjunction with measurements in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$, these results establish the linear relation between ${\left({\mathrm{}\left|M\right|\mathrm{}}^2\right)}^{\frac{1}{2}}$ and $T_z$ for $\Delta T=0\mathrm{}$, $E2\mathrm{}$ analog transitions. These results and other data for neighboring $s-d$-shell nuclei show that the isoscalar strenghts of $2_1^{+}$→$0_1^{+}$ transitions are less enhanced for $T=1\mathrm{}$ than for $T=0\mathrm{}$ nuclei.

The target-$A$ dependence of cross sections for emission of energetic $Z=1\mathrm{}$, 2 particles from 100-MeV/u ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ on Al, Ni, Sn, and Au targets is found to vary from an $A^{\frac{1}{3}}$ dependence at small angles to $\approx A^{\frac{2}{3}}$ at $\theta >45\mathrm{}°$, suggesting a smooth transition from peripheral to central collisions. The $A$ dependence of ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ yields indicate that target neutrons contribute to the formation of these particles. Velocity and temperature parameters of a heated, moving source are given for projectile energies from 7.5 to 147 MeV/u.

The tensor polarization $t_{20}$ of ${\pi }^{+}-d$ elastic scattering has been measured at 120 and 138 MeV as a function of scattering angle. While at the higher energy a strong oscillatory behavior prevails over the angular range measured (105°-180° c.m.), a considerable flattening is observed at the lower energy over the angular range 140°-170° c.m. This energy dependence and other observations are believed to manifest further evidence for the presence of nonconventional dynamics in this energy region.

A distorted-wave formulation of simple direct nuclear reactions, using Dirac wave functions, is presented. The resulting amplitude contains interior damping due to relativistic Darwin terms. The calculations are compared with standard Schrödinger results and significant differences are found.

Hadron scattering is shown to be sensitive to the relative sign of neutron and proton transition matrix elements. The relative signs for the $2_2^{+}$ states are determined to be positive for ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, and negative for ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ on the basis of proton differential cross-section measurements at 650 and 800 MeV. Suppression of the one-step amplitude in the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ $2_2^{+}$ state causes the interference of one-step and multistep reactions to be experimentally apparent.

Beta-decay half-lives have been measured for eight neutron-rich isotopes produced in the fragmentation of 11.4-GeV ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$. The experiment used a new measurement technique designed to observe very short half-lives. The previously unknown half-lives of ${}_{}{}^{22}{}_{}{}^{}\mathrm{O}$ (910 ± 350 ms) and ${}_{}{}^{32}{}_{}{}^{}\mathrm{Al}$ (35 ± 5 ms) have been obtained, as well as six known half-lives to provide a check of the procedure.

The Ginzburg-Landau equation with periodic boundary conditions on the interval [0, $\frac{2\pi }{q}$] is integrated numerically for large times. As $q$ is decreased, the motion in phase space exhibits a sequence of bifurcations from a limit cycle to a two-torus to a three-torus to a chaotic regime. The three-torus is observed for a finite range of $q$ and transition to chaotic flow is preceded by frequency locking.

An experiment on electromagnetically driven flows shows sequences of instabilities involving overstability and slow oscillations of the cellular structure before the onset of turbulence.

The first direct measurement of fuel density-radius product $\rho R$ in laser-fusion experiments is obtained by measuring the number of deuterium and tritium ions elastically scattered out of the fuel by 14-MeV fusion neutrons. They were recorded with the solid-state track detector CR-39. The energy spectrum of these particles is found to agree well with the theoretical result. This diagnostic was used in low- and high-compression experiments and gave measured $\rho R$ values of 1.3×${10}^{-4\mathrm{}}$ and 1.2×${10}^{-3\mathrm{}}$ g/${\mathrm{cm}}^2$, with an uncertainty of ∼ 20%.

The dynamic structure factor of a three-dimensional crystal, with an interpenetrating set of atomic chains which form one-dimensional fluids, is studied. At high frequencies there are two longitudinal acoustic modes arising from the separate motion of the lattice and fluid. At low frequencies there is one combined propagating longitudinal acoustic mode and a diffusive excitation due to particle motion. The crossover between these regions is predicted to occur at a frequency ∼ MHz in ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$.

The hydrogen pair correlation function of liquid water has been measured by time-of-flight neutron diffraction. The isotope substitution technique has been used to cancel the problematic hydrogen incoherent and inelastic scattering without introducing a dynamical model of the liquid. The results are in remarkable agreement with computer simulations of water using model potentials, although the short-range structure is more tightly coordinated than predicted.

Unusual features of radiation spectra from relativistic positrons channeled in the ionic crystal LiF have been observed.

The finite-size scaling of Fisher and Barber is extended to infinitely coordinated systems. Near $T_c$ and for a large number of elements $N$, a critical quantity $A$ behaves as ${|T-T_c|}^{a}f\left(\frac{N}{N_c}\right)$ with $N_c\sim {|T-T_c|}^{-{\nu }^{*}}$. An argument gives ${\nu }^{*}={\nu }_{\mathrm{MF}}{d}_c$, where ${\nu }_{\mathrm{MF}}$ is the mean-field coherence-length exponent and $d_c$ the upper critical dimensionality of the corresponding short-range system. This is checked on spin systems at $T\ne 0$ and on the Ising-$\mathrm{XY}$ quantum spin system in a transverse field at $T=0\mathrm{}$ for which calculations are reported.

The antiferromagnetic ordering in Pr due to the coupling of the $4f$ electronic system to the nuclei and to magnetic Nd impurities has been studied by neutron diffraction. A pure monocrystal of Pr develops true long-range order at about 50-60 mK. The ordering in both this crystal and a $P\mathcal{r}\mathrm{Nd}$ alloy is, however, presaged by unusually intense and longrange magnetic fluctuations, which are ascribed to the special form of the exchange interactions.

Electronic wave functions are studied on dilute lattices, at dimensionalities $1<~d<~8$. Generalized average inverse participation ratios are expanded in powers of the bond concentration, $p$. $Dlog$ Padé approximants indicate that these ratios diverge as ${(p_q-p)}^{{\gamma }_q}$, signaling the appearance of extended states for $p>\mathrm{}{p}_q$. These Anderson transitions occur above classical percolation. No divergence is detected at $d=2\mathrm{}$. These results are consistent with the existence of localized states at the center of the band.