Observations were made 1570 meters of water equivalent underground with an 8000-metric-ton water Cherenkov detector. During a live time of 80 d no events consistent with the decay $p\to e^{+}{\pi }^0$ were found in a fiducial mass of 3300 metric tons. It is concluded that the limit on the lifetime for bound plus free protons divided by the $e^{+}{\pi }^0$ branching ratio is $\frac{\tau }{B}>6.5\mathrm{}\times {10}^{31}$ yr; for free protons the limit is $\frac{\tau }{B}>1.9\mathrm{}\times {10}^{31}$ yr (90% confidence). Observed cosmic-ray muons and neutrinos are compatible with expectations.

A method for solving the inverse problem of certain hyperbolic as well as elliptic systems of $n$ equations in the plane is given. This result can be used to linearize the initial-value problem of several physically significant nonlinear evolution equations in two spatial and one temporal dimension.

Dielectronic recombination cross sections for the Li-like ions ${\mathrm{B}}^{2+}$ and ${\mathrm{C}}^{3+}$ via $1s^{2}2s\to 1s^{2}2p$ excitation are reported. The amount of electron capture attending the passage of megaelectronvolt/(atomic mass unit) ion beams through a collinear, magnetically confined, space-charge-limited electron beam is observed as a function of relative energy. The results agree well with distorted-wave calculations.

It has been found that a standing-wave pulse may be employed to produce an easily detectable, backward-propagating, phase-conjugate "replica" of any traditional gas-phase photon-echo signal. Standing-wave—induced backward two-pulse photon echoes have been observed in lithium vapor while only apertures were used to block laser background. An interesting dependence of backward echo intensity on standing-wave orientation is observed and discussed.

Two steps have been taken towards determining if the flux absorption and relaxation properties of a spheromak will allow dc-powered electrodes to form and sustain a steady-state spheromak. Without changing the physical properties of the spheromak, the formation time was increased from an Alfvén time to a tearing time, reducing the coaxial source power from ∼ 10 GW to ∼ 500 MW. With use of ∼ 50 MW, spheromaks were formed and then sustained at constant density and field for 1 ms, much longer than a magnetic-energy decay time.

With use of low-energy ${\mathrm{Ne}}^{+}$ scattering and low-energy electron diffraction both long-range order and Au segregation have been found at the ${\mathrm{Cu}}_3$Au(001) surface. The Au concentrations in the first and second layers are essentially constant at 0.5 and 0, respectively, for $T<~400°$C, beyond which they approach each other. Calculations of shadowing for the ordered surface agree with experiment, e.g., for shadowing of Cu atoms in the second and third layers by Au atoms in the first layer.

The model of Fukuyama and Lee for the pinning of the charge-density-wave phase by impurities is investigated. The current-current correlation function, related to the force-force correlation function by the equation of motion, is calculated to fourth order in the impurity concentration $n_0$. It is found that the threshold electric field is proportional to ${n_0}^2$, and above threshold, the resulting current is periodic in time, exhibiting many harmonics.

It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.

Explicit calculations reported here show that in the classical undamped Heisenberg ferromagnet with orthorhombic anisotropy, the critical slowing down accompanying the energetic instability of the static domain walls is not marked (as one would expect) by a localized soft dynamic mode of the wall, but is realized by a new mechanism which here is called "softening of the velocity change." The model-independent character of this behavior of ferromagnetic domain walls is conjectured.

Torque measurements have been made as a function of temperature on a Cu-2-at.%-Mn and a Au-18-at.%-Fe alloy. At a field-dependent temperature $T^{*}\mathrm{}\left(H\right)\mathrm{}$ torque effects go to zero indicating the frontier for the low-temperature strong-irreversibility regime. For the $\mathrm{Cu}\mathrm{Mn}$ sample the present experimental $T^{*}\mathrm{}\left(H\right)\mathrm{}$ curve coincides with the calculated mean-field-model de Almeida-Thouless line. For the $\mathrm{Au}\mathrm{Fe}$, $T^{*}\mathrm{}\left(H\right)\mathrm{}$ also follows the behavior predicted for the strong-irreversibility crossover on the mean-field model.

Large final-state effects have been observed in the $3p$, $3s$, and $2p$ electron energyloss spectra of vanadium as the incident-electron energy was reduced from 1500 eV to about 50 eV above the core threshold. Changes in the line shapes for the onset of $2p_{\frac{3}{2}}$ excitation and changes in measured threshold energies for $2p_{\frac{3}{2}}$, $3s$, and $3p$ excitation show the significance of the transition from sudden to adiabatic excitation. Strong excitations due to exchange effects are also observed in the $3p$ spectra at low incident energies.

A general method is given for solving certain inverse problems in the plane. The results can be used to construct the solution to the initial-value problems of related nonlinear evolution equations in two spatial and one temporal dimension. The method also allows one to compute lumps, i.e., multidimensional solitons tending to zero in all spatial directions.

An improved Coulomb potential is presented for use in the relativistic Schrödinger equation. This potential takes into account contributions of all two-photon exchange diagrams and gives the lowest-order relativistic corrections to the static Coulomb potential for arbitrary masses of the two particles. The cases spin 0-spin 0, spin 0-spin ½, and spin ½-spin ½ are considered. When the mass of one of the particles goes to infinity, then the well-known corrections to the binding energy and to the phase shifts as obtained with either the Klein-Gordon or the Dirac equation are reproduced.

Spontaneous compactification of $d=11\mathrm{}$ supergravity on the squashed seven-sphere ($S^7$) yields a spontaneously broken phase of the $N=8\mathrm{}$ theory on the round $S^7$ with SO(8) broken to SO(5) ⊗ SU(2) and with $N=1\mathrm{}$ or $N=0\mathrm{}$ supersymmetry according as the squashing is left or right handed. A feature unique to Kaluza-Klein supergravity is that the massless gravitino of the $N=1\mathrm{}$ phase comes from a massive $N=8\mathrm{}$ supermultiplet, as do the Higgs scalars. A solution is found with squashing and torsion but only in the right-squashed ($N=0\mathrm{}$) case.

A new spontaneous-symmetry-breaking mechanism is formulated for SU(3), which is used to describe the formation of bags around quarks. The Higgs field is replaced by the scalar product of two colored fermion fields. This model gives mass only to one gluon (equivalent to ${A_{\mu }}^8$) when spontaneously broken. The consequences of this scheme are discussed, and it is argued that it can explain several puzzling high-energy heavy-ion experiments.

With use of the MARK-J detector at $\sqrt{s}=34.7\mathrm{}$ GeV 21 000 $e^{+}{e}^{-}\to \mathrm{hadron}$ events have been collected. By measurement of the asymmetry in angular energy correlations the strong coupling constant ${\alpha }_s=0.13\mathrm{}\pm 0.01 \left(\mathrm{statistical}\right)\pm 0.02 \left(\mathrm{systematic}\right)$ is determined, in complete second order, and independent of the fragmentation models and QCD cutoff values used.

Identification of muons in hadronic events from $e^{+}{e}^{-}$ annihilation observed in the MAC detector at the storage ring PEP provides flavor tagging of heavy primary quarks. A sample enriched in events from $b\overline{b}$ production is obtained and the $b$-quark fragmentation function is inferred from the momentum spectrum of the muons. The $b$ quark is found to fragment predominantly with high values of $z$, with $〈z_b〉=0.8\mathrm{}\pm 0.1$, and to have an over-all semimuonic branching fraction of (${15.5}_{-2.9\mathrm{}}^{+5.4\mathrm{}}$)%.

The inelastic cross section of $p$-air collisions [${\sigma }_{\mathrm{in}}(p-\mathrm{air})$] between ${10}^{16}$ and ${10}^{18}$ eV is estimated by the observation of extensive air showers at Akeno. The flux of air showers at different zenith angles is analyzed with both a fixed muon number and a fixed electron number. ${\sigma }_{\mathrm{in}}(p-\mathrm{air})$ increases with energy as $290\times E_{\mathrm{lab}}^{0.06\pm 0.01}$ mb ($E_{\mathrm{lab}}$ in teraelectron-volts) up to ${10}^{18}$ eV with the assumptions of Feynman scaling in the fragmentation region and at least 10% of the primary particles being protons.

Two unusually-high-multiplicity interactions of high-energy heavy nuclei are observed in a balloon-borne emulsion chamber: A Si + Ag Br event (4 TeV/nucleon) and a Ca + C event (100 TeV/nucleon), with 1015 and 760 charged particles, respectively. The multiplicities and rapidity distributions favor the multichain model but not the wounded-nucleon superposition model. The high average $P_T$ (550-700 MeV/c) and the rapidity fluctuations of the events are not readily understood in terms of any superposition models.

It is found that just below nuclear saturation density more stable forms of dense matter exist than the near-spherical nuclei or bubbles customarily assumed. Because of the large effect of the Coulomb lattice energy, cylindrical and planar geometries can occur, both as nuclei and as bubbles. It is suggested that in order to approximate more complicated kinds of short-range order, the dimensionality should be regarded as a continuous variable ranging from $d=3\mathrm{}$ (spheres) to $d=1\mathrm{}$ (planes). The dependence of $d$ on density is illustrated, and its dependence on nuclear models discussed.