Recently, Berry recognized in quantum mechanics a topological phase factor arising from the adiabatic transport of a system around a closed circuit, which is essentially the Aharonov-Bohm effect in parameter space. Here we consider manifestations of this phase factor for a photon in a state of adiabatically invariant helicity. An interferometer is suggested to see this phase. Also, an effective optical activity for a helical optical fiber is predicted. These effects emerge on a classical level as topological features of Maxwell's theory.

We report the first experimental verification of Berry's topological phase. The key element in the experiment was a single-mode, helically wound optical fiber, inside which a photon of a given helicity could be adiabatically transported around a closed path in momentum space. The experiment confirmed at the classical level that the angle of rotation of linearly polarized light in this fiber gives a direct measure of Berry's phase. The topological nature of this effect was also verified, i.e., the rotation was found to be independent of deformations of fiber path if the solid angle of the path in momentum space stayed constant.

I consider a connected self-avoiding polymer network made of identical long chains, with fixed topology. Using renormalization theory and conformal invariance, I conjecture in 2D, and give in $d=4-\epsilon$, to order $O\left(\epsilon \right)$, the exact value of its critical exponent $\gamma$ as a function of the topological invariants. In 2D, the exact result fits with recent numerical data for three- and four-leg stars by Lipson et al.

We compare the particle flow in the event plane of three-jet $q\overline{q}g$ (quark-antiquark-gluon) events with the particle flow in radiative annihilation events $q\overline{q}\gamma$ (quark-antiquark-photon) for similar kinematic configurations. In the angular region between quark and antiquark jet, we find a significant decrease in particle density for $q\overline{q}g$ as compared to $q\overline{q}\gamma$. This effect is predicted in QCD as a result of destructive interference between soft-gluon radiation from quark, antiquark, and hard gluon.

The ${\Sigma }^0-\Lambda$ transition magnetic moment has been measured to be $\left|\mu \right({\Sigma }^0-\Lambda \left)\right|=1.59\mathrm{}\pm 0.05\pm 0.07$ nuclear magnetons. The ${\Sigma }^0$ lifetime is $\tau \left({\Sigma }^0\right)=(0.76\mathrm{}\pm 0.05\pm 0.07)\times {10}^{-19\mathrm{}}$ see. The uncertainties are statistical and systematic, respectively.

Hadron mass calculations are carried out in lattice QCD on a $9^3$ × 18 lattice for flavor-nonsinglet mesons and baryons. Dynamical quark loops are fully incorporated with the Langevin technique. The contribution of dynamical quark loops significantly modifies the hadron masses in lattice units, but its dominant part can be absorbed into a shift of the coupling constant for the quark mass range we explored.

Dynamical chiral-symmetry breaking in asymptotically free theories with a slowly running coupling is analyzed. When the confinement scale $\Lambda$ is much less than the cutoff $M$ beyond which the theory cannot be used in isolation, the dynamical mass $\Sigma \mathrm{}\left(p\right)\mathrm{}$ starts from a value $\approx \Lambda$ for momenta $p\lesssim \Lambda$ and falls slowly for a significant range $p>\mathrm{}\Lambda$. It then takes on the asymptotic form $\frac{{\left(\ln p\right)}^a}{p^2}$ where $a>\mathrm{}1\mathrm{}$. In hypercolor theories this behavior generates sufficiently large fermion masses for a higher value of $M$ than naively expected. This in turn could allow for an adequate suppression of flavor-changing neutral currents.

We discuss muon and electron lepton-number nonconservation due to renormalization effects of the scalar-lepton mass matrix in spontaneously broken $N=1\mathrm{}$ supergravity theories. Differently from the case of massless or Dirac neutrinos, we find that if neutrinos are Majorana particles in a "seesaw" scheme the couplings photino-lepton-scalar-lepton lead to sizable rates for the processes $\mu \to e\gamma$ and $\mu +\mathrm{nucleus}\to e+\mathrm{nucleus}$. We discuss the constraints derived from the present experimental bounds.

In a recent experiment, Simpson found an excess intensity in the measured tritium beta spectrum below 1.5 keV. A detailed account of the decay energy and Coulomb-screening effects raises the theoretical curve in precisely this energy range, so that little, if any, of the excess remains. This correction is shown to be approximately given by a simple analytical expression.

A two-delta ($\Delta \Delta$) process and a new two-nucleon ($\mathrm{NN}$) process are proposed for neutrinoless $\left(0_{\nu }\right)\beta \beta$ decay. The conventional $\mathrm{NN}$ mechanism is also examined. The $N\Delta$ interaction and the integration over virtual neutrino momenta lead to the dominance of the $\Delta \Delta$ process. This dominance enables one to relate $0_{\nu }\beta \beta$ decay rates and forward-angle double-charge-exchange cross sections for $0^{+}$ (g.s.) → $0^{+}$ (g.s.) transitions, and to use this relation to obtain limits on lepton-number nonconservation from experimental double-charge-exchange cross sections in a nearly nuclear-structure-model-independent way.

We report the measurement of the differential scattering cross section for coherent photon scattering (nuclear Compton scattering) from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at an average energy of 180 MeV. This represents the first direct observation of the coherent process on a complex nucleus above the pion threshold. The results are compared with the prediction of a calculation utilizing the isobar-hole formalism.

Photodissociation of mass-selected ${{\left({\mathrm{CO}}_2\right)}_n}^{-}$ clusters, $n<~40$ at 355 and 308 nm reveals that the same "magic numbers" are present in the fragmentation pattern as in the mass spectrum, demonstrating that these intensity anomalies are due to relative ionic stabilities. The photon energy dependence of the fragmentation pattern shows that photodissociation proceeds by an evaporative mechanism and yields an upper bound, 0.22 ± 0.01 eV, for the binding energy of a neutral C${\mathrm{O}}_2$ onto the ionic cluster in the large-cluster limit.

The internuclear separation is used as a continuous parameter to vary the coupling strength between resonances of different autoionizing series in order to study the interference effects and the validity of independent-resonance models. This interference can have profound effects on the autoionization mechanism, which are demonstrated for $e^{-}+\mathrm{H}_2^{}{}_{}{}^{+}$ collisions. The new feature predicted by our calculations is the analog in the resonance case of avoided crossings for bound states and opens new avenues for an understanding of the autoionization process and has interesting experimental implications.

We show that the use of the interelectronic vector as adiabatic axis allows two-electron states of atoms to be described in terms of molecular orbitals. The associated potential curves can be obtained by scaling calculations on the ${\mathrm{H}}_2^{+}$ molecular ion and show for doubly excited states a strong similarity to adiabatic curves obtained from an analysis in hyperspherical coordinates. We associate a definite molecular symmetry with each two-electron state.

Fluorescent $\mathrm{Cl} K\alpha$ x-ray spectra were observed with a double-crystal spectrometer. $K\alpha$ line shapes appeared asymmetrically smeared by the presence of the shakeoff satellites within the natural width of main lines. Bonding effects of $K{M}^n\to L{M}^n$ satellites—parasites—of chlorine were observed ($n=1,2\mathrm{}$) for the first time. The relative intensities of parasites were measured in a number of chlorine compounds. Except for RbCl and CsCl, the relative intensities were found to be related to the covalency of the compounds.

Autoionization-ejected electrons from the configuration $1s^{2}2pnl$ produced by transfer and excitation in 2.5-3.5-MeV ${\mathrm{C}}^{3+}$ +He collisions were measured. Several peaks produced by autoionization are seen to be strongly enhanced in the backward direction. At these peaks, it is found that two autoionizing states with opposite parities overlap within their natural widths (i.e., overlapping resonances). This results in a strong forward-backward asymmetry, which is explained by the fast decay of a polarized electron state.

We consider the longitudinal dispersion of dynamically neutral tracer placed in a fluid flowing within a porous medium. For a random tube network, we derive the exact rules for tracer motion under the combined action of molecular diffusion and convection, and we introduce an efficient "probability propagation" algorithm which permits an (in principle) exact calculation of the first-passage-time distribution of the tracer as it flows through the medium. With our formalism, we exhibit both linear and nonlinear dispersion phenomena in two-dimensional random networks.

A recent exact multidimensional inverse-scattering method, developed for Schrödinger's equation, establishes a linear integral equation which determines the wave field at all space-time points from the scattering data. We present a new derivation of this integral equation which depends only on very general features of the scattering process such as causality, linearity, and the far-field decay of the wave field. Consequently, this integral equation is shown to hold for a wide class of wave equations (including, for example, the acoustic wave equation).

It is conjectured that the component wave functions of the Rabi Hamiltonian in Bargmann's Hilbert space are terminating series of spheroidal wave functions and generalized spheroidal wave functions of Leitner and Meixner. Numerical calculations strongly support the conjecture.

We study the statistical mechanics of two-dimensional surfaces of fixed connectivity embedded in $d$ dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. Without self-avoidance, entropy generates elastic interactions at large distances, and the radius of gyration $R_G$ increases as ${\left(\ln L\right)}^{\frac{1}{2}}$, where $L$ is the linear size of the uncrumpled surface. With self-avoidance $R_G$ grows as $L^{\nu }$, with $\nu =\frac{4}{\mathrm{}(d+2\mathrm{})\mathrm{}}$ as obtained from a Flory theory and in good agreement with our Monte Carlo results for $d=3\mathrm{}$.