Charge Symmetry Violation in Nuclear Physics

The study of charge symmetry violation in nuclear physics is a potentially enormous subject. Through a few topical examples we aim to show that it is not a subject of peripheral interest but rather goes to the heart of our understanding of hadronic systems.Comment: Invited talk at the Int. Conference on Weak and Electromagnetic Interactions in Nuclei, Osaka, June 12-16 199

Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants

Quandle 2-cocycles define invariants of classical and virtual knots, and extensions of quandles. We show that the quandle 2-cocycle invariant with respect to a non-trivial $2$-cocycle is constant, or takes some other restricted form, for classical knots when the corresponding extensions satisfy certain algebraic conditions. In particular, if an abelian extension is a conjugation quandle, then the corresponding cocycle invariant is constant. Specific examples are presented from the list of connected quandles of order less than 48. Relations among various quandle epimorphisms involved are also examined

Quark-Meson Coupling Model for a Nucleon

The quark-meson coupling model for a nucleon is considered. The model describes a nucleon as an MIT bag, in which quarks are coupled to scalar and vector mesons. A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent way. It is shown that the mass of a nucleon as a dressed MIT bag interacting with sigma- and omega-meson fields significantly differs from the mass of a free MIT bag. A few sets of model parameters are obtained so that the mass of a dressed MIT bag becomes the nucleon mass. The results of our calculations imply that the self-energy of the bag in the quark-meson coupling model is significant and needs to be considered in doing the nuclear matter calculations.Comment: 3 figure

Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators

The paper analyses the decay of any zero modes that might exist for a massless Dirac operator H:= \ba \cdot (1/i) \bgrad + Q, where $Q$ is $4 \times 4$-matrix-valued and of order O(|\x|^{-1}) at infinity. The approach is based on inversion with respect to the unit sphere in $\R^3$ and establishing embedding theorems for Dirac-Sobolev spaces of spinors $f$ which are such that $f$ and $Hf$ lie in $(L^p(\R^3))^4, 1\le p<\infty.$Comment: 11 page

Effect of nucleon structure variation on the longitudinal response function

Using the quark-meson coupling (QMC) model, we study the longitudinal response function for quasielastic electron scattering from nuclear matter. In QMC the coupling constant between the scalar ($\sigma$) meson and the nucleon is expected to decrease with increasing nuclear density, because of the self-consistent modification of the structure of the nucleon. The reduction of the coupling constant then leads to a smaller contribution from relativistic RPA than in the Walecka model. However, since the electromagnetic form factors of the in-medium nucleon are modified at the same time, the longitudinal response function and the Coulomb sum are reduced by a total of about 20% in comparison with the Hartree contribution. We find that the relativistic RPA and the nucleon structure variation both contribute about fifty-fifty to the reduction of the longitudinal response.Comment: 14 pages, including 3 ps file

Variation of hadron masses in finite nuclei

Using a self-consistent, Hartree description for both infinite nuclear matter and finite nuclei based on a relativistic quark model (the quark-meson coupling model), we investigate the variation of the masses of the non-strange vector mesons, the hyperons and the nucleon in infinite nuclear matter and in finite nuclei.Comment: 4 pages plus one ps file, to appear in Proc. of International Symposium on Non-Nucleonic Degrees of Freedom Detected in Nucleus (NNDF '96) at Osaka, Japa

Self-consistent description of finite nuclei based on a relativistic quark model

Relativistic Hartree equations for spherical nuclei have been derived from a relativistic quark model of the structure of bound nucleons which interact through the (self-consistent) exchange of scalar ($\sigma$) and vector ($\omega$ and $\rho$) mesons. The coupling constants and the mass of the $\sigma$-meson are determined from the properties of symmetric nuclear matter and the rms charge radius in $^{40}$Ca. Calculated properties of static, closed-shell nuclei from $^{16}$O to $^{208}$Pb are compared with experimental data and with results of Quantum Hadrodynamics (QHD). The dependence of the results on the nucleon size and the quark mass is investigated. Several possible extensions of the model are also discussed.Comment: 37 pages, 17 postscript figures are included, uses epsfig.sty, uuencoded Z-compressed .tar file (uufiles

Dyadic Green's Functions and Guided Surface Waves for a Surface Conductivity Model of Graphene

An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper transverse-electric (TE) surface wave exists if and only if the imaginary part of conductivity is positive (associated with interband conductivity), and a proper transverse-magnetic (TM) surface wave exists when the imaginary part of conductivity is negative (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of the imaginary part of conductivity can be varied, allowing for some control over surface wave properties.Comment: 9 figure