NN Core Interactions and Differential Cross Sections from One Gluon Exchange

We derive nonstrange baryon-baryon scattering amplitudes in the nonrelativistic quark model using the ``quark Born diagram" formalism. This approach describes the scattering as a single interaction, here the one-gluon-exchange (OGE) spin-spin term followed by constituent interchange, with external nonrelativistic baryon wavefunctions attached to the scattering diagrams to incorporate higher-twist wavefunction effects. The short-range repulsive core in the NN interaction has previously been attributed to this spin-spin interaction in the literature; we find that these perturbative constituent-interchange diagrams do indeed predict repulsive interactions in all I,S channels of the nucleon-nucleon system, and we compare our results for the equivalent short-range potentials to the core potentials found by other authors using nonperturbative methods. We also apply our perturbative techniques to the N$\Delta$ and $\Delta\Delta$ systems: Some $\Delta\Delta$ channels are found to have attractive core potentials and may accommodate ``molecular" bound states near threshold. Finally we use our Born formalism to calculate the NN differential cross section, which we compare with experimental results for unpolarised proton-proton elastic scattering. We find that several familiar features of the experimental differential cross section are reproduced by our Born-order result.Comment: 27 pages, figures available from the authors, revtex, CEBAF-TH-93-04, MIT-CTP-2187, ORNL-CCIP-93-0

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Mapping Bathymetry and Depositional Facies on Great Bahama Bank

Satellite imagery and an extensive set of water-depth measurements have been used to map and critically evaluate the magnitude and patterns of bathymetry across Great Bahama Bank. Descriptions of previously collected sediment samples were combined with satellite imagery to map and refine the interpreted distribution of surficial carbonate sediments (depositional facies). Data reveal that 60% of Great Bahama Bank lies in 5 m or less of water. The deep portion occurs mainly in a generally east–west trending area in the southern portion of the platform. The re-evaluation of the facies reveals that Great Bahama Bank is essentially a very grainy platform with muddier accumulations primarily in the lee of Andros Island. This area of Great Bahama Bank also experiences currents related to an excursion of the Florida Current onto the platform top; possibly enhancing sediment mud production through the generation of whitings. Sediment equivalents to mudstones, wackestones and mud-rich packstones cover 8%, 5% and 14%, respectively, of the platform top, whereas sediment equivalents to mud-poor packstones, grainstones and rudstones account for 20%, 45% and 3% of the surface area. Boundstones (reefs) were not specifically mapped in this study due to the resolution of the mapping. There is a poor relationship between the occurrence of the depositional texture and water depth, in that the grainier sediment types are abundant across the full range of water depths. The most abrupt lateral facies changes portrayed on the facies maps are observed leeward of islands, areas which also hold the highest diversity in facies type. The majority of the islands on the platform align with the north-west/south-east strike of the platform margin and these islands, in turn, exert control on the shape and orientation of facies belts that develop in proximity to them. For this reason, regions of the platform that contain principal islands host facies belts that align with the principal axis of the platform, whereas for regions lacking islands, the facies belts adopt an east–west trend consistent with prevailing winds and currents. There is a clear trend that the wide southern portion of the platform hosts the most continuous expanses of grain-rich sediments