Chiral 3π\pi-exchange NN-potentials: Results for dominant next-to-leading order contributions

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$-excitation). A similar feature has been observed for the chiral $2\pi$-exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review

Three-pion exchange: a gap in the nucleon-nucleon potential

The leading contribution to the three-pion exchange nucleon-nucleon potential is calculated in the framework of chiral symmetry. It has pseudoscalar and axial components and is dominated by the former, which has a range of about 1.5 fm and tends to enhance the OPEP. The strength of this force does not depend on the pion mass and hence it survives in the chiral limit.Comment: 20 pages, 5 figures, 1 tabl

Three-pion-exchange potential

Using the chiral symmetry, we calculated the dominant contribution to the nucleon - nucleon potential due to the exchange of three non-correlated pions. This contribution is isovetor with pseudoscalar and axial components. The pseudoscalar component is dominant, it has a range of 1.0 fm and it contributes in the pion channel

Chiral symmetry and pion-nucleon scattering

In this work, we study the influence of the way pious couple to nucleons in perturbative calculation of an observable in the pion-nucleon scattering

Mechanisms of enrichment of natural radioactivity along the beaches of the Camargue, France

A field study was carried out along the Golfe du Lion, that focussed on the beaches of the Camargue, to locate the main areas where enriched U and Th are found, and to better understand the processes that concentrate radioactivity on beaches. Indeed enriched areas are observed on some Camargue beaches, where high-dose rates are recorded due to excess U and Th activity (>1000 Bq kg-1). The coastline was mapped by means of an aerial gamma survey and the results indicated that the main actinides deposits occurred in the Camargue area. This concentrating effect is possibly due to a greater sedimentary contribution from the River Rhone relative to other minor Mediterranean rivers. Across the along-shore profile, the variability in actinides observed at the eastern part of Beauduc spit is mainly explained by variations in heavy and light mineral contents. Such variability can be accounted for by redistribution of the sand caused by erosion/deposition processes occurring in the eastern part of the spit. Further parameters such as grain size and heavy minerals content were studied in connection with the distribution of U, Th and 40K in the field at a more localised level (i.e. across-shore beach profile). The <200-μm fraction contains more than 50% of the radioactivity and heavy minerals (especially zircon) are the main contributors to the high levels of external radiation. Therefore the enriched areas, where U and Th exceed 1000 Bq kg-1, presumably result from the sorting of sand grains according to their size and density. © 2006 Elsevier Ltd. All rights reserved