13,934 research outputs found

    Chiral 2π2\pi-exchange NN-potentials: Two-loop contributions

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    We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to 62.362.3 MeV at r=1.0r=1.0 fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants dˉj\bar d_j entering the chiral πN\pi N-scattering amplitude. We also evaluate the one-loop 2π2\pi-exchange diagram with two second order chiral ππNN\pi \pi NN-vertices proportional to the low energy constants c1,2,3,4c_{1,2,3,4} as well as the first relativistic 1/M-correction to the 2π2\pi-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.Comment: 6 pages, 2 figure

    Resummation of in-medium ladder diagrams: s-wave effective range and p-wave interaction

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    A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by considering the effective range correction in the s-wave interaction and a (spin-independent) p-wave contact-interaction. A two-component recursion generates the in-medium T-matrix at any order when off-shell terms spoil the factorization of multi-loop diagrams. The resummation to all orders is achieved in the form of a geometrical series for the particle-particle ladders, and through an arctangent-function for the combined particle-particle and hole-hole ladders. One finds that the effective range correction changes the results in the limit of large scattering length considerably, with the effect that the Bertsch parameter ξn\xi_n nearly doubles. Applications to the equation of state of neutron matter at low density are also discussed. For the p-wave contact-interaction the resummation to all orders is facilitated by decomposing tensorial loop-integrals with a transversal and a longitudinal projector. The enhanced attraction provided by the p-wave ladder series has its origin mainly in the coherent sum of Hartree and Fock contributions.Comment: 17 pages, 7 figures, to be published in Eur. Phys. J.

    Parity-violating two-pion exchange nucleon-nucleon interaction

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    We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of r=mπ11.4r= m_\pi^{-1} \simeq 1.4 fm they amount to about ±16\pm 16% of the parity-violating 1π1\pi-exchange potential. We evaluate also the parity-violating effects arising from 2π2\pi-exchange with excitation of virtual Δ(1232)\Delta(1232)-isobars. These come out to be relatively small in comparison to those from diagrams with only nucleon intermediate states. The reason for this opposite behavior to the parity-conserving case is the blocking of the dominant isoscalar central channel by CP-invariance. Furthermore, we calculate the T-matrix related to the iteration of the parity-violating 1π1\pi-exchange with the parity-conserving one. The analytical results presented in this work can be easily implemented into calculations of parity-violating nuclear observables.Comment: 7 pages, 3 figures, 1 table, published in: Phys. Rev. C76. 047001 (2007

    Third-order particle-hole ring diagrams with contact-interactions and one-pion exchange

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    The third-order particle-hole ring diagrams are evaluated for a NN-contact interaction of the Skyrme type. The pertinent four-loop coefficients in the energy per particle Eˉ(kf)kf5+2n\bar E(k_f) \sim k_f^{5+2n} are reduced to double-integrals over cubic expressions in euclidean polarization functions. Dimensional regularization of divergent integrals is performed by subtracting power-divergences and the validity of this method is checked against the known analytical results at second-order. The complete O(p2){\cal O}(p^2) NN-contact interaction is obtained by adding two tensor terms and their third-order ring contributions are also calculated in detail. The third-order ring energy arising from long-range 1π1\pi-exchange is computed and it is found that direct and exchange contributions are all attractive. The very large size of the pion-ring energy, Eˉ(kf0)92\bar E(k_{f0})\simeq -92\,MeV at saturation density, is however in no way representative for that of realistic chiral NN-potentials. Moreover, the third-order (particle-particle and hole-hole) ladder diagrams are evaluated with the full O(p2){\cal O}(p^2) contact interaction and the simplest three-ring contributions to the isospin-asymmetry energy A(kf)kf5A(k_f)\sim k_f^5 are studied.Comment: 20 pages, 3 figure

    Pion-photon exchange nucleon-nucleon potentials

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    We calculate in chiral perturbation theory the dominant next-to-leading order correction to the πγ\pi\gamma-exchange NN-potential proportional to the large isovector magnetic moment κv=4.7\kappa_v = 4.7 of the nucleon. The corresponding spin-spin and tensor potentials V~S,T(r)\widetilde V_{S,T}(r) in coordinate space have a very simple analytical form. At long distances r2r \simeq 2 fm these potentials are of similar size (but opposite in sign) as the leading order πγ\pi\gamma-exchange potentials. We consider also effects from virtual Δ\Delta-isobar excitation as well as other isospin-breaking contributions to the 2π2\pi-exchange NN-potential induced by additional one-photon exchange.Comment: 7 pages, 2 figures, to be published in Phys. Rev. C (2006) Brief Report

    Chiral four-body interactions in nuclear matter

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    An exploratory study of chiral four-nucleon interactions in nuclear and neutron matter is performed. The leading-order terms arising from pion-exchange in combination with the chiral 4π4\pi-vertex and the chiral NN3π3\pi-vertex are found to be very small. Their attractive contribution to the energy per particle stays below 0.60.6\,MeV in magnitude for densities up to ρ=0.4\rho =0.4\,fm3^{-3}. We consider also the four-nucleon interaction induced by pion-exchange and twofold Δ\Delta-isobar excitation of nucleons. For most of the closed four-loop diagrams the occurring integrals over four Fermi spheres can either be solved analytically or reduced to easily manageable one- or two-parameter integrals. After summing the individually large contributions from 3-ring, 2-ring and 1-ring diagrams of alternating signs, one obtains at nuclear matter saturation density ρ0=0.16\rho_0=0.16\,fm3^{-3} a moderate contribution of 2.352.35\,MeV to the energy per particle. The curve Eˉ(ρ)\bar E(\rho) rises rapidly with density, approximately with the third power of ρ\rho. In pure neutron matter the analogous chiral four-body interactions lead, at the same density ρn\rho_n, to a repulsive contribution that is about half as strong. The present calculation indicates that long-range multi-nucleon forces, in particular those provided by the strongly coupled πNΔ\pi N \Delta-system with its small mass-gap of 293293\,MeV, can still play an appreciable role for the equation of state of nuclear and neutron matter.Comment: 19 pages, 15 figures, to be published in Eur. Phys. J.