13,130 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

    Twice-iterated boson-exchange scattering amplitudes

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    We calculate at two-loop order the complex-valued scattering amplitude related to the twice-iterated scalar-isovector boson-exchange between nucleons. In comparison to the once-iterated boson-exchange amplitude it shows less dependence on the scattering angle. We calculate also the iteration of the (static) irreducible one-loop potential with the one-boson exchange and find similar features. Together with the irreducible three-boson exchange potentials and the two-boson exchange potentials with vertex corrections, which are also evaluated analytically, our results comprise all nonrelativistic contributions from scalar-isovector boson-exchange at one- and two-loop order. The applied methods can be straightforwardly adopted to the pseudoscalar pion with its spin- and momentum-dependent couplings to the nucleon.Comment: 9 pages, 7 figures, to be published in Physical Review C (2006

    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

    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.

    Spin-asymmetry energy of nuclear matter

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    We calculate the density-dependent spin-asymmetry energy S(kf)S(k_f) of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to S(kf)S(k_f) originate from one-pion exchange, iterated one-pion exchange, and (irreducible) two-pion exchange with no, single, and double virtual Δ\Delta-isobar excitation. We find that the truncation to 1π1\pi-exchange and iterated 1π1\pi-exchange terms (which leads already to a good nuclear matter equation of state) is spin-unstable, since S(kf0)<0S(k_{f0})<0. The inclusion of the chiral πNΔ\pi N\Delta-dynamics guarantees the spin-stability of nuclear matter. The corresponding spin-asymmetry energy S(kf)S(k_f) stays positive within a wide range of an undetermined short-range parameter S5S_5 (which we also estimate from realistic NN-potentials). Our results reemphasize the important role played by two-pion exchange with virtual Δ\Delta-isobar excitation for the nuclear matter many-body problem. Its explicit inclusion is essential in order to obtain good bulk and single-particle properties.Comment: 11 pages, 6 figuers, accepted for publication in Physical Review