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

Abstract

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 EΛ‰(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 1Ο€1\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, EΛ‰(kf0)β‰ƒβˆ’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

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