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 $\bar{E}(k_f)\sim k_f^{5+2n}$ 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 $\mathcal{O}(p^2)$ 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 $1\pi$-exchange is computed and it is found that direct and exchange contributions are all attractive. The very large size of the pion-ring energy, $\bar{E}(k_{f0})\simeq -92$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 $\mathcal{O}(p^2)$ contact interaction and the simplest three-ring contributions to the isospin-asymmetry energy $A(k_f)\sim k_f^5$ are studied.

20 pages, 3 figures

References in corpus (7)

• Chiral effective field theory and nuclear forces
• The Skyrme Interaction in finite nuclei and nuclear matter
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Neutron matter from chiral two- and three-nucleon calculations up to N${}^3$LO
• Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT
• Towards order-by-order calculations of the nuclear and neutron matter equations of state in chiral effective field theory
• Next-to-next-to-leading order Skyrme interaction in nuclear matter: Nuclear bulk quantities at second order in perturbation theory

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• Effective field theory for dilute Fermi systems at fourth order
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• Ground state energy of the polarized diluted gas of interacting spin $1/2$ fermions
• Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory