Density-dependent NN-interaction from subleading chiral 3N-forces: Long-range terms

Abstract

We derive from the subleading contributions to the chiral three-nucleon force (long-range terms, published in Phys.\,Rev.\,C\,77, 064004 (2008)) a density-dependent two-nucleon interaction $V_{\text{med}}$ in isospin-symmetric, spin-saturated nuclear matter. Following the division of the pertinent 3N-diagrams into two-pion exchange topology, two-pion-one-pion exchange topology and ring topology, we evaluate for these all self-closings and concatenations of nucleon-lines to an in-medium loop. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and ${\vec{\tau }}_1\cdot {\vec{\tau }}_2$) and five independent spin-structures are expressed in terms of functions, which are either given in closed analytical form or require at most one numerical integration. In the same way we treat the $2\pi$-exchange 3N-force up to fourth order. Our results for $V_{\text{med}}$ are most helpful to implement the long-range subleading chiral 3N-forces into nuclear many-body calculations.

19 pages, 1 figure, 1 table, typo in eq.(82) corrected

References in corpus (7)

• Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation
• Subleading contributions to the chiral three-nucleon force I: long-range terms
• Neutron matter from chiral two- and three-nucleon calculations up to N${}^3$LO
• Four-nucleon force using the method of unitary transformation
• Pairing in neutron matter: New uncertainty estimates and three-body forces
• Three-nucleon force in chiral EFT with explicit $\Delta (1232)$ degrees of freedom: Longest-range contributions at fourth order
• Density-dependent NN-interaction from subleading chiral 3N-forces: short-range terms and relativistic corrections

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