Density-dependent NN interaction from subleading chiral three-nucleon forces: Long-range terms

N. Kaiser, B. Singh

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17 Scopus citations


We derive from the subleading contributions to the chiral three-nucleon (3N) force [long-range terms; published by V. Bernard, Phys. Rev. C 77, 064004 (2008)PRVCAN0556-281310.1103/PhysRevC.77.064004] a density-dependent two-nucleon interaction Vmed 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 kf-dependent potentials associated with the isospin operators (1 and τ - 1·τ - 2) and five independent spin structures are expressed in terms of functions which either are given in closed analytical form or require at most one numerical integration. In the same way we treat the 2π-exchange 3N force at sub-subleading order. Our results for Vmed are most helpful to implement long-range subleading chiral 3N forces into nuclear many-body calculations.

Original languageEnglish
Article number014002
JournalPhysical Review C
Issue number1
StatePublished - 22 Jul 2019


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