Density-dependent NN interaction from subsubleading chiral 3N forces: Intermediate-range contributions

From the subsubleading chiral three-nucleon forces [intermediate-range contributions, published in Phys. Rev. C 87, 054007 (2013)PRVCAN0556-281310.1103/PhysRevC.87.054007] a density-dependent NN-interaction Vmed is derived in isospin-symmetric nuclear matter. Following the division of the pertinent 3N diagrams into two-pion-one-pion exchange topology and ring topology, one evaluates for these all self-closings and concatenations of nucleon lines to an in-medium loop. In the case of the 2π1π-exchange topology, the momentum- and kf-dependent potentials associated with the isospin operators (1 and τ - 1·τ - 2) and five independent spin structures require at most one numerical integration. For the more challenging (concatenations of the) ring diagrams proportional to c1,2,3,4, one ends up with regularized double-integrals ∫0λdrr∫0π/2dψ from which the λ2 divergence has been subtracted and the logarithmic piece ∼ln(mπ/λ) is isolated. The derived semianalytical results are most helpful to implement the subsubleading chiral 3N forces into nuclear many-body calculations.