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

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From the subsubleading chiral three-nucleon forces intermediate-range contributions, published in Phys. Rev. C 87, 054007 (2013) a density-dependent NN-interaction V-med 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 2 pi 1 pi-exchange topology, the momentum- and k(f)-dependent potentials associated with the isospin operators (1 and (tau) over right arrow (1).(tau) over right arrow (2)) and five independent spin structures require at most one numerical integration. For the more challenging (concatenations of the) ring diagrams proportional to c(1,2,3,4), one ends up with regularized double-integrals integral(lambda)(0) dr r integral(pi/2)(0) d psi from which the lambda(2) divergence has been subtracted and the logarithmic piece similar to ln(m(pi)/lambda) is isolated. The derived semianalytical results are most helpful to implement the subsubleading chiral 3N forces into nuclear many-body calculations.

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