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We derive from the subleading contributions to the chiral three-nucleon force(long-range terms, published in Phys.\,Rev.\,C\,77, 064004 (2008)) adensity-dependent two-nucleon interaction $V_\text{med}$ in isospin-symmetric,spin-saturated nuclear matter. Following the division of the pertinent3N-diagrams into two-pion exchange topology, two-pion-one-pion exchangetopology and ring topology, we evaluate for these all self-closings andconcatenations 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 areexpressed in terms of functions, which are either given in closed analyticalform 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 $V_\text{med}$ aremost helpful to implement the long-range subleading chiral 3N-forces intonuclear many-body calculations.

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