Density-dependent NN-interaction from subleading chiral 3N-forces: short-range terms and relativistic corrections

We derive from the subleading contributions to the chiral three-nucleon force (short-range terms and relativistic corrections, published in Phys. Rev. C84, 054001 (2011)) a density-dependent two-nucleon interaction $V_{\text{med}}$ in isospin-symmetric nuclear matter. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and ${\vec{\tau }}_1\text{\hspace{0.17em}⁣}\cdot \text{\hspace{0.17em}⁣}{\vec{\tau }}_2$) and five independent spin-structures are expressed in terms of loop functions, which are either given in closed analytical form or require at most one numerical integration. Our results for $V_{\text{med}}$ are most helpful to implement subleading chiral 3N-forces into nuclear many-body calculations.