Polarization Contributions to the Spin Dependence of the Effective Interaction in Neutron Matter

We calculate the modification of the effective interaction of particles on the Fermi surface due to polarization contributions, with particular attention to spin-dependent forces. In addition to the standard spin-spin, tensor, and spin-orbit forces, spin nonconserving effective interactions are induced by screening in the particle-hole channels. Furthermore, a novel long-wavelength tensor force is generated. We compute the polarization contributions to second order in the low-momentum interaction $V_{\mathrm{l}\mathrm{o}\mathrm{w}k}$ and find that the medium-induced spin-orbit interaction leads to a reduction of the ${}^{3}P_2$ pairing gap for neutrons in the interior of neutron stars.