Excitation modes and pairing interaction in the inner crust of neutron stars

We perform a detailed calculation of the pairing properties of the inner crust of a neutron star. We focus on a specific density, and take into account the coexistence of a nuclear lattice with a superfluid gas of neutrons. The Hartree-Fock-Bogoliubov (HFB) equations are solved adding the matrix elements of the direct nucleon-nucleon interaction and those of the interaction induced by medium-polarization effects. The latter are obtained after a detailed calculation of the excited states of the system, within the random phase approximation. It is concluded that for the density considered, polarization processes reduce the pairing gap of about a factor of 2.