  The 1S0 pairing gap associated with the inner crust of a neutron star is
calculated, taking into account the coexistence of the nuclear lattice with the
sea of free neutrons (finite size effects), as well as medium polarization
effects associated with the exchange of density and spin fluctuations. Both
effects are found to be important and to lead to an overall quenching of the
pairing gap. This result, whose quantitative value is dependent on the
effective interaction used to generate the single-particle levels, is a
consequence of the balance between the attractive (repulsive) induced
interaction arising from the exchange of density (spin) modes, balance which in
turn is influenced by the presence of the protons and depends on the
single-particle structure of the system.
