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We present a new semiclassical theory for describing pairing in finite Fermisystems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit ofthe gap equation written in the basis of the mean field (weak coupling). Inaddition to the position dependence of the Fermi momentum, the size dependenceof the pairing force is also taken into account in this theory. Along isotopicchains the Thomas-Fermi gaps average the well known arch structure shown by thequantal gaps. This structure can be almost recovered in our formalism if someshell fluctuations are included in the level density. We point out that at thedrip line nuclear pairing is strongly reduced. This fact is illustrated withthe behavior of the gap in the inner crust of neutron stars.

Thomas-Fermi approximation to pairing in finite Fermi systems. The weak coupling regime