Semi-Classical Description of the Average Pairing Properties in Nuclei

We present a new semi-classical theory for describing pairing in finite Fermi systems. It is based in taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvement of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.