On the nuclear curvature energy

The curvature energy coefficient of the nuclear mass formulaa _c is first calculated for the model case of a Fermi gas bounded by an external Woods-Saxon potential. The semiclassical theory of Wigner and Kirkwood is used anda _c is found to be close to zero. It is, however, shown that this low value is due to the lack of selfconsistency of the potential. When available, the results of the model compare very well with quantal values and the extrapolation to the spherical cavity (billiard) checks with the value fora _c known from the Balian-Bloch theory. Second, the selfconsistent case is generalised to finite range forces. No indication is found that this modifies the fact that all theoretical values for a _c are larger than about 7 MeV which is an order of magnitude above the empirical value.