ON THE NUCLEAR CURVATURE ENERGY

The curvature energy coefficient of the nuclear mass formula a(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 and a(c) is found to be close to zero. It is, however, shown that this low value is due to the lack of self-consistency 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 for a(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.