Short-range forces and surface tension in nuclei

Abstract

Consider an atomic nucleus, or any closed system of Fermions under the influence of a saturating short-range interaction. If the range is sufficiently short, one finds that the thickness of the surface layer is not determined by the range of this force, but by a new,quantum mechanical characteristic length, L=(ħ²/8mF)^1/3, whereF is the restoring force generated at the boundary by the self-consistent potential acting on the most energetic particles. Moreover, in equilibrium, thisforce adjusts itself in such a manner that k _F L ∼ 1 wherek _F is the Fermi wave number. As a consequence, one is now able to compute the binding energy, and thus the volume and surface energy coefficients in an explicit analytical fashion as a function of the coupling constants of the interaction, which in the present case is a modified Skyrme interaction. In addition, speculations are made on the existence ofsurface isomers. These are nuclei at several hundred MeV excitation with essentially the same central density, but with an increased surface region.