Surface Effects on the Energy Gap in Nuclear Matter

Abstract

The energy gap in the intrinsic excitation spectra of even-even nuclei is calculated in the BCS approximation starting from separable interactions adjusted to fit 'So nucleon scattering data. Simplified nuclear models are used to investigate the relation between the surface properties and the value of the energy gap in finite nuclei and, in particular, we consider a slab model of infinite extent in two directions but finite in the third direction and of variable surface thickness. An effective length of the slab is defined and this is held constant while the density profile is varied. For a fixed effective mass, it is found that the energy gap is essentially determined by the effective length for a particular interaction. On the other hand, radically diverse variations of the energy gap with effective length are obtained for potentials that differ appreciably in their repulsive character in infinite nuclear matter. This sensitivity may be fortuitous however, as the slab model underestimates the finite volume contribution to the pairing matrix elements and overestimates the importance of the infinite matter properties of the potential.