Coupling of surface and bulk vibrations in the nuclear breathing mode

We treat a general class of dynamical couplings of the surface to the bulk of a spherical nucleus during isoscalar breathing vibrations. Compressibilities are evaluated in the extended Thomas-Fermi approximation using a realistic Skyrme force (SkMsup(*)). Inertial parameters are obtained in a hydrodynamical framework. The lower of the two eigenmodes is found to be close in energy to the pure bulk vibration (and to the scaling mode), and to be in excellent agreement with the experimental giant monopole resonance energies. The coupling of surface and bulk vibrations shifts the pure surface mode to appreciably higher energies (approx.= 25 MeV in 208Pb). This upper mode which has a pronounced anti-scaling behaviour, might be identified through the analysis of its transition density. (orig.)