Abstract
Abstract Explicit analytic expressions are derived for the cubic energy-weighted sum rule in RPA and for Skyrme interactions. From these and the once energy-weighted sum rule an average energy for the giant resonance is estimated. The contributions from the deformation of the Fermi sea, and also from the Coulomb, surface and effective mass terms in the interaction are explicitly evaluated. The limited validity of estimates based on the assumption of a uniform density distribution is stressed. The important role of the surface for modes of high multipolarity is shown quantitatively. Using a leptodermous expansion the true volume, surface and higher order terms are obtained.
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