Giant monopole resonance and nuclear incompressibility within the Fermi-liquid drop model

We study the important effects of Fermi surface distortion on the isoscalar giant monopole resonance (ISGMR), within a Fermi-liquid drop model, by considering consistently the effects on nuclear incompressibility coefficients and the boundary conditions needed to determine the energy of the ISGMR. There is a significant difference between the static nuclear incompressibility K, derived as a stiffness coefficient with respect to an adiabatic change in the bulk density, and the dynamic one K' associated with the zero sound velocity. We show that the enhancement in the energy of the ISGMR, the lowest breathing mode, which is due to the renormalization of K into K' is strongly suppressed by the effects of the Fermi surface distortion on the boundary condition. This is not the case for higher breathing modes such as the overtone. We also discuss, in particular, the effects of the Fermi surface distortion on energy weighted sums for the monopole mode and on the constrained and the scaling incompressibility coefficients and their relation to the liquid drop one.