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 con sidering consistently the effects on nuclear incompressibility coefficients and the boundary conditions needed to determine the energy of the ISGMR. T here is a significant difference between the static nuclear incompressibili ty K, derived as a stiffness coefficient with respect to an adiabatic chang e in the bulk density, and the dynamic one K' associated with the zero soun d velocity. We show that the enhancement in the energy of the ISGMR, the lo west breathing mode, which is due to the renormalization of K into K' is st rongly suppressed by the effects of the Fermi surface distortion on the bou ndary condition. This is not the case for higher breathing modes such as th e overtone. We also discuss, in particular, the effects of the Fermi surfac e distortion on energy weighted sums for the monopole mode and on the const rained and the scaling incompressibility coefficients and their relation to the liquid drop one.