ISGDR- bulk or surface mode ?

A polarization and response function for finite systems and temperatures is derived from linearizing the Vlasov equation. Besides the Lindhard response function in local density approximation we obtain an additional contribution due to the surface. This formula is applied to isoscalar giant resonances which we consider as next harmonics to the basic dipole mode. The spurious center of mass motion is subtracted within the polarization. The results based on simple Fermi liquid considerations are in reasonable agreement with experimental data.