Isoscalar compression modes within fluid dynamic approach

Abstract

We study the nuclear isoscalar monopole and dipole compression modes in nuclei within the fluid dynamic approach (FDA) with and without the effect of relaxation. For a wide region of the medium and heavy nuclei, the FDA predicts that the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) exhaust about 90% of the corresponding model-independent sum rules. In the case of neglecting the effect of relaxation, the FDA, when adjusted to reproduce the centroid energy $E0$ of the ISGMR, results with centroid energy $E1$ of the ISGDR which is in agreement with the predictions of the self-consistent Hartree-Fock random-phase approximation calculations and the scaling model but significantly larger than the experimental value. We also show that the FDA leads to the correct hydrodynamic limit for the ratio ${(E1/E0)}_{\mathrm{FDA}}.$ We find that the ratio ${(E1/E0)}_{\mathrm{FDA}}$ depends on the relaxation time and approaches the preliminary experimental value ${(E1/E0)}_{\mathrm{exp}}=1.5\ifmmode\pm\else\textpm\fi{}0.1$ in a short relaxation time limit.