Single- and double-phonon giant monopole resonances in a nonlinear approach

Isoscalar monopole density vibrations in spherical nuclei with a sharp surface are studied in a nonlinear hydrodynamical approach. The frequency shift of the one- and two-phonon excitations due to nonlinear terms is obtained. The frequencies of one- ~two-! phonon giant isoscalar monopole resonances calculated in the nonlinear hydrodynamic theory increase by ’2%(8%) in heavy nuclei and by ’14‐18 % ~50%! in light nuclei compared to the linear approximation. The frequency shift is a function of both the mass number A and the parameters of the nucleon-nucleon interaction.