N-phonon giant resonances in the nonlinear hydrodynamic approach and the nucleon-nucleon interaction

Isoscalar and isovector density vibrations in a slab with sharp edges are studied in a nonlinear hydrodynamic approach. The frequency shift of the N-phonon excitation due to nonlinear terms is obtained. The frequencies of one-and two-phonon vibrations calculated in the nonlinear hydrodynamic theory are reduced by approximate to 5-30 % for isoscalar and by approximate to 1-8 % for isovector resonances as compared to the linear approximation. The frequency shift is a function of both the slab thickness and the parameters of the nucleon-nucleon interaction. Experimental data on the frequency shift of the N-phonon states due to the nonlinear terms in the case N greater than or equal to 7 may be used for selecting of the set of nucleon-nucleon interaction parameters.