Evaluation of the escape widths of the giant dipole resonances in the fermi-liquid theory

Abstract

In the theory of the finite fermi-systems [1], it was shown that giant resonances in nuclei can be consider as the zero-sound excitations which exhaust the large part of the energy-weighted sum rules. In the framework of [1] the solutions of the zero-sound dispersion equation in the symmetric nuclear matter, \omega_s(k), are considered. The method of calculation of these solutions is based on the analytical structure of the polarization operators \Pi(\omega,k). The solutions of the dispersion equation, which are real at small k, become complex with k increasing when the overlapping of the collective and 1p1h modes starts. The imaginary part of \omega_s(k) is the result of the collective zero-sound excitation decay to the real particle-hole pairs and can be compared with the escape width of resonances. We compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with Re\omega_s(k) and Im\omega_s(k) taken at a definite wave vector k=k_A.