A semiclassical collective response of heated, asymmetric, and rotating nuclei

Abstract

The quasiparticle Landau Fermi-liquid and periodic orbit theories are presented for the semi-classical description of collective excitations in nuclei, which are close to one of the main topics of the fruitful activity of S.T. Belyaev. Density-density response functions are studied at low temperatures within the temperature-dependent collisional Fermi-liquid theory in the relaxation time approximation. The isothermal, isolated (static) and adiabatic susceptibilities for nuclear matter show the ergodicity property. Temperature corrections to the response function, viscosity and thermal conductivity coefficients have been derived, also in the long wavelength (hydrodynamic) limit. The relaxation and correlation functions are obtained through the fluctuation-dissipation theorem and their properties are discussed in connection to the static susceptibilities and ergodicity of the Fermi systems. Transport coefficients, such as nuclear friction and inertia as functions of the temperature for the hydrodynamic (heat-pole and first sound) and Fermi surface distortion zero-sound modes are derived within the Fermi-liquid droplet model. They are shown to be in agreement with the semi-microscopical calculations based on the nuclear shell model (SM) for large temperatures. This kinetic approach is extended to the study of the neutron-proton correlations in asymmetric neutron-rich nuclei. The surface symmetry binding-energy constants are presented as functions of the Skyrme-force parameters in the approximation of a sharp-edged proton-neutron asymmetric nucleus and applied to calculations of the isovector giant dipole resonance. The energies, sum rules, and transition densities of these resonances obtained by using analytical expression for these surface constants in terms of the Skyrme-force parameters are in fairly good agreement with the experimental data. An analysis of the experimental data, in particular the specific structure of these resonances in terms of a main, and some satellite peaks, in comparison with our analytical approach and other theoretical semimicroscopical models, might turn out to be of capital importance for a better understanding of the values of the fundamental surface symmetry-energy constant. The semiclassical collective moment of inertia is derived analytically beyond the quantum perturbation approximation of the cranking model for any potential well as a mean field. It is shown that this moment of inertia can be approximated by its rigid-body value for the rotation with a given frequency within the ETF and more general periodic orbit theories in the nearly local long-length approximation. Its semiclassical shell-structure components are derived in terms of the periodic-orbit free-energy shell corrections. An enhancement of the moment of inertia near the symmetrybreaking bifurcation deformations was found. We obtained good agreement between the semiclassical and quantum shell-structure components of the moment of inertia for several critical bifurcation deformations for the completely analytically solved example of the harmonic oscillator mean field.