Self-consistent pairing interaction and collective motion in nuclei: a semiclassical approach

The solutions of the semiclassical time-dependent Hartree-Fock-Bogoliubov equations of motion are studied in a linear approximation in which the pairing field is allowed to oscillate and to become complex. The pairing field fluctuations are derived from the self-consistent relation (the gap equation of the BCS type), while the static pairing field is approximated with a phenomenological constant Delta. The self-consistent pairing-field fluctuations introduce possibility of new collective modes of the system. We have found out the dispersion relation which determines possible collective modes of the system generated by the pairing interaction. The obvious solution of our dispersion relation at (omega=0 corresponds to the Anderson-Goldstone-Nambu mode and is related to gauge symmetry. The solutions of dispersion relation have been studied in a simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter characterized by parameters (size, density, pairing gap) typical of heavy nuclei. We have found that the dispersion relation has approximate solution at h omega approximate to 2 Delta for the monopole channel Our semiclassical approach is valid for both weak and strong pairing. Here we focus on weak pairing which is suitable for systems with size and pairing parameter appropriated to nuclei.