Kinetic model of excitation of pairing vibrations in superfluid nuclei

Excitation of pairing vibrations in superfluid nuclei is studied by using a kinetic model based on the Vlasov equation with pairing, derived from the time-dependent Hartree-Fock-Bogolyubov theory. The anomalous density response function is used to find the monopole pairing mode and the dynamic variation of the pairing gap associated with this mode. The spectroscopic factor for the excitation of monopole pairing vibrations in two-neutron transfer reaction is estimated. It is found that the pairing correlations give rise to the same coherent contribution to the semiclassical spectroscopic factor as to the corresponding quantum expression, which is essentially determined by the distribution of the neutron levels near the Fermi energy. A numerical evaluation of the reduced spectroscopic factor for the excitation of monopole pairing vibrations in two-neutron transfer reaction in superfluid nuclei shows that it does not exceed several percent of the spectroscopic factor for the transfer of two neutrons to the ground state. This estimate is in agreement with the experimental data obtained for the ratio of the cross section for the excitation of 0+state in the (p,t) reaction in the energy region of double pairing gap to the cross section for the excitation of the ground state for superfluid nuclei of the rare-earth and actinide regions.