Excitation of monopole pairing vibrations in two-neutron transfer reaction: a semiclassical approach

For studying the collective pairing excitations of nuclei, the two-nucleon transfer reactions in superfluid nuclei (the pairing gap of the ground state is not zero), in particular, the (p,t) reaction, are of the greatest interest. A simple model of monopole pairing excitations in superfluid nuclei on the basis of the semiclassical time-dependent Hartree-Fock-Bogolyubov theory in the limit of small amplitudes is considered. Using the anomalous density response function, the monopole pairing mode in the energy region of double pairing gap and the variation of the pairing gap associated with this mode are found. The ratio of the spectroscopic factor for the excitation of monopole pairing vibrations in the (p,t) reaction in even superfluid nuclei to the spectroscopic factor for the transfer of two neutrons to the ground state of the daughter nucleus (the relative spectroscopic factor) is estimated. For this, it is assumed that the relative spectroscopic factor is proportional to the pairing gap variation associated with the monopole pairing vibrations in agreement with the corresponding quantum expression. Numerical estimate of the relative spectroscopic factors for superfluid nuclei of the rare-earth and actinide regions shows that the spectroscopic factor for the two-neutron transfer, leading to the excitation of the monopole pairing vibrations, does not exceed several percent of the spectroscopic factor for the transfer of two neutrons to the ground state. This semiclassical estimate is in agreement with the experimental rations of the cross sections for the excitation of 0+states in the energy region of double pairing gap to the cross sections for the excitation of the ground states for superfluid nuclei of the rare-earth and actinide regions.