Pair Transfer and Reaction Dynamics in $^{40,48}$Ca + $^{96}$Zr Collisions Below the Coulomb Barrier

Sub-barrier fusion reactions are ideal for probing the effects of pairing correlations on simultaneous neutron transfer. Previous calculations using the BCS approximation showed an enhancement of pair transfer, relative to treatments with no pairing, but failed to reproduce the observed enhancement factor between one- and two-neutron transfer probabilities. This work aims to microscopically investigate the dynamics of $^{40,48}$Ca + $^{96}$Zr head-on collisions below the Coulomb barrier, focusing on the role of pairing correlations in neutron transfer. We employ time-dependent energy density functional theory extended to superfluid systems, TDSLDA. Transfer probabilities, including contributions to specific $K$-angular momentum projections, are extracted using projection operators and compared to results from calculations without pairing. Our calculations show that pairing is correlated to the dynamic deformability of the nucleus, which influences mean neutron transfer in sub-barrier reactions. We also show that TDSLDA reproduces the experimentally observed enhancement factor by significantly increasing the probability of transferring a neutron pair in the $K = 0$ spin channel. These results confirm the strong influence of pairing and structure on sub-barrier multi-nucleon transfer, and demonstrate that TDSLDA provides a reliable microscopic framework for describing the interplay between nuclear superfluidity and reaction dynamics.