Role of the isospin diffusion on cluster transfer in $^{12,14}$C + $^{209}$Bi reactions

Heavy-ion collisions at near-barrier energies provide a crucial pathway for investigating nucleon correlations and clustering structures. Recent experimental results showed that the valence neutrons in light projectiles obviously enhance the $\alpha$ transfer. This finding is extremely puzzled and fascinating, because it violates the ground-state $Q$ value systematics unexpectedly. In this work, the time-dependent Hartree-Fock approach is utilized to investigate the cluster transfer. By comparing the reactions $^{12,14}$C + $^{209}$Bi, we discover that above puzzling behavior is because of the strong correlation between isospin diffusion and clustering. Our calculations clearly show that the equilibrium of neutron-to-proton ratio strongly inhibits the clustering. This work opens a prospect for investigating the clustering in open quantum system.