Role of the isospin diffusion on the cluster transfer in ${}^{12,14}\mathrm{C}+{}^{209}\mathrm{Bi}$ 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 puzzling 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 ${}^{12,14}\mathrm{C}+{}^{209}\mathrm{Bi}$, 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 an open quantum system.

Figure 1

Two-dimensional density distribution for the linear-chain structure of ${}^{12}\mathrm{C}^{\mathrm{Lin}.}$(a), ${}^{14}\mathrm{C}^{\mathrm{Lin}.}$(b), and the difference between them (c) in the static HF calculations and the triangular structure of ${}^{12}\mathrm{C}^{\mathrm{Tri}.}$(d), ${}^{14}\mathrm{C}^{\mathrm{Tri}.}$(e), and the difference between them (f) in the DC-HF calculations with the SLy5 parametrization of the Skyrme EDF.

Figure 2

The DC-TDHF potential (upper panels) calculated for the ${}^{12}\mathrm{C}^{\mathrm{Lin}.}+{}^{209}\mathrm{Bi}$ at $E_{\mathrm{c}.\mathrm{m}.}=75$ MeV and the corresponding particle number (lower panels) of nucleon transfer from of projectile to target as functions of distance of the center of mass at impact parameter $b=5.5$ fm (a), (b) and $b=6.5$ fm (c), (d). The snapshots of density distribution are also shown.

Figure 3

The nucleon transfer number as functions of three reaction systems at $E_{\mathrm{c}.\mathrm{m}.}=70$ MeV, $b=6$ fm. The nucleon transfer from the projectile to the target (a), from the target to the projectile (b) and the net transfer number are both shown.

Figure 4

Time evolution of the excitation energy from DC-TDHF (a), the net nucleon transferring number from the projectile to the target (b), and the isospin variation of projectile-like fragments (c) for ${}^{12}\mathrm{C}^{\mathrm{Lin}.}+{}^{209}\mathrm{Bi}$ (circles), ${}^{14}\mathrm{C}^{\mathrm{Lin}.}+{}^{209}\mathrm{Bi}$ (lower triangles), and ${}^{14}\mathrm{C}_{\mathrm{T}}^{\mathrm{Lin}.}+{}^{209}\mathrm{Bi}$ (upper triangles) at $E_{\mathrm{c}.\mathrm{m}.}=70$ MeV, $b=6$ fm.

Figure 5

The transfer probabilities of ${}^4\mathrm{He}$ (upper panels) and ${}^8\mathrm{Be}$ (lower panels) as functions of impact parameter $b$. The dots with a horizontal line, open dots and solid dots denote ${}^{12}\mathrm{C}, {}^{14}\mathrm{C}$, and ${}^{14}\mathrm{C}^{\mathrm{T}}$ projectiles, respectively. Circles, squares and diamonds denote $E_{\mathrm{c}.\mathrm{m}.}=70$ MeV, 75 MeV and 80 MeV, respectively. The open triangles and solid triangles denote ${}^{12}\mathrm{C}^{\mathrm{Tri}.}$ and ${}^{14}\mathrm{C}^{\mathrm{Tri}.}$ at $E_{\mathrm{c}.\mathrm{m}.}=80$ MeV, respectively. The lines are only to guide the eyes.