Multinucleon transfer in the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ reaction

The dynamic mechanics in the multinucleon transfer reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ at an incident energy of $E_{\mathrm{c}.\mathrm{m}.}=450$ MeV is investigated by using the improved quantum molecular dynamics model (ImQMD). The lifetime of the neck directly influences the nucleon exchange and energy dissipation between the projectile and the target. The total-kinetic-energy–mass distributions and excitation energy division of primary binary fragments and the mass distributions of primary fragments at different impact parameters are calculated. The thermal equilibrium between two reaction partners has been observed at the lifetime of a neck larger than $480\mathrm{fm}/c$. By using the statistical decay code gemini to describe the de-excitation process of the primary fragments, the isotope production cross sections from Pt to At are compared with the prediction by the dinuclear system and GRAZING model. The calculations indicate that the GRAZING model is suitable for estimating the isotope production cross sections only for $\mathrm{\Delta }Z=-1$ to +2; the DNS + gemini calculations underestimate the cross sections in the neutron-rich and neutron-deficient regions; and the ImQMD + gemini calculations give reasonable predictions of the isotope production cross sections for $\mathrm{\Delta }Z=-3$ to 0.

Figure 1

Time evolution of density distribution for three typical events of the reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ at $b=1$ (top panels), 5 (middle panels), and 8 (bottom panels) fm.

Figure 2

(a) Lifetime of the neck calculated by the ImQMD model as a function of impact parameters. (b) Nucleon transfer ratio $\eta$ as a function of impact parameters. $\eta =(\delta N_p-\delta N_t)/(\delta N_p+\delta N_t)$, where $\delta N_p+\delta N_t$ is the total nucleon number of PLFs (or TLFs). $\delta N_p$ and $\delta N_t$ denote the number of nucleons that come from the original projectile and target, respectively. The dashed line denotes the value of the nucleon exchange equilibrium between the projectile and target which is $-0.21$.

Figure 3

TKE-mass distributions of primary binary fragments in different impact parameter regions.

Figure 4

TKEL distributions of primary binary fragments. The solid circles denote all the binary events; solid line denotes the Gaussian fitting for the quasielastic events.

Figure 5

(a) Average excitation energy of PLFs and TLFs as a function of neck lifetime. (b) $\langle E_{\mathrm{TLF}}^{*}\rangle /\langle E_{\mathrm{TLF}}^{*}\rangle$ as a function of neck lifetime. The dashed line denotes the value of thermal equilibrium between the TLFs and PLFs.

Figure 6

(a) Mass distributions of primary binary fragments at different impact parameter regions from the ImQMD model. (b) Mass distributions of primary binary fragments calculated with the ImQMD (thick solid line), DNS (thin solid line), and GRAZING (dash-dot line) model. The experimental data (open circles) are from Ref. [14].

Figure 7

Isotopic production cross sections from Pt to At. The thick solid line, thin solid line, and dash-dot line denote the calculation results from the combinations of ImQMD + gemini and DNS + gemini, and from the GRAZING model with inclusion of evaporation for secondary fragments. The experimental data (solid circles) are from Ref. [14].