Examining the effect of a binding-energy-dependent clusterization algorithm on isospin-sensitive observables in heavy-ion collisions

The phase space obtained using the isospin quantum molecular dynamical (IQMD) model is analyzed by applying the binding energy cut in the most commonly and widely used secondary cluster recognition algorithm. In addition, for the present study, the energy contribution from momentum-dependent and symmetry potentials is also included during the calculation of total binding energy, which was absent in clusterization algorithms used earlier. The stability of fragments and isospin effects are explored by using the new clusterization algorithm. The findings are summarized as follows: (1) The clusterization algorithm identifies the fragments at quite early time. (2) It is more sensitive for free nucleons and light charged particles compared to intermediate mass fragments, which results in the enhanced (reduced) production of free nucleons (light charged particles, or LCPs). (3) It has affected the yield of isospin-sensitive observables—neutrons ($n$), protons ($p$), ${}^3\mathrm{H},{}^3\mathrm{He}$, and the single ratio $\left[R\right(n/p\left)\right]$—to a greater extent in the mid-rapidity and low kinetic energy region. In conclusion, the inclusion of the binding energy cut in the clusterization algorithm is found to play a crucial role in the study of isospin physics. This study will give another direction for the determination of symmetry energy in heavy-ion collisions at intermediate energies.

Figure 1

Upper panels: Comparison of charge distribution of experimental data of ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ and ${}^{129}\mathrm{Xe}+{}^{\mathrm{nat}}\text{Sn}$ with the results obtained using MST and MSTB algorithms. Here the theoretical calculations are of ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ for the right panel. Bottom left (right) panels: Comparison of the results of $Z_{\mathrm{bound}}(Z_{\mathrm{bound}}/Z_{\mathrm{projectile}})$ dependence of $M_{\mathrm{IMFs}}(Z_{\mathrm{Max}}/Z_{\mathrm{projectile}})$ with the experimental data of GSI for the projectile fragmentation of ${}^{124}\mathrm{Sn}$.

Figure 2

The time evolution of different kinds of fragments: free nucleons (upper), LCPs (middle), and IMFs (bottom) for central collisions at 50 MeV/nucleon with MST and MSTB algorithms. The left (right) panels are for neutron-poor (neutron-rich) ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ (${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$) reaction systems. All the results are with soft symmetry energy.

Figure 3

The rapidity distribution of neutrons, protons, and ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ particles for neutron-poor and neutron-rich reaction systems with MST and MSTB algorithms. The results for the differential rapidity distributions of $(n-p)$ and ${(}^3\text{H}-{}^3\mathrm{He})$ are also presented in the right top and bottom panels, respectively.

Figure 4

Same as in Fig. 3, but for the kinetic energy dependence instead of rapidity distribution dependence.

Figure 5

The kinetic energy dependence of single $n/p$ (${}^3\mathrm{H}/{}^3\mathrm{He}$) in the top (bottom) panels for neutron-poor and neutron-rich reaction systems with MST and MSTB algorithms.

Figure 6

Isospin-asymmetry dependence of yield of neutrons and protons (${}^3\mathrm{H}$ and ${}^3\mathrm{He}$) with MST and MSTB algorithms in the top left (right) panels. The corresponding $n/p$ (${}^3\mathrm{H}/{}^3\mathrm{He}$) dependence is shown in the bottom left (right) panels. All the lines are fitted with a power law of the form $Y=A{X}^{\tau }$.

Figure 7

Incident energy dependences of the power-law-fitted parameter $\tau$ [from isospin asymmetry dependence of $n/p$ and (${}^3\mathrm{H}/{}^3\mathrm{He}$) at different incident energies] with MST and MSTB algorithms.