Nuclear cluster structure effect on elliptic and triangular flows in heavy-ion collisions

The initial geometry effect on collective flows, which are inherited from initial projectile structure, is studied in relativistic heavy-ion collisions of ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ by using a multiphase transport model (AMPT). Elliptic flow ($v_2$) and triangular flow ($v_3$) which are significantly resulted from the chain and triangle structure of ${}^{12}\mathrm{C}$ with three-$\alpha$ clusters, respectively, in central ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions are compared with the flow from the Woods-Saxon distribution of nucleons in ${}^{12}\mathrm{C}$. $v_3/v_2$ is proposed as a probe to distinguish the pattern of $\alpha$-clustered ${}^{12}\mathrm{C}$. This study demonstrates that the initial geometry of the collision zone inherited from nuclear structure can be explored by collective flow at the final stage in heavy-ion collisions.

Figure 1

In the most central collisions, initial intrinsic nucleon distribution of the ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ system (upper panels), and the participant distributions (lower panels): (a) and (d) for the ${}^{12}\mathrm{C}$ with the chain $\alpha$-clustering structure, (b) and (e) for the triangle $\alpha$-clustering structure, (c) and (f) for the Woods-Saxon nucleon distribution. The nucleon distribution in ${}^{197}\mathrm{Au}$ always take the Woods-Saxon form.

Figure 2

The $N_{\mathrm{track}}$ distribution in ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV (a) and 10 GeV (b), respectively; Average $N_{\mathrm{track}}$ ($〈N_{\mathrm{track}}〉$) as a function of impact parameter $b$ at (c) 200 GeV and (d) 10 GeV, respectively.

Figure 3

In ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV (upper panels) and 10 GeV (lower panels), $v_2$ as function of $N_{\mathrm{track}}$: (a) and (e) for initial partons, (b) and (f) for the freeze-out partons, (c) and (g) for the hadrons without hadronic rescattering, and (d) and (h) for the final-state hadrons.

Figure 4

Same as Fig. 3 but for $v_3$.

Figure 5

In ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV (upper panels) and 10 GeV (lower panels), second- and third-order participant eccentricity coefficients, (a) and (c) for ${\epsilon }_2\left\{PP\right\}$, (b) and (d) for ${\epsilon }_3\left\{PP\right\}$, as function of $N_{\mathrm{track}}$.

Figure 6

In ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV (upper panels) and 10 GeV (lower panels), (a) and (c) $v_2/{\epsilon }_2\left\{PP\right\}$, (b) and (d) $v_3/{\epsilon }_3\left\{PP\right\}$ of final hadrons as function of $N_{\mathrm{track}}$.

Figure 7

In ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV (upper panels) and 10 GeV (lower panels), (a) and (c) ${\epsilon }_3\left\{PP\right\}/{\epsilon }_2\left\{PP\right\}$, (b) and (d) $v_3/v_2$ of final hadrons as function of $N_{\mathrm{track}}$.