Determining the neutron skin thickness by relativistic semi-isobaric collisions

The neutron skin thickness of the benchmark nucleus ${}^{208}\mathrm{Pb}$ is crucial for our understanding of the equation of state of nuclear matter. In this paper, we discuss the effect of the neutron skin on the flow ratio observables in the semi-isobaric collisions ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ and ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ using iebe-vishnu hydrodynamic simulations. Our results suggest that ${}^{208}\mathrm{Pb}$ and ${}^{197}\mathrm{Au}$ should have the same magnitude of neutron skin thickness to describe the anisotropic flow ratios between the semi-isobaric systems. Our method provides an unconventional way to determine the neutron skin with the existing relativistic heavy ion collision data.

Figure 1

Different symmetric collision systems at RHIC and the LHC.

Figure 2

Charged particle production with different sizes of neutron skin in (a) ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV and ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, and (b) their ratios.

Figure 3

Flow harmonics $v_2\left\{2\right\}$, $v_2\left\{4\right\}$, and $v_3\left\{2\right\}$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV and $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV, calculated from iebe-vishnu hydrodynamic simulations with different sizes of neutron skin for the colliding nuclei.

Figure 4

The flow ratios of $v_2\left\{2\right\}/v_3\left\{2\right\}$ and $v_2\left\{4\right\}/v_3\left\{2\right\}$ in (a) $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200$ GeV and (b) $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV from iebe-vishnu hydrodynamic simulations with different sizes of neutron skin for the colliding nuclei.

Figure 5

The ratios of (a) individual flow observables $v_2\left\{2\right\}$, $v_2\left\{4\right\}$, $v_3\left\{2\right\}$ and (b) their double ratios in semi-isobaric collisions, calculated from iebe-vishnu hydrodynamic simulations with different sizes of neutron skin for the ${}^{208}\mathrm{Pb}$ nuclei. The neutrons skin for ${}^{197}\mathrm{Au}$ is fixed to $\mathrm{\Delta }{r}_{\mathrm{np}}=0.17$ fm.

Figure 6

The approximate scaling law in the isobaric ratio of $v_2\left\{2\right\},v_2\left\{4\right\},v_3\left\{2\right\},v_2\left\{2\right\}/v_3\left\{2\right\},v_2\left\{4\right\}/v_3\left\{2\right\}$ when ${}^{208}\mathrm{Pb}$ and ${}^{197}\mathrm{Au}$ have the same neutron skin size.