Observable effects of symmetry energy in heavy-ion collisions at intermediate energies

Within an isospin-dependent transport model for nuclear reactions induced by neutron-rich nuclei, we perform a comparative study of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Zn}$ reactions at beam energies of $30\text{MeV}∕\text{nucleon}$ and $400\text{MeV}∕\text{nucleon}$ to identify optimal experimental conditions and observables for investigating the equation of state (EOS) of neutron-rich matter at the Rare Isotope Accelerator (RIA). Several observables known to be sensitive to the density dependence of the symmetry energy are examined as a function of impact parameter for both reaction systems. In particular, the strength of isospin transport∕diffusion is studied by using rapidity distributions of free nucleons and their isospin asymmetries. An approximate isospin equilibrium is established even for peripheral collisions with a very soft symmetry energy at $30\text{MeV}∕\text{nucleon}$. At $400\text{MeV}∕\text{nucleon}$, however, a strong isospin translucency is observed even in most central collisions with either soft or stiff symmetry energies. Origins of these observations and their implications to determining the EOS of neutron-rich matter at the RIA are discussed.

Figure 1

Symmetry energy (upper window) and symmetry potentials as a function of density for an isospin asymmetry of $\delta =0.2$ and the $\gamma$ parameter of 0.5 and 2.0, respectively.

Figure 2

(Color online) Rapidity distributions of neutrons (left) and protons (right) in the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $30\text{MeV}∕\text{nucleon}$.

Figure 3

(Color online) Rapidity distributions of neutrons (left) and protons (right) in the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $400\text{MeV}∕\text{nucleon}$.

Figure 4

(Color online) Rapidity distributions of isospin asymmetry of free nucleons in the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $30\text{MeV}∕\text{nucleon}$.

Figure 5

(Color online) Rapidity distributions of isospin asymmetry of free nucleons in the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $400\text{MeV}∕\text{nucleon}$.

Figure 6

(Color online) Transverse momentum dependence of the neutron∕proton ratio at midrapidity for the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $30\text{MeV}∕\text{nucleon}$.

Figure 7

(Color online) Transverse momentum dependence of the neutron∕proton ratio at midrapidity for the reaction of ${}^{100}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $400\text{MeV}∕\text{nucleon}$.

Figure 8

(Color online) Neutron-proton differential flow for the reaction of ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $30\text{MeV}∕\text{nucleon}$.

Figure 9

(Color online) Neutron-proton differential flow for the reaction of ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $400\text{MeV}∕\text{nucleon}$.

Figure 10

(Color online) ${\pi }^{-}∕{\pi }^{+}$ ratio as a function of impact parameter in the reaction of ${}^{100}\mathrm{Zn}+{}^{124}\mathrm{Sn}$ at a beam energy of $400\text{MeV}∕\text{nucleon}$.