Probing the symmetry energy and the degree of isospin equilibrium

The rapidity dependence of the single and double neutron-to-proton ratios of nucleon emission from isospin-asymmetric but mass-symmetric reactions Zr+Ru and Ru+Zr at the energy range $100A\sim 800A$ MeV and impact parameter range $0\sim 8$ fm is investigated. The reaction system with isospin asymmetry and mass symmetry has the advantage of simultaneously showing the dependence on symmetry energy and the degree of the isospin equilibrium. We find that the beam-energy and impact-parameter dependences of the slope parameter of the double neutron-to-proton ratio ($F_D$) as a function of rapidity are quite sensitive to the density dependence of symmetry energy, especially at energies $E_b\sim 400A$ MeV and reduced impact parameters around 0.5. Here, the symmetry energy effect on $F_D$ is enhanced, as compared to the single neutron-to-proton ratio. The degree of equilibrium with respect to isospin (isospin mixing) in terms of $F_D$ is addressed, and its dependence on symmetry energy is also discussed.

Figure 1

(a)–(d): Rapidity dependence of $n/p$ with symmetry energies of $\gamma =0.5$ and $1.5$ for Zr + Ru and Ru + Zr reactions with varied $E_b$ and $b/b_0$, as shown in each plot. (e)–(f): Corresponding double $n/p$ ratios, $(n/p){}_{\text{ZrRu}}/(n/p){}_{\text{RuZr}}$, for (a) and (d) cases.

Figure 2

(a): Beam-energy dependence of the slope parameter $F_D$ with symmetry energies with $\gamma =0.5$ and $1.5$, for impact parameters $b/b_0=0$ and $0.5$. $F_D$ values at $E_b=400A$ MeV and at $b/b_0=0.5$ with SM-EOS are shown with open symbols. (b): Centrality dependence of $F_D$ at $E_b=400A$ MeV.