and double neutron-to-proton ratios from different neutron-rich systems to the high-density behavior of symmetry energy, and then compare the sensitivity of symmetry energy from the neutron-to-proton ratio with that from the pion ratio. This study is similar to recent studies using the pion ratio [@Li03; @Wolt09; @Li09; @Feng10]. ]{}

For the present study, the isospin quantum molecular dynamics (IQMD) model is used to generate the phase space of nucleons, which is discussed in Sec. II. The results are discussed in sec. III, and we summarize the results in sec. IV .

Methodology: ISOSPIN QUANTUM MOLECULAR DYNAMICS MODEL {#IQMD}
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In the IQMD model [@Hart98; @Kuma10], nucleons are represented by wave packets, just as in the QMD model of Aichelin [@Aich91]. These wave packets of the target and projectile interact via the full Skyrme potential energy, which is represented by $U$ and is given as: $$U~=~U_{\rho} + U_{Coul}\cdot$$ Here $U_{Coul}$ is the Coulomb energy and $U_{\rho}$ originates from the density dependence of the nucleon optical potential, and is given as $$U_{\rho}~=~\frac{\alpha}{2}\frac{\rho^2}{\rho_0}~+~\frac{\beta}{\gamma+1}
\frac{\rho^{\gamma+1}}{\rho_0^{\gamma}}+
E^{pot}_{Sym}(\rho)\rho\delta^2 .
\label{equation2}$$

The first two of the three parameters of Eq. \[equation2\] ($\alpha$ and $\beta$) are determined by demanding that, at normal nuclear matter densities, the binding energy 