The isospin effects in proton-induced reactions on isotopes of ${}^{112-132}\mathrm{Sn}$ and the corresponding $\beta$-stable isobars are studied by means of the improved quantum molecular dynamics model and some sensitive probes for the density dependence of the symmetry energy at subnormal densities are proposed. The beam energy range is chosen to be 100–300 MeV. Our study shows that the system size dependence of the reaction cross sections for $p+{}^{112-132}\mathrm{Sn}$ deviates from the Carlson's empirical expression obtained by fitting the reaction cross sections for proton on nuclei along the $\beta$-stability line and sensitively depends on the stiffness of the symmetry energy. We also find that the angular distribution of elastic scattering for $p+{}^{132}\mathrm{Sn}$ at large impact parameters is very sensitive to the density dependence of the symmetry energy, which is uniquely due to the effect of the symmetry potential with no mixture of the effect from the isospin dependence of the nucleon-nucleon cross sections. The isospin effects in neutron-induced reactions are also studied and it is found that the effects are just opposite to that in proton-induced reactions. We find that the difference between the peaks of the angular distributions of elastic scattering for $p+{}^{132}\mathrm{Sn}$ and $n+{}^{132}\mathrm{Sn}$ at $E_{p,n}=100$ MeV and $b=7.5$ fm is positive for soft symmetry energy $U_{\mathrm{sym}}^{\mathrm{sf}}$ and negative for super-stiff symmetry energy $U_{\mathrm{sym}}^{\mathrm{nlin}}$ and close to zero for linear density dependent symmetry energy $U_{\mathrm{sym}}^{\mathrm{lin}}$, which seems very useful for constraining the density dependence of the symmetry energy at subnormal densities.

• Received 8 April 2008

DOI:https://doi.org/10.1103/PhysRevC.78.044609