  Within an isospin-dependent transport model for nuclear reactions induced by
neutron-rich nuclei, we perform a comparative study of $^{100}Sn+^{124}Sn$ and
$^{100}Zn+^{124}Sn$ reactions at beam energies of 30 MeV/A and 400 MeV/A to
identify optimal experimental conditions and observables for investigating the
equation of state (EOS) of neutron-rich matter at 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 MeV/A. At 400 MeV/A, 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 Rare Isotope
Accelerator (RIA) are discussed.
