Much effort has been undertaken recently to improve constraints on the symmetry energy term in the Nuclear Equation of State (EOS). Specifically, the behavior of the symmetry energy above and below nuclear saturation density plays a significant role in the properties of neutron stars, the structure of heavy nuclei, and the dynamics of nuclear reactions. The tendency for neutrons to drift from a neutron-rich region to a neutron-deficient region during a peripheral collision of heavy nuclei is known as isospin diffusion, and has been previously shown to be a sensitive observable for the study of the symmetry energy at sub-saturation densities.Projectile fragmentation reactions with beams of $^{112,118,124}$Sn at 70MeV/u on targets of $^{112,118,124}$Sn have been measured at Michigan State University, in order to understand the effect of the isospin asymmetry on the reaction dynamics. Heavy fragments with $Z>20$ were detected and isotopically identified using the S800 Spectrometer, and the momentum distributions of these fragments were reconstructed. Additionally, light charged particles and intermediate mass fragments were detected in an array of Si-CsI telescopes to simultaneously determine the isotopic distributions of fragments with $Z<8$. The impact parameter of the collision was characterized by a measurement of the charged particle multiplicity in a $4\pi$ scintillator array. These data provide a detailed picture of the evolution of the projectile-like residue over a range of isospin asymmetries and impact parameter.The measured yield ratios have been used to extract information about the diffusion of neutrons between the projectile and target during peripheral collisions. The validity of using isotopic yield ratios as a surrogate for the isospin asymmetry of the compound system are discussed, and the associated isospin diffusion results are presented.
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