There are two distinct components involved in using heavy ion collisions to constrain the density dependence of the symmetry energy. On one hand, observables sensitive to the symmetry energy must be identified and measured with enough precision to provide meaningful constraints. On the other hand, nuclear reaction simulations are used to predict those observables for different possible forms of the symmetry energy. Examination of both components and the interface between them is important to improve the constraints. This thesis contributes to both the experimental and theoretical parts of this endeavor.First, we examine the uncertainties in the simulation of the isospin diffusion observable by varying the input physics within the pBUU transport code. In addition to the symmetry energy, several other uncertain parts of the calculation affect isospin diffusion, most notably the in-medium nucleon-nucleon cross sections and light cluster production. There is also a difference in the calculated isospin transport ratios depending on whether they are computed using the isospin asymmetry of the heavy residue or of all forward-moving fragments. We suggest that measurements comparing these two quantities would help place constraints on the input physics, including the density dependence of the symmetry energy.Second, we present a measurement of the neutron and proton kinetic energy spectra emitted from central collisions of 124Sn + 124Sn and 112Sn + 112Sn at beam energies of 50 MeV per nucleon and 120 MeV per nucleon. Previous transport simulations indicate that ratios of these spectra are sensitive to the density dependence of the symmetry energy and to the isovector momentum dependence of the mean field. Protons were detected in the Large Area Silicon Strip Array (LASSA) and neutrons were detected in the MSU Neutron Walls. The multiplicity of charged particles detected in the MSU Miniball was used to determine the impact parameter of the collisions. Several thin scintillators were used to provide the start time for the neutron measurement, determine the charged particle background in the neutron detector, and measure the beam rate.We construct ratios of the neutron and proton spectra between the two reaction systems and compare them to recent ImQMD-Sky transport model simulations and to previous data, where available. The new data with beam energy of 50 MeV per nucleon represents a substantial increase in precision and an extension to higher kinetic energies compared to the previous data. No previous data exists near a beam energy of 120 MeV per nucleon. The simulations indicate a strong dependence of the spectral ratios on the effective mass splitting and to a lesser extent on the density dependence of the symmetry energy. However, significant differences exist between the simulations and the measurement. We present arguments and coalescence invariant spectra to indicate that a major source of the discrepancy is clustering effects. The theoretical treatment of these effects must be considered in more detail before constraints on the equation of state can be extracted from this or other measurements of proton and neutron emission from heavy ion collisions.
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