This dissertation focuses on the study of the nuclear equation of state, with an emphasis on the extraction of effective mass splitting between neutron and proton. A series of experiments was proposed and approved to use the neutron-to-proton (n/p) ratios from heavy-ion collisions as a probe to constrain the nuclear equation of state. The latest experiments were carried out at the National Superconducting Cyclotron Laboratory (NSCL) using three detection systems: the Microball, for extracting impact parameter information, the HiRA10 silicon array, for detecting light charged particles from hydrogen to helium isotopes, and the vLANA neutron wall, for measuring neutrons.Each of the two calcium isotope beams, 40Ca and 48Ca, were delivered at two different energies, 56 MeV/u and 140 MeV/u, and targeted onto stationary targets. These targets were enriched with either nickel isotopes, 58Ni and 68Ni, or tin isotopes, 112Sn and 124Sn, to produce a range of isospin asymmetries, (N −Z)/A, with values ranging from 0.02 to 0.14. A total of 16 beam-target configurations were explored in the experiment, but this dissertation primarily analyzes beam-target pairs with the extreme asymmetry values, specifically, 40Ca + 58Ni, 48Ca + 64Ni, 40Ca + 112Sn, and 48Ca + 124Sn, at both beam energies.Key findings include the successful reconstruction of light charged particle spectra with HiRA10 and the revelation of the isoscaling property across the entire measured range. The isoscaling of charged particles enables the construction of pseudo-neutron and corresponding coalescence-invariant (CI) neutron spectra. Due to large systematic errors, the CI n/p ratios from one single reaction may not be reliable. These limitations were greatly mitigated by constructing the double ratio of CI n/p ratios from the most and the least neutron-rich systems. The double ratio was then analyzed through a Bayesian framework informed by the Improved Quantum Molecular Dynamics (ImQMD) model, showing sensitivity to the nucleon effective mass splitting.The second part of this work dedicated significant effort towards the calibration and data analysis of vLANA, a neutron wall array equipped with a veto wall to discriminate against charged particles. The in-depth calibration resulted in improvements in accuracy, precision, and effective handling of large variety of data obtained over a period of two months when the experiments were performed. The intrinsic efficiency of neutron detection was evaluated through a sophisticated simulation using a newly developed neuSIM4 code. The study culminated with the presentation of neutron spectra for the Ca+Ni systems at incident energy of 140 MeV/u, confirming the isoscaling property of neutrons. Furthermore, the substitution of pseudo-neutrons with actual reconstructed neutrons in the CI n/p double ratio suggested Δm∗np/δ = −0.10 ± 0.09, aligning with the findings from the light charged particle analysis and previous works.In summary, the methodology developed in this dissertation paves a way for future investigations of effective mass splitting, contributing to our understanding of the nuclear equation of state. It also underscores the need for ongoing collaboration with theorists and calls for further exploration using other theoretical models.
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