Effects of Initial Nucleon-Nucleon Correlations on Light Nuclei Production in Au+Au Collisions at $\sqrt{s_\mathrm{NN}} = 3\ $ GeV

Light nuclei production in heavy-ion collisions serves as a sensitive probe of the QCD phase structure. In coalescence models, triton ($N_t$) and deuteron ($N_d$) yields depend on the spatial separation of nucleon pairs ($\Delta r$) in Wigner functions, yet the impact of initial two-nucleon correlations $\rho(\Delta r)$ remains underexplored. We develop a method to sample nucleons in $^{197}$Au nuclei that simultaneously satisfies both the single-particle distribution $f(r)$ and the two-nucleon correlation $\rho(\Delta r)$. Using these nuclei, we simulate Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV via the SMASH transport model (mean-field mode) to calculate proton, deuteron, and triton yields. Simulations reveal a 36% enhancement in mid-rapidity deuteron yields across all centrality ranges and a 33% rise in mid-rapidity triton production for 0-10% central collisions. Calculated transverse momentum of light nuclei aligns with STAR data. We further analyze impacts of baryon conservation, spectator exclusion, and centrality determination via charged multiplicity. Notably, observed discrepancies in the double yield ratio suggest unaccounted physical mechanisms, such as critical fluctuations or inaccuracies in coalescence parameters or light nuclei cross-sections. This underscores the critical role of initial nucleon-nucleon correlations, linking microscopic nuclear structure to intermediate-energy collision dynamics.