Probing $\alpha$ clustering in $^{12}\mathrm{C}$ at CSR energies using the Jet AA Microscopic Transport Model

We investigate the sensitivity of low-energy nuclear collisions to intrinsic nuclear structure by studying the interplay between initial-state geometry and final-state observables in C+C and C+Pb collisions at $\sqrt{s_{NN}}=2.36$~GeV, relevant for experiments at the Cooling Storage Ring (CSR) facility in Lanzhou and forthcoming experiments at the High Intensity heavy-ion Accelerator Facility (HIAF) in Huizhou. Calculations are performed within the Jet AA Microscopic Transport Model (JAM) using Woods--Saxon and triangular $\alpha$-clustered configurations for the $^{12}C$ nucleus. The initial geometry is characterized in terms of transverse size, compactness, eccentricities, and their ensemble-averaged fluctuations. We find that $\alpha$ clustering leads to a more compact participant configuration than the Woods--Saxon case, while transverse-size and eccentricity fluctuations show only weak sensitivity to clustering. At this beam energy, radial observables remain sensitive to geometric compactness, with the ensemble-averaged proton mean transverse momentum $\langle p_T \rangle$ enhanced for $\alpha$-clustered configurations, whereas pions show little sensitivity. The anisotropic response is examined using flow harmonic coefficients. We find an enhancement of the root-mean-square flow magnitudes, $v_n\{2\} = \sqrt{\langle v_n^2\rangle}$, for $\alpha$-clustered configurations at large $N_{part}$, while the ensemble-averaged fluctuation strength of individual harmonics remains small. Symmetric cumulants of the initial-state eccentricities show sensitivity to clustering, whereas the corresponding ensemble-averaged correlations among final-state flow harmonics do not exhibit a comparably strong separation. These results indicate that radial observables and correlation-based flow measurements provide complementary probes of $\alpha$ clustering in low-energy nuclear collisions.