Probing the $\alpha$ cluster of $^{ 16}$O with the relativistic $^{ 16}$O+$^{ 16}$O collisions has raised great interest in the heavy ion community. However, the effects of the $\alpha$ cluster on the soft hadron observables vary largely among different studies. In this paper, we explain the differences by the compactness of the $\alpha$ cluster in oxygen, using iEBE-VISHNU hydrodynamic simulations with different initial state $\alpha$ cluster configurations. We also find several observables, such as the intensive skewness of the $[p_{ \rm T}]$ correlator $\Gamma_{ p_{ \rm T}}$, the harmonic flows $v_2\{ 2\}$, $v_2\{ 4\}$, $v_3\{ 2\}$, and the $v_n^2-\delta[p_{ \rm T}]$ correlations $\rho(v_{ 2}^{ 2}, [p_{ \rm T}])$, $\rho(v_{ 3}^{ 2}, [p_{ \rm T}])$ in $^{ 16}$O+$^{ 16}$O collisions are sensitive to the compactness of the $\alpha$ cluster in the colliding nuclei, which can be used to constrain the configurations of $^{ 16}$O in the future. Our study serves as an important step toward the quantitative exploration of the $\alpha$ cluster configuration in the light nuclei with relativistic heavy ion collisions.
Categories: nucl-th nucl-ex