Systematic investigation of the nuclear multipole deformations in $U+U$ collisions with a multi-phase transport model

Relativistic heavy ion collisions provide a unique opportunity to study the shape of colliding nuclei, even up to higher-order multipole deformations. In this work, several observables that are sensitive to quadrupole and hexadecapole deformations of uranium-238 in relativistic $\text{U}+\text{U}$ collisions have been systematically investigated with a multi-phase transport model. We find that the flow harmonic $v_2$, the $v_2$ and mean transverse momentum correlation, and the three-particle asymmetry cumulant ${\mathrm{ac}}_2\left\{3\right\}$ are sensitive to nuclear quadrupole deformation, while ${\mathrm{ac}}_2\left\{3\right\}$ and nonlinear response coefficient ${\chi }_{4,22}$ are sensitive to nuclear hexadecapole deformation. Our results from transport model studies are in qualitative agreement with previous hydrodynamic studies. The results indicate that the uncertainties of the hexadecapole deformation of uranium on the quadrupole deformation determination can be reduced by the abundance of correlation observables provided by the relativistic heavy ion collisions.