Shape of atomic nuclei in heavy ion collisions
In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flows v n are linearly related to the strengths of the multipole shape of the distribution of nucleons in the transverse plane, ε n : v n ∝ε n . The ε n , for n=1, 2, 3, 4, are sensitive to the shapes of the colliding ions, characterized by the quadrupole β 2 , octupole β 3 , and hexadecapole β 4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langleε^{2}_{n}\rangle$ = $a^{'}_{n} + b^{'}_{n}β^{2}_{n}$, for events in a fixed centrality. The $\langleε^{2}_{1}\rangle$ has a contribution from β 3 and β 4 , and $\langleε^{2}_{3}\rangle$ from β 4 . In ultracentral collisions, there are little cross contributions between β 2 and ε 3 and between β 3 and ε 2 , but clear cross contributions are present in noncentral collisions. Additionally, $\langleε^{2}_{n}\rangle$ are insensitive to nonaxial shape parameters such as the triaxiality. This is good news because the measurements of v 2 , v 3 , and v 4 can be used to constrain simultaneously the β 2 , β 3 , and β 4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a^{'}_{n}$, to obtain a simple equation that relates the β n of the two species. Finally, this opens up the possibility to map the shape of the atomic nuclei at a timescale (<10 –24 s) much shorter than probed by low-energy nuclear structure physics (<10 –21 s), which ultimately may provide information complementary to that obtained in the nuclear structure experiments.