Shape of atomic nuclei in heavy ion collisions

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow vn are linearly related to the strength of the multi-pole shape of the nucleon density distribution in the transverse plane εn, vn ∝ εn for n = 1,2,3,4. The εn are sensitive to the shape of the colliding ions, characterized by the quadrupole β2, octupole β3 and hexadecapole β4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model, and we observe a robust linear relation, ⟨εn⟩ = an + bnβ n, for events in fixed centrality. The ⟨ε1⟩ has a contribution from β3 and β4, and ⟨ε3⟩ from β4, but there are little cross contributions between β2 and ε3 and between β3 and ε2. Additionally, ⟨εn⟩ are insensitive to non-axial shape parameters such as the triaxiality. These are good news because we can use measurements of v2, v3 and v4 to constrain simultaneously the β2, β3, and β4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical an, to obtain simple equation that relates the βn of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale (< 10−24s) much shorter than nuclear structure physics (< 10−21s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.