Shape of atomic nuclei in heavy ion collisions

Jiangyong Jia

doi:10.1103/PhysRevC.105.014905

paper

Shape of atomic nuclei in heavy ion collisions

arXiv:2106.08768 · doi:10.1103/PhysRevC.105.014905

Abstract

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow $v_{n}$ are linearly related to the strength of the multi-pole shape of the distribution of nucleons in the transverse plane $ε_{n}$ , $v_{n} \propto ε_{n}$ . The $ε_{n}$ , for $n = 1, 2, 3, 4$ , are sensitive to the shape 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, $⟨ ε_{n}^{2} ⟩ = a_{n}^{'} + b_{n}^{'} β_{n}^{2}$ , for events in a fixed centrality. The $⟨ ε_{1}^{2} ⟩$ has a contribution from $β_{3}$ and $β_{4}$ , and $⟨ ε_{3}^{2} ⟩$ from $β_{4}$ . In the ultra-central 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 non-central collisions. Additionally, $⟨ ε_{n}^{2} ⟩$ are insensitive to non-axial 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 simple equation that relates the $β_{n}$ of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale ( $< 1 0^{- 24}$ s) much shorter than probed by low-energy nuclear structure physics ( $< 1 0^{- 21}$ s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.

arXiv comment18 pages, 9 figures plus two appendixes, published version

Shape of atomic nuclei in heavy ion collisions

Abstract

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