Shape of atomic nuclei in heavy ion collisions

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 ${\epsilon }_n$, $v_n\propto {\epsilon }_n$. The ${\epsilon }_n$, for $n=1,2,3,4$, are sensitive to the shape of the colliding ions, characterized by the quadrupole ${\beta }_2$, octupole ${\beta }_3$ and hexadecapole ${\beta }_4$ deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $⟨{\epsilon }_n^2⟩=a_n^{\prime }+b_n^{\prime }{\beta }_n^2$, for events in a fixed centrality. The $⟨{\epsilon }_1^2⟩$ has a contribution from ${\beta }_3$ and ${\beta }_4$, and $⟨{\epsilon }_3^2⟩$ from ${\beta }_4$. In the ultra-central collisions, there are little cross contributions between ${\beta }_2$ and ${\epsilon }_3$ and between ${\beta }_3$ and ${\epsilon }_2$, but clear cross contributions are present in non-central collisions. Additionally, $⟨{\epsilon }_n^2⟩$ 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 ${\beta }_2$, ${\beta }_3$, and ${\beta }_4$ values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a_n^{\prime }$, to obtain simple equation that relates the ${\beta }_n$ of the two species. 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 those obtained in the nuclear structure experiments.

18 pages, 9 figures plus two appendixes, published version

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