Shape of atomic nuclei in heavy ion collisions

TL;DR

This paper investigates how the shape deformations of atomic nuclei influence the anisotropic flow in heavy ion collisions, revealing linear relationships that can help map nuclear shapes at extremely short timescales.

Contribution

It demonstrates a robust linear relation between shape deformations and flow parameters, enabling nuclear shape constraints through heavy ion collision measurements.

Findings

Linear relation between $ angle ext{varepsilon}_n^2 angle$ and $eta_n^2$

Insensitivity of $ angle ext{varepsilon}_n^2 angle$ to non-axial shape parameters

Potential to map nuclear shapes at ultra-short timescales

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 $\varepsilon_n$, $v_n\propto \varepsilon_n$. The $\varepsilon_n$, 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, $\langle\varepsilon_n^2\rangle = a_n'+b_n'\beta_n^2$, for events in a fixed centrality. The $\langle\varepsilon_1^2\rangle$ has a contribution from $\beta_3$ and $\beta_4$, and $\langle\varepsilon_3^2\rangle$ from $\beta_4$. In the ultra-central collisions, there are little cross contributions between $\beta_2$ and $\varepsilon_3$ and between $\beta_3$ and $\varepsilon_2$, but clear cross contributions are present in non-central collisions. Additionally, $\langle\varepsilon_n^2\rangle$ 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 $a_n'$, 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.