Orateur
Description
The $^{238}$U nucleus is well deformed with a large quadruple deformation $\beta_2=0.286$. However, its hexadecapole deformation $\beta_{\rm 4,U}$ is not well determined, mainly because it is overshadowed by the large $\beta_{\rm 2,U}$ in experimental observables that are typically sensitive to both. A recent study (Ryssens, et.al., Phys.Rev.Lett. 130, 212302) proposes a smaller $\beta_2$ for U to explain the $v_{2}$ differences between $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions, and thereby a finite $\beta_{\rm 4,U}$ to compensate the smaller $\beta_{\rm 2,U}$ in order to still describe the experimental quadruple moment. This is, however, rather indirect as $v_{2}$ is nearly insensitive to $\beta_4$, and the $v_{2}$ differences between the two systems can simply be explained by a larger $\beta_{\rm 2, Au}$ as our knowledge of the $\beta_{2}$ of odd-Z nuclei is poor. In this talk, we present three truly $\beta_4$-sensitive observables, the flow harmonic correlation ${\rm ac}_{2}\{3\}$, the event-plane correlation $\langle\cos(4\Phi_2-4\Phi_4)\rangle$, and the nonlinear response coefficient $\chi_{4,22}$. The $\chi_{4,22}$ observable is even insensitive to the quadruple deformation and the system size, providing an unique opportunity to precisely extract the $\beta_{\rm 4,U}$ from relativistic heavy ion collisions.
