Hexadecapole deformation of $^{238}$U from relativistic heavy-ion collisions using a nonlinear response coefficient

The hexadecapole deformation ($\beta_4$) of the $^{238}$U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation ($\beta_2$) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic $^{238}$U+ $^{238}$U collisions that is solely sensitive to $\beta_4$ and insensitive to $\beta_2$. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the $\beta_4$ of $^{238}$U in heavy-ion data at the Relativistic Heavy Ion Collider.