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.