Hexadecapole Deformation of U238 from Relativistic Heavy-Ion Collisions Using a Nonlinear Response Coefficient

The hexadecapole deformation (β₄) of the ²³⁸U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation (β₂) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic U+U collisions that is solely sensitive to β₄ and insensitive to β₂. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the β₄ of ²³⁸U in heavy-ion data at the Relativistic Heavy Ion Collider.