Hexadecapole Deformation of ^{238}U from Relativistic Heavy-Ion Collisions Using a Nonlinear Response Coefficient

The hexadecapole deformation (β_{4}) of the ^{238}U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation (β_{2}) 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 β_{4} and insensitive to β_{2}. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the β_{4} of ^{238}U in heavy-ion data at the Relativistic Heavy Ion Collider.