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

The hexadecapole deformation (β_4) of the ^238U 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 ^238U+ ^238U 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 ^238U in heavy-ion data at the Relativistic Heavy Ion Collider.