Hexadecapole Deformation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">U</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>238</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> from Relativistic Heavy-Ion Collisions Using a Nonlinear Response Coefficient
H. Xu, J. Zhao, F. Wang
Abstract
The hexadecapole deformation (${\ensuremath{\beta}}_{4}$) of the $^{238}\mathrm{U}$ nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation (${\ensuremath{\beta}}_{2}$) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic $\mathrm{U}+\mathrm{U}$ collisions that is solely sensitive to ${\ensuremath{\beta}}_{4}$ and insensitive to ${\ensuremath{\beta}}_{2}$. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the ${\ensuremath{\beta}}_{4}$ of $^{238}\mathrm{U}$ in heavy-ion data at the Relativistic Heavy Ion Collider.