Impact of Nuclear Deformation on Relativistic Heavy-Ion Collisions: Assessing Consistency in Nuclear Physics across Energy Scales

In the hydrodynamic framework of heavy-ion collisions, elliptic flow v₂ is sensitive to the quadrupole deformation β of the colliding ions. This enables one to test whether the established knowledge on the low-energy structure of nuclei is consistent with collider data from high-energy experiments. We derive a formula based on generic scaling laws of hydrodynamics to relate the difference in v₂ measured between collision systems that are close in size to the value of β of the respective species. We validate our formula in simulations of ²³⁸U+²³⁸U and ¹⁹⁷Au+¹⁹⁷Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to experimental data. Using the deformation of ²³⁸U from low-energy experiments, we find that RHIC v₂ data implies 0.16≲|β|≲0.20 for ¹⁹⁷Au nuclei, i.e., significantly more deformed than reported in the literature, posing an interesting issue in nuclear phenomenology.