Testing microscopic nuclear-density inputs for deformation-sensitive observables in relativistic $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions

Recent STAR measurements of $^{238}$U+$^{238}$U/$^{197}$Au+$^{197}$Au ratios provide a sensitive test of nuclear deformation in relativistic heavy-ion collisions, but the elliptic-flow, triangular-flow, and transverse-momentum-related observables are not simultaneously described within existing calculations. We use three-dimensional lattice covariant density functional theory (CDFT) with pairing correlations to provide microscopic density distributions of both $^{238}$U and $^{197}$Au for event-by-event hydrodynamic simulations. The CDFT densities substantially improve the description of the ultracentral elliptic-flow ratio, while the octupole-deformed uranium configuration yields a larger triangular-flow ratio than the reflection-symmetric configuration. In contrast, the transverse-momentum-related ratios remain difficult to describe within the present framework. We further show that variations of the density of the odd-mass $^{197}$Au reference nucleus can produce changes in the triangular-flow ratio comparable to the separation between the two uranium configurations. These results demonstrate that both the uranium structure and the reference-nucleus density must be controlled before quantitative nuclear-structure constraints can be extracted from high-energy collisions.