Investigation of the shape of uranium in relativistic $^{238}$U+$^{238}$U collisions with nuclear densities from covariant density functional theory

TL;DR

This work addresses how nuclear deformation, especially in $^{238}$U, shapes observables in relativistic heavy-ion collisions. It combines 3D lattice covariant density functional theory (CDFT) densities, including $\beta_{20}$, $\beta_{30}$, and $\beta_{40}$ components, with event-by-event hydrodynamic simulations (iEBE-VISHNU) of $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au at $\sqrt{s_{NN}}=200$ GeV, using two Au density parameter sets to test sensitivity. The main findings are that CDFT densities improve the description of the elliptic-flow ratio $v_{2}^{2}\{2\}$ and help resolve the ultracentral $v_2$ puzzle, but tensions with transverse-momentum observables such as $\langle v_{2}^{2}\delta p_T \rangle$ and $\langle(\delta p_T)^2\rangle$ persist, and the extraction of octupole deformation from $R(v_{3}^{2})$ is highly dependent on the poorly constrained $^{197}$Au structure. These results highlight the necessity of realistic nuclear densities for both colliding species and the need for integrated nuclear-structure–heavy-ion modeling to use relativistic collisions as precision probes of deformation.

Abstract

Relativistic $^{238}$U+$^{238}$U collisions have recently been used to extract the quadrupole shape of $^{238}$U. In this study, we employ state-of-the-art three-dimensional (3D) lattice covariant density functional theory (CDFT) with pairing correlations to calculate the density of uranium, including its octupole and hexadecaople deformations, as input for hydrodynamic simulations of these collisions. We find that while the CDFT density well describes elliptic flow, a clear mismatch emerges with transverse-momentum-related observables, indicating a tension in the effective quadrupole deformation. Furthermore, constraining the octupole deformation with triangular flow $v_{3}$ proves to be difficult due to significant sensitivity to the uncertain nuclear structure of the gold reference system. Our results underscore the necessity of realistic nuclear densities for both colliding species and highlight the need for further investigation of correlations related to both flow and transverse momentum to fully characterize nuclear deformation.

Figures (5)

• Figure 1: (Color online) Density distributions of $^{238}$U obtained from covariant density functional theory calculations for an octupole-deformed configuration ($\beta_{20}=0.29$, $\beta_{30}=0.09$, upper panels (a)–(c)) and the corresponding purely prolate configuration ($\beta_{20}=0.29$, $\beta_{30}=0$, lower panels (d)–(f)).
• Figure 2: (Color online) Centrality dependence of the $v_{2}^{2}\{2\}$ (or $\varepsilon_{2}^{2}$) ratio between U+U and Au+Au collisions obtained from iEBE-VISHNU (or initial TRENTo) simulations. The results in panels (a) and (b) are generated using the ${\rm Au}_{\rm default}$ and ${\rm Au}_{\rm new}$ parameter sets, respectively. Experiment data from the STAR Collaboration are taken from Ref. STAR:2024wgy.
• Figure 3: (Color online) Centrality dependence of the $v_{3}^{2}\{2\}$ (or $\varepsilon_{3}^{2}$) ratio between U+U and Au+Au collisions obtained from iEBE-VISHNU (or initial TRENTo) simulations. The results in panels (a) and (b) are generated using the ${\rm Au}_{\rm default}$ and ${\rm Au}_{\rm new}$ parameter sets, respectively. Experiment data from the STAR Collaboration are taken from Ref. STAR:2025elk.
• Figure 4: (Color online) Centrality dependence of the $\langle v_{2}^{2}\delta p_{\mathrm T} \rangle$ ratio between U+U and Au+Au collisions, obtained from iEBE-VISHNU simulations. Experiment data from the STAR collaboration are taken from Ref. STAR:2024wgy.
• Figure 5: (Color online) Centrality dependence of the $\langle(\delta p_{\mathrm T})^{2}\rangle$ ratio between U+U and Au+Au collisions, obtained from iEBE-VISHNU simulations. Experiment data from the STAR Collaboration are taken from Ref. STAR:2024wgy.