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

TL;DR

This paper uses advanced covariant density functional theory to model uranium densities in relativistic collisions, revealing insights into nuclear deformation and highlighting challenges in matching experimental flow observables.

Contribution

It introduces detailed 3D covariant density functional calculations of uranium densities, including octupole and hexadecapole deformations, for collision simulations.

Findings

CDFT density describes elliptic flow well

Mismatch with transverse-momentum observables indicates deformation tension

Difficulty constraining octupole deformation due to nuclear structure uncertainties

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.