Evidence for modest octupole deformation in $^{238}$U from high-energy heavy-ion collisions

TL;DR

This work develops an imaging-by-smashing approach to extract ground-state nuclear shapes from high-energy heavy-ion collisions by leveraging ratios of $v_n$- and $p_T$-based observables between $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au to cancel common nonshape effects. The method uses a Woods-Saxon density with deformations and demonstrates near-linear relationships between observables and deformation parameters, enabling extraction of $β_{2\mathrm{U}}$, $β_{3\mathrm{U}}$, and the triaxiality $γ_{\mathrm{U}}$ through hydrodynamic and initial-state modeling. The analysis yields $β_{2\mathrm{U}}=0.286\pm0.025$, $γ_{\mathrm{U}}=8.7\pm4.5^{\circ}$, and evidence for a modest octupole deformation $β_{3\mathrm{U}}\sim0.08$–$0.10$, broadly consistent with low-energy data under a rigid-rotor framework. This demonstrates that high-energy collisions provide direct sensitivity to ground-state nuclear shapes on femtosecond timescales and offers a path to map deformation across nuclei, with future work planned on other collision systems to refine the technique.

Abstract

We present a novel ``imaging-by-smashing" approach for probing nuclear deformation in high-energy heavy-ion collisions. By analyzing anisotropic-flow ($v_n$) and mean transverse momentum ($\left[p_T\right]$)-based observables in collisions of highly deformed $^{238} \mathrm{U}$ nucleus and nearly spherical $^{197} \mathrm{Au}$ nucleus, we extract the deformation parameters of $^{238}$U. The key observables include the variances $\left\langle v_n^2\right\rangle,\left\langle\left(δp_T\right)^2\right\rangle$, and the covariance $\left\langle v_n^2 δp_T\right\rangle$. Ratios of these observables between $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions largely cancel final-state effects, thereby isolating the influence of nuclear deformation. We further report the first experimental indication of octupole deformation in $^{238}$U via $v_3$-based observables~\cite{2025rot}. The extracted deformation parameters, comparing with state-of-the-art hydrodynamic model calculations, are consistent with low-energy nuclear structure data. These results establish high-energy collisions as a powerful probe of nuclear shapes on femtosecond timescales.

Figures (2)

• Figure 1: Centrality dependence of ratios of one-and two-particle observables, $\left\langle v_2^2\right\rangle,\left\langle\left(\delta p_{\mathrm{T}}\right)^2\right\rangle$, $\left\langle v_3^2\right\rangle,\left\langle v_4^2\right\rangle$, and $\left\langle p_{\mathrm{T}}\right\rangle$, between $^{238}\mathrm{U}+^{238}\mathrm{U}$ and $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions in four $p_{\mathrm{T}}$ ranges. Figure is from Ref. 2025rot.
• Figure 2: Centrality dependence of ratios of three-particle observable, $\left\langle v_2^2 \delta p_{\mathrm{T}}\right\rangle$ (left) and $\left\langle v_3^2 \delta p_{\mathrm{T}}\right\rangle$ (right) between $^{238}\mathrm{U}+^{238}\mathrm{U}$ and $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions, obtained for four $p_{\mathrm{T}}$ intervals. Figure is from Ref. 2025rot.