Imaging nuclear shape through anisotropic and radial flow in high-energy heavy-ion collisions

TL;DR

This work uses ultra-central collisions of deformed $^{238}$U nuclei and near-spherical $^{197}$Au to image nuclear shapes by linking anisotropic flow $v_n$ and radial flow through the observable $[p_T]$. By constructing ratios and normalized correlators of $⟨v_n^2⟩$, $⟨(δp_T)^2⟩$, and $⟨v_n^2 δp_T⟩$, the study largely suppresses final-state effects and isolates initial-condition-driven deformation signals. Comparisons with IP-Glasma+MUSIC and Glauber models yield quantitative constraints on uranium deformation: $β_{2 m U} = 0.300 \pm 0.016$ and $γ_{ m U} = 8.3 \\pm 4.7^ ext{o}$, with evidence for modest octupole deformation $β_{3 m U}$ from $v_3$ observables. These results validate imaging nuclear shapes at femtosecond timescales and demonstrate a path to calibrate high-energy nuclear structure studies against low-energy measurements, with implications for both nuclear structure and QGP initial-state modelling.

Abstract

Most atomic nuclei exhibit ellipsoidal shapes characterized by quadrupole deformation $β_2$ and triaxiality $γ$, and sometimes even a pear-like octupole deformation $β_3$. The STAR experiment introduced a new "imaging-by-smashing" technique [arXiv:2401.06625, arXiv:2501.16071] to image the nuclear global shape by colliding nuclei at ultra-relativistic speeds and analyzing outgoing debris. Features of nuclear shape manifest in collective observables like anisotropic flow $v_n$ and radial flow via mean transverse momentum $[p_{\mathrm{T}}]$. We present new measurements of the variances of $v_n$ ($n=2$, 3, and 4) and $[p_{\mathrm{T}}]$, and the covariance of $v_n^2$ with $[p_{\mathrm{T}}]$, in collisions of highly deformed $^{238}$U and nearly spherical $^{197}$Au. Ratios of these observables between the two systems effectively suppress common final-state effects, isolating the strong impact of uranium's deformation. By comparing results with state-of-the-art hydrodynamic model calculations, we extract $β_{2\mathrm{U}}$ and $γ_{\mathrm{U}}$ values consistent with those deduced from low-energy nuclear structure measurements. Measurements of $v_3$ and its correlation with $[p_{\mathrm{T}}]$ also provide the first experimental suggestion of a possible octupole deformation for $^{238}$U. These findings provide significant support for using high-energy collisions to explore nuclear shapes on femtosecond timescales, with implications for both nuclear structure and quark-gluon plasma studies.

Figures (38)

• Figure 1: Illustration of how collision geometry and collective expansion are impacted by quadrupole deformation in collisions of prolate (a) and oblate (b) nuclei. The configurations vary between body-body and tip-tip, which are selected based on the momentum distribution of final state particles. The negative (positive) correlation between ellipticity and inverse size in (a) ((b)) drives the negative (positive) correlation between elliptic flow and radial flow in the final state, highlighting the potential of constraining the triaxiality. The dashed grey circles represent the baseline shape of the QGP for spherical nuclei.
• Figure 2: Distributions of reconstructed TPC track multiplicity ($\hbox{$N_{\mathrm{ch}}^{\mathrm{rec}}$}$) in $|\eta|<0.5$ and $p_{\mathrm{T}}> 0.15$ GeV/$c$ (left), and efficiency-corrected TPC track multiplicity ($\hbox{$N_{\mathrm{ch}}$}$) for $|\eta|<0.5$ and $p_{\mathrm{T}}> 0.2$ GeV/$c$ (right), in U+U and Au+Au collisions.
• Figure 3: Relationship between centrality and $\hbox{$N_{\mathrm{ch}}^{\mathrm{rec}}$}$ (left), and mapping between $\hbox{$N_{\mathrm{ch}}^{\mathrm{rec}}$}$ and $\hbox{$N_{\mathrm{ch}}$}$ (right) in U+U and Au+Au collisions.
• Figure 4: $\left\langle v_2^2\right\rangle$ (left) and $\left\langle (\delta p_{\mathrm{T}})^2\right\rangle$ (right) as a function of centrality in U+U and Au+Au collisions for charged hadrons in $0.2<p_{\mathrm{T}}<3$ GeV/$c$. Results are obtained using the two-subevent method.
• Figure 5: The $\left\langle v_3^2\right\rangle$ (left), $\left\langle v_4^2\right\rangle$ (middle) and $\left\langle p_{\mathrm{T}}\right\rangle$ (right) as a function of centrality in U+U and Au+Au collisions for charged hadrons in $0.2<p_{\mathrm{T}}<3$ GeV/$c$.