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

Abstract

Most atomic nuclei exhibit ellipsoidal shapes characterized by quadrupole deformation $\beta_2$ and triaxiality $\gamma$, and sometimes even a pear-like octupole deformation $\beta_3$. 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 $\beta_{2\mathrm{U}}$ and $\gamma_{\mathrm{U}}$ 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.