Imaging nuclear shape through anisotropic and radial flow in high-energy heavy-ion collisions
The Star Collaboration
Abstract
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 ((STAR Collaboration) 2024 Nature 635 67; Jia 2025 Rep. Prog. Phys. 88 092301) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:math> . We present new measurements of the variances of v n ( n = 2, 3, and 4) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:math> , and the covariance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>β</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mi mathvariant="normal">U</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">U</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> values consistent with those deduced from low-energy nuclear structure measurements. Measurements of v 3 and its correlation with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> </mml:math> 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.