[Paper Review] The impact of nuclear deformation on relativistic heavy-ion collisions: assessing consistency in nuclear physics across energy scales

Giuliano Giacalone, J. Jia+1 more|arXiv (Cornell University)|May 4, 2021

High-Energy Particle Collisions ResearchPhysics and Astronomy41 references95 citations

TL;DR

This paper proposes a hydrodynamic scaling method to test consistency between low-energy nuclear deformation data and high-energy relativistic heavy-ion collision data. By relating elliptic flow (v2) differences between 197Au+197Au and 238U+238U collisions to nuclear quadrupole deformation β, it finds that RHIC data implies β ≈ 0.16–0.20 for gold, significantly larger than literature values, challenging current nuclear phenomenology.

ABSTRACT

In the hydrodynamic framework of heavy-ion collisions, elliptic flow, $v_2$, is sensitive to the quadrupole deformation, $\beta$, of the colliding ions. This enables one to test whether the established knowledge on the low-energy structure of nuclei is consistent with collider data from high-energy experiments. We derive a formula based on generic scaling laws of hydrodynamics to relate the difference in $v_2$ measured between collision systems that are close in size to the value of $\beta$ of the respective species. We validate our formula in simulations of 238U+238U and 197Au+197Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to experimental data. Using the deformation of 238U from low-energy experiments, we find that RHIC $v_2$ data implies $0.16 \lesssim |\beta| \lesssim 0.20$ for 197Au nuclei, i.e., significantly more deformed than reported in the literature, posing an interesting puzzle in nuclear phenomenology.

Motivation & Objective

• To assess whether low-energy nuclear deformation parameters (β) are consistent with high-energy heavy-ion collision data.
• To develop a hydrodynamic scaling method that relates v2 differences between collision systems to their deformation parameters.
• To test whether the established β values from low-energy experiments match the effective β inferred from RHIC v2 measurements.
• To identify potential inconsistencies in nuclear structure models when extrapolated to ultra-short time-scale QGP dynamics.
• To provide a quantitative framework for cross-scale validation of nuclear physics.

Proposed method

• Derives a scaling law: ⟨v2²⟩ = a + bβ², relating mean-squared elliptic flow to nuclear deformation β.
• Defines ratios rv2², rb, ra, rY to compare v2 between two systems (e.g., 197Au+197Au and 238U+238U) and express βY as a linear function of βX.
• Uses hydrodynamic simulations (AMPT model) with varying β values to validate the scaling formula in 238U+238U and 197Au+197Au collisions at √sNN = 193–200 GeV.
• Estimates coefficients a and b using viscous hydrodynamics scaling laws, with corrections from v3 flow data and mass number dependence.
• Applies the validated formula to experimental RHIC v2 data to infer β for 197Au, using 238U’s known β from low-energy data.
• Performs numerical checks including event-by-event fluctuations and impact parameter dependence to ensure robustness.

Experimental results

Research questions

• RQ1 Is the β value inferred from RHIC v2 data consistent with the β value measured in low-energy nuclear experiments?
• RQ2 Can a hydrodynamic scaling law reliably relate v2 differences between two heavy-ion systems to their respective deformation parameters?
• RQ3 Does the observed v2 in 197Au+197Au collisions imply a larger deformation than currently reported in the literature?
• RQ4 To what extent do viscous damping and mass number scaling affect the consistency of β extraction across energy scales?
• RQ5 What is the impact of nuclear deformation on initial-state eccentricity fluctuations in high-energy collisions?

Key findings

• The derived scaling formula rv2² = (rv2²ra − 1)/rY + (rv2²rb)βX² successfully predicts v2 differences in AMPT simulations across various β values.
• The method is robust under variations in impact parameter and event-by-event fluctuations, confirming its validity in hydrodynamic frameworks.
• Using 238U’s known β ≈ 0.3 from low-energy data, the analysis infers that 197Au must have |β| ≈ 0.16–0.20 to reproduce RHIC v2 data.
• This inferred β for 197Au is significantly larger than the literature value of β ≈ 0.13, indicating a potential inconsistency in nuclear structure models.
• The result challenges the assumption that low-energy nuclear deformation parameters directly translate to high-energy QGP dynamics.
• The discrepancy suggests that either the current β value for 197Au is underestimated, or the hydrodynamic response to deformation is not fully captured by existing models.