arXiv subjects

Hao-jie Xu

Publications and source records attributed to Hao-jie Xu.

At least 19 recordsLinked to original sources

arXiv2026

Investigation of Nonlinear Collective Dynamics in Relativistic Heavy-Ion Collisions Using A Multi-Phase Transport Model

The nonlinear response coefficient, $χ_{4,22}$, is a crucial observable for probing the dynamical properties of the quark-gluon plasma (QGP). Although traditionally interpreted as a signature of medium response, recent studies suggest that $χ_{4,22}$ also encodes information about the intrinsic initial-state configuration of the colliding nuclei. In this study, we use the A Multi-Phase Transport (AMPT) model to investigate the microscopic origin and stage-by-stage development of $χ_{4,22}$ in $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. By tracking flow observables through the partonic cascade, quark coalescence, and hadronic rescattering phases, we map the conversion of initial geometric eccentricities into final-state momentum anisotropies. Our results demonstrate that the absolute magnitude of $χ_{4,22}$ increases continuously during collective expansion, confirming its nature as a dynamically generated medium response. In contrast, the relative ratio of this coefficient between the U+U and Au+Au systems, $R(χ_{4,22})$, exhibits approximate stage independence over a broad centrality range, as quantified by a constant-fit test across the three AMPT evolution stages. This indicates that the ratio reduces common medium-response effects, such as overall amplification efficiency and viscous attenuation, and therefore retains stronger sensitivity to the relative initial-state geometry. These findings provide theoretical support for using nonlinear flow ratios to constrain higher-order nuclear structure, such as hexadecapole deformation, while also clarifying the residual stage dependence and nonflow limitations relevant to precision extractions.

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arXiv2026

Testing microscopic nuclear-density inputs for deformation-sensitive observables in relativistic $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions

Recent STAR measurements of $^{238}$U+$^{238}$U/$^{197}$Au+$^{197}$Au ratios provide a sensitive test of nuclear deformation in relativistic heavy-ion collisions, but the elliptic-flow, triangular-flow, and transverse-momentum-related observables are not simultaneously described within existing calculations. We use three-dimensional lattice covariant density functional theory (CDFT) with pairing correlations to provide microscopic density distributions of both $^{238}$U and $^{197}$Au for event-by-event hydrodynamic simulations. The CDFT densities substantially improve the description of the ultracentral elliptic-flow ratio, while the octupole-deformed uranium configuration yields a larger triangular-flow ratio than the reflection-symmetric configuration. In contrast, the transverse-momentum-related ratios remain difficult to describe within the present framework. We further show that variations of the density of the odd-mass $^{197}$Au reference nucleus can produce changes in the triangular-flow ratio comparable to the separation between the two uranium configurations. These results demonstrate that both the uranium structure and the reference-nucleus density must be controlled before quantitative nuclear-structure constraints can be extracted from high-energy collisions.

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arXiv2026

Probing the tetrahedral $α$ clusters in relativistic $^{16}$O + $^{16}$O collisions

Relativistic $^{16}$O +$^{16}$O collisions provide a valuable opportunity to study both the quark-gluon plasma formed in small systems and the intrinsic structure of $^{16}$O. Recent implementations of \textit{ab initio} nuclear configurations in heavy-ion simulations have produced different predictions for cluster-sensitive observables, making it difficult to identify the origin of possible $α$-cluster signals. In this work, we introduce a controlled sampling scheme that varies the compactness of $α$-cluster-induced multi-nucleon correlations while keeping the one-body density distribution of $^{16}$O fixed. This allows us to separate effects driven by the tetrahedral one-body density from those driven by genuine multi-nucleon correlations. We show that the normalized ratios ${\rm Norm}(v_{2}\{2\}/v_{2}\{4\})$ and ${\rm Norm}(v_{2}\{2\}/v_{3}\{2\})$, together with their initial-state eccentricity counterparts, provide complementary constraints on initial-condition model dependence and cluster compactness. Hybrid hydrodynamic simulations and comparisons with recent LHC measurements further clarify the extent to which the initial-state signals survive final-state evolution. Our results provide a framework for using relativistic light-ion collisions to constrain cluster correlations in $^{16}$O.

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arXiv2026

Resolution-matched nuclear geometry and the nucleon-size ambiguity in relativistic heavy-ion collisions

Nuclear structure theory provides point-nucleon densities, whereas high-energy nuclear collisions probe nuclei through finite-resolution hadronic interactions. This resolution mismatch becomes a physical ambiguity when point densities are embedded in Monte Carlo initial-state models with a finite transverse nucleon profile. A parameter intended to describe the effective interaction range can then also reshape the nuclear surface, blurring the separation between nuclear structure and collision dynamics. I show that this ambiguity can largely account for the strong nucleon-width dependence of the ${}^{208}$Pb+${}^{208}$Pb hadronic cross section ($σ_{\rm AA}$) reported in recent Bayesian analyses. Fixing the folded density that enters the Glauber phase shift removes this ambiguity at the level of nuclear geometry. The corrected cross section becomes nearly insensitive to a Gaussian nucleon width and instead probes the nuclear surface. Within a two-component estimate for ${}^{208}$Pb, the current experimental uncertainty of $σ_{\rm AA}$ translates into a broad neutron-skin interval, $Δr_{\rm np}\in[0,0.21]$ fm. These results reframe $σ_{\rm AA}$ as a surface-sensitive bridge between point-nucleon nuclear structure and finite-resolution high-energy initial conditions, rather than as a standalone nucleon-size observable. This establishes resolution matching as a necessary step for using relativistic heavy-ion collisions as quantitative probes of nuclear structure.

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arXiv2026

Quantum Symmetry Restoration and Emergent Effective Deformation in Relativistic Heavy-Ion Collisions

Classically deformed nuclear geometries are commonly employed in standard descriptions of relativistic collisions between two even-even nuclei, despite the fact that their exact ground states are rotationally invariant $0^+$ states. In this paper, we formulate the collision geometry directly from the eikonal scattering matrix based on a nonorthogonal Generator Coordinate Method construction of rotationally invariant ground states. In the optical limit, using a localized transported-density approximation for the collision-channel one-body response, rotational overlap localization generates an effective one-body density associated with the scattering process. Within this approximation, using the Gaussian Overlap Approximation and its heat-kernel representation, we show that rotational symmetry restoration acts as a geometric low-pass filter which exponentially suppresses effective deformation modes. The classical rigid-rotor limit is recovered for large intrinsic angular momentum fluctuations. We establish a microscopic framework connecting rotational symmetry restoration, collective overlap localization, and the effective deformation geometries of nuclei in high energy collisions.

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arXiv2026

Nonlinear response of flow harmonics in Gubser flow with participant-reaction planes mismatch

We investigate the nonlinear response of flow harmonics $v_2,v_4$ to initial-state eccentricities $ε_2,ε_4$ within the Gubser-flow framework. By extending the perturbative solutions of Gubser flow, we derive analytic nonlinear response relations connecting the eccentricities $ε_2,ε_4$ to the flow harmonics $v_2,v_4$. Our results reproduce the well-known result $v_4/v_2^2 \to 1/2$ in large transverse momentum $p_T$ limit. Furthermore, we study the effects of a mismatch between the participant and reaction planes. We find that the conventional nonlinear response coefficients acquire an additional factor determined by the participant-plane angles, which is often approximated as statistical noise driven by event-by-event fluctuations. This factor can modify both the strength but even the sign of the effective nonlinear response coefficient, making it sensitive to the initial configuration of the colliding nuclei. Our study provides new analytical insight into the origin of collective phenomena in relativistic heavy-ion collisions.

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arXiv2026

Impact of Geometric Inflation on Nucleon Size Sensitivity in Relativistic Heavy-Ion Collisions

The intrinsic transverse size of nucleons, parameterized by a Gaussian width $w$, is a critical yet uncertain input in the initial-state modeling of relativistic heavy-ion collisions. Using a finite $w$ in standard initial geometry models introduces an unintentional ``geometric inflation'' that alters the initial nuclear density profile. In this study, we implement a self-consistent density correction to eliminate this artifact and investigate its impact on final-state observables. Through hybrid (viscous hydrodynamics + hadronic transport) simulations of $^{208}$Pb+$^{208}$Pb collisions at the LHC, we demonstrate that removing geometric inflation significantly modifies the sensitivity of observables to the nucleon width $w$. While elliptic flow and mean transverse momentum ($\langle [p_{\rm T}]\rangle$) become less sensitive to variations in $w$, the Pearson correlation coefficient $ρ(v_{n}^{2}, δp_{\rm T})$, $[p_{\rm T}]$ fluctuations, and triangular flow exhibit enhanced sensitivity to fluctuations in nucleon positions. Our results indicate that uncorrected geometric inflation can bias the extraction of nucleon structure and quark-gluon plasma properties. This underscores the necessity of a self-consistent initial-state geometry for reliable Bayesian inference in heavy-ion collisions.

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arXiv2025

A "breathing'' octupole $^{208}$Pb nucleus: resolving the elliptical-to-triangular azimuthal anisotropy puzzle in ultracentral relativistic heavy ion collisions

Relativistic heavy ion collisions provide a unique opportunity to probe the nuclear structure by taking an instantaneous snapshot of the colliding nuclei and converting it into momentum anisotropies of final emitted hadrons. A long-standing puzzle of too large a ratio of the elliptical-to-triangular ($v_{2}$-to-$v_{3}$) anisotropies in ultracentral $^{208}$Pb+$^{208}$Pb collisions at the Large Hadron Collider(LHC) cannot be solved simply by hydrodynamic simulations with initial conditions containing the spherical or certain deformed shape of $^{208}$Pb. In this Letter, using the iEBE-VISHNU relativistic viscous hydrodynamic hybrid model simulations with the Trento initial condition, we show that a dynamic octupole deformation--a shape-breathing of $^{208}$Pb --could potentially solve the $v_{2}$-to-$v_{3}$ puzzle and simultaneously describe the $v_3\{4\}$ data measured in experiment. Our results highlight the unique capability of capturing transient collective properties of nuclei on yoctosecond ($10^{-24}$~s) timescales, unfeasible with low-energy nuclear reactions.

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arXiv2024

Exploring the Nuclear Shape Phase Transition in Ultra-Relativistic $^{129}$Xe+$^{129}$Xe Collisions at the LHC

The shape phase transition for certain isotope or isotone chains, associated with the quantum phase transition of finite nuclei, is an intriguing phenomenon in nuclear physics. A notable case is the Xe isotope chain, where the structure transits from a $γ$-soft rotor to a spherical vibrator, with the second-order shape phase transition occurring in the vicinity of $^{128-130}$Xe. In this letter, we focus on investigating the $γ$-soft deformation of $^{129}$Xe associated with the second-order shape phase transition by constructing novel correlators for ultra-relativistic $^{129}$Xe+$^{129}$Xe collisions. In particular, our iEBE-VISHNU model calculations show that the $v_2^2-[p_T]$ correlation $ρ_{2}$ and the mean transverse momentum fluctuation $Γ_{p_T}$, which were previously interpreted as the evidence for the rigid triaxial deformation of $^{129}$Xe, can also be well explained by the $γ$-soft deformation of $^{129}$Xe. We also propose two novel correlators $ρ_{4,2}$ and $ρ_{2,4}$, which carry non-trivial higher-order correlations and show unique capabilities to distinguish between the $γ$-soft and the rigid triaxial deformation of $^{129}$Xe in $^{129}$Xe+$^{129}$Xe collisions at the LHC. The present study also provides a novel way to explore the second-order shape phase transition of finite nuclei with ultra-relativistic heavy ion collisions.

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arXiv2024

Systematic investigation of the nuclear multiple deformations in U+U collisions with A Multi-Phase Transport model

Relativistic heavy ion collisions provide a unique opportunity to study the shape of colliding nuclei, even up to higher-order multiple deformations. In this work, several observables that are sensitive to quadrupole and hexadecapole deformations of Uranium-238 in relativistic U+U collisions have been systematically investigated with A Multi-Phase Transport model. We find that the flow harmonic $v_{2}$, the $v_{2}$ and mean transverse momentum correlation, and the three-particle asymmetry cumulant ${\rm ac}_{2}\{3\}$ are sensitive to nuclear quadrupole deformation, while ${\rm ac}_{2}\{3\}$ and nonlinear response coefficient $χ_{4,22}$ are sensitive to nuclear hexadecapole deformation. Our results from transport model studies are in qualitative agreement with previous hydrodynamic studies. The results indicate that the uncertainties of the hexadecapole deformation of Uranium on the quadrupole deformation determination can be reduced by the abundance of correlation observables provided by the relativistic heavy ion collisions.

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arXiv2024

Impact of initial fluctuations and nuclear deformations in isobar collisions

Relativistic isobar ($^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr) collisions have revealed intricate differences in their nuclear size and shape, inspiring unconventional studies of nuclear structure using relativistic heavy ion collisions. In this study, we investigate the relative differences in the mean multiplicity ($R_{\langle N_{\rm ch}\rangle}$) and the second- ($R_{ε_{2}}$) and third-order eccentricity ($R_{ε_{3}}$) between isobar collisions using initial state models. It is found that initial fluctuations and nuclear deformations have negligible effects on $R_{\langle N_{\rm ch}\rangle}$ in most central collisions, while both are important for the $R_{ε_{2}}$ and $R_{ε_{3}}$, the degree of which is sensitive to the underlying nucleonic or sub-nucleonic degree of freedom. These features, compared to real data, may probe the particle production mechanism and the physics underlying nuclear structure.

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arXiv2024

Hexadecapole deformation of $^{238}$U from relativistic heavy-ion collisions using a nonlinear response coefficient

The hexadecapole deformation ($β_4$) of the $^{238}$U nucleus has not been determined because its effect is overwhelmed by those from the nucleus' large quadrupole deformation ($β_2$) in nuclear electric transition measurements. In this Letter, we identify the nonlinear response of the hexadecapole anisotropy to ellipticity in relativistic $^{238}$U+ $^{238}$U collisions that is solely sensitive to $β_4$ and insensitive to $β_2$. We demonstrate this by state-of-the-art hydrodynamic calculations and discuss the prospects of discovering the $β_4$ of $^{238}$U in heavy-ion data at the Relativistic Heavy Ion Collider.

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arXiv2024

Exploring the compactness of $α$ cluster in $^{16}$O nuclei with relativistic $^{16}$O+$^{16}$O collisions

Probing the $α$ cluster of $^{16}$O with the relativistic $^{16}$O+$^{16}$O collisions has raised great interest in the heavy ion community. However, the effects of the $α$ cluster on the soft hadron observables vary largely among different studies. In this paper, we explain the differences by the compactness of the $α$ cluster in oxygen, using iEBE-VISHNU hydrodynamic simulations with different initial state $α$ cluster configurations. We also find several observables, such as the intensive skewness of the $[p_{\rm T}]$ correlator $Γ_{p_{\rm T}}$, the harmonic flows $v_2\{2\}$, $v_2\{4\}$, $v_3\{2\}$, and the $v_n^2-δ[p_{\rm T}]$ correlations $ρ(v_{2}^{2}, [p_{\rm T}])$, $ρ(v_{3}^{2}, [p_{\rm T}])$ in $^{16}$O+$^{16}$O collisions are sensitive to the compactness of the $α$ cluster in the colliding nuclei, which can be used to constrain the configurations of $^{16}$O in the future. Our study serves as an important step toward the quantitative exploration of the $α$ cluster configuration in the light nuclei with relativistic heavy ion collisions.

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arXiv2024

Determining the neutron skin thickness by relativistic semi-isobaric collisions

The neutron skin thickness of the benchmark nucleus $^{208}$Pb is crucial for our understanding of the equation of state of nuclear matter. In this paper, we discuss the effect of the neutron skin on the flow ratio observables in the semi-isobaric collisions $^{208}$Pb+$^{208}$Pb and $^{197}$Au+$^{197}$Au using iEBE-VISHNU hydrodynamic simulations. Our results suggest that $^{208}$Pb and $^{197}$Au should have the same magnitude of neutron skin thickness to describe the anisotropic flow ratios between the semi-isobaric systems. Our method provides an unconventional way to determine the neutron skin with the existing relativistic heavy ion collision data.

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arXiv2023

Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs

$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between these two collision systems and demonstrate that the ratios of ${\rm ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences between $^{96}$Ru and $^{96}$Zr. We also study the nonlinear response coefficients $χ_{4,22}$, which show insensitivity to the deformation effect.

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arXiv2023

Probing neutron skin and symmetry energy with relativistic isobar collisions

In these proceedings, we present the three proposed observables to probe the neutron skin and symmetry energy with relativistic isobar collisions, namely, the isobar ratios of the produced hadron multiplicities ($N_{\rm ch}$), the mean transverse momenta ($\langle p_{\perp} \rangle$), and the net charge multiplicities ($ΔQ$). Our findings suggest potentially significant improvement to neutron skin and symmetry energy determination over traditional low energy methods.

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arXiv2022

Measuring neutron skin by grazing isobaric collisions

Neutron skin thickness ($Δr_{\rm np}$) of nuclei and the inferred nuclear symmetry energy are of critical importance to nuclear physics and astrophysics. It is traditionally measured by nuclear processes with significant theoretical uncertainties. We recently proposed an indirect measurement of the $Δr_{\rm np}$ by charged hadron multiplicities in central isobaric collisions at relativistic energies, which are sensitive to nuclear densities. In this Letter, we propose a direct measurement of the $Δr_{\rm np}$ by using net-charge multiplicities in ultra-peripheral (grazing) collisions of those isobars, under the assumption that they are simple superimposition of nucleon-nucleon interactions. We illustrate this novel approach by the TRENTO and URQMD models.

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arXiv2021

Probing nuclear structure with mean transverse momentum in relativistic isobar collisions

Transverse momentum ($p_{T}$) generation in relativistic heavy ion collisions is sensitive to the initial geometry and the final-state bulk evolution. We demonstrate with hydrodynamic calculations that the mean $p_T$ ratio ($R_{\langle p_{T}\rangle}$) between the highly similar isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions is insensitive to the bulk evolution and remains sensitive to the small difference in the initial nuclear structure (neutron skin and deformation) between the Ru and Zr nuclei.We further find that nuclear deformation can produce an anticorrelation between $R_{\langle p_{T}\rangle}$ and eccentricity (or elliptic flow) in central collisions. These findings suggest that the $R_{\langle p_{T}\rangle}$ between the isobar systems can be used to measure the neutron skin thickness and deformation parameters, which can in turn constrain the nuclear symmetry energy slope parameter.

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