Article

Elliptic flow fluctuations in central collisions of spherical and deformed nuclei

February 2019
Physical Review C 99(2)

DOI:10.1103/PhysRevC.99.024910

Authors:

Elliptic flow (v2) fluctuations in central heavy-ion collisions are direct probes of the fluctuating geometry of the quark-gluon plasma and, as such, are strongly sensitive to any deviation from spherical symmetry in the shape of the colliding nuclei. I investigate the consequences of nuclear deformation for v2 fluctuations, and I assess whether current models of medium geometry are able to predict and capture such effects. Assuming linear hydrodynamic response between v2 and the eccentricity of the medium, ɛ2, I perform accurate comparisons between model calculations of ɛ2 fluctuations and STAR data on cumulants of elliptic flow in central Au+Au and U+U collisions. From these comparisons, I evince that the most distinct signatures of nuclear deformation appear in the non-Gaussianities of v2 fluctuation, and I show, in particular, that the non-Gaussian v2 fluctuations currently observed in central Au+Au collisions are incompatible with model calculations that implement a quadrupole coefficient of order 12% in the Au197 nuclei. Finally, I make robust predictions for the behavior of higher order cumulants of v2 in collisions of nonspherical nuclei.

Impact parameter dependence of anisotropic flow: Bayesian reconstruction in ultracentral nucleus-nucleus collisions

Preprint

Full-text available

Jul 2024

Peculiar phenomena have been observed in analyses of anisotropic flow (

v_n

) fluctuations in ultracentral nucleus-nucleus collisions: The fourth-order cumulant of the elliptic flow (

v_2

) distribution changes sign. In addition, the ATLAS collaboration has shown that cumulants of

v_n

fluctuations of all orders depend significantly on the centrality estimator. We show that these peculiarities are due to the fact that the impact parameter b always spans a finite range for a fixed value of the centrality estimator. We provide a quantitative determination of this range through a simple Bayesian analysis. We obtain excellent fits of STAR and ATLAS data, with a few parameters, by assuming that the probability distribution of

v_n

solely depends on b at a given centrality. This probability distribution is almost Gaussian, and its parameters depend smoothly on b, in a way that is constrained by symmetry and scaling laws. We reconstruct, thus, the impact parameter dependence of the mean elliptic flow in the reaction plane in a model-independent manner, and assess the robustness of the extraction using Monte Carlo simulations of the collisions where the impact parameter is known. We argue that the non-Gaussianity of

v_n

fluctuations gives direct information on the hydrodynamic response to initial anisotropies, ATLAS data being consistent with a smaller response for n=4 than for n=2 and n=3, in agreement with hydrodynamic calculations.

Momentum dependent flow correlations in deformed nuclei collision at RHIC energy

Preprint

Full-text available

Jan 2023

Flow fluctuations in ultra-relativistic heavy-ion collision can be probed by studying the momentum dependent correlations or the factorization-breaking coefficients between flow harmonics in separate kinematic bins (transverse momentum or pseudorapidity). We study such factorization-breaking coefficients for collisions of deformed U+U nuclei to see the effect of the nuclear deformation on momentum dependent coefficients. We also study momentum dependent mixed-flow correlations for the isobar collision system : Ru+Ru and Zr+Zr, which have the same mass number but different nuclear structure, thus providing the ideal scenario to study nuclear deformation effect on such observables. We use the TRENTO + MUSIC model for simulations and event-by-event analysis of those observables. We find that these momentum dependent correlation coefficients are not only excellent candidates to probe the fluctuation in heavy-ion collision, but also show significant sensitivity to the nuclear deformation.

Impact of Nuclear Deformation on Relativistic Heavy-Ion Collisions: Assessing Consistency in Nuclear Physics across Energy Scales

Article

Full-text available

Dec 2021

In the hydrodynamic framework of heavy-ion collisions, elliptic flow v2 is sensitive to the quadrupole deformation β 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 v2 measured between collision systems that are close in size to the value of β of the respective species. We validate our formula in simulations of U238+U238 and Au197+Au197 collisions at top Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to experimental data. Using the deformation of U238 from low-energy experiments, we find that RHIC v2 data implies 0.16≲|β|≲0.20 for Au197 nuclei, i.e., significantly more deformed than reported in the literature, posing an interesting issue in nuclear phenomenology.

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

Preprint

Full-text available

May 2021

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.

Question de forme : observer la déformation des noyaux atomiques aux collisionneurs des hautes énergies

Thesis

Nov 2020

Giuliano Giacalone

Collider experiments conducted atthe BNL RHIC and at the CERN LHC show thatthe the emission of particles following the interactionof two nuclei at relativistic energy is highlyanisotropic in azimuthal angle. This observationis compatible with a hydrodynamic paradigm, accordingto which the final-state hadrons are emittedfollowing the expansion of a fluidlike systemcreated in the interaction region. Withinthis paradigm, anisotropy in the emission of particlesis enhanced whenever the colliding nucleihave deformed ground states. By meansof high-quality comparisons between the predictionsof hydrodynamic models and particle colliderdata, I study the phenomenological manifestationsof the quadrupole deformation of atomicnuclei in relativistic ¹⁹⁷Au+¹⁹⁷Au, ²³⁸U+²³⁸U,and ¹²⁹Xe+¹²⁹Xe collisions. This analysis demonstratesthat a deep understanding of the structureof the colliding ions is required for the interpretationof data in high-energy experiments. RHICdata confirms in particular the well-known factthat the geometry of ²³⁸U nuclei is that of a welldeformedellipsoid, while indicating that ¹⁹⁷Au nuclei are nearly spherical, a result which is atodds with the estimates of mean-field and empiricalnuclear models. LHC data brings instead evidenceof quadrupole deformation in the groundstate of ¹²⁹Xe nuclei, ascribable to the first visiblemanifestation of shape coexistence phenomena inhigh-energy nuclear experiments. I introduce asimple method to isolate collision configurationsthat maximally break azimuthal symmetry dueto the orientation of the deformed nuclei. Thisallows me to define observables with an unprecedentedsensitivity to the deformation of the collidingspecies, thus paving the way for quantitativestudies of nuclear structure at high energy.

A matter of shape: seeing the deformation of atomic nuclei at high-energy colliders

Preprint

Jan 2021

Giuliano Giacalone

This work establishes a deep connection between two seemingly distant branches of nuclear physics: nuclear structure and relativistic heavy-ion collisions. At the heart of this connection is the recent discovery made at particle colliders that the elliptic flow of outgoing hadrons in central nucleus-nucleus collisions is strongly impacted by the quadrupole deformation of the colliding nuclear species. I review the physics of the soft sector of relativistic heavy-ion collisions, and I explain that the interpretation of elliptic flow data in central

^{197}

Au+

^{197}

Au,

^{238}

U+

^{238}

U, and

^{129}

Xe+

^{129}

Xe collisions requires a deep understanding the structure of these ions. Subsequently, I introduce a technique that permits one to isolate collision configurations in which the deformed shapes of the colliding nuclei maximally break rotational (azimuthal) symmetry in the interaction region. This allows me to construct observables that possess an unparalleled sensitivity to the quadrupole deformation of the colliding ions, and thus to conclude that nuclear experiments at high energy can be used to place new quantitative constraints on the deformation of atomic nuclei. I emphasize the great opportunities offered by potential collider experiments aimed at the systematic study of nuclear deformation across the valley of stability.

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Preprint

Full-text available

Sep 2021

Jiangyong Jia

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength

\beta_2

and triaxiality

\gamma

. The deformation can be accessed in high-energy heavy-ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity

\varepsilon_2

and the density gradient

d_{\perp}

in the initial state. Using analytical estimate and a Glauber model, we show that the variances,

\langle\varepsilon_2^2\rangle

\langle(\delta d_{\perp}/d_{\perp})^2\rangle

, and skewnesses,

\langle\varepsilon_2^2\delta d_{\perp}/d_{\perp}\rangle

\langle(\delta d_{\perp}/d_{\perp})^3\rangle

, have a simple analytical form of

a'+b'\beta_2^2

and

a'+(b'+c'\cos(3\gamma))\beta_2^3

, respectively. From these, we constructed several normalized skewnesses to isolate the

\gamma

dependence from that of

\beta_2

, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the

\beta_2

and

\gamma

. Assuming a linear relation with elliptic flow

v_2

and mean-transverse momentum

[p_{\mathrm{T}}]

of final state particles,

v_2\propto \varepsilon_2

and

\delta d_{\perp}/d_{\perp} \propto \delta[p_{\mathrm{T}}]/[p_{\mathrm{T}}]

, similar conclusions are also expected for the variances and skewnesses of

v_2

and

[p_{\mathrm{T}}]

, which can be measured precisely in top RHIC and LHC energies. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate,

\cos(3\gamma)=1

, and oblate nuclei,

\cos(3\gamma)=-1

, with well known

\beta_2

values to calibrate the coefficients

b'

and

c'

, followed by collisions of species of interest especially those with known

\beta_2

but unknown

\gamma

Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart

Article

Full-text available

Dec 2024
NUCL SCI TECH

Lihua Sun

High-energy nuclear collisions encompass three key stages: the structure of the colliding nuclei, informed by low-energy nuclear physics, the initial condition, leading to the formation of quark–gluon plasma (QGP), and the hydrodynamic expansion and hadronization of the QGP, leading to final-state hadron distributions that are observed experimentally. Recent advances in both experimental and theoretical methods have ushered in a precision era of heavy-ion collisions, enabling an increasingly accurate understanding of these stages. However, most approaches involve simultaneously determining both QGP properties and initial conditions from a single collision system, creating complexity due to the coupled contributions of these stages to the final-state observables. To avoid this, we propose leveraging established knowledge of low-energy nuclear structures and hydrodynamic observables to independently constrain the QGP’s initial condition. By conducting comparative studies of collisions involving isobar-like nuclei—species with similar mass numbers but different ground-state geometries—we can disentangle the initial condition’s impacts from the QGP properties. This approach not only refines our understanding of the initial stages of the collisions but also turns high-energy nuclear experiments into a precision tool for imaging nuclear structures, offering insights that complement traditional low-energy approaches. Opportunities for carrying out such comparative experiments at the Large Hadron Collider and other facilities could significantly advance both high-energy and low-energy nuclear physics. Additionally, this approach has implications for the future electron-ion collider. While the possibilities are extensive, we focus on selected proposals that could benefit both the high-energy and low-energy nuclear physics communities. Originally prepared as input for the long-range plan of U.S. nuclear physics, this white paper reflects the status as of September 2022, with a brief update on developments since then.

Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart

Article

Full-text available

Dec 2024
NUCL SCI TECH

High-energy nuclear collisions encompass three key stages: the structure of the colliding nuclei, informed by low-energy nuclear physics, the initial condition , leading to the formation of quark–gluon plasma (QGP), and the hydrodynamic expansion and hadronization of the QGP, leading to final-state hadron distributions that are observed experimentally. Recent advances in both experimental and theoretical methods have ushered in a precision era of heavy-ion collisions, enabling an increasingly accurate understanding of these stages. However, most approaches involve simultaneously determining both QGP properties and initial conditions from a single collision system, creating complexity due to the coupled contributions of these stages to the final-state observables. To avoid this, we propose leveraging established knowledge of low-energy nuclear structures and hydrodynamic observables to independently constrain the QGP’s initial condition. By conducting comparative studies of collisions involving isobar-like nuclei—species with similar mass numbers but different ground-state geometries—we can disentangle the initial condition’s impacts from the QGP properties. This approach not only refines our understanding of the initial stages of the collisions but also turns high-energy nuclear experiments into a precision tool for imaging nuclear structures, offering insights that complement traditional low-energy approaches. Opportunities for carrying out such comparative experiments at the Large Hadron Collider and other facilities could significantly advance both high-energy and low-energy nuclear physics. Additionally, this approach has implications for the future electron-ion collider. While the possibilities are extensive, we focus on selected proposals that could benefit both the high-energy and low-energy nuclear physics communities. Originally prepared as input for the long-range plan of U.S. nuclear physics, this white paper reflects the status as of September 2022, with a brief update on developments since then.

Energy dependence of the deformed nuclear structure at small-$x

Preprint

Full-text available

Nov 2024

We quantify the effect of high-energy JIMWLK evolution on the deformed structure or heavy (Uranium) and intermediate (Ruthenium) nuclei. The soft gluon emissions in the high-energy evolution are found to drive the initially deformed nuclei towards a more spherical shape, although the evolution is slow ,especially for the longest distance-scale quadrupole deformation. We confirm a linear relationship between the squared eccentricity

\varepsilon_n^2

and the deformation parameter

\beta_n^2

in central collisions across the energy range covered by the RHIC and LHC measurements. The applied JIMWLK evolution is found to leave visible signatures in the eccentricity evolution that can be observed if the same nuclei can be collided at RHIC and at the LHC, or in rapidity-dependent flow measurements. Our results demonstrate the importance of including the Bjorken-x dependent nuclear geometry when comparing simulations of the Quark Gluon Plasma evolution with precise flow measurements at high collision energies.

The unexpected uses of a bowling pin: anisotropic flow in fixed-target

^{208}

Pb+

^{20}

Ne collisions as a probe of quark-gluon plasma

Preprint

Full-text available

May 2024

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies (

\sqrt{s_{\rm NN}}\sim100

GeV in the centre-of-mass). With input from \textit{ab initio} calculations of the structure of

^{16}

O and

^{20}

Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions, to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma (QGP) formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow (

v_2

) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of

^{20}

Ne, which is deformed in a bowling-pin geometry. Owing to the large

^{208}

Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow (

v_4

) of Pb+Ne collisions via non-linear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution (

c_2\{4\}

). Exploiting the shape of

^{20}

Ne proves thus an ideal method to investigate the formation of QGP in fixed-target experiments at LHCb, and demonstrates the power of SMOG2 as a tool to image nuclear ground states.

Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plasmas to hadron distributions

Article

Full-text available

Dec 2023
EUR PHYS J A

Giuliano Giacalone

It is an experimental fact that multi-particle correlations in the final states of high-energy nucleus-nucleus collisions are sensitive to collective correlations of nucleons in the wave functions of the colliding nuclei. Here, I show that this connection is more direct than it intuitively seems. With an energy deposition scheme inspired by high-energy quantum chromodynamics, and within a linearized description of initial-state fluctuations in the quark-gluon plasma, I exhibit relations between N -particle correlations in the final states of nuclear collisions and N -nucleon density distributions in the colliding nuclei. This result formally justifies the sensitivity of the outcome of high-energy collisions to features such as nuclear deformations. It paves the way, thus, to systematic studies of the impact of state-of-the-art nuclear interactions in such processes.

Impact of quadrupole deformation on intermediate-energy heavy-ion collisions

Preprint

Aug 2023

This study employs the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to simulate intermediate-energy heavy-ion collisions between prolate nuclei

^{24}

Mg. The emphasis is on investigating the influence of centrality and orientation in several collision scenarios. The final-state particle multiplicities and anisotropic flows are primarily determined by the eccentricity and the area of the initial overlap. This not only provides feedback on the collision systems, but also, to some extent, provides a means to explore the fine structure inside deformed nuclei. Additionally, non-polarized collisions have been further discussed. These results contribute to the understanding of the geometric effects in nuclear reactions, and aid in the exploration of other information on reaction systems, such as the equation of state and nuclear high-momentum tail.

Measures of azimuthal anisotropy in high-energy collisions

Preprint

Aug 2023

Jean-Yves Ollitrault

Azimuthal anisotropy is a key observation made in ultrarelativistic heavy-ion collisions. This phenomenon has played a crucial role in the development of the field over the last two decades. In addition to its interest for studying the quark-gluon plasma, which was the original motivation, it is sensitive to the properties of incoming nuclei, in particular to the nuclear deformation and to the nuclear skin. The azimuthal anisotropy is therefore of crucial importance when relating low-energy nuclear structure to high-energy nuclear collisions. This article is an elementary introduction to the various observables used in order to characterize azimuthal anisotropy, which go under the names of

v_2\{2\}

v_3\{2\}

v_2\{4\}

, etc. The intended audience is primarily physicists working in the field of nuclear structure.

Spectator Matter in Collisions of Relativistic Deformed Nuclei

Article

Full-text available

Jul 2023

Many-body correlations for nuclear physics across scales: from nuclei to quark-gluon plasmas to hadron distributions

Preprint

May 2023

Giuliano Giacalone

It is an experimental fact that multi-particle correlations in the final states of high-energy nucleus-nucleus collisions are sensitive to collective correlations of nucleons in the wave functions of the colliding nuclei. Here, I show that this connection is more direct than it intuitively seems. With an energy deposition scheme inspired by high-energy quantum chromodynamics, and within a linearized description of initial-state fluctuations in the quark-gluon plasma, I exhibit relations between N-particle correlations in the final states of nuclear collisions and N-nucleon density distributions in the colliding nuclei. This result formally justifies the sensitivity of the outcome of high-energy collisions to features such as nuclear deformations. It paves the way, thus, to systematic studies of the impact of state-of-the-art nuclear interactions in such processes.

Predictions for the sPHENIX physics program

Preprint

Full-text available

May 2023

sPHENIX is a next-generation detector experiment at the Relativistic Heavy Ion Collider, designed for a broad set of jet and heavy-flavor probes of the Quark-Gluon Plasma created in heavy ion collisions. In anticipation of the commissioning and first data-taking of the detector in 2023, a RIKEN-BNL Research Center (RBRC) workshop was organized to collect theoretical input and identify compelling aspects of the physics program. This paper compiles theoretical predictions from the workshop participants for jet quenching, heavy flavor and quarkonia, cold QCD, and bulk physics measurements at sPHENIX.

Flow Distribution Analysis as A Probe of Nuclei Deformity

Preprint

Full-text available

Jan 2023

We study the flow harmonic distribution in deformed nuclei. To do this, we use the standard Gram-Charlier method to find the higher-order correction to the well-known Bessel-Gaussian distribution. We find that, apart from the necessity of including a shift parameter

\bar v_n

, the modified flow distribution describes the flow distribution of quadrupole and octupole deformation accurately. Using the shifted radial distribution, arising from this method, we scrutinize the effect of deformation on flow distribution. Assuming a linear relation between observables of spherical and deformed collisions,

\mathcal{O}_D=\mathcal{O}_S+\left(\sum_{m=2}a_{k,m} \beta_m\right)^{2k}

, for events with a fixed centrality, we compare the flow distribution of deformed and spherical nuclei. We also propose a way to measure

\bar{v}_2

in asymmetric nuclei collisions.

Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart

Preprint

Full-text available

Sep 2022

A major goal of the hot QCD program, the extraction of the properties of the quark gluon plasma (QGP), is currently limited by our poor knowledge of the initial condition of the QGP, in particular how it is shaped from the colliding nuclei. To attack this limitation, we propose to exploit collisions of selected species to precisely assess how the initial condition changes under variations of the structure of the colliding ions. This knowledge, combined with event-by-event measures of particle correlations in the final state of heavy-ion collisions, will provide in turn a new way to probe the collective structure of nuclei, and to confront and exploit the predictions of state-of-the-art ab initio nuclear structure theories. The US nuclear community should capitalize on this interdisciplinary connection by pursuing collisions of well-motivated species at high-energy colliders.

Structure of

^{128,129,130}

Xe through multi-reference energy density functional calculations

Preprint

Jul 2022

Recently, values for the Kumar quadrupole deformation parameters of the nucleus

^{130}

Xe have been computed from the results of a Coulomb excitation experiment, indicating that this xenon isotope has a prominent triaxial ground state. Within a different context, it was recently argued that the analysis of particle correlations in the final states of ultra-relativistic heavy-ion collisions performed at the Large Hadron Collider (LHC) points to a similar structure for the adjacent isotope,

^{129}

Xe. In the present work, we report on state-of-the-art multi-reference energy density functional calculations that combine projection on proton and neutron number as well as angular momentum with shape mixing for the three isotopes

^{128,129,130}

Xe using the Skyrme-type pseudo-potential SLyMR1. Exploring the triaxial degree of freedom, we demonstrate that the ground states of all three isotopes display a very pronounced triaxial structure. Moreover, comparison with experimental results shows that the calculations reproduce fairly well the low-energy excitation spectrum of the two even-mass isotopes. By contrast, the calculation of

^{129}

Xe reveals some deficiencies of the effective interaction.

Separating the impact of nuclear skin and nuclear deformation on elliptic flow and its fluctuations in high-energy isobar collisions

Preprint

Full-text available

Jun 2022

Bulk nuclear structure properties, such as radii and deformations, leave distinct signatures in the final states of relativistic heavy-ion collisions. Collisions of isobars, in particular, offer an easy route to establish clear correspondences between the structure of colliding nuclei and the final state observables. Here we investigate the impact of nuclear skin and nuclear deformations on elliptic flow (

v_2

) and its fluctuations in high-energy

^{96}

Ru+

^{96}

Ru and

^{96}

Zr+

^{96}

Zr collisions, for which experimental data is available. We show that the difference in skin thickness between these isobars impacts the intrinsic ellipticity of the collision systems, or reaction-plane flow,

v_2^{\mathrm{rp}}

. In contrast, differences in nuclear deformations impact only the fluctuations of

v_2

around

v_2^{\mathrm{rp}}

. Through isobar collisions, one can separate the influence of nuclear skin and nuclear deformations in the

v_2

data. This is a significant step towards assessing the consistency of nuclear phenomena across energy scales.

Impact of nuclear deformation on collective flow observables in relativistic U+U collisions

Preprint

Jun 2022

Niseem Magdy Abdelrahman

A Multi-Phase Transport (AMPT) model is used to investigate the efficacy of several flow observables to constrain the initial-state deformation of the Uranium nuclei in U+U collisions at nucleon-nucleon center-of-mass energy

\sqrt{s_{\mathrm{NN}}}

= 193 GeV. The multiparticle azimuthal cumulant method is used to investigate the sensitivity of (I) a set of quantities that are sensitive to both initial- and final-state effects as well as (II) a set of dimensionless quantities that are more sensitive to initial-state effects to the Uranium nuclei quadrupole shape deformation. I find that the combined use of the flow harmonics, flow fluctuations and correlations, linear and nonlinear flow correlations to the quadrangular flow harmonic, and the correlations between elliptic flow and the mean-transverse momentum could serve to constrain the nuclear deformation of the Uranium nuclei. Therefore, a comprehensive set of measurements of such observables can provide a quantifying tool for the quadrupole shape deformation via data-model comparisons

Correlations between flow and transverse momentum in Xe+Xe and Pb+Pb collisions at the LHC with the ATLAS detector: a probe of the heavy-ion initial state and nuclear deformation

Preprint

Full-text available

Apr 2022

ATLAS Collaboration

The correlations between flow harmonics

v_n

for n=2, 3 and 4 and mean transverse momentum

[p_\mathrm{T}]

^{129}

Xe+

^{129}

Xe and

^{208}

Pb+

^{208}

Pb collisions at

\sqrt{s_{\mathrm{NN}}}=5.44

TeV and 5.02 TeV, respectively, are measured using charged particles with the ATLAS detector. The correlations are sensitive to the shape and size of the initial geometry, nuclear deformation, and initial momentum anisotropy. The effects from non-flow and centrality fluctuations are minimized, respectively, via a subevent cumulant method and event activity selection based on particle production in the very forward rapidity. The results show strong dependences on centrality, harmonic number n,

p_{\mathrm{T}}

and pseudorapidity range. Current models describe qualitatively the overall centrality- and system-dependent trends but fail to quantitatively reproduce all the data. In the central collisions, where models generally show good agreement, the

v_2

[p_\mathrm{T}]

correlations are sensitive to the triaxiality of the quadruple deformation. The comparison of model to the Pb+Pb and Xe+Xe data suggests that the

^{129}

Xe nucleus is a highly deformed triaxial ellipsoid that is neither a prolate nor an oblate shape. This provides strong evidence for a triaxial deformation of

^{129}

Xe nucleus using high-energy heavy-ion collision.

Evidence of Quadrupole and Octupole Deformations in Zr 96 + Zr 96 and Ru 96 + Ru 96 Collisions at Ultrarelativistic Energies

Article

Full-text available

Jan 2022

In the hydrodynamic model description of heavy-ion collisions, the elliptic flow v2 and triangular flow v3 are sensitive to the quadrupole deformation β2 and octupole deformation β3 of the colliding nuclei. The relations between vn and βn have recently been clarified and were found to follow a simple parametric form. The STAR Collaboration has just published precision vn data from isobaric Ru96+Ru96 and Zr96+Zr96 collisions, where they observe large differences in central collisions v2,Ru>v2,Zr and v3,Ru<v3,Zr. Using a transport model simulation, we show that these orderings are a natural consequence of β2,Ru≫β2,Zr and β3,Ru≪β3,Zr. We reproduce the centrality dependence of the v2 ratio qualitatively and v3 ratio quantitatively and extract values of β2 and β3 that are consistent with those measured at low-energy nuclear structure experiments. STAR data provide the first direct evidence of strong octupole correlations in the ground state of Zr96 in heavy-ion collisions. Our analysis demonstrates that flow measurements in high-energy, heavy-ion collisions, especially using isobaric systems, are a new precision tool to study nuclear structure physics.

Evidence of quadrupole and octupole deformations in

^{96}

Zr+

^{96}

Zr and

^{96}

Ru+

^{96}

Ru collisions at ultra-relativistic energies

Preprint

Full-text available

Sep 2021

In the hydrodynamic model description of heavy ion collisions, the elliptic flow

v_2

and triangular flow

v_3

are sensitive to the quadrupole deformation

\beta_2

and octupole deformation

\beta_3

of the colliding nuclei. The relations between

v_n

and

\beta_n

have recently been clarified and were found to follow a simple parametric form. The STAR Collaboration have just published precision

v_n

data from isobaric

^{96}

Ru+

^{96}

Ru and

^{96}

Zr+

^{96}

Zr collisions, where they observe large differences in central collisions

v_{2,\mathrm{Ru}}>v_{2,\mathrm{Zr}}

and

v_{3,\mathrm{Ru}}<v_{3,\mathrm{Zr}}

. Using a transport model simulation, we show that these orderings are a natural consequence of

\beta_{2,\mathrm{Ru}}\gg\beta_{2,\mathrm{Zr}}

and

\beta_{3,\mathrm{Ru}}\ll\beta_{3,\mathrm{Zr}}

. We are able to reproduce the centrality dependence of the

v_2

ratio qualitatively and

v_3

ratio quantitatively, and extract values of

\beta_2

and

\beta_3

that are consistent with those measured at low energy nuclear structure experiments. STAR data provide the first direct evidence of strong octupole correlations in the ground state of

^{96}

Zr in heavy ion collisions. Our analysis demonstrates that flow measurements in high-energy heavy ion collisions, especially using isobaric systems, are a new precision tool to study nuclear structure physics.

Shape of atomic nuclei in heavy ion collisions

Preprint

Full-text available

Jun 2021

Jiangyong Jia

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow

v_n

are linearly related to the strength of the multi-pole shape of the nucleon density distribution in the transverse plane

\varepsilon_n

v_n\propto \varepsilon_n

for n=1,2,3,4. The

\varepsilon_n

are sensitive to the shape of the colliding ions, characterized by the quadrupole

\beta_2

, octupole

\beta_3

and hexadecapole

\beta_4

deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model, and we observe a robust linear relation,

\langle\varepsilon_n^2\rangle = a_n'+b_n'\beta_n^2

, for events in fixed centrality. The

\langle\varepsilon_1^2\rangle

has a contribution from

\beta_3

and

\beta_4

, and

\langle\varepsilon_3^2\rangle

from

\beta_4

, but there are little cross contributions between

\beta_2

and

\varepsilon_3

and between

\beta_3

and

\varepsilon_2

. Additionally,

\langle\varepsilon_n^2\rangle

are insensitive to non-axial shape parameters such as the triaxiality. These are good news because we can use measurements of

v_2

v_3

and

v_4

to constrain simultaneously the

\beta_2

\beta_3

, and

\beta_4

values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical

a_n'

, to obtain simple equation that relates the

\beta_n

of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale (

<10^{-24}

s) much shorter than nuclear structure physics (

<10^{-21}

s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.

Constraining nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in nuclear collisions

Preprint

Full-text available

May 2021

In heavy ion collisions, elliptic flow

v_2

and radial flow, characterized by event-wise average transverse momentum

[p_{\mathrm{T}}]

, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between

v_2

and

[p_{\mathrm{T}}]

\rho_2

, was found to be particularly sensitive to the quadrupole deformation parameter

\beta

that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation

\beta>0

reduces the

\rho_2

in ultra-central collisions (UCC), we show that the prolate deformation

\beta<0

enhances the value of

\rho_2

. As

\beta>0

and

\beta<0

are the two extremes of triaxiality, the strength and sign of

v_2^2-[p_{\mathrm{T}}]

correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale (

<10^{-24}

s).

Accessing the shape of atomic nuclei with relativistic collisions of isobars

Preprint

Feb 2021

Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to obtain quantitative information about the geometric shape of atomic nuclei.

Ultracentral Collisions of Small and Deformed Systems at RHIC

Article

Jan 2021
NUCL PHYS A

We study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-pT “(semi)dilute-(semi)dilute” regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in 0–1% ultracentral symmetric collisions of small deformed ions and in 0–10% d¹⁹⁷Au collisions. The collision systems we consider are ²³⁸U²³⁸U, d¹⁹⁷Au, ⁹Be¹⁹⁷Au, ⁹Be⁹Be, ³He³He, and ³He¹⁹⁷Au.

Turning up and down strong magnetic fields in relativistic nuclear collisions

Article

Full-text available

Dec 2020
PHYS LETT B

Giuliano Giacalone

I show that the average transverse momentum, 〈pt〉, of the hadrons emitted in relativistic nuclear collisions can be used as a “knob” to control the strength of the magnetic field induced by the spectator and the participant protons over the overlap region. I thus argue that any observable sensitive to this magnetic field is nontrivially correlated with 〈pt〉 at a given collision centrality.

Anisotropic Flow in Fixed-Target Pb 208 + Ne 20 Collisions as a Probe of Quark-Gluon Plasma

Article

Feb 2025
PHYS REV LETT

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies (sqrt[s_{NN}]∼100 GeV in the center of mass). With input from ab initio calculations of the structure of ^{16}O and ^{20}Ne, we compute 3+1D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow (v_{2}) in Pb+Ne collisions is greatly enhanced compared to the Pb+O baseline due to the shape of ^{20}Ne, which is deformed in a bowling-pin geometry. Owing to the large ^{208}Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow (v_{4}) of Pb+Ne collisions via nonlinear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution (c_{2}{4}). Exploiting the shape of ^{20}Ne proves thus an ideal method to investigate the formation of quark-gluon plasma in fixed-target experiments at LHCb, and demonstrates the power of System for Measuring Overlap with Gas as a tool to image nuclear ground states.

Benchmarking nuclear matrix elements of

0\nu\beta\beta

decay with high-energy nuclear collisions

Preprint

Feb 2025

Reducing uncertainties in the nuclear matrix element (NME) remains a critical challenge in designing and interpreting experiments aimed at discovering neutrinoless double beta (

0\nu\beta\beta

) decay. Here, we identify a class of observables, distinct from those employed in low-energy nuclear structure applications, that are strongly correlated with the NME: momentum correlations among hadrons produced in high-energy nuclear collisions. Focusing on the

^{150}

\rightarrow

^{150}

Sm transition, we combine a Bayesian analysis of the structure of

^{150}

Nd with simulations of high-energy

^{150}

Nd+

^{150}

Nd collisions. We reveal prominent correlations between the NME and features of the quark-gluon plasma (QGP) formed in these processes, such as spatial gradients and anisotropies, which are accessible via collective flow measurements. Our findings demonstrate collider experiments involving

0\nu\beta\beta

decay candidates as a platform for benchmarking theoretical predictions of the NME.

On sensitivity of nucleus deformation on final-state flow harmonics

Article

Feb 2025
CHINESE PHYS C

In this work, we explore the effect of deformation of the nuclei on collective flow in relativistic heavy-ion collisions. The parameter associated with the geometrical deformation in the Glauber model is tuned to reproduce the empirical multiplicity probability distributions correctly. Subsequently, the particle spectra and collective flows for Au+Au and U+U collisions are evaluated using a hybrid hydrodynamic code CHESS. We analyze the effects of the degrees of freedom associated with the IC on the final-state flow harmonics by exploring the parameter space of the former. The connection between the deformation parameters, specifically

\beta_2

and

\beta_4

, and the flow anisotropies is scrutinized. In particular, deviations in elliptic flow at

p_{\mathrm{T}}\sim 2

GeV are observed at smaller values of

\beta_2

in Au+Au collisions. On the other hand, for U+U collisions, the averaged overall flow harmonics are found to be less sensitive to the geometrical parameters. Despite the difference in the model's specifications, our findings largely confirm those obtained in the literature employing different approaches, which indicate that flow harmonics can be used as a sensible probe for the initial geometry fluctuations and to discriminate between different theoretical models.

Impact parameter dependence of anisotropic flow: Bayesian reconstruction in ultracentral nucleus-nucleus collisions

Article

Dec 2024

Momentum-dependent flow correlations in deformed nuclei at collision energies available at the BNL Relativistic Heavy Ion Collider

Article

May 2023

Flow fluctuations in ultrarelativistic heavy-ion collisions can be probed by studying the momentum dependent correlations or the factorization-breaking coefficients between flow harmonics in separate kinematic bins (transverse momentum p or pseudorapidity η). We study such factorization-breaking coefficients for collisions of deformed U238+U238 nuclei to see the effect of the nuclear deformation on momentum dependent coefficients. We also study momentum dependent mixed-flow correlations for the isobar collision system: Ru96+Ru96 and Zr96+Zr96, which have the same mass number but different nuclear structure, thus providing the ideal scenario to study nuclear deformation effect on such observables. We use the TRENTO + MUSIC model for simulations and event-by-event analysis of those observables. We find that these momentum dependent correlation coefficients are not only excellent candidates to probe the fluctuation in heavy-ion collision, but also show significant sensitivity to the nuclear deformation.

Predicting quadrupole deformation via anisotropic flow and transverse momentum spectra in isotopic

\mathbf {{}^{128-135}_{\qquad \,54}\textrm{Xe}}

collisions at LHC

Article

Full-text available

May 2024
EUR PHYS J C

In the hydrodynamical description of heavy-ion collisions, the elliptic flow

{\textrm{v}}_{2}

v 2 and triangular flow

{\textrm{v}}_{3}

v 3 are sensitive to the quadrupole deformation

{\beta _{2}}

β 2 of the colliding nuclei. We produce

{\textrm{v}}_{2}

v 2 and

{\textrm{v}}_{3}

v 3 ratios qualitatively and quantitatively in most-central Xe–Xe collisions at 5.44 TeV. By employing HYDJET++ model, we study the sensitivity of anisotropic flow coefficients and mean transverse momentum to the quadrupole deformation and system-size in isotopic Xe–Xe collisions. Flow observables strongly depend on the strength of nucleon–nucleon scattering occurring in even-A and odd-A nuclei. Flow for odd-A nuclei is suppressed in comparison to flow in even-A collisions. There exists a linear inter-dependence between

{\textrm{p}}_{\textrm{T}}

p T integrated anisotropic flow and nuclear deformation. Mean transverse momentum signifies the fireball temperature in body–body and tip–tip collisions. There exists a negative linear correlation of

\langle {\textrm{p}}_{\textrm{T}}\rangle

⟨ p T ⟩ with collision system-size and a positive correlation with nuclear deformation. Flow measurements in high-energy, heavy-ion collisions using isotopic collision systems, offer a new precision tool to study nuclear structure physics. Observation of nuclear structure properties like nuclear deformation in a heavy-ion collision such as this would be very interesting.

Predictions for the sPHENIX physics program

Article

Mar 2024
NUCL PHYS A

Study of Octupole deformations in Pb-Pb collisions at 5.02 TeV

Article

Full-text available

Dec 2023
PHYS LETT B

Measures of azimuthal anisotropy in high-energy collisions

Article

Oct 2023
EUR PHYS J A

Jean-Yves Ollitrault

v_2\{2\}

v_3\{2\}

v_2\{4\}

, etc. The intended audience is primarily physicists working in the field of nuclear structure.

Impact of quadrupole deformation on intermediate-energy heavy-ion collisions

Article

Sep 2023

This study employs the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to simulate intermediate-energy heavy-ion collisions between prolate nuclei Mg24. The emphasis is on investigating the influence of centrality and orientation in several collision scenarios. The final-state particle multiplicities and anisotropic flows are primarily determined by the eccentricity and the area of the initial overlap. This not only provides feedback on the collision systems, but also, to some extent, provides a means to explore the fine structure inside deformed nuclei. Additionally, nonpolarized collisions are further discussed. These results contribute to the understanding of the geometric effects in nuclear reactions, and aid in the exploration of other information on reaction systems, such as the equation of state and nuclear high-momentum tail.

Flow distribution analysis as a probe of nuclear deformation

Article

Sep 2023

We study the flow harmonic distribution in collisions of deformed nuclei. To do this, we use the standard Gram-Charlier method to find the higher-order correction to the well-known Bessel-Gaussian distribution. We find that, apart from the necessity of including a shift parameter v¯n, the modified flow distribution accurately describes the distribution of flow harmonics in a system formed after collisions of deformed nuclei with quadrupole and octupole deformity. Using the shifted radial distribution arising from this method, we scrutinize the effect of deformation on flow distribution. We also propose a way to measure v¯2 in deformed-nucleus collisions.

Separating the Impact of Nuclear Skin and Nuclear Deformation in High-Energy Isobar Collisions

Article

Jul 2023

Bulk nuclear structure properties, such as radii and deformations, leave distinct signatures in the final state of relativistic heavy-ion collisions. Isobaric collisions offer an easy route to establish explicit connections between the colliding nuclei’s structure and the observable outcomes. Here, we investigate the effects of nuclear skin thickness and nuclear deformations on the elliptic flow (v2) and its fluctuations in high-energy Ru96+Ru96 and Zr96+Zr96 collisions. Our findings reveal that the difference in skin thickness between these isobars only influences the inherent ellipticity of the collision systems, v2rp. In contrast, differences in nuclear deformations solely impact the fluctuations of v2 around v2rp. Hence, we have identified a data-driven method to disentangle the effects of nuclear skin and nuclear deformations, marking a significant step toward assessing the consistency of nuclear phenomena across energy scales.

Impact of nuclear deformation on collective flow observables in relativistic U+U collisions

Article

Mar 2023
EUR PHYS J A

Niseem Magdy Abdelrahman

\sqrt{\textit{s}_{NN}}

= 193 GeV. The multiparticle azimuthal cumulant method is used to investigate the sensitivity of (I) a set of quantities that are sensitive to both initial- and final-state effects as well as (II) a set of dimensionless quantities that are more sensitive to initial-state effects to the Uranium nuclei quadrupole shape deformation. We find that the combined use of the flow harmonics, flow fluctuations and correlations, linear and non-linear flow correlations to the quadrangular flow harmonic, and the correlations between elliptic flow and the mean-transverse momentum could serve to constrain the nuclear deformation of the Uranium nuclei. Therefore, a comprehensive set of measurements of such observables can provide a quantifying tool for the quadrupole shape deformation via data-model comparisons.

Accessing the shape of atomic nuclei with relativistic collisions of isobars

Article

Oct 2021

Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to gain precise knowledge of the geometric shape of atomic nuclei.

Structure of

^{128,129,130}

Xe through multi-reference energy density functional calculations

Article

Sep 2022
EUR PHYS J A

Recently, values for the Kumar quadrupole deformation parameters of the nucleus

^{130}

^{129}

^{128,129,130}

^{129}

Xe reveals some deficiencies of the effective interaction.

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Article

Apr 2022

Jiangyong Jia

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β2 and triaxiality γ. The deformation can be accessed in high-energy heavy ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ɛ2 and the density gradient d⊥ in the initial state. Using an analytical estimate and a Glauber model, I show that the variances 〈ɛ22〉 or 〈(δd⊥/d⊥)2〉 and skewnesses 〈ɛ22δd⊥/d⊥〉 or 〈(δd⊥/d⊥)3〉 have a simple analytical form of a′+b′β22 and a′+[b′+c′cos(3γ)]β23, respectively. From these, I constructed several normalized skewnesses to isolate the γ dependence from that of β2 and show that the correlations between a normalized skewness and a variance can constrain simultaneously β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [pT] of final-state particles, v2∝ɛ2 and δ[pT]/[pT]∝δd⊥/d⊥, similar conclusions are also expected for the variances and skewnesses of v2 and [pT], i.e., a+bβ22 for 〈v22〉 and 〈(δ[pT]/[pT])2〉 and a+[b+ccos(3γ)]β23 for 〈v22δ[pT]/[pT]〉 or 〈(δ[pT]/[pT])3〉. My findings motivate a dedicated system scan of high-energy heavy ion collisions at RHIC and LHC to measure triaxiality of atomic nuclei: one first determines the coefficients b and c by collisions of isobaric near prolate nuclei, cos(3γ)≈1, and near oblate nuclei, cos(3γ)≈−1, with known β2 values, followed by collisions of other species of interest with similar mass number. The (β2,γ) values for this species can be inferred directly from the measured variance and skewness observables from these collisions. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

Shape of atomic nuclei in heavy ion collisions

Article

Jan 2022

Jiangyong Jia

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flows vn are linearly related to the strengths of the multipole shape of the distribution of nucleons in the transverse plane, ɛn: vn∝ɛn. The ɛn, for n=1,2,3,4, are sensitive to the shapes of the colliding ions, characterized by the quadrupole β2, octupole β3, and hexadecapole β4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, 〈ɛn2〉=an′+bn′βn2, for events in a fixed centrality. The 〈ɛ12〉 has a contribution from β3 and β4, and 〈ɛ32〉 from β4. In ultracentral collisions, there are little cross contributions between β2 and ɛ3 and between β3 and ɛ2, but clear cross contributions are present in noncentral collisions. Additionally, 〈ɛn2〉 are insensitive to nonaxial shape parameters such as the triaxiality. This is good news because the measurements of v2, v3, and v4 can be used to constrain simultaneously the β2, β3, and β4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical an′, to obtain a simple equation that relates the βn of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale (<10−24s) much shorter than probed by low-energy nuclear structure physics (<10−21s), which ultimately may provide information complementary to that obtained in the nuclear structure experiments.

Probing the Neutron Skin with Ultrarelativistic Isobaric Collisions

Article

Nov 2020

Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.

Possible octupole deformation of Pb 208 and the ultracentral v 2 to v 3 puzzle

Article

Nov 2020

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of nonspherical nuclei. In the case of Xe129 collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In Pb208 collisions a discrepancy exists in similar centralities, where either elliptic flow is overpredicted or triangular flow is underpredicted by hydrodynamic models; this is known as the v2-to-v3 puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that Pb208 nuclei could have a pear-shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we reexamine the v2-to-v3 puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio v34/v32 and comparing two different hydrodynamic models. We find that while an octupole deformation would slightly improve the ratio between v2 and v3, it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with β3≲0.0375 for Pb208, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. The v2-to-v3 puzzle remains a challenge for hydrodynamic models.

Constraining the quadrupole deformation of atomic nuclei with relativistic nuclear collisions

Article

Aug 2020

Giuliano Giacalone

Preliminary data by the STAR collaboration at the BNL Relativistic Heavy Ion Collider shows that the elliptic flow, v2, and the average transverse momentum, 〈pt〉, of final-state hadrons produced in high-multiplicity U238+U238 collisions are negatively correlated. This observation brings experimental evidence of a significant prolate deformation, β≈0.3, in the colliding U238 nuclei. I show that a quantitative description of this new phenomenon can be achieved within the hydrodynamic framework of heavy-ion collisions, and that thus such kind of data in the context of high-energy nuclear experiments can help constrain the quadrupole deformation of the colliding species.

Multiparticle azimuthal correlations for extracting event-by-event elliptic and triangular flow in Au + Au collisions at s N N = 200 GeV

Article

Full-text available

Feb 2019

We present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity 1<|η|<3 in Au + Au collisions at sNN=200 GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients v2{2},v2{4},v2{6}, and v2{8}, and triangular flow coefficients v3{2} and v3{4}. Using the small-variance limit, we estimate the mean and variance of the event-by-event v2 distribution from v2{2} and v2{4}. In a complementary analysis, we also use a folding procedure to study the distributions of v2 and v3 directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final-state momentum distributions are discussed.

Non-Gaussian elliptic-flow fluctuations in PbPb collisions at s NN = 5.02 TeV

Article

Full-text available

Feb 2019
PHYS LETT B

Event-by-event fluctuations in the elliptic-flow coefficient v2 are studied in PbPb collisions at √sNN = 5.02 TeV using the CMS detector at the CERN LHC. Elliptic-flow probability distributions p(v2) for charged particles with transverse momentum 0.3 < pT < 3.0 GeV/c and pseudorapidity |η| < 1.0 are determined for different collision centrality classes. The moments of the p(v2) distributions are used to calculate the v2 coefficients based on cumulant orders 2, 4, 6, and 8. A rank ordering of the higher-order cumulant results and nonzero standardized skewness values obtained for the p(v2) distributions indicate nonGaussian initial-state fluctuations. Bessel–Gaussian and elliptic power fits to the flow distributions are studied to characterize the initial-state spatial anisotropy.

Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at s N N = 5.02

\sqrt{s_{\mathrm{NN}}}=5.02

and 2.76 TeV

Article

Full-text available

Jul 2018
J HIGH ENERGY PHYS

A bstract Measurements of anisotropic flow coefficients with two- and multi-particle cumulants for inclusive charged particles in Pb-Pb collisions at

\sqrt{s_{\mathrm{NN}}}=5.02

s N N = 5.02 and 2.76 TeV are reported in the pseudorapidity range | η | < 0.8 and transverse momentum 0.2 < p T < 50 GeV/ c . The full data sample collected by the ALICE detector in 2015 (2010), corresponding to an integrated luminosity of 12.7 (2.0) μ b ⁻¹ in the centrality range 0-80%, is analysed. Flow coefficients up to the sixth flow harmonic ( v 6 ) are reported and a detailed comparison among results at the two energies is carried out. The p T dependence of anisotropic flow coefficients and its evolution with respect to centrality and harmonic number n are investigated. An approximate power-law scaling of the form v n ( p T ) ∼ p T n /3 is observed for all flow harmonics at low p T (0.2 < p T < 3 GeV/ c ). At the same time, the ratios v n / v m n / m are observed to be essentially independent of p T for most centralities up to about p T = 10 GeV/ c . Analysing the differences among higher-order cumulants of elliptic flow ( v 2 ), which have different sensitivities to flow fluctuations, a measurement of the standardised skewness of the event-by-event v 2 distribution P ( v 2 ) is reported and constraints on its higher moments are provided. The Elliptic Power distribution is used to parametrise P ( v 2 ), extracting its parameters from fits to cumulants. The measurements are compared to different model predictions in order to discriminate among initial-state models and to constrain the temperature dependence of the shear viscosity to entropy-density ratio.

Anisotropic flow in Xe–Xe collisions at s NN = 5.44 TeV

Article

Full-text available

Jun 2018
PHYS LETT B

The first measurements of anisotropic flow coefficients vn for mid-rapidity charged particles in Xe–Xe collisions at sNN=5.44 TeV are presented. Comparing these measurements to those from Pb–Pb collisions at sNN=5.02 TeV, v2 is found to be suppressed for mid-central collisions at the same centrality, and enhanced for central collisions. The values of v3 are generally larger in Xe–Xe than in Pb–Pb at a given centrality. These observations are consistent with expectations from hydrodynamic predictions. When both v2 and v3 are divided by their corresponding eccentricities for a variety of initial state models, they generally scale with transverse density when comparing Xe–Xe and Pb–Pb, with some deviations observed in central Xe–Xe and Pb–Pb collisions. These results assist in placing strong constraints on both the initial state geometry and medium response for relativistic heavy-ion collisions.

Predictions for multiplicities and flow harmonics in 5.44 TeV Xe+Xe collisions at the CERN Large Hadron Collider

Article

Full-text available

Nov 2017

We present the next-to-leading-order event-by-event EKRT model predictions for the centrality dependence of the charged hadron multiplicity in the pseudorapidity interval

|\eta|\le 0.5

, and for the centrality dependence of the charged hadron flow harmonics

v_n\{2\}

obtained from 2-particle cumulants, in

\sqrt{s_{NN}}=5.44

TeV Xe+Xe collisions at the CERN Large Hadron Collider. Our prediction for the 0-5 \% central charged multiplicity is

dN_{\rm ch}/d\eta =1218\pm 46

. We also predict

v_n\{2\}

in Xe+Xe collisions to increase more slowly from central towards peripheral collisions than those in a Pb+Pb system. We find that at

10 \dots 50

\% centralities

v_2\{2\}

is smaller and

v_3\{2\}

is larger than in the Pb+Pb system while

v_4\{2\}

is of the same magnitude in both systems. We also find that the ratio of flow harmonics in Xe+Xe collisions and in Pb+Pb collisions shows a slight sensitivity to the temperature dependence of the shear-viscosity-to-entropy ratio. As we discuss here, the new nuclear mass-number systematics especially in the flow harmonics serves as a welcome further constraint for describing the space-time evolution of a heavy-ion system and for determining the shear viscosity and other transport properties of strongly interacting matter.

Hydrodynamic predictions for 5.44 TeV Xe+Xe collisions

Article

Full-text available

Nov 2017

We argue that relativistic hydrodynamics is able to make robust predictions for soft particle production in Xe+Xe collisions at the CERN Large Hadron Collider (LHC). The change of system size from Pb+Pb to Xe+Xe provides a unique opportunity to test the scaling laws inherent to fluid dynamics. Using event-by-event hydrodynamic simulations, we make quantitative predictions for several observables: Mean transverse momentum, anisotropic flow coefficients, and their fluctuations. Results are shown as function of collision centrality.

Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions

Article

Full-text available

Nov 2017

The QCD equation of state at zero baryon chemical potential is the only element of the standard dynamical framework to describe heavy ion collisions that can be directly determined from first principles. Continuum extrapolated lattice QCD equations of state have been computed using 2+1 quark flavors (up/down and strange) as well as 2+1+1 flavors to investigate the effect of thermalized charm quarks on QCD thermodynamics. Lattice results have also indicated the presence of new strange resonances that not only contribute to the equation of state of QCD matter but also affect hadronic afterburners used to model the later stages of heavy ion collisions. We investigate how these new developments obtained from first principles calculations affect multiparticle correlations in heavy ion collisions. We compare the commonly used equation of state S95n-v1, which was constructed using what are now considered outdated lattice results and hadron states, to the current state-of-the-art lattice QCD equations of state with 2+1 and 2+1+1 flavors coupled to the most up-to-date hadronic resonances and their decays. New hadronic resonances lead to an enhancement in the hadronic spectra at intermediate

p_T

. Using an outdated equation of state can directly affect the extraction of the shear viscosity to entropy density ratio,

\eta/s

, of the quark-gluon plasma and results for different flow observables. The effects of the QCD equation of state on multiparticle correlations of identified particles are determined for both AuAu

\sqrt{s_{NN}}=200

GeV and PbPb

\sqrt{s_{NN}}=5.02

TeV collisions. New insights into the

v_2\{2\}

v_3\{2\}

puzzle in ultracentral collisions are found. Flow observables of heavier particles exhibit more non-linear behavior regardless of the assumptions about the equation of state, which may provide a new way to constrain the temperature dependence of

\eta/s

Relative flow fluctuations as a probe of initial state fluctuations

Article

Full-text available

Feb 2017

Elliptic flow,

v_2

, and triangular flow,

v_3

, are to a good approximation linearly proportional to the corresponding spatial anisotropies of the initial density profile,

\varepsilon_2

and

\varepsilon_3

. Using event-by-event hydrodynamic simulations, we point out when deviations from this linear scaling are to be expected. When these deviations are negligible, relative

v_n

fluctuations are equal to relative

\varepsilon_n

fluctuations, and one can directly probe models of initial conditions using ratios of cumulants, for instance

v_n\{4\}/v_n\{2\}

. We argue that existing models of initial conditions tend to overestimate flow fluctuations in central Pb+Pb collisions, and to underestimate them in peripheral collisions. We make predictions for

v_3\{6\}

in noncentral Pb+Pb collisions, and for

v_3\{4\}

and

v_3\{6\}

in high-multiplicity p+Pb collisions.

Initial partonic eccentricity fluctuations in a multi-phase transport model

Article

Full-text available

Oct 2016

Initial partonic eccentricities in Au+Au collisions at center-of-mass energy

\sqrt{s_{NN}}

= 200 GeV are investigated using a multi-phase transport model with string melting scenario. The initial eccentricities in different order of harmonics are studied using participant and cumulant definitions. Eccentricity in terms of second-, fourth- and sixth order cumulants as a function of number of participant nucleons are compared systematically with the traditional participant definition. The ratio of the cumulant eccentricities

\varepsilon\left\{4\right\}/\varepsilon\left\{2\right\}

and

\varepsilon\left\{6\right\}/\varepsilon\left\{4\right\}

are studied in comparison with the ratio of the corresponding flow harmonics. The conversion coefficients (

v_n/\varepsilon_n

) are explored up to fourth order harmonic based on cumulant method. Furthermore, studies on transverse momentum (

p_T

) and pseudo-rapidity (

\eta

) dependencies of eccentricities and their fluctuations are presented. As in ideal hydrodynamics initial eccentricities are expected to be closely related to the final flow harmonics in relativistic heavy-ion collisions, studies of the fluctuating initial condition in the AMPT model will shed light on the tomography properties of the initial source geometry.

The skewness of elliptic flow fluctuations

Article

Full-text available

Aug 2016

Using event-by-event hydrodynamic calculations, we find that the fluctuations of the elliptic flow (

v_2

) in the reaction plane have a negative skew. Comparing the skewness of the

v_2

fluctuations to that of the initial eccentricity fluctuations, we show that skewness is the main effect that separates higher-order cumulants. Furthermore, negative skew corresponds to the hierarchy

v_2\{4\}>v_2\{6\}

observed in Pb+Pb collisions at the LHC. We describe how the skewness can be measured experimentally and show that hydrodynamics naturally reproduces its magnitude and centrality dependence.

Linear and cubic response to the initial eccentricity in heavy-ion collisions

Article

Full-text available

Nov 2015

We study the relation between elliptic flow,

v_2

and the initial eccentricity,

\varepsilon_2

, in heavy-ion collisions, using hydrodynamic simulations. Significant deviations from linear eccentricity scaling are seen in more peripheral collisions. We identify the mechanism responsible for these deviations as a cubic response, which we argue is a generic property of the hydrodynamic response to the initial density profile. The cubic response increases elliptic flow fluctuations, thereby improving agreement of initial condition models with experimental data.

Azimuthal anisotropy in U+U and Au+Au collisions at RHIC

Article

Full-text available

May 2015

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants,

v_2\{2\}

and

v_2\{4\}

, for charged hadrons from U+U collisions at

\sqrt{s_{\rm NN}}

= 193 GeV and Au+Au collisions at

\sqrt{s_{\rm NN}}

= 200 GeV. Nearly fully overlapping collisions are selected based on the amount of energy deposited by spectators in the STAR Zero Degree Calorimeters (ZDCs). Within this sample, the observed dependence of

v_2\{2\}

on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. An initial-state model with gluon saturation describes the slope of

v_2\{2\}

as a function of multiplicity in central collisions better than one based on Glauber with a two-component multiplicity model.

Viscous Effects on the Mapping of the Initial to Final State in Heavy Ion Collisions

Article

Full-text available

Nov 2014

We investigate the correlation between various aspects of the initial geometry of heavy ion collisions at the Relativistic Heavy Ion Collider energies and the final anisotropic flow, using v-USPhydro, a 2+1 event-by-event viscous relativistic hydrodynamical model. We test the extent of which shear and bulk viscosity affect the prediction of the final flow harmonics,

v_n

, from the initial eccentricities,

\varepsilon_n

. We investigate in detail the flow harmonics

v_1

through

v_5

where we find that

v_1

v_4

, and

v_5

are dependent on more complicated aspects of the initial geometry that are especially important for the description of peripheral collisions, including a non-linear dependence on eccentricities as well as a dependence on shorter-scale features of the initial density. Furthermore, we compare our results to previous results from NeXSPheRIO, a 3+1 relativistic ideal hydrodynamical model that has a non-zero initial flow contribution, and find that the combined contribution from 3+1 dynamics and non-zero, fluctuating initial flow decreases the predictive ability of the initial eccentricities, in particular for very peripheral collisions, but also disproportionately in central collisions.

Parameterization of Deformed Nuclei for Glauber Modeling in Relativistic Heavy Ion Collisions

Article

Full-text available

Sep 2014
PHYS LETT B

The density distributions of large nuclei are typically modeled with a Woods-Saxon distribution characterized by a radius

R_{0}

and skin depth a. Deformation parameters

\beta

are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics

R_{0}(1+\beta_2Y^0_2+\beta_4Y^0_4)

. But when a nucleus is non-spherical, the

R_{0}

and a inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods-Saxon distribution. In addition, the

\beta_2

values typically derived from the reduced electric quadrupole transition probability B(E2)

\uparrow

are not directly related to the

\beta_2

values used in the spherical harmonic expansion. B(E2)

\uparrow

is more accurately related to the intrinsic quadrupole moment

Q_{0}

than to

\beta_2

. One can however calculate

Q_0

for a given

\beta_2

and then derive B(E2)

\uparrow

from

Q_0

. In this paper we calculate and tabulate the

R_0

, a, and

\beta_2

values that when used in a Woods-Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the eccentricity

\varepsilon_2

and

\varepsilon_3

with the new and old parameters. We find that

\varepsilon_3

is particularly senstive to a.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at

\sqrt{s_{NN}}=2.76

TeV with the ATLAS detector

Article

Full-text available

Aug 2014

ATLAS measurements of the azimuthal anisotropy in lead-lead collisions at

\sqrt{s_{NN}}=2.76

TeV are shown using a dataset of approximately 7

\mu

^{-1}

collected at the LHC in 2010. The measurements are performed for charged particles with transverse momenta

0.5<p_T<20

GeV and in the pseudorapidity range

|\eta|<2.5

. The anisotropy is characterized by the Fourier coefficients,

v_n

, of the charged-particle azimuthal angle distribution for n = 2-4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the

v_n

coefficients are presented. The elliptic flow,

v_2

, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients,

v_3

and

v_4

, are determined with two- and four-particle cumulants. Flow harmonics

v_n

measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to

v_n

measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multi-particle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Improved version of the PHOBOS Glauber Monte Carlo

Article

Full-text available

Aug 2014

Glauber models are used to calculate geometric quantities in the initial state of heavy ion collisions, such as impact parameter, number of participating nucleons and initial eccentricity. Experimental heavy-ion collaboration, in particular at RHIC and LHC, use Glauber Model calculations for various geometric observables. In this document, we describe the assumptions inherent to the approach, and provide an updated implementation (v2) of the Monte Carlo based Glauber Model calculation, which originally was used by the PHOBOS collaboration. The main improvement w.r.t. the earlier version (arXiv:0805.4411) are the inclusion of tritium, Helium-3, and Uranium, as well as the treatment of deformed nuclei and Glauber-Gribov fluctuations of the proton in p+A collisions. A users' guide (updated to reflect changes in v2) is provided for running various calculations.

Azimuthal Anisotropy Distributions in High-Energy Collisions

Article

Full-text available

Aug 2014
PHYS LETT B

Elliptic flow in ultrarelativistic heavy-ion collisions results from the hydrodynamic response to the spatial anisotropy of the initial density profile. A long-standing problem in the interpretation of flow data is that uncertainties in the initial anisotropy are mingled with uncertainties in the response. We argue that the non-Gaussianity of flow fluctuations in small systems can be used to disentangle the initial state from the response. We apply this method to recent measurements of anisotropic flow in Pb+Pb and p+Pb collisions at the LHC. The response coefficient is found to decrease mildly as the system becomes smaller. This mild decrease is consistent with a low value of the ratio of viscosity over entropy.

Continuous description of fluctuating eccentricities

Article

Full-text available

May 2014
PHYS LETT B

We consider the initial energy density in the transverse plane of a high energy nucleus-nucleus collision as a random field \rho(\x), whose probability distribution

P[\rho]

, the only ingredient of the present description, encodes all possible sources of fluctuations. We argue that it is a local Gaussian, with a short-range 2-point function, and that the fluctuations relevant for the calculation of the eccentricities that drive the anisotropic flow have small relative amplitudes. In fact, this 2-point function, together with the average density, contains all the information needed to calculate the eccentricities and their variances, and we derive general model independent expressions for these quantities. The short wavelength fluctuations are shown to play no role in these calculations, except for a renormalization of the short range part of the 2-point function. As an illustration, we compare to a commonly used model of independent sources, and recover the known results of this model.

Elliptic flow in U + U collisions at s NN = 200 GeV and in Pb + Pb collisions at s NN = 2.76 TeV: Prediction from a hybrid approach

Article

Full-text available

Feb 2011

We predict the elliptic flow parameter v in U+U collisions at (s{sub NN})=200 GeV and in Pb+Pb collisions at (s{sub NN})=2.76 TeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state and the subsequent hadronic stage is described by a hadron cascade model.

Triangularity and Dipole Asymmetry in Heavy Ion Collisions

Article

Full-text available

Jun 2011

We introduce a cumulant expansion to parametrize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion the cumulants characterize the triangularity and the dipole asymmetry of the initial entropy distribution. We show that for midperipheral collisions the orientation angle of the dipole asymmetry psi1,3 has a 20% preference out of plane. This leads to a small net v1 out of plane. In peripheral and midcentral collisions the orientation angles psi1,3 and psi3,3 are strongly correlated, but this correlation disappears towards central collisions. We study the ideal hydrodynamic response to these cumulants and determine the associated v1/ε1 and v3/ε3 for a massless ideal gas equation of state. The space time development of v1 and v3 is clarified with figures. These figures show that v1 and v3 develop toward the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for v3 are provisionally compared to Alver and Roland fit of STAR inclusive two-particle correlation functions. Finally, we propose to measure the v1 associated with the dipole asymmetry and the correlations between psi1,3 and psi3,3 by measuring a two-particle correlation with respect to the participant plane . The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration . This experimental measurement would provide convincing evidence for the hydrodynamic and geometric interpretation of two-particle correlations at RHIC.

Photoactivation experiment on^{197} Au and its implications for the dipole strength in heavy nuclei

Article

Full-text available

Nov 2008

The 197Au(γ,n) reaction is used as an activation standard for photodisintegration studies on astrophysically relevant nuclei. At the bremsstrahlung facility of the superconducting electron accelerator ELBE (Electron Linear accelerator of high Brilliance and low Emittance) of Forschungszentrum Dresden-Rossendorf, photoactivation measurements on 197Au have been performed with bremsstrahlung endpoint energies from 8.0 to 15.5 MeV. The measured activation yield is compared with previous experiments as well as with calculations using Hauser-Feshbach statistical models. It is shown that the experimental data are best described by a two-Lorentzian parametrization with taking the axial deformation of 197Au into account. The experimental 197Au(γ,n) reaction yield measured at ELBE via the photoactivation method is found to be consistent with previous experimental data using photon scattering or neutron detection methods.

Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions

Article

Full-text available

Jan 2008

In this paper, we investigate various ways of defining the initial source eccentricity using the Monte Carlo Glauber (MCG) approach. In particular, we examine the participant eccentricity, which quantifies the eccentricity of the initial source shape by the major axes of the ellipse formed by the interaction points of the participating nucleons. We show that reasonable variation of the density parameters in the Glauber calculation, as well as variations in how matter production is modeled, do not significantly modify the already established behavior of the participant eccentricity as a function of collision centrality. Focusing on event-by-event fluctuations and correlations of the distributions of participating nucleons we demonstrate that, depending on the achieved event-plane resolution, fluctuations in the elliptic flow magnitude

v_2

lead to most measurements being sensitive to the root-mean-square, rather than the mean of the

v_2

distribution. Neglecting correlations among participants, we derive analytical expressions for the participant eccentricity cumulants as a function of the number of participating nucleons, \Npart,keeping non-negligible contributions up to \ordof{1/\Npart^3}. We find that the derived expressions yield the same results as obtained from mixed-event MCG calculations which remove the correlations stemming from the nuclear collision process. Most importantly, we conclude from the comparison with MCG calculations that the fourth order participant eccentricity cumulant does not approach the spatial anisotropy obtained assuming a smooth nuclear matter distribution. In particular, for the Cu+Cu system, these quantities deviate from each other by almost a factor of two over a wide range in centrality.

Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions

Article

Full-text available

Dec 2012

Relativistic dissipative fluid dynamics is a common tool to describe the space-time evolution of the strongly interacting matter created in ultrarelativistic heavy-ion collisions. For a proper comparison to experimental data, fluid-dynamical calculations have to be performed on an event-by-event basis. Therefore, fluid dynamics should be able to reproduce, not only the event-averaged momentum anisotropies,

<v_{n}>

, but also their distributions. In this paper, we investigate the event-by-event distributions of the initial-state and momentum anisotropies

\epsilon_n

and

v_n

, and their correlations. We demonstrate that the event-by-event distributions of relative

v_n

fluctuations are almost equal to the event-by-event distributions of corresponding

\epsilon_n

fluctuations, allowing experimental determination of the relative anisotropy fluctuations of the initial state. Furthermore, the correlation

c(v_2,v_4)

turns out to be sensitive to the viscosity of the fluid providing an additional constraint to the properties of the strongly interacting matter.

Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions

Article

Full-text available

Nov 2011

We investigate how the initial geometry of a heavy-ion collision is transformed into final flow observables by solving event-by-event ideal hydrodynamics with realistic fluctuating initial conditions. We study quantitatively to what extent anisotropic flow (v_n) is determined by the initial eccentricity epsilon_n for a set of realistic simulations, and we discuss which definition of epsilon_n gives the best estimator of v_n. We find that the common practice of using an r^2 weight in the definition of varepsilon_n in general results in a poorer predictor of v_n than when using r^n weight, for n > 2. We similarly study the importance of additional properties of the initial state. For example, we show that in order to correctly predict v_4 and v_5 for non-central collisions, one must take into account nonlinear terms proportional to (epsilon_2)^2 and (epsilon_2)*(epsilon_3), respectively. We find that it makes no difference whether one calculates the eccentricities over a range of rapidity, or in a single slice at z=0, nor is it important whether one uses an energy or entropy density weight. This knowledge will be important for making a more direct link between experimental observables and hydrodynamic initial conditions, the latter being poorly constrained at present.

Predictions of Elliptic flow and nuclear modification factor from 200 GeV U + U collisions at RHIC

Article

Full-text available

Jul 2009
PHYS LETT B

Predictions of elliptic flow (

v_2

) and nuclear modification factor (

R_{AA}

) are provided as a function of centrality in U + U collisions at

\sqrt{s_{_{NN}}}

= 200 GeV. Since the

^{238}

U nucleus is naturally deformed, one could adjust the properties of the fireball, density and duration of the hot and dense system, for example, in high energy nuclear collisions by carefully selecting the colliding geometry. Within our Monte Carlo Glauber based approach, the

v_2

with respect to the reaction plane

v_2^{RP}

in U + U collisions is consistent with that in Au + Au collisions, while the

v_2

with respect to the participant plane

v_2^{PP}

increases

\sim

30-60% at top 10% centrality which is attributed to the larger participant eccentricity at most central U + U collisions. The suppression of

R_{AA}

increases and reaches

\sim

0.1 at most central U + U collisions that is by a factor of 2 more suppression compared to the central Au + Au collisions due to large size and deformation of Uranium nucleus. Comment: 14 pages, 6 figures; typo added, fix the systematic error on the v2^{PP}

System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow

Article

Full-text available

Jul 2007

This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.

Kurtosis of elliptic flow fluctuations

Article

Jan 2019

Elliptic flow (v2) in ultrarelativistic nucleus-nucleus collisions fluctuates event to event, both in magnitude and in orientation with respect to the reaction plane. Even though the reaction plane is not known event to event in experiment, we show that the statistical properties of v2 fluctuations in the reaction plane can be precisely extracted from experimental data. Previous studies have shown how to measure the mean, variance and skewness using the first three cumulants v2{2}, v2{4}, and v2{6}. We complement these studies by providing a formula for the kurtosis, which requires an accurate determination of the next cumulant v2{8}. Using existing data, we show that the kurtosis is positive for most centralities, in contrast with the kurtosis of triangular flow fluctuations, which is negative. We argue that these features are robust predictions of fluid-dynamical models.

Centrality or volume fluctuations in heavy-ion collisions

Article

Mar 2018

Centrality or volume fluctuations (VF) is one of the main uncertainties for interpreting the centrality dependence of many experimental observables. The VF is constrained by centrality selection based on particle multiplicity in a reference subevent, and contributes to observables measured in another subevent. Using a Glauber-based independent source model, we study the influence of VF on several distributions of multiplicity N and eccentricities

\epsilon_n

: p(N),

p(\epsilon_n)

p(\epsilon_n,\epsilon_m)

and

p(N,\epsilon_n)

, where the effects of VF is quantified using multi-particle cumulants of these distributions. In mid-central collisions, a general relation is established between the multiplicity fluctuation and resulting VF in the reference subevent. In ultra-central collisions, where distribution of particle production sources is strongly distorted, we find these cumulants exhibit rich sign-change patterns, due to observable-dependent non-Gaussianity in the underlying distributions. The details of sign-change pattern change with the size of the collision systems. Simultaneous comparison on these different types cumulants between model prediction and experimental data can be used to constrain the VF and particle production mechanism in heavy-ion collisions. Since the concept of centrality and VF are expected to fluctuate in the longitudinal direction within a single event, we propose to use pseudorapidity-separated subevent cumulant method to explore the nature of intra-event fluctuations of centrality and collective dynamics. The subevent method can be applied for any bulk observable that is sensitive to centrality, and has the potential to separate different mechanisms for multiplicity and flow fluctuations happening at different time scales. The forward detector upgrades at RHIC and LHC will greatly enhance such studies in the future.

Effects of initial-state dynamics on collective flow within a coupled transport and viscous hydrodynamic approach

Article

Oct 2017

We evaluate the effects of preequilibrium dynamics on observables in ultrarelativistic heavy-ion collisions. We simulate the initial nonequilibrium phase within A MultiPhase Transport (AMPT) model, while the subsequent near-equilibrium evolution is modeled using (2+1)-dimensional relativistic viscous hydrodynamics. We match the two stages of evolution carefully by calculating the full energy-momentum tensor from AMPT and using it as input for the hydrodynamic evolution. With a shear viscosity to entropy density ratio of 0.12, our model describes quantitatively a large set of experimental data on Pb+Pb collisions at the Large Hadron Collider(LHC) over a wide range of centrality: differential anisotropic flow

v_n(p_T) ~(n=2-6)

, event-plane correlations, correlation between

v_2

and

v_3

, and cumulant ratio

v_2\{4\}/v_2\{2\}

Relating centrality to impact parameter in nucleus-nucleus collisions

Article

Jul 2017

In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision using a single observable, say n, typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between n and the impact parameter, b, of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about b can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of n is Gaussian for a fixed b, we show that the probability distribution of impact parameter in a narrow centrality bin can be accurately reconstructed up to

5\%

centrality. We apply our methodology to Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) data. We propose a simple measure of the precision of the centrality determination, which can be used to compare different experiments.

Standardized Cumulants of Flow Harmonic Fluctuations

Article

Apr 2017

The distribution of flow harmonics in heavy ion experiment can be characterized by standardized cumulants. We first use the Elliptic-Power distribution together with the hydrodynamic linear response to study the two dimensional standardized cumulants of elliptic and triangular flow (

v_2

and

v_3

) distribution. Using this, the 2q-particle correlation functions

c_3\{2\}

c_3\{4\}

and

c_3\{6\}

, are related to the second, forth and sixth standardized cumulants of the

v_3

distribution, respectively. The

c_{n}\{2q\}

can be also written in terms of cumulants

v_n\{2q\}

. Specifically,

-(v_3\{4\}/v_3\{2\})^4

turns out to be the kurtosis of the

v_3

event-by-event fluctuation distribution. We introduce a new probability distribution

p(v_3)

with

v_3\{2\}

, kurtosis and sixth order standardized cumulant as its free parameters. Compared to the Gaussian distribution, it indicates a more accurate fit with experimental results. Finally, we compare the kurtosis obtained from simulation with that of extracted from experimental data for the

v_3

distribution.

Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium

Article

May 2016

We quantitatively estimate properties of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions utilizing Bayesian statistics and a multi-parameter model-to-data comparison. The study is performed using a recently developed parametric initial condition model, TRENTO, which interpolates among a general class of particle production schemes, and a modern hybrid model which couples viscous hydrodynamics to a hadronic cascade. We calibrate the model to multiplicity, transverse momentum, and flow data and report constraints on the parametrized initial conditions and the temperature-dependent transport coefficients of the quark-gluon plasma. We show that initial entropy deposition is consistent with a saturation-based picture, extract a relation between the minimum value and slope of the temperature-dependent specific shear viscosity, and find a clear signal for a nonzero bulk viscosity.

Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions

Article

Jul 2015

We introduce a new parametric initial-condition model for high-energy nuclear collisions based on eikonal entropy deposition via a "reduced-thickness" function. The model simultaneously describes experimental proton-proton, proton-nucleus, and nucleus-nucleus multiplicity distributions and generates nucleus-nucleus eccentricity harmonics consistent with experimental flow constraints. In addition, the model is compatible with ultracentral uranium-uranium data unlike existing models that include binary collision terms.

Nuclear ground-state masses and deformations: FRDM(2012)

Article

Aug 2015

We tabulate the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground-state microscopic corrections, and nuclear ground-state deformations of 9318 nuclei ranging from

^{16}

O to A=339. The calculations are based on the finite-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model. Relative to our FRDM(1992) mass table in {\sc Atomic Data and Nuclear Data Tables} [{\bf 59} 185 (1995)], the results are obtained in the same model, but with considerably improved treatment of deformation and fewer of the approximations that were necessary earlier, due to limitations in computer power. The more accurate execution of the model and the more extensive and more accurate experimental mass data base now available allows us to determine one additional macroscopic-model parameter, the density-symmetry coefficient L, which was not varied in the previous calculation, but set to zero. Because we now realize that the FRDM is inaccurate for some highly deformed shapes occurring in fission, because some effects are derived in terms of perturbations around a sphere, we only adjust its macroscopic parameters to ground-state masses. The values of ten constants are determined directly from an optimization to fit ground-state masses of 2149 nuclei ranging from

^{16}

O to

^{265}_{106}

Sg and

^{264}_{108}

Hs. The error of the mass model is 0.5595~MeV. We also provide masses in the FRLDM, which in the more accurate treatments now has an error of 0.6618 MeV. But in contrast to the FRDM, it is suitable for studies of fission and has been extensively so applied elsewhere, with FRLDM(2002) constants. The FRLDM(2012) fits 31 fission barrier heights from

^{70}

Se to

^{252}

Cf with a root-mean-square deviation of 1.052 MeV.

Intrinsic Fluctuations of the Proton Saturation Momentum Scale in High Multiplicity p+p Collisions

Article

Aug 2015
NUCL PHYS A

High multiplicity events in p+p collisions are studied using the theory of the Color Glass Condensate. We show that intrinsic fluctuations of the proton saturation momentum scale are needed in addition to the sub-nucleonic color charge fluctuations to explain the very high multiplicity tail of distributions in p+p collisions. The origin of such intrinsic fluctuations are presumably non-perturbative in nature. Classical Yang Mills simulations using the IP-Glasma model are performed to make quantitative estimations. We find that fluctuations as large as

\cal O

(1) of the average values of the saturation momentum scale can lead to rare high multiplicity events seen in p+p data at RHIC and LHC energies. Using the available data on multiplicity distributions we try to constrain the distribution of the proton saturation momentum scale and make predictions for the multiplicity distribution in 13 TeV p+p collisions.

Event-by-event fluctuations in perturbative QCD + saturation + hydro model: pinning down QCD matter shear viscosity in ultrarelativistic heavy-ion collisions

Article

May 2015

We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order perturbative QCD using a saturation conjecture to control soft particle production, and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries, against the LHC and RHIC measurements. We compare also the computed event-by-event probability distributions of relative fluctuations of elliptic flow, and event-plane angle correlations, with the experimental data from Pb+Pb collisions at the LHC. We show how such a systematic multi-energy and multi-observable analysis tests the initial state calculation and the applicability region of hydrodynamics, and in particular how it constrains the temperature dependence of the shear viscosity-to-entropy ratio of QCD matter in its different phases in a remarkably consistent manner.

Initial-state geometry and fluctuations in Au + Au, Cu + Au, and U + U collisions at energies available at the BNL Relativistic Heavy Ion Collider

Article

Jun 2014

We study within the IP-Glasma and two-component MC-Glauber models the effects of initial-state geometry and fluctuations on multiplicities and eccentricities for several collision species at the Relativistic Heavy Ion Collider (RHIC). These include copper-gold (Cu + Au), gold-gold (Au + Au), and uranium-uranium (U + U) collisions. The multiplicity densities per participant pair are very similar in all systems studied. Ellipticities vary strongly between collision systems, most significantly for central collisions, while fluctuation driven odd moments vary little between systems. Event-by-event distributions of eccentricities in mid-central collisions are wider in Cu + Au relative to Au + Au and U + U systems. An anticorrelation between multiplicity and eccentricity is observed in ultracentral U + U collisions which is weaker in the IP-Glasma model than the two-component MC-Glauber model. In ultracentral Au + Au collisions the two models predict opposite signs for the slope of this correlation. Measurements of elliptic flow as a function of multiplicity in such central events can therefore be used to discriminate between models with qualitatively different particle production mechanisms.

Collision Geometry and Flow in Uranium+Uranium Collisions

Article

Feb 2015

Using event-by-event viscous fluid dynamics to evolve fluctuating initial density profiles from the Monte-Carlo Glauber model for U+U collisions, we report a "knee"-like structure in the elliptic flow as a function of collision centrality, located near 0.5% centrality as measured by the final charged multiplicity. This knee is due to the preferential selection of tip-on-tip collision geometries by a high-multiplicity trigger. Such a knee structure is not seen in the STAR data. This rules out the two-component MC-Glauber model for initial energy and entropy production. An enrichment of tip-tip configurations by triggering solely on high-multiplicity in the U+U collisions thus does not work. On the other hand, using the Zero Degree Calorimeters (ZDCs) coupled with event-shape engineering, we identify the selection purity of body-body and tip-tip events in the full-overlap U+U collisions. With additional constraints on the asymmetry of the ZDC signals one can further increases the probability of selecting tip-tip events in U+U collisions.

GLISSANDO 2: GLauber initial-state simulation and mOre..., ver. 2

Article

Oct 2013
COMPUT PHYS COMMUN

We present an extended version of GLISSANDO, a Monte-Carlo generator for Glauber-like models of the initial stage of relativistic heavy-ion collisions. The increased functionality of the code incorporates a parametrization of shape of nuclei, including light nuclei needed in the NA61 experiment, the nuclear deformation, a possibility of using correlated distributions of nucleons in nuclei read from external files, an option of overlaying distributions of produced particles dependent on the space-time rapidity, the inclusion of the core-corona effect, or the output of the source distributions that can be used in event-by-event hydrodynamics. Together with other features, such as incorporation of various variants of Glauber models, or the implementation of a realistic NN collision profile, the generator offers a realistic and practical approach to describe the early phase of the collision in 3+1 dimensions; the predictions may later be used in modeling the intermediate evolution phase, e.g., with hydrodynamics. The software is integrated with the ROOT platform. The supplied scripts compute and plot numerous features of the distributions, such as the multiplicity distributions and centrality classes, harmonic asymmetry coefficients and their correlations, forward-backward correlations, etc. The code can also be used for the proton-nucleus and deuteron-nucleus collisions.

Universal Fluctuation-Driven Eccentricities in Proton-Proton, Proton-Nucleus, and Nucleus-Nucleus Collisions

Article

Dec 2013

We show that the statistics of fluctuation-driven initial-state anisotropies in proton-nucleus and nucleus-nucleus collisions is to a large extent universal. We propose a simple parameterization for the probability distribution of the Fourier coefficient

\varepsilon_n

in harmonic n, which is in good agreement with Monte-Carlo simulations. Our results provide a simple explanation for the 4-particle cumulant of triangular flow measured in Pb-Pb collisions, and for the 4-particle cumulant of elliptic flow recently measured in p-Pb collisions. Both arise as natural consequences of the condition that initial anisotropies are bounded by unity. We argue that the initial rms anisotropy in harmonic n can be directly extracted from the measured ratio

v_n\{4\}/v_n\{2\}

: this gives direct access to a property of the initial density profile from experimental data. We also make quantitative predictions for the small lifting of degeneracy between

v_n\{4\}

v_n\{6\}

and

v_n\{8\}

. Our result support the picture that long-range correlations observed in p-Pb collisions at the LHC originate from collective flow proportional to the initial anisotropy.

Influence of initial fluctuations on geometry measures in relativistic U-U and Cu-Au collisions

Article

Nov 2012

In the framework of the Glauber approach we investigate the influence of the initial fluctuations on various measures of the initial-state geometry in 63Cu+197Au and 238U+238U relativistic ion collisions. Comparing variants of Glauber model (the wounded-nucleon model, the mixed model, and the hot-spot model) we indicate sensitivity of certain observables, in particular for the azimuthal eccentricity parameters as well as for the correlation of directions of the principal axes associated with the Fourier components. We apply GLISSANDO in our analysis.

Gluon Saturation Effects in Relativistic U+U Collisions

Article

Jul 2006
PHYS LETT B

We examine entropy production in relativistic U + U collisions on the basis of a color glass condensate (CGC) type picture as implemented in the Kharzeev–Levin–Nardi model (KLN). In this framework, we find that the peak entropy density produced in tip-on-tip U + U collisions is about 30% greater than that seen in central Au + Au collisions. Although the resulting difference in the produced charged particle multiplicity between tip-on-tip and side-on-side collisions is smaller than that predicted by previous Glauber model estimates, it is still large enough to allow for experimental discrimination between average orientations of the uranium nuclei. We also point out that in the saturation/CGC approach the collision geometry plays a more important role than previously believed, and that the observed centrality dependence of the produced particle multiplicity per participant in Au + Au collisions can be qualitatively reproduced even without running coupling effects.

Fluctuating Glasma Initial Conditions and Flow in Heavy Ion Collisions

Article

Feb 2012

We compute initial conditions in heavy-ion collisions within the Color Glass Condensate (CGC) framework by combining the impact parameter dependent saturation model (IP-Sat) with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this IP-Glasma description includes quantum fluctuations of color charges on the length-scale determined by the inverse nuclear saturation scale Q_s. The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity is close to that in a model tuned to reproduce experimental flow data. We compare transverse momentum spectra and v_(2,3,4)(p_T) of pions from different models of initial conditions using relativistic viscous hydrodynamic evolution.

Determining initial-state fluctuations from flow measurements in heavy-ion collisions

Article

Apr 2011

We present a number of independent flow observables that can be measured using multiparticle azimuthal correlations in heavy-ion collisions. Some of these observables are already well known, such as v2{2} and v2{4}, but most are new--in particular, joint correlations between v1, v2 and v3. Taken together, these measurements will allow for a more precise determination of the medium properties than is currently possible. In particular, by taking ratios of these observables, we construct quantities which are less sensitive to the hydrodynamic response of the medium, and thus more directly characterize the initial-state fluctuations of the event shape, which may constrain models for early-time, non-equilibrium QCD dynamics. We present predictions for these ratios using two Monte-Carlo models, and compare to available data.

Anisotropy as a signature of transverse collective flow

Article

Aug 1992

Jean-Yves Ollitrault

We show that anisotropies in transverse-momentum distributions provide an unambiguous signature of transverse collective flow in ultrarelativistic nucleus-nucleus collisions. We define a measure of the anisotropy from experimental observables. The anisotropy coming from collective effects is estimated quantitatively using a hydrodynamical model, and compared to the anisotropy originating from finite multiplicity fluctuations. We conclude that collective behavior could be seen in Pb-Pb collisions if a few hundred particle momenta were measured in a central event.

Anisotropic Flow and Jet Quenching in Ultrarelativistic U + U Collisions

Article

May 2005

Full-overlap U+U collisions provide significantly larger initial energy densities at comparable spatial deformation, and significantly larger deformation and volume at comparable energy density, than semi-central Au+Au collisions. We show quantitatively that this provides a long lever arm for studying the hydrodynamic behavior of elliptic flow in much larger and denser collision systems and the predicted nonlinear path-length dependence of radiative parton energy loss.

Nuclear Ground-State Masses and Deformations

Article

Aug 1993

We tabulate the atomic mass excesses and nuclear ground-state deformations of 8979 nuclei ranging from

^{16}

O to A=339. The calculations are based on the finite-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model. Relative to our 1981 mass table the current results are obtained with an improved macroscopic model, an improved pairing model with a new form for the effective-interaction pairing gap, and minimization of the ground-state energy with respect to additional shape degrees of freedom. The values of only 9 constants are determined directly from a least-squares adjustment to the ground-state masses of 1654 nuclei ranging from

^{16}

O to

^{263}

106 and to 28 fission-barrier heights. The error of the mass model is 0.669~MeV for the entire region of nuclei considered, but is only 0.448~MeV for the region above N=65. Comment: 50 pages plus 20 PostScript figures and 160-page table obtainable by anonymous ftp from t2.lanl.gov in directory masses, LA-UR-93-3083

Effects of fluctuations on the initial eccentricity from the Color Glass Condensate in heavy ion collisions

Article

Dec 2006

We introduce a modified form of the Kharzeev-Levin-Nardi (KLN) approach for nuclear collisions. The new ansatz for the unintegrated gluon distribution function preserves factorization, and the saturation scale is bound from below by that for a single nucleon. It also reproduces the correct scaling with the number of collisions at high transverse momentum. The corresponding Monte Carlo implementation allows us to account for fluctuations of the hard sources (nucleons) in the transverse plane. We compute various definitions of the eccentricity within the new approach, which are relevant for the interpretation of the elliptic flow. Our approach predicts breaking of the scaling of the eccentricity with the Glauber eccentricity at the level of about 30%.

Multiplicity distribution and source deformation in full-overlap U+U collisions

Article

Jun 2005

We present a full Monte Carlo simulation of the multiplicity and eccentricity distributions in U+U collisions at sqrt(s) = 200 A GeV. While unavoidable trigger inefficiencies in selecting full-overlap U+U collisions cause significant modifications of the multiplicity distribution shown in PRL94, 132301 (2005), a selection of source eccentricities by cutting the multiplicity distribution is still possible. Comment: 4 pages. Corrected error in Eq. (4), recalculated Figs. 2-4 and added Fig. 5 and more discussion. As a result of correcting this error, the spectator cut for a useful definition of "full-overlap" collisions had to be tightened by a factor 10, to the 0.5% of events with the lowest number of spectators

Advantage of U+U over Au+Au collisions at constant beam energy

Article

Jan 2006

Collisions of deformed uranium nuclei are studied in a Monte-Carlo Glauber model. For U+U at zero impact parameter (b=0) in the most favorable orientation (tip-to-tip), the transverse particle density (charged-particle rapidity density per weighted transverse area of the initial participant zone) increases by about 35% compared to Au+Au at b=0. To estimate the advantage of U+U over Au+Au in the context of real experiments at the Relativistic Heavy Ion Collider, we examine the effect of a range of centrality cuts on the event sample. In terms of the transverse particle density, the predicted advantage of U+U is about 16%. Comment: Title changed, ref 8 changed, two sentences are added at the end of the section III

Elliptic flow fluctuations in central collisions of spherical and deformed nuclei

Abstract

No full-text available

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