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Constraining the quadrupole deformation of atomic nuclei with relativistic nuclear collisions
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Abstract
Preliminary data by the STAR collaboration at the BNL Relativistic Heavy Ion Collider show that the elliptic flow, , and the average transverse momentum, , of final-state hadrons produced in high-multiplicity U+U collisions are negatively correlated. This observation brings experimental evidence of a significant prolate deformation, , in the colliding U nuclei. I show that a quantitative description of STAR data 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.
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Collisions between heavy atomic nuclei at ultrarelativistic energies are carried out at particle colliders to produce the quark–gluon plasma, a state of matter where quarks and gluons are not confined into hadrons, and colour degrees of freedom are liberated. This state is thought to be produced as a transient phenomenon before it fragments into thousands of particles that reach the particle detectors. Despite two decades of investigations, one of the big open challenges¹ is to obtain an experimental determination of the temperature reached in a heavy-ion collision, and a simultaneous determination of another thermodynamic quantity, such as the entropy density, that would give access to the number of degrees of freedom. Here, we obtain such a determination, utilizing state-of-the-art hydrodynamic simulations². We define an effective temperature, averaged over the spacetime evolution of the medium. Then, using experimental data, we determine this temperature and the corresponding entropy density and speed of sound in the matter created in lead–lead collisions at the Large Hadron Collider. Our results agree with first-principles calculations from lattice quantum chromodynamics³ and confirm that a deconfined phase of matter is indeed produced.
This paper describes the measurements of flow harmonics v2–v6 in 3μb−1 of Xe+Xe collisions at sNN=5.44 TeV performed using the ATLAS detector at the Large Hadron Collider (LHC). Measurements of the centrality, multiplicity, and pT dependence of the vn obtained using two-particle correlations and the scalar product technique are presented. The measurements are also performed using a template-fit procedure, which was developed to remove nonflow correlations in small collision systems. This nonflow removal is shown to have a significant influence on the measured vn at high pT, especially in peripheral events. Comparisons of the measured vn with measurements in Pb+Pb collisions and p+Pb collisions at sNN=5.02 TeV are also presented. The vn values in Xe+Xe collisions are observed to be larger than those in Pb+Pb collisions for n=2, 3, and 4 in the most central events. However, with decreasing centrality or increasing harmonic order n, the vn values in Xe+Xe collisions become smaller than those in Pb+Pb collisions. The vn in Xe+Xe and Pb+Pb collisions are also compared as a function of the mean number of participating nucleons, 〈Npart〉, and the measured charged-particle multiplicity in the detector. The v3 values in Xe+Xe and Pb+Pb collisions are observed to be similar at the same 〈Npart〉 or multiplicity, but the other harmonics are significantly different. The ratios of the measured vn in Xe+Xe and Pb+Pb collisions, as a function of centrality, are also compared to theoretical calculations.
A bstract
Multi-particle azimuthal cumulants are measured as a function of centrality and transverse momentum using 470 μ b − 1 of Pb+Pb collisions at s NN = 5 . 02 TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of harmonic flow coefficients v n and correlated fluctuations between two harmonics v n and v m . For the first time, a non-zero four-particle cumulant is observed for dipolar flow, v 1 . The four-particle cumulants for elliptic flow, v 2 , and triangular flow, v 3 , exhibit a strong centrality dependence and change sign in ultra-central collisions. This sign change is consistent with significant non-Gaussian fluctuations in v 2 and v 3 . The four-particle cumulant for quadrangular flow, v 4 , is found to change sign in mid-central collisions. Correlations between two harmonics are studied with three- and four-particle mixed-harmonic cumulants, which indicate an anti-correlation between v 2 and v 3, and a positive correlation between v 2 and v 4 . These correlations decrease in strength towards central collisions and either approach zero or change sign in ultra-central collisions. To investigate the possible flow fluctuations arising from intrinsic centrality or volume fluctuations, the results are compared between two different event classes used for centrality definitions. In peripheral and mid-central collisions where the cumulant signals are large, only small differences are observed. In ultra-central collisions, the differences are much larger and transverse momentum dependent. These results provide new information to disentangle flow fluctuations from the initial and final states, as well as new insights on the influence of centrality fluctuations.
To assess the properties of the quark–gluon plasma formed in ultrarelativistic ion collisions, the ATLAS experiment at the LHC measures a correlation between the mean transverse momentum and the flow harmonics. The analysis uses data samples of lead–lead and proton–lead collisions obtained at the centre-of-mass energy per nucleon pair of 5.02 TeV, corresponding to total integrated luminosities of 22~\upmu \text {b}^{-1} and , respectively. The measurement is performed using a modified Pearson correlation coefficient with the charged-particle tracks on an event-by-event basis. The modified Pearson correlation coefficients for the 2nd-, 3rd-, and 4th-order flow harmonics are measured in the lead–lead collisions as a function of event centrality quantified as the number of charged particles or the number of nucleons participating in the collision. The measurements are performed for several intervals of the charged-particle transverse momentum. The correlation coefficients for all studied harmonics exhibit a strong centrality evolution, which only weakly depends on the charged-particle momentum range. In the proton–lead collisions, the modified Pearson correlation coefficient measured for the 2nd-order flow harmonics shows only weak centrality dependence. The lead-lead data is qualitatively described by the predictions based on the hydrodynamical model.
Azimuthal correlations of charged particles in xenon-xenon collisions at a center-of-mass energy per nucleon pair of sNN=5.44 TeV are studied. The data were collected by the CMS experiment at the LHC with a total integrated luminosity of 3.42μb−1. The collective motion of the system formed in the collision is parametrized by a Fourier expansion of the azimuthal particle density distribution. The azimuthal anisotropy coefficients v2, v3, and v4 are obtained by the scalar-product, two-particle correlation, and multiparticle correlation methods. Within a hydrodynamic picture, these methods have different sensitivities to noncollective and fluctuation effects. The dependence of the Fourier coefficients on the size of the colliding system is explored by comparing the xenon-xenon results with equivalent lead-lead data. Model calculations that include initial-state fluctuation effects are also compared to the experimental results. The observed angular correlations provide new constraints on the hydrodynamic description of heavy ion collisions.
Ultrarelativistic collisions of heavy atomic nuclei produce an extremely hot and dense phase of matter, known as quark–gluon plasma (QGP), which behaves like a near-perfect fluid with the smallest specific shear viscosity—the ratio of the shear viscosity to the entropy density—of any known substance¹. Due to its transience (lifetime ~ 10⁻²³ s) and microscopic size (10⁻¹⁴ m), the QGP cannot be observed directly, but only through the particles it emits; however, its characteristics can be inferred by matching the output of computational collision models to experimental observations. Previous work, using viscous relativistic hydrodynamics to simulate QGP, has achieved semiquantitative constraints on key physical properties, such as its specific shear and bulk viscosity, but with large, poorly defined uncertainties2–8. Here, we present the most precise estimates so far of QGP properties, including their quantitative uncertainties. By applying established Bayesian parameter estimation methods⁹ to a dynamical collision model and a wide variety of experimental data, we extract estimates of the temperature-dependent specific shear and bulk viscosity simultaneously with related initial-condition properties. The method is extensible to other collision models and experimental data and may be used to characterize additional aspects of high-energy nuclear collisions.
In recent years the understanding of the limits of the smallest possible droplet of the quark gluon plasma has been called into question. Experimental results from both the Large Hadron Collider and the Relativistic Heavy Ion Collider have provided hints that the quark gluon plasma may be produced in systems as small as that formed in pPb or dAu collisions. Yet alternative explanations still exist from correlations arising from quarks and gluons in a color glass condensate picture. In order to resolve these two scenarios, a system-size scan has been proposed at the Large Hadron Collider for collisions of ArAr and OO. Here we make predictions for a possible future run of ArAr and OO collisions at the Large Hadron Collider and study the system-size dependence of a variety of flow observables. We find that linear response (from the initial conditions to the final flow harmonics) becomes more dominant in smaller systems, whereas the linear+cubic response can accurately predict multiparticle cumulants for a wide range of centralities in large systems.
High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in classical field simulations to the subsequent hydrodynamic evolution. We build such a framework using nonequilibrium Green’s functions, calculated in QCD kinetic theory, to propagate the initial energy-momentum tensor to the hydrodynamic phase. We demonstrate that this approach can be easily incorporated into existing hydrodynamic simulations, leading to stronger constraints on the energy density at early times and the transport properties of the QCD medium. Based on (conformal) scaling properties of the Green’s functions, we further obtain pragmatic bounds for the applicability of hydrodynamics in nuclear collisions.
In the context of ultra-relativistic nuclear collisions, we present a fast method for calculating the final particle spectra after the direct decay of resonances from a Cooper–Frye integral over the freeze-out surface. The method is based on identifying components of the final particle spectrum that transform in an irreducible way under rotations in the fluid-restframe. Corresponding distribution functions can be pre-computed including all resonance decays. Just a few of easily tabulated scalar functions then determine the Lorentz invariant decay spectrum from each space-time point, and simple integrals of these scalar functions over the freeze-out surface determine the final decay products. This by-passes numerically costly event-by-event calculations of the intermediate resonances. The method is of considerable practical use for making realistic data to model comparisons of the identified particle yields and flow harmonics, and for studying the viscous corrections to the freeze-out distribution function.
In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, dNch/dη and total charged-particle multiplicity, Nchtot, in Xe–Xe collisions at a centre-of-mass energy per nucleon–nucleon pair of sNN=5.44TeV. The measurements are performed as a function of collision centrality over a wide pseudorapidity range of −3.5<η<5. The values of dNch/dη at mid-rapidity and Nchtot for central collisions, normalised to the number of nucleons participating in the collision (Npart) as a function of sNN follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of Npart, and up to the 5% most central collisions the trends are the same as the ones observed in Pb–Pb at a similar energy. For more central collisions, the Xe–Xe scaled multiplicities exceed those in Pb–Pb for a similar Npart. The results are compared to phenomenological models and theoretical calculations based on different mechanisms for particle production in nuclear collisions. All considered models describe the data reasonably well within 15%.
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.
This publication describes the methods used to measure the centrality of inelastic Pb-Pb collisions at a center-of-mass energy of 2.76 TeV per colliding nucleon pair with ALICE. The centrality is a key parameter in the study of the properties of QCD matter at extreme temperature and energy density, because it is directly related to the initial overlap region of the colliding nuclei. Geometrical properties of the collision, such as the number of participating nucleons and the number of binary nucleon-nucleon collisions, are deduced from a Glauber model with a sharp impact parameter selection and shown to be consistent with those extracted from the data. The centrality determination provides a tool to compare ALICE measurements with those of other experiments and with theoretical calculations.
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.
We present transverse momentum distributions of charged hadrons produced in Au+Au collisions at GeV. The spectra were measured for transverse momenta pT from 0.25 to 4.5 GeV/c in a pseudorapidity range of 0.2<η<1.4. The evolution of the spectra is studied as a function of collision centrality, from 65 to 344 participating nucleons. The results are compared to data from proton–antiproton collisions and Au+Au collisions at lower RHIC energies. We find a significant change of the spectral shape between proton–antiproton and semi-peripheral Au+Au collisions. Comparing semi-peripheral to central Au+Au collisions, we find that the yields at high pT exhibit approximate scaling with the number of participating nucleons, rather than scaling with the number of binary collisions.
We present results for two-particle transverse momentum correlations, <Delta p(t,i)Delta p(t,j)>, as a function of event centrality for Au+Au collisions at root SNN = 20, 62, 130, and 200 GeV at the BNL Relativistic Heavy Ion Collider. We observe correlations decreasing with centrality that are similar at all four incident energies. The correlations multiplied by the multiplicity density increase with incident energy, and the centrality dependence may show evidence of processes such as thermalization, jet production, or the saturation of transverse flow. The square root of the correlations divided by the event-wise average transverse momentum per event shows little or no beam energy dependence and generally agrees with previous measurements made at the CERN Super Proton Synchrotron.
Relativistic heavy ion collisions generate nuclear-sized droplets of quark-gluon plasma (QGP) that exhibit nearly inviscid hydrodynamic expansion. Smaller collision systems such as p+Au, d+Au, and He3+Au at the BNL Relativistic Heavy Ion Collider, as well as p+Pb and high-multiplicity p+p at the CERN Large Hadron Collider may create even smaller droplets of QGP. If so, the standard time evolution paradigm of heavy ion collisions may be extended to these smaller systems. These small systems present a unique opportunity to examine pre-hydrodynamic physics and extract properties of the QGP, such as the bulk viscosity, where the short lifetimes of the small droplets make them more sensitive to these contributions. Here, we focus on the influence of bulk viscosity, its temperature dependence, and the implications of negative pressure and potential cavitation effects on the dynamics in small and large systems using the publicly available hydrodynamic codes sonic and music. We also discuss pre-hydrodynamic physics in different frameworks including anti–de Sitter/conformal field theory strong coupling, ip-glasma weak coupling, and free streaming.
We posit a unified hydrodynamic and microscopic description of the quark-gluon plasma (QGP) produced in ultrarelativistic p−Pb and Pb-Pb collisions at sNN=5.02TeV and evaluate our assertion using Bayesian inference. Specifically, we model the dynamics of both collision systems using initial conditions with parametric nucleon substructure, a preequilibrium free streaming stage, event-by-event viscous hydrodynamics, and a microscopic hadronic afterburner. Free parameters of the model, which describe the initial state and QGP medium are then simultaneously calibrated to fit charged-particle yields, mean pT, and flow cumulants. We argue that the global agreement of the calibrated model with the experimental data strongly supports the existence of hydrodynamic flow in small collision systems at ultrarelativistic energies, and that the flow produced develops at length scales smaller than a single proton. Posterior estimates for the model's input parameters are obtained, and new insights into the temperature dependence of the QGP transport coefficients and event-by-event structure of the proton are discussed.
We present an introductory review of the early-time dynamics of high-energy heavy-ion collisions and the kinetics of high-temperature quantum chromodynamic matter. The equilibration mechanisms in the quark–gluon plasma uniquely reflect the nonabelian and ultrarelativistic character of the many-body system. Starting with a brief exposé of the key theoretical and experimental questions, we provide an overview of the theoretical tools employed in weak coupling studies of the early-time nonequilibrium dynamics. We highlight theoretical progress in understanding different thermalization mechanisms in weakly coupled nonabelian plasmas, and discuss their relevance in describing the approach to local thermal equilibrium during the first fm/ c of a heavy-ion collision. We also briefly discuss some important connections to the phenomenology of heavy-ion collisions.
Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 69 is October 21, 2019. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
We present two-particle pt correlations as a function of event centrality for Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These results are compared to previous measurements from CERES at the Super Proton Synchrotron and from ALICE at the Large Hadron Collider. The data are compared with UrQMD model calculations and with a model based on a Boltzmann-Langevin approach incorporating effects from thermalization. The relative dynamical correlations for Au+Au collisions at sNN=200 GeV show a power-law dependence on the number of participant nucleons and agree with the results for Pb+Pb collisions at sNN=2.76TeV from ALICE. As the collision energy is lowered from sNN=200 to 7.7 GeV, the centrality dependence of the relative dynamical correlations departs from the power-law behavior observed at the higher collision energies. In central collisions, the relative dynamical correlations increase with collision energy up to sNN=200 GeV in contrast to previous measurements that showed little dependence on the collision energy.
We study multiparticle azimuthal correlations in relativistic heavy-ion collisions at a center-of-mass energy of 200 GeV. We use the impact parameter-dependent Glasma model to initialize the viscous hydrodynamic simulation MUSIC and employ the UrQMD transport model for the low-temperature region of the collisions. In addition, we study effects of local charge and global momentum conservation among the sampled particles. With the exception of the lowest-order three-particle correlator C112, our framework provides a good description of the existing charge-inclusive azimuthal correlation data for Au+Au and U+U collisions at the Relativistic Heavy-Ion Collider (RHIC). We also present results for charge-dependent two- and three-particle correlators in Au+Au and U+U collisions and make predictions for isobar (Ru+Ru and Zr+Zr) collisions to provide a much-needed baseline for the search for the chiral magnetic effect at RHIC.
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.
We describe ultrarelativistic heavy ion collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider with a hybrid model using the IP-Glasma model for the earliest stage and viscous hydrodynamics and microscopic transport for the later stages of the collision. We demonstrate that within this framework the bulk viscosity of the plasma plays an important role in describing the experimentally observed radial flow and azimuthal anisotropy simultaneously. We further investigate the dependence of observables on the temperature below which we employ the microscopic transport description.
A decade ago, a brief summary of the field of the relativistic heavy ion physics could be formulated as the discovery of strongly coupled quark-gluon plasma, sQGP for short, a near-perfect fluid with surprisingly large entropy-density-to-viscosity ratio. Since 2010, the LHC heavy ion program added excellent new data and discoveries. Significant theoretical efforts have been made to understand these phenomena. Now there is a need to consolidate what we have learned and formulate a list of issues to be studied next. Studies of angular correlations of two and more secondaries reveal higher harmonics of flow, identified as the sound waves induced by the initial state perturbations. As in cosmology, detailed measurements and calculations of these correlations helped to make our knowledge of the explosion much more quantitative. In particular, their damping had quantified the viscosity. Other kinetic coefficients—the heavy-quark diffusion constants and the jet quenching parameters—also show enhancements near the critical point T≈Tc. Since densities of QGP quarks and gluons strongly decrease at this point, these facts indicate large role of nonperturbative mechanisms, e.g., scattering on monopoles. New studies of the pp and pA collisions at high multiplicities reveal collective explosions similar to those in heavy ion AA collisions. These “smallest drops of the sQGP” revived debates about the initial out-of-equilibrium stage of the collisions and mechanisms of subsequent equilibration.
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.
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.
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.
Initial eccentricity and eccentricity fluctuations of the interaction volume created in relativistic collisions of deformed 197Au and 238U nuclei are studied using optical and Monte Carlo (MC) Glauber simulations. It is found that the nonsphericity noticeably influences the average eccentricity in central collisions, and eccentricity fluctuations are enhanced from deformation. Quantitative results are obtained for Au+Au and U+U collisions at energy √sNN=200 GeV.
A new method of determining nuclear shapes is proposed which avoids the assumption of a specific nuclear model. The concept of an equivalent ellipsoid, whose charge and moments equal those of the nucleus, is employed. But the method is equally valid for spherical, deformed, and intermediate nuclei. It can be employed for any nucleus (evev-evevn, odd-A, or odd-odd) provided enough E2 matrix elements are available. The example of 152Sm is discussed.
The space-time evolution of the hadronic matter produced in the central rapidity region in extreme relativistic nucleus-nucleus collisions is described. We find, in agreement with previous studies, that quark-gluon plasma is produced at a temperature ≳200-300 MeV, and that it should survive over a time scale ≳5 fm/c. Our description relies on the existence of a flat central plateau and on the applicability of hydrodynamics.
This chapter discusses nuclear shapes studied by Coulomb excitation. Nuclear E2 properties are a direct and an unambiguous measure of the collective shape parameters for quadrupole collectivity. Coulomb excitation selectively excites collective states with cross sections that are a direct measure of the E2 matrix elements. Advances in the field of Coulomb excitation make it feasible to measure essentially all the E2 matrix elements for low-lying nuclear levels. The completeness and extent of this E2 information add a new dimension to the study of quadrupole collectivity in nuclei. In particular, now it is practical to use a model-independent method for extracting the collective shape parameters directly from this large body of E2 data. Coulomb excitation can now be used to address open questions such as those regarding the limits of the validity of macroscopic collective models, the role of symmetries in collective motion, and the role of shape transitions and shape coexistence in nuclear structure. It is possible to exploit the model-independent sum rule method to project the significant quadrupole collective shape degrees of freedom directly from the data. The power of the sum rule technique is that it allows a wealth of data to be transformed into a form that clearly shows the extent to which the data are correlated because of collectivity.
Large-scale axial mean-field calculations from proton to neutron drip lines have been performed within the Hartree-Fock-Bogoliubov
method based on the D1S Gogny force. Nearly 7000 nuclides have been studied under the axial symmetric hypothesis and various
properties are displayed on an Internet web site for every individual nucleus. Some global properties are presented such as
the positions of the drip lines, the nuclide ground-state deformations and binding energies as well as regions where possible
super- or hyper-deformation might be encountered.
Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.
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.
We show that the event-by-event fluctuations of the transverse size of the
initial source, which follow directly from the Glauber treatment of the
earliest stage of relativistic heavy-ion collisions, cause, after hydrodynamic
evolution, fluctuations of the transverse flow velocity at hadronic freeze-out.
This in turn leads to event-by-event fluctuations of the average transverse
momentum, p_T. Simulations with GLISSANDO for the Glauber phase, followed by a
realistic hydrodynamic evolution and statistical hadronization carried out with
THERMINATOR, lead to agreement with the RHIC data. In particular, the magnitude
of the effect, its centrality dependence, and the weak dependence on the
incident energy are properly reproduced. Our results show that bulk of the
observed event-by-event p_T fluctuations may be explained by the fluctuations
of the size of the initial source.
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.
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
The assumption of simultaneous chemical and thermal freeze-outs of the hadron gas leads to a surprisingly accurate, albeit entirely conventional, explanation of the recently-measured RHIC pT spectra. The original thermal spectra are supplied with secondaries from decays of all resonances, and subsequently folded with a suitably parameterized expansion involving longitudinal and transverse flow. The predictions of this thermal approach, with various parametrizations for the expansion, are in a striking quantitative agreement with the data in the whole available range of 0 < pT < 3.5GeV. Comment: Published version, minor changes (revtex, 6 pages, 2 figures)
This is a review of the theoretical background, experimental techniques, and phenomenology of what is called the "Glauber Model" in relativistic heavy ion physics. This model is used to calculate "geometric" quantities, which are typically expressed as impact parameter (b), number of participating nucleons (N_part) and number of binary nucleon-nucleon collisions (N_coll). A brief history of the original Glauber model is presented, with emphasis on its development into the purely classical, geometric picture that is used for present-day data analyses. Distinctions are made between the "optical limit" and Monte Carlo approaches, which are often used interchangably but have some essential differences in particular contexts. The methods used by the four RHIC experiments are compared and contrasted, although the end results are reassuringly similar for the various geometric observables. Finally, several important RHIC measurements are highlighted that rely on geometric quantities, estimated from Glauber calculations, to draw insight from experimental observables. The status and future of Glauber modeling in the next generation of heavy ion physics studies is briefly discussed.
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