The unambiguous observation of a Chiral Magnetic Effect (CME)-driven charge separation is the core aim of the isobar program at RHIC consisting of ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr and ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru collisions at $\sqrt {s_{\rm NN}}\!=\!200$ GeV. We quantify the role of the spatial distributions of the nucleons in the isobars on both eccentricity and magnetic field strength within a relativistic hadronic transport approach (SMASH, Simulating Many Accelerated Strongly-interacting Hadrons). In particular, we introduce isospin-dependent nucleon-nucleon spatial correlations in the geometric description of both nuclei, deformation for ${^{96}_{44}}$Ru and the so-called neutron skin effect for the neutron-rich isobar i.e. ${^{96}_{40}}$Zr. The main result of this study is a reduction of the magnetic field strength difference between ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru and ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr by a factor of 2, from $10\%$ to $5\%$ in peripheral collisions when the neutron-skin effect is included. Further, we find an increase of eccentricity by up to 10$\%$ when deformation is taken into account while neither the neutron skin effect nor the nucleon-nucleon correlations result into a significant modification of this observable with respect to the traditional Woods-Saxon modeling. Our results suggest a significantly smaller CME signal to background ratio for the experimental charge separation measurement in peripheral collisions with the isobar systems than previously expected.
In these proceedings, we present the three proposed observables to probe the neutron skin and symmetry energy with relativistic isobar collisions, namely, the isobar ratios of the produced hadron multiplicities ($N_{\rm ch}$), the mean transverse momenta ($\langle p_{\perp} \rangle$), and the net charge multiplicities ($ΔQ$). Our findings suggest potentially significant improvement to neutron skin and symmetry energy determination over traditional low energy methods.
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.
Neutron skin thickness ($Δr_{\rm np}$) of nuclei and the inferred nuclear symmetry energy are of critical importance to nuclear physics and astrophysics. It is traditionally measured by nuclear processes with significant theoretical uncertainties. We recently proposed an indirect measurement of the $Δr_{\rm np}$ by charged hadron multiplicities in central isobaric collisions at relativistic energies, which are sensitive to nuclear densities. In this Letter, we propose a direct measurement of the $Δr_{\rm np}$ by using net-charge multiplicities in ultra-peripheral (grazing) collisions of those …
The effects of neutron skin on the multiplicity ($N_{\rm ch}$) and eccentricity($ε_2$) in relativistic $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV are investigated with the Trento model. It is found that the Ru+Ru/Zr+Zr ratios of the $N_{\rm ch}$ distributions and $ε_{2}$ in mid-central collisions are exquisitely sensitive to the neutron skin type (skin vs.~halo). The state-of-the-art calculations by energy density functional theory (DFT) favor the halo-type neutron skin and can soon be confronted by experimental data. It is demo…
The STAR collaboration is currently pursuing the blind analysis of the data for isobar collisions that was performed at RHIC in the year 2018 to make a decisive test of the Chiral Magnetic Effect (CME). Why is it so difficult to detect signals of CME in the experiment? Do we really understand different sources of background? Why observing similar charge separation between p/d+A and A+A does not stop us from pursuing the search for CME? In this contribution, I attempt to address some of these questions and briefly outline a few recent STAR analyses based on new methods and observables to isolat…
The charge-exchange (3He,t) scattering to the isobaric analog state (IAS) of the target can be considered as "elastic" scattering of 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross- section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target is related directl…
Neutron skin impurity from Coulomb core polarization in $^{208}\text{Pb}$: Insights from PREX-II and validation via the $(^{3}\text{He}, t)$ isobaric analog state reaction
$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between these two collision systems and demonstrate that the ratios of ${\rm ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences betwee…
We show that the yield ratio of free spectator neutrons produced in high-energy $^{96}$Zr+$^{96}$Zr to $^{96}$Ru+$^{96}$Ru collisions is a clean probe of the neutron-skin thickness of colliding nuclei and the slope parameter $L$ of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions via a state-of-the-art Skyrme-Hartree-Fock-Bogolyubov calculation. Among spectator nucleons given by the Glauber model, free spectator neutrons include those from direct production that survive from clusterization as well as those from deexcitation of heavy clusters d…
In these proceedings, we present the measurements of neutron skin thickness and nuclear deformation using isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV by the STAR detector. The significant deviations from unity of the isobar ratios of elliptic flow $v_{2}$, triangular flow $v_{3}$, mean $p_{\rm T}$ fluctuations $\langleδp_{\rm T}^{2}\rangle/\langle p_{\rm T}\rangle^{2}$, and asymmetric cumulant ${\rm ac}_{2}\{3\}$ indicate large differences in their quadrupole and octuple deformations. The significant deviations of the isob…
\item[Purpose] We suppose that the IYR(m) depends on the neutron-skin thickness ($δ_{np}$) of the projectile, and check the idea of whether the neutron-skin thickness effects can fully explain the systematic dependence of the IYR(m). \item[Methods] A modified statistical abrasion-ablation model is used to calculate the reactions induced by projectiles of three series. \item[Results] The IYR(m) shows a distribution of a linear part in the small-$x$ fragments, and a nonlinear part in the large-$x$ fragments. The linear part of IYR(m) is fitted. (1) In the calcium isotopic reactions, the IYR(m) d…
We report the measurements of spin alignment ($ρ_{00}$) for $K^{*0}$, $\overline{K^{*0}}$, $K^{*+}$, and $K^{*-}$ vector mesons in RHIC isobar collisions (Zr+Zr and Ru+Ru) at $\sqrt{s_{\mathrm {NN}}}$ = 200 GeV. We observe the first non-zero spin alignment for $K^{*\pm}$ in heavy-ion collisions. The $K^{*\pm}$ $ρ_{00}$ is about 3.9$σ$ larger than that of $K^{*0}$. The observed difference and the ordering between $K^{*\pm}$ and $K^{*0}$ are surprising, and require further inputs from theory. When comparing between the isobar and Au+Au collisions, no significant system size dependence in $K^{*0}…
The isobaric collision experiment at RHIC provides the unique opportunity to detect the possible signal of Chiral Magnetic Effect (CME) in heavy ion collisions. The idea is to contrast the correlation observables of the two colliding systems that supposedly have identical flow-driven background contributions while quite different CME signal contributions due to the 10% variation in their nuclear charge and thus magnetic field strength. With the recently developed quantitative simulation tool for computing CME signal, the Anomalous-Viscous Fluid Dynamics (AVFD), we demonstrate that a joint (mul…
In these proceedings we discuss the recent precision measurements of charge separation difference between Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\rm NN}}=200$ GeV by STAR collaboration. The measurements indicate that the magnitude of the difference in the charge separation attributable to the magnetic fields between the two systems is smaller than previously expected. We also present charge separation measurements on the Chiral Magnetic Effect search from the RHIC BES-II experiment using the Event Plane Detectors (EPD) from Au+Au collisions at $\sqrt{s_{\rm NN}} =$ 27 GeV.
We report the measurements of global spin polarization of hyperons ($P_Λ$) from FAIR, RHIC and LHC energies. The $P_Λ$ continue to follow an increasing trend at $\sqrt{s_{\mathrm NN}}$ < 7.7 GeV indicating that enormous vorticity prevail even in hadronic dominant region. New measurements of local spin polarization ($P_{z,2}$) from isobar collisions follow the same pattern observed in previous RHIC and LHC energies. An observable motivated by predicted baryonic Spin Hall Effect, the net local polarization ($P_{z,2}^{\mathrm{net}}$), shows negative value in Au+Au collisions at $\sqrt{s_{\mathrm …
In this report, we briefly examine the current status of the study of the chiral magnetic effect including theory and experimental progress. We recommend future strategies for resolving uncertainties in interpretation including recommendations for theoretical work, recommendations for measurements based on data collected in the past five years, and recommendations for beam use in the coming years of RHIC. We have specifically investigated the case for colliding nuclear isobars (nuclei with the same mass but different charge) and find the case compelling. We recommend that a program of nuclear …
Isobar collisions which were thought to have the same background and different magnetic fields provide an opportunity to verify the chiral magnetic effect (CME) in relativistic heavy-ion collisions. However, the first result from the RHIC-STAR isobar experiment did not observe the CME signal, but discovered that the backgrounds are different between $_{44}^{96}\textrm{Ru}+_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+_{40}^{96}\textrm{Zr}$ collisions. We test eighteen cases of Woods-Saxon parameter settings resulting from different nuclear deformation or nuclear structure effects using a m…
The quark-gluon matter produced in relativistic heavy-ion collisions may contain local domains in which P and CP symmetries are not preserved. When coupled with an external magnetic field, such P- and CP-odd domains will generate electric currents along the magnetic field --- a phenomenon called the chiral magnetic effect (CME). Recently, the STAR Collaboration at RHIC and the ALICE Collaboration at the LHC released data of charge-dependent azimuthal-angle correlators with features consistent with the CME expectation. However, the experimental observable is contaminated with significant backgr…
We construct a nuclear interaction in chiral effective field theory with explicit inclusion of the $Δ$-isobar $Δ(1232)$ degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon ($πN$) low-energy constants (LECs) from a Roy-Steiner analysis of $πN$ scattering data, optimize the LECs in the contact potentials up to NNLO to reproduce low-energy nucleon-nucleon scattering phase shifts, and constrain the three-nucleon interaction at NNLO to reproduce the binding energy and point-proton radius of $^{4}$He. For heavier nuclei we use the coupled-cluster method to…
Disentangling nuclear structure through multiparticle azimuthal correlations in high-energy isobar collisions
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), and Institute of Modern Physics, Fudan University（核物理与离子束应用教育部重点实验室，复旦大学现代物理研究所）；Department of Chemistry, Stony Brook University（石溪大学化学系）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委员会理论物理上海研究中心，复旦大学）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理部）；School of Physics, East China Normal University（华东师范大学物理学院）
The ratios of bulk observables, such as harmonic flow $v_2$ and $v_3$, between high-energy $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr collisions were recently argued to be a clean probe of the nuclear structure differences between $^{96}$Ru and $^{96}$Zr. Using a transport model simulation of isobar collisions, we quantify this claim from the dependence of the ratios $v_{2,\mathrm{Ru}}/v_{2,\mathrm{Zr}}$ and $v_{3,\mathrm{Ru}}/v_{3,\mathrm{Zr}}$ on various final state effects, such as the shear viscosity, hadronization and hadronic cascade. Although the $v_2$ and $v_3$ change by more than 50%…
We investigate the static properties of the nucleon in the presence of strong magnetic fields and discuss the consequent changes of the nucleon structure, based on the Skyrme model. The results show that at large values of the magnetic field ($\sim10^{17}$ to $10^{18} \mathrm{G}$), which is supposed to appear in heavy-ion collision experiments at RHIC energies, the soliton starts to deviate from the spherically symmetric form and its size starts to change. At extremely large values of the magnetic field ($\sim 10^{19}$ G), which may be found at the LHC experiments, the soliton becomes more com…
The neutron skin in deformed nuclei is generally not uniformly distributed but has an angular distribution, depending on both the spin-dependent nuclear interaction and the nuclear symmetry energy. To extract the information of the deformed neutron skin, we have explored the possibility of using free spectator nucleons in central tip-tip and body-body collisions at top RHIC energy with four typical deformed nuclei. The density distributions of neutrons and protons are consistently obtained from the Skyrme-Hartree-Fock-Bogolyubov calculation, and the angular distribution of the neutron skin can…
The Gamow-Teller resonances (GTR) and isobaric analog states (IAS) of a sequence of even-even Sn target nuclei are calculated by using the framework of the relativistic Hartree-Bogoliubov model plus proton-neutron quasiparticle random-phase approximation. The calculation reproduces the experimental data on ground-state properties, as well as the excitation energies of the isovector excitations. It is shown that the isotopic dependence of the energy spacings between the GTR and IAS provides direct information on the evolution of neutron skin-thickness along the Sn isotopic chain. A new method i…
Using two-nucleon and three-nucleon interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit $Δ$ isobar contributions, we calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach. In particular, we present for the first time nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with $Δ$ isobar intermediate states (N3LO$Δ$) recently developed by Piar…
We study multi-particle azimuthal correlations in relativistic heavy-ion collisions at a center of mass energy of 200 GeV. We use the IP-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 $C_{112}$, our framework provides a good description of the existing charge inclusive azimuthal correlation data for Au+Au and U+U col…
The $^{208}$Pb($p$,$nγ\bar p$) $^{207}$Pb reaction at a beam energy of 30 MeV has been used to excite the anti-analog of the giant dipole resonance (AGDR) and to measure its $γ$-decay to the isobaric analog state in coincidence with proton decay of IAS. The energy of the transition has also been calculated with the self-consistent relativistic random-phase approximation (RRPA), and found to be linearly correlated to the predicted value of the neutron-skin thickness ($ΔR_{pn}$). By comparing the theoretical results with the measured transition energy, the value of 0.190 $\pm$ 0.028 fm has been …
The PHENIX experiment at BNL-RHIC recently reported the single transverse spin asymmetry $A_N$ for forward neutrons measured in polarized proton-nucleus collisions at $\sqrt{s_{NN}} = 200\,$GeV; $A_N$ in proton-aluminum and proton-gold collisions are -0.015 and 0.18, respectively, which are clearly different from $A_N=-0.08$ in proton-proton collisions. In this paper, we propose large $A_N$ for forward neutrons in ultraperipheral polarized proton-nucleus collisions as an explanation of the PHENIX measurements. The proposed model is demonstrated using two Monte Carlo simulations organized as fo…
We investigate properties of the Delta(1232) and nucleon spectral functions at finite temperature and baryon density within a hadronic model. The medium modifications of the Delta consist of a renormalization of its pion-nucleon cloud and resonant pi-Delta scattering. Underlying coupling constants and form factors are determined by the elastic π-N scattering phase shift in the isobar channel, as well as empirical partial decay widths of excited baryon resonances. For cold nuclear matter the model provides reasonable agreement with photoabsorption data on nuclei in the Delta-resonance region. I…
Neutron Skin Effects on Particle Emission in Heavy-Ion Collisions: A Topic Review with Astrophysical and Nuclear Structure Connections
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（复旦大学现代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（复旦大学理论核物理上海研究中心）；School of Physics, East China Normal University（华东师范大学物理系）
Besides the yield ratio of free spectator neutrons produced in ultracentral $^{96}$Zr+$^{96}$Zr to $^{96}$Ru+$^{96}$Ru collisions, we propose that the yield ratio $N_n/N_p$ of free spectator neutrons to protons in a single collision system at RHIC and LHC can be a more sensitive probe of the neutron-skin thickness $Δr_{\mathrm{np}}$ and the slope parameter $L$ of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions of colliding nuclei obtained from Skyrme-Hartree-Fock-Bogolyubov calculations, and a Glauber model that provides information of specta…
We investigate the impact of the neutron-skin thickness Delta(R) on the energy difference between the anti-analog giant dipole resonance (AGDR), E(AGDR), and the isobaric analog state (IAS), E(IAS), in a heavy nucleus such as 208Pb. For guidance, we first develop a simple and analytic, yet physical, approach based on the Droplet Model that linearly connects the energy difference E(AGDR)-E(IAS) with Delta(R). To test this correlation on more fundamental grounds, we employ a family of systematically varied Skyrme energy density functionals where variations on the value of the symmetry energy at …
Based on the deformed nucleon distributions obtained from the constrained Skyrme-Hartree-Fock-Bogolyubov calculation using different nuclear symmetry energies, we have investigated the effects of the neutron skin and the collision geometry on the yield of free spectator nucleons as well as the yield ratio $N_n/N_p$ of free spectator neutrons to protons in collisions of deformed nuclei at RHIC energies. We found that tip-tip (body-body) collisions with prolate (oblate) nuclei lead to fewest free spectator nucleons, compared to other collision configurations. While the $N_n/N_p$ ratio is sensiti…
Impacts of nuclear structure on multiplicity ($N_{ch}$) and anisotropic flows ($v_{2}$ and $v_{3}$) in the isobaric collisions of $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4 and 200 GeV are investigated by using the string melting version of A MultiPhase Transport (AMPT) model. In comparison with the experimental data released recently by the STAR collaboration, it is found that the impact of quadrupole deformation $β_{2}$ on the $v_{2}$ difference is mainly manifested in the most central collisions, while the octupole deformation $β_{…
The chiral magnetic effect (CME) is predicted to occur as a consequence of a local violation of $\cal P$ and $\cal CP$ symmetries of the strong interaction amidst a strong electro-magnetic field generated in relativistic heavy-ion collisions. Experimental manifestation of the CME involves a separation of positively and negatively charged hadrons along the direction of the magnetic field. Previous measurements of the CME-sensitive charge-separation observables remain inconclusive because of large background contributions. In order to better control the influence of signal and backgrounds, the S…
We perform a systematic analysis of the density dependence of the nuclear symmetry energy within the microscopic Brueckner--Hartree--Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three body force of Urbana type. Our results are compared thoroughly to those arising from several Skyrme and relativistic effective models. The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion col…
The chiral magnetic effect (CME) is a novel transport phenomenon, arising from the interplay between quantum anomalies and strong magnetic fields in chiral systems. In high-energy nuclear collisions, the CME may survive the expansion of the quark-gluon plasma fireball and be detected in experiments. Over the past decade, the experimental searches for the CME have aroused extensive interest at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The main goal of this article is to investigate three pertinent experimental approaches: the $γ$ correlator, the $R$ correla…
In this contribution we report a recently developed Anomalous-Viscous Fluid Dynamics (AVFD) framework, which simulates the evolution of fermion currents in QGP on top of the bulk expansion from data-validated VISHNU hydrodynamics. With reasonable estimates of initial conditions and magnetic field lifetime, the predicted CME signal is quantitatively consistent with change separation measurements in 200GeV Au-Au collisions at RHIC. We further develop the event-by-event AVFD simulations that allow direct evaluation of two-particle correlations arising from CME signal as well as the non-CME backgr…
