Determination of the Neutron Skin of

Emergent bulk properties of matter governed by the strong nuclear force give rise to physical phenomena across vastly different scales, ranging from the shape of atomic nuclei to the masses and radii of neutron stars. They can be accessed on Earth by measuring the spatial extent of the outer skin made of neutrons that characterizes the surface of heavy nuclei. The isotope ^{208}Pb, owing to its simple structure and neutron excess, has been in this context the target of many dedicated efforts. Here, we determine the neutron skin from measurements of particle distributions and their collective flow in ^{208}Pb+^{208}Pb collisions at ultrarelativistic energy performed at the Large Hadron Collider, which are mediated by interactions of gluons and thus sensitive to the overall size of the colliding ^{208}Pb ions. By means of state-of-the-art global analysis tools within the hydrodynamic model of heavy-ion collisions, we infer a neutron skin Δr_{np}=0.217±0.058 fm, consistent with nuclear theory predictions, and competitive in accuracy with a recent determination from parity-violating asymmetries in polarized electron scattering. We establish thus a new experimental method to systematically measure neutron distributions in the ground state of atomic nuclei.

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

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 (v_{2}) and its fluctuations in high-energy ^{96}Ru+^{96}Ru and ^{96}Zr+^{96}Zr collisions. Our findings reveal that the difference in skin thickness between these isobars only influences the inherent ellipticity of the collision systems, v_{2}^{rp}. In contrast, differences in nuclear deformations solely impact the fluctuations of v_{2} around v_{2}^{rp}. 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.

Evidence of Hexadecapole Deformation in Uranium-238 at the Relativistic Heavy Ion Collider.

State-of-the-art hydrodynamic simulations of the quark-gluon plasma are unable to reproduce the elliptic flow of particles observed at the BNL Relativistic Heavy Ion Collider (RHIC) in relativistic ^{238}U+^{238}U collisions when they rely on information obtained from low-energy experiments for the implementation of deformation in the colliding ^{238}U ions. We show that this is due to an inappropriate treatment of well-deformed nuclei in the modeling of the initial conditions of the quark-gluon plasma. Past studies have identified the deformation of the nuclear surface with that of the nuclear volume, though these are different concepts. In particular, a volume quadrupole moment can be generated by both a surface hexadecapole and a surface quadrupole moment. This feature was so far neglected in the modeling of heavy-ion collisions, and is particularly relevant for nuclei like ^{238}U, which is both quadrupole deformed and hexadecapole deformed. With rigorous input from Skyrme density functional calculations, we show that correcting for such effects in the implementation of nuclear deformations in hydrodynamic simulations restores agreement with BNL RHIC data. This brings consistency to the results of nuclear experiments across energy scales, and demonstrates the impact of the hexadecapole deformation of ^{238}U on high-energy collisions.

Evidence of the Triaxial Structure of

The interpretation of the emergent collective behavior of atomic nuclei in terms of deformed intrinsic shapes is at the heart of our understanding of the rich phenomenology of their structure, ranging from nuclear energy to astrophysical applications across a vast spectrum of energy scales. A new window into the deformation of nuclei has been recently opened with the realization that nuclear collision experiments performed at high-energy colliders, such as the CERN Large Hadron Collider (LHC), enable experimenters to identify the relative orientation of the colliding ions in a way that magnifies the manifestations of their intrinsic deformation. Here we apply this technique to LHC data on collisions of ^{129}Xe nuclei to exhibit the first evidence of nonaxiality in the ground state of ions collided at high energy. We predict that the low-energy structure of ^{129}Xe is triaxial (a spheroid with three unequal axes) and show that such deformation can be determined from high-energy data. This result demonstrates the unique capabilities of precision collider machines such as the LHC as new means to perform imaging of the collective structure of atomic nuclei.

Constraining the Nucleon Size with Relativistic Nuclear Collisions.

The notion of the "size" of nucleons and their constituents plays a pivotal role in the current paradigm of the formation and the fluctuations of the quark-gluon plasma produced in high-energy nuclear collision experiments. We report on state-of-the-art hydrodynamic results showing that the correlation between anisotropic flow v_{n}^{2} and the mean transverse momentum of hadrons [p_{t}] possesses a unique sensitivity to the nucleon size in off-central heavy-ion collisions. We argue that existing experimental measurements of this observable support a picture where the relevant length scale characterizing the colliding nucleons is of order 0.5 fm or smaller, and we discuss the broad implications of this finding for future global Bayesian analyses aimed at extracting initial-state and medium properties from nucleus-nucleus collision data, including v_{n}^{2}-[p_{t}] correlations. Determinations of the nucleon size in heavy-ion collisions will provide a solid independent constraint on the initial state of small system collisions and will establish a deep connection between collective flow data in nucleus-nucleus experiments and data on deep inelastic scattering on protons and nuclei.

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

In the hydrodynamic framework of heavy-ion collisions, elliptic flow v_{2} is sensitive to the quadrupole deformation ß 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 ß of the respective species. We validate our formula in simulations of ^{238}U+^{238}U and ^{197}Au+^{197}Au collisions at top Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to experimental data. Using the deformation of ^{238}U from low-energy experiments, we find that RHIC v_{2} data implies 0.16≲|ß|≲0.20 for ^{197}Au nuclei, i.e., significantly more deformed than reported in the literature, posing an interesting issue in nuclear phenomenology.

Observable Signatures of Initial State Momentum Anisotropies in Nuclear Collisions.

We show that the correlation between the elliptic momentum anisotropy v_{2} and the average transverse momentum [p_{T}] at fixed multiplicity in small system nuclear collisions carries information on the origin of the observed momentum anisotropy. A calculation using a hybrid IP-Glasma+music+UrQMD model that includes contributions from final state response to the initial geometry as well as initial state momentum anisotropies of the color glass condensate predicts a characteristic sign change of the correlator ρ[over ^](v_{2}^{2},[p_{T}]) as a function of charged particle multiplicity in p+Au and d+Au collisions at sqrt[s]=200 GeV, and p+Pb collisions at sqrt[s]=5.02 TeV. This sign change is absent in calculations without initial state momentum anisotropies. The model further predicts a qualitative difference between the centrality dependence of ρ[over ^](v_{2}^{2},[p_{T}]) in Au+Au collisions at sqrt[s]=200 GeV and Pb+Pb collisions at sqrt[s]=5.02 TeV, with only the latter showing a sign change in peripheral events. Predictions for O+O collisions at different collision energy show a similar behavior. Experimental observation of these distinct qualitative features of ρ[over ^](v_{2}^{2},[p_{T}]) in small and large systems would constitute strong evidence for the presence and importance of initial state momentum anisotropies predicted by the color glass condensate effective theory.

Observing the Deformation of Nuclei with Relativistic Nuclear Collisions.

I show that particle collider experiments on relativistic nuclear collisions can serve as direct probes of the deformation of the colliding nuclear species. I argue that collision events presenting very large multiplicities of particles and very small values of the average transverse momentum of the emitted hadrons probe collision geometries in which the nuclear ellipsoids fully overlap along their longer side. By looking at these events one selects interaction regions whose elliptic anisotropy is determined by the deformed nuclear shape, which becomes accessible experimentally through the measurement of the elliptic flow of outgoing hadrons.

Hydrodynamic Attractors, Initial State Energy, and Particle Production in Relativistic Nuclear Collisions.

We exploit the concept of hydrodynamic attractors to establish a macroscopic description of the early time out-of-equilibrium dynamics of high energy heavy-ion collisions. One direct consequence is a general relation between the initial state energy and the produced particle multiplicities measured in experiments. When combined with an ab initio model of energy deposition, the entropy production during the preequilibrium phase naturally explains the universal centrality dependence of the measured charged particle yields in nucleus-nucleus collisions. Further, we estimate the energy density of the far-from-equilibrium initial state and discuss how our results can be used to constrain nonequilibrium properties of the quark-gluon plasma.