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Keywords = Cold Nuclear Matter

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18 pages, 780 KB  
Article
Equation of State of Highly Asymmetric Neutron Star Matter from Liquid Drop Model and Meson Polytropes
by Elissaios Andronopoulos and Konstantinos N. Gourgouliatos
Symmetry 2026, 18(2), 225; https://doi.org/10.3390/sym18020225 - 27 Jan 2026
Viewed by 644
Abstract
We present a unified description of dense matter and neutron star structure based on simple but physically motivated models. Starting from the thermodynamics of degenerate Fermi gases, we construct an equation of state for cold, catalyzed matter by combining relativistic fermion statistics with [...] Read more.
We present a unified description of dense matter and neutron star structure based on simple but physically motivated models. Starting from the thermodynamics of degenerate Fermi gases, we construct an equation of state for cold, catalyzed matter by combining relativistic fermion statistics with the liquid drop model of nuclear binding. The internal stratification of matter in the outer crust is described by the β-equilibrium, neutron drip and a gradual transition to supranuclear matter. Short-range repulsive interactions inspired by Quantum Hadrodynamics are incorporated at high densities in order to ensure stability and causality. The resulting equation of state is used as input in the Tolman–Oppenheimer–Volkoff equations, yielding self-consistent neutron star models. We compute macroscopic stellar properties including the mass–radius relation, compactness and surface redshift that can be compared with recent observational data. Despite the simplicity of the underlying microphysics, the model produces neutron star masses and radii compatible with current observational constraints from X-ray timing and gravitational-wave measurements. This work demonstrates that physically transparent models can capture the essential features of neutron star structure and provide valuable insight into the connection between dense-matter physics and astrophysical observables; they can also be used as easy-to-handle models to test the impact of more complicated phenomena and variations in neutron stars. Full article
(This article belongs to the Special Issue Nuclear Symmetry Energy: From Finite Nuclei to Neutron Stars)
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42 pages, 11490 KB  
Review
Experimental Review of the Quarkonium Physics at the LHC
by Yiyang Zhao, Jinfeng Liu, Xing Cheng, Chi Wang and Zhen Hu
Symmetry 2025, 17(9), 1521; https://doi.org/10.3390/sym17091521 - 12 Sep 2025
Cited by 2 | Viewed by 2003
Abstract
We review recent heavy quarkonium measurements in pp, pPb, and PbPb collisions at the LHC by the ALICE, ATLAS, CMS, and LHCb collaborations using Run-2 and early Run-3 data. Production studies include present differential cross-sections and polarization measurements [...] Read more.
We review recent heavy quarkonium measurements in pp, pPb, and PbPb collisions at the LHC by the ALICE, ATLAS, CMS, and LHCb collaborations using Run-2 and early Run-3 data. Production studies include present differential cross-sections and polarization measurements of charmonium and bottomonium, providing precise tests of QCD theoretical calculations and unveiling symmetry relations among spin and orbital configurations. Notably, a tt¯ quasi-bound-state has been observed at the LHC recently. Suppression analyses quantify the sequential melting of bottomonium states in PbPb collisions, serving as a probe of the deconfined quark–gluon plasma. Cold nuclear matter effects are constrained through comparisons of quarkonium yields in pPb and pp collisions. Furthermore, multi-quarkonium investigations observe di- and tri-quarkonium production processes and resonances, exploring multi-parton interactions and the symmetry structure underlying exotic hadron states. Full article
(This article belongs to the Special Issue Symmetry in Hadron Physics)
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57 pages, 2571 KB  
Review
Heavy–Heavy and Heavy–Light Mesons in Cold Nuclear Matter
by J. J. Cobos-Martínez, Guilherme N. Zeminiani and Kazuo Tsushima
Symmetry 2025, 17(5), 787; https://doi.org/10.3390/sym17050787 - 19 May 2025
Cited by 1 | Viewed by 1330
Abstract
We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and [...] Read more.
We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons, K,K,D,D,B,B,η,η,ϕ,ηc,J/ψ,ηb,Υ, and Bc, where our emphasis is on the heavy mesons. In addition, we also present some new results for the Bc-nucleus bound states. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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9 pages, 340 KB  
Article
A Systematic Approach to Studying Quark Energy Loss in Nuclei Using Positive Pions
by Nicolás Zambra-Gómez, William K. Brooks and Nicolás Viaux
Particles 2025, 8(2), 44; https://doi.org/10.3390/particles8020044 - 15 Apr 2025
Viewed by 1081
Abstract
Our objective is to test the published models of partonic energy loss, particularly those describing the energy loss mechanisms of quarks traversing nuclear matter, within the framework of semi-inclusive deep inelastic scattering. Our methodological approach focuses on quantifying the quark energy loss in [...] Read more.
Our objective is to test the published models of partonic energy loss, particularly those describing the energy loss mechanisms of quarks traversing nuclear matter, within the framework of semi-inclusive deep inelastic scattering. Our methodological approach focuses on quantifying the quark energy loss in cold matter by analyzing the positive pions (π+) produced in various nuclear targets, including deuterium, carbon, iron and lead, while our first approach only includes deuterium and carbon. Before normalizing the pions’ energy distribution to unity to perform a shape analysis, acceptance corrections were performed to account for the detector’s efficiency and ensure accurate comparisons of the spectra. By normalizing the energy spectra of π+ produced from these distinct targets and based on the Baier–Dokshitzer–Mueller–Peigné–Schiff theory, which posits that quark energy loss depends only on nuclear size, it is assumed that the energy distributions of the targets will exhibit similar behavior. For this normalization, an energy shift between these distributions, corresponding to the quark energy loss, is identified. To ensure accuracy, statistical techniques such as the Kolmogorov–Smirnov test are used. The data used to test and explore the analysis technique and method were from the CLAS6 EG2 dataset collected using Jefferson Lab’s CLAS detector. Full article
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19 pages, 703 KB  
Article
Surface and Curvature Tensions of Cold, Dense Quark Matter: A Term-by-Term Analysis Within the Nambu–Jona–Lasinio Model
by Ana Gabriela Grunfeld, María Florencia Izzo Villafañe and Germán Lugones
Universe 2025, 11(2), 29; https://doi.org/10.3390/universe11020029 - 21 Jan 2025
Cited by 2 | Viewed by 1274
Abstract
In this paper, we conduct a thorough investigation of the surface and curvature tensions, σ and γ, of three-flavor cold quark matter using the Nambu–Jona–Lasinio (NJL) model with vector interactions. Our approach ensures both local and global electric charge neutrality, as well [...] Read more.
In this paper, we conduct a thorough investigation of the surface and curvature tensions, σ and γ, of three-flavor cold quark matter using the Nambu–Jona–Lasinio (NJL) model with vector interactions. Our approach ensures both local and global electric charge neutrality, as well as chemical equilibrium under weak interactions. By employing the multiple reflection expansion formalism to account for finite size effects, we explore the impact of specific input parameters, particularly the vector coupling constant ratio ηV, the radius R of quark matter droplets, as well as the charge-per-baryon ratio ξ of the finite size configurations. We focus on the role of the contributions of each term of the NJL Lagrangian to the surface and curvature tensions in the mean field approximation. We find that the total surface tension exhibits two different density regimes: it remains roughly constant at around 100MeVfm2 up to approximately 2–4 times the nuclear saturation density, and beyond this point, it becomes a steeply increasing function of nB. The total surface and curvature tensions are relatively insensitive to variations in R but are affected by changes in ξ and ηV. We observe that the largest contribution to σ and γ comes from the regularized divergent term, making these quantities significantly higher than those obtained within the MIT bag model. Full article
(This article belongs to the Special Issue Universe: Feature Papers 2024 – Compact Objects)
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21 pages, 1039 KB  
Article
Charmonium Transport in Heavy-Ion Collisions at the LHC
by Biaogang Wu and Ralf Rapp
Universe 2024, 10(6), 244; https://doi.org/10.3390/universe10060244 - 31 May 2024
Cited by 12 | Viewed by 1609
Abstract
We provide an update on our semi-classical transport approach for quarkonium production in high-energy heavy-ion collisions, focusing on J/ψ and ψ(2S) mesons in 5.02 TeV Pb-Pb collisions at the Large Hadron Collider (LHC) at both forward and [...] Read more.
We provide an update on our semi-classical transport approach for quarkonium production in high-energy heavy-ion collisions, focusing on J/ψ and ψ(2S) mesons in 5.02 TeV Pb-Pb collisions at the Large Hadron Collider (LHC) at both forward and mid-rapidity. In particular, we employ the most recent charm-production cross sections reported in pp collisions, which are pivotal for the magnitude of the regeneration contribution, and their modifications due to cold-nuclear-matter (CNM) effects. Multi-differential observables are calculated in terms of nuclear modification factors as a function of centrality, transverse momentum, and rapidity, including the contributions from feeddown from bottom hadron decays. For our predictions for ψ(2S) production, the mechanism of sequential regeneration relative to the more strongly bound J/ψ meson plays an important role in interpreting recent ALICE data. Full article
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8 pages, 748 KB  
Communication
Experimental Study of Cold Dense Nuclear Matter
by Maria Patsyuk, Timur Atovullaev, Goran Johansson, Dmitriy Klimanskiy, Vasilisa Lenivenko, Sergey Nepochatykh and Eli Piasetzky
Particles 2024, 7(1), 229-236; https://doi.org/10.3390/particles7010013 - 8 Mar 2024
Viewed by 2196
Abstract
The fundamental theory of nuclear interactions, Quantum Chromodynamics (QCD), operates in terms of quarks and gluons at higher resolution. At low resolution the relevant degrees of freedom are nucleons. Two-nucleon Short-Range Correlations (SRC) help to interconnect these two descriptions. SRCs are temporary fluctuations [...] Read more.
The fundamental theory of nuclear interactions, Quantum Chromodynamics (QCD), operates in terms of quarks and gluons at higher resolution. At low resolution the relevant degrees of freedom are nucleons. Two-nucleon Short-Range Correlations (SRC) help to interconnect these two descriptions. SRCs are temporary fluctuations of strongly interacting close pairs of nucleons. The distance between the two nucleons is comparable to their radii and their relative momenta are larger than the fermi sea level. According to the electron scattering experiments held in the last decade, SRCs have far-reaching impacts on many-body systems, the nucleon-nucleon interactions, and nuclear substructure. The modern experiments with ion beams and cryogenic liquid hydrogen target make it possible to study properties of the nuclear fragments after quasi-elastic knockout of a single nucleon or an SRC pair. Here we review the status and perspectives of the SRC program in so-called inverse kinematics at JINR (Dubna, Russia). The first SRC experiment at the BM@N spectrometer (2018) with 4 GeV/c/nucleon carbon beam has shown that detection of an intact 11B nucleus after interaction selects out the quasi-elastic knockout reaction with minimal contribution of initial- and final-state interactions. Also, 25 events of SRC-breakups showed agreement in SRC properties as known from electron beam experiments. The analysis of the second measurement of SRC at BM@N held in 2022 with an improved setup is currently ongoing. The SRC project at JINR moved to a new experimental area in 2023, where the next measurement is being planned in terms of experimental setup and physics goals. Full article
(This article belongs to the Special Issue Infinite and Finite Nuclear Matter (INFINUM))
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28 pages, 5465 KB  
Review
Towards Experimental Confirmation of Quarkonia Melting in Quark–Gluon Plasma: A Review of Recent Measurements of Quarkonia Production in Relativistic Heavy-Ion Collisions
by Kara R. Mattioli
Symmetry 2024, 16(2), 225; https://doi.org/10.3390/sym16020225 - 13 Feb 2024
Cited by 1 | Viewed by 2301
Abstract
The dissociation, or “melting”, of heavy quarkonia states due to color charge screening is a predicted signature of quark–gluon plasma (QGP) formation, with a quarkonium state predicted to dissociate when the temperature of the medium is higher than the binding energy of the [...] Read more.
The dissociation, or “melting”, of heavy quarkonia states due to color charge screening is a predicted signature of quark–gluon plasma (QGP) formation, with a quarkonium state predicted to dissociate when the temperature of the medium is higher than the binding energy of the quarkonium state. A conclusive experimental observation of quarkonium melting coupled with a detailed theoretical understanding of the melting mechanism would enable the use of quarkonia states as temperature probes of the QGP, a long-sought goal in the field of relativistic heavy-ion collisions. However, the interpretation of quarkonia suppression measurements in heavy-ion collisions is complicated by numerous other cold nuclear matter effects that also result in the dissociation of bound quarkonia states. A comprehensive understanding of these cold nuclear matter effects is therefore needed in order to correctly interpret quarkonia production measurements in heavy-ion collisions and to observe the melting of quarkonium states experimentally. In this review, recent measurements of quarkonia production in pA and AA collisions and their state-of-the-art theoretical interpretations will be discussed, as well as the future measurements needed to further the knowledge of cold nuclear matter effects and realize a measurement of quarkonia melting in heavy-ion collisions. Full article
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19 pages, 6448 KB  
Article
Constraints on Phase Transitions in Neutron Star Matter
by Len Brandes and Wolfram Weise
Symmetry 2024, 16(1), 111; https://doi.org/10.3390/sym16010111 - 18 Jan 2024
Cited by 30 | Viewed by 4058
Abstract
Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known [...] Read more.
Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities cs2>0.1 in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range Δρ/ρ<0.2 (at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined. Full article
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14 pages, 549 KB  
Article
Dense Cold Quark–Gluon Matter Clusters and Their Study at the NICA Collider
by Vladimir Vechernin, Svetlana Belokurova and Semyon Yurchenko
Symmetry 2024, 16(1), 79; https://doi.org/10.3390/sym16010079 - 6 Jan 2024
Cited by 2 | Viewed by 1697
Abstract
In this paper, the production of particles outside the region of nucleon–nucleon kinematics due to interactions involving dense cold clusters of quark-gluon matter in nuclei is calculated. The possibility of observing this process in the region of central rapidities and large transverse momenta [...] Read more.
In this paper, the production of particles outside the region of nucleon–nucleon kinematics due to interactions involving dense cold clusters of quark-gluon matter in nuclei is calculated. The possibility of observing this process in the region of central rapidities and large transverse momenta in heavy ion collisions at low energies with MPD detector at the NICA collider is demonstrated. Full article
(This article belongs to the Section Physics)
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16 pages, 2302 KB  
Article
Toward the System Size Dependence of Anisotropic Flow in Heavy-Ion Collisions at sNN= 2–5 GeV
by Mikhail Mamaev and Arkadiy Taranenko
Particles 2023, 6(2), 622-637; https://doi.org/10.3390/particles6020036 - 2 Jun 2023
Cited by 9 | Viewed by 2548
Abstract
The study of the high-density equation of state (EOS) and the search for a possible phase transition in dense baryonic matter is the main goal of beam energy scan programs with relativistic heavy ions at energies sNN= 2–5 GeV. The [...] Read more.
The study of the high-density equation of state (EOS) and the search for a possible phase transition in dense baryonic matter is the main goal of beam energy scan programs with relativistic heavy ions at energies sNN= 2–5 GeV. The most stringent constraints currently available on the high-density EOS of symmetric nuclear matter come from the present measurements of directed (v1) and elliptic flow (v2) signals of protons in Au + Au collisions. In this energy range, the anisotropic flow is strongly affected by the presence of cold spectators due to the sizable passage time. The system size dependence of anisotropic flow may help to study the participant–spectator contribution and improve our knowledge of the EOS of symmetric nuclear matter. In this work, we discuss the layout of the upgraded BM@N experiment and the anticipated performance for differential anisotropic flow measurements of identified hadrons at Nuclotron energies: sNN= 2.3–3.5 GeV. Full article
(This article belongs to the Special Issue Selected Papers from "Physics Performance Studies at FAIR and NICA")
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10 pages, 396 KB  
Article
Hydromagnetic Waves in Cold Nuclear Matter
by Şerban Mişicu
Magnetism 2023, 3(2), 148-157; https://doi.org/10.3390/magnetism3020012 - 29 May 2023
Cited by 1 | Viewed by 1998
Abstract
I consider a proton–neutron fluid mixture placed in an ultra-strong external static magnetic field and derive the spin-independent, small-amplitude disturbances in infinitely extended systems. As a theoretical framework I adopt a hydrodynamical model for the proton and neutron fluids moving in a Skyrme [...] Read more.
I consider a proton–neutron fluid mixture placed in an ultra-strong external static magnetic field and derive the spin-independent, small-amplitude disturbances in infinitely extended systems. As a theoretical framework I adopt a hydrodynamical model for the proton and neutron fluids moving in a Skyrme mean-field derived from the time-dependent Hartree Fock formulation of the many-body nuclear problem. From the mass, momentum balance, and Maxwell equations, I set up a system of equations governing the electromagnetic field and the continuum-mechanical fields of the mixture. Next, the hydromagnetic equations are linearized, and the occurrence of small-amplitude distortions of the velocity field is analyzed for various orientations of the constant external magnetic induction with respect to the wave propagation vector. The derivation of the above equations is carried out for the inviscid case. Full article
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48 pages, 6164 KB  
Review
Skyrme Crystals, Nuclear Matter and Compact Stars
by Christoph Adam, Alberto García Martín-Caro, Miguel Huidobro and Andrzej Wereszczynski
Symmetry 2023, 15(4), 899; https://doi.org/10.3390/sym15040899 - 12 Apr 2023
Cited by 14 | Viewed by 3405
Abstract
A general review of the crystalline solutions of the generalized Skyrmemodel and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground [...] Read more.
A general review of the crystalline solutions of the generalized Skyrmemodel and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrmemodel on the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first-order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass–radius curves already reasonably satisfy current astrophysical constraints. Full article
(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)
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23 pages, 10179 KB  
Review
Recent Quarkonia Measurements in Small Systems at RHIC and LHC Energies
by Krista L. Smith
Universe 2023, 9(4), 174; https://doi.org/10.3390/universe9040174 - 3 Apr 2023
Viewed by 1730
Abstract
Heavy-ion research at the Relativistic Heavy Ion Collider (RHIC) during the first decade of data collection, approximately during the years 2000–2010, was primarily focused on the study of Au+Au collisions. The search for evidence of quark-gluon plasma (QGP), a state of matter where [...] Read more.
Heavy-ion research at the Relativistic Heavy Ion Collider (RHIC) during the first decade of data collection, approximately during the years 2000–2010, was primarily focused on the study of Au+Au collisions. The search for evidence of quark-gluon plasma (QGP), a state of matter where quarks and gluons become unbound within a high energy density environment, which was at the forefront of research efforts. However, studies of the azimuthal anisotropy parameter v2 in p/d+Pb collisions from the Large Hadron Collider (LHC) yielded results consistent with the hydrodynamic flow, one of the signatures of quark-gluon plasma formation in heavy-ion collisions. Since the publication of these findings, the field of heavy-ion physics has made subsequent measurements in small system collisions to study cold nuclear matter effects as well as look for additional evidence of hot nuclear matter effects. Quarkonia, a bound state of a cc¯ or bb¯ pair, has often been used to probe a wide range of nuclear effects in both large and small collision systems. Here we will review recent quarkonia measurements in small system collisions at RHIC and LHC energies and summarize the experimental conclusions. Full article
(This article belongs to the Special Issue Jet and Heavy Flavor Production)
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5 pages, 711 KB  
Proceeding Paper
Nuclear Pasta in Cold Non-Accreting Neutron Stars: Symmetry Energy Effects
by Nikolai N. Shchechilin, John M. Pearson and Nicolas Chamel
Phys. Sci. Forum 2023, 7(1), 10; https://doi.org/10.3390/ECU2023-14017 - 15 Feb 2023
Cited by 2 | Viewed by 1955
Abstract
The densest part of neutron star crusts may contain very exotic nuclear configurations, so-called nuclear pasta. We investigate the effect of nuclear symmetry energy on the existence of such phases in cold non-accreting neutron stars. For this purpose, we apply three Brussels–Montreal functionals [...] Read more.
The densest part of neutron star crusts may contain very exotic nuclear configurations, so-called nuclear pasta. We investigate the effect of nuclear symmetry energy on the existence of such phases in cold non-accreting neutron stars. For this purpose, we apply three Brussels–Montreal functionals based on generalized Skyrme effective interactions, whose parameters were accurately calibrated to reproduce both experimental data on nuclei and realistic neutron-matter equations of state. These functionals differ in their predictions for the density dependence of the symmetry energy. Within the fourth-order extended Thomas–Fermi method, we find that pasta occupies a wider region of the crust for models with a lower slope of the symmetry energy (and higher symmetry energy at relevant densities) in agreement with previous studies based on pure Thomas–Fermi approximation and compressible liquid-drop models. However, the incorporation of microscopic corrections consistently calculated with the Strutinsky integral method leads to a significant shift of the onset of the pasta phases to higher densities due to the enhanced stability of spherical clusters. As a result, the pasta region shrinks substantially and the role of symmetry energy weakens. This study sheds light on the importance of quantum effects for reliably describing pasta phases in neutron stars. Full article
(This article belongs to the Proceedings of The 2nd Electronic Conference on Universe)
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