Showing papers on "Nuclear matter published in 2020"

Evidence for quark-matter cores in massive neutron stars

Abstract: The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (M⊙) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars5,6 with mass M ≈ 2M⊙, the presence of quark matter is found to be linked to the behaviour of the speed of sound cs in strongly interacting matter. If the conformal bound $${c}_{\rm{s}}^{2}\le 1/3$$ (ref. 7) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant. The cores of neutron stars could be made of hadronic matter or quark matter. By combining first-principles calculations with observational data, evidence for the presence of quark matter in neutron star cores is found.

Postmerger Gravitational-Wave Signatures of Phase Transitions in Binary Mergers

Abstract: With the first detection of gravitational waves from a binary system of neutron stars GW170817, a new window was opened to study the properties of matter at and above nuclear-saturation density. Reaching densities a few times that of nuclear matter and temperatures up to 100 MeV, such mergers also represent potential sites for a phase transition (PT) from confined hadronic matter to deconfined quark matter. While the lack of a postmerger signal in GW170817 has prevented us from assessing experimentally this scenario, two theoretical studies have explored the postmerger gravitational-wave signatures of PTs in mergers of a binary system of neutron stars. We here extend and complete the picture by presenting a novel signature of the occurrence of a PT. More specifically, using fully general-relativistic hydrodynamic simulations and employing a suitably constructed equation of state that includes a PT, we present the occurrence of a ``delayed PT,'' i.e., a PT that develops only some time after the merger and produces a metastable object with a quark-matter core, i.e., a hypermassive hybrid star. Because in this scenario, the postmerger signal exhibits two distinct fundamental gravitational-wave frequencies---before and after the PT---the associated signature promises to be the strongest and cleanest among those considered so far, and one of the best signatures of the production of quark matter in the present Universe.

Neutron Star Extreme Matter Observatory: A kilohertz-band gravitational-wave detector in the global network

Abstract: Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly-rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2-4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a neutron star extreme matter observatory (NEMO): a gravitational-wave interferometer optimized to study nuclear physics with merging neutron stars. The concept uses high circulating laser power, quantum squeezing and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above one kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year, and potentially allows for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

Neutron Star Extreme Matter Observatory: A kilohertz-band gravitational-wave detector in the global network

Abstract: Gravitational waves from coalescing neutron stars encode information about nuclear matter at extreme densities, inaccessible by laboratory experiments. The late inspiral is influenced by the presence of tides, which depend on the neutron star equation of state. Neutron star mergers are expected to often produce rapidly rotating remnant neutron stars that emit gravitational waves. These will provide clues to the extremely hot post-merger environment. This signature of nuclear matter in gravitational waves contains most information in the 2–4 kHz frequency band, which is outside of the most sensitive band of current detectors. We present the design concept and science case for a Neutron Star Extreme Matter Observatory (NEMO): a gravitational-wave interferometer optimised to study nuclear physics with merging neutron stars. The concept uses high-circulating laser power, quantum squeezing, and a detector topology specifically designed to achieve the high-frequency sensitivity necessary to probe nuclear matter using gravitational waves. Above 1 kHz, the proposed strain sensitivity is comparable to full third-generation detectors at a fraction of the cost. Such sensitivity changes expected event rates for detection of post-merger remnants from approximately one per few decades with two A+ detectors to a few per year and potentially allow for the first gravitational-wave observations of supernovae, isolated neutron stars, and other exotica.

Studying strong phase transitions in neutron stars with gravitational waves

Abstract: The composition of neutron stars at the extreme densities reached in their cores is currently unknown. Besides nuclear matter of normal neutrons and protons, the cores of neutron stars might harbor exotic matter such as deconfined quarks. In this paper we study strong hadron-quark phase transitions in the context of gravitational wave observations of inspiraling neutron stars. We consider upcoming detections of neutron star coalescences and model the neutron star equations of state with phase transitions through the Constant-Speed-of-Sound parametrization. We use the fact that neutron star binaries with one or more hadron-quark hybrid stars can exhibit qualitatively different tidal properties than binaries with hadronic stars of the same mass, and hierarchically model the masses and tidal properties of simulated populations of binary neutron star inspiral signals. We explore the parameter space of phase transitions and discuss under which conditions future observations of binary neutron star inspirals can identify this effect and constrain its properties, in particular the threshold density at which the transition happens and the strength of the transition. We find that if the detected population of binary neutron stars contains both hadronic and hybrid stars, the onset mass and strength of a sufficiently strong phase transition can be constrained with 50-100 detections. If the detected neutron stars are exclusively hadronic or hybrid, then it is possible to place lower or upper limits on the transition density and strength.

Quantifying uncertainties and correlations in the nuclear-matter equation of state

Abstract: We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\ensuremath{\chi}\mathrm{EFT}$ expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\ensuremath{\chi}\mathrm{EFT}$ breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

Probing the core of the strong nuclear interaction

Abstract: The strong nuclear interaction between nucleons (protons and neutrons) is the effective force that holds the atomic nucleus together. This force stems from fundamental interactions between quarks and gluons (the constituents of nucleons) that are described by the equations of Quantum Chromodynamics (QCD). However, as these equations cannot be solved directly, physicists resort to describing nuclear interactions using effective models that are well constrained at typical inter-nucleon distances in nuclei but not at shorter distances. This limits our ability to describe high-density nuclear matter such as in the cores of neutron stars. Here we use high-energy electron scattering measurements that isolate nucleon pairs in short-distance, high-momentum configurations thereby accessing a kinematical regime that has not been previously explored by experiments, corresponding to relative momenta above 400 MeV/c. As the relative momentum between two nucleons increases and their separation thereby decreases, we observe a transition from a spin-dependent tensor-force to a predominantly spin-independent scalar-force. These results demonstrate the power of using such measurements to study the nuclear interaction at short-distances and also support the use of point-like nucleons with two- and three-body effective interactions to describe nuclear systems up to densities several times higher than the central density of atomic nuclei.

Symmetric Nuclear Matter from the Strong Interaction.

Abstract: We study the equation of state of symmetric nuclear matter at zero temperature over a wide range of densities using two complementary theoretical approaches. At low densities, up to twice nuclear saturation density, we compute the energy per particle based on modern nucleon-nucleon and three-nucleon interactions derived within chiral effective field theory. For higher densities, we derive for the first time constraints in a Fierz-complete setting directly based on quantum chromodynamics using functional renormalization group techniques. We find remarkable consistency of the results obtained from both approaches as they come together in density and the natural emergence of a maximum in the speed of sound c_{S} at supranuclear densities. The presence of this maximum appears tightly connected to the formation of a diquark gap. Notably, this maximum is observed to exceed the asymptotic value c_{S}^{2}=1/3 while its exact position in terms of the density cannot yet be determined conclusively.

Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals

Abstract: Gravitational waves (GWs) from binary neutron stars encode unique information about ultra-dense matter through characterisic signatures associated with a variety of phenomena including tidal effects during the inspiral. The main tidal signature depends predominantly on the equation of state (EoS)-related tidal deformability parameter Λ, but at late times is also characterised by the frequency of the star's fundamental oscillation mode (f-mode). In General Relativity and for nuclear matter, Λ and the f-modes are related by universal relations which may not hold for alternative theories of gravity or exotic matter. Independently measuring Λ and the f-mode frequency enables tests of gravity and the nature of compact binaries. Here we present directly measured constraints on the f-mode frequencies of the companions of GW170817. We also show that future GW detector networks will measure f-mode frequencies to within tens of Hz, enabling precision GW asteroseismology with binary inspiral signals alone.

Measurement and microscopic description of odd–even staggering of charge radii of exotic copper isotopes

Abstract: Nuclear charge radii globally scale with atomic mass number A as A1∕3, and isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. This odd–even staggering, ubiquitous throughout the nuclear landscape1, varies with the number of protons and neutrons, and poses a substantial challenge for nuclear theory2–4. Here, we report measurements of the charge radii of short-lived copper isotopes up to the very exotic 78Cu (with proton number Z = 29 and neutron number N = 49), produced at only 20 ions s–1, using the collinear resonance ionization spectroscopy method at the Isotope Mass Separator On-Line Device facility (ISOLDE) at CERN. We observe an unexpected reduction in the odd–even staggering for isotopes approaching the N = 50 shell gap. To describe the data, we applied models based on nuclear density functional theory5,6 and A-body valence-space in-medium similarity renormalization group theory7,8. Through these comparisons, we demonstrate a relation between the global behaviour of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects, naturally emerge from A-body calculations fitted to properties of A ≤ 4 nuclei. Isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. In charge radii of short-lived copper isotopes, a reduction of this effect is observed when the neutron number approaches fifty.

Accurate bulk properties of nuclei from A = 2 to ∞ from potentials with Δ isobars

Abstract: We optimize $\mathrm{\ensuremath{\Delta}}$-full nuclear interactions from chiral effective field theory The low-energy constants of the contact potentials are constrained by two-body scattering phase shifts, and by properties of bound state of $A=2$ to 4 nucleon systems and nuclear matter The pion-nucleon couplings are taken from a Roy-Steiner analysis The resulting interactions yield accurate binding energies and radii for a range of nuclei from $A=16$ to $A=132$, and provide accurate equations of state for nuclear matter and realistic symmetry energies Selected excited states are also in agreement with data

Gravitational waves from holographic neutron star mergers

Abstract: We present simulations of binary neutron star mergers with equations of state (EoSs) that have input from holography, and analyze the spectral properties of the resulting waveforms. These EoSs consist of a standard nuclear matter EoS at low densities, transitioning to a state-of-the-art holographic EoS with first-order deconfinement phase transition in the otherwise intractable high-density regime. Depending on the transition density, the characteristic frequencies in the spectrum produced from the hybrid EoSs are shifted to significantly lower values. Equal-mass binaries with a total mass of $2.8\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ reach densities in the quark matter phase in the core of the transient hypermassive neutron star, which then induces an immediate gravitational collapse.

Bayesian Inference of the Symmetry Energy of Super-Dense Neutron-Rich Matter from Future Radius Measurements of Massive Neutron Stars

Abstract: Using an explicitly isospin-dependent parametric Equation of State (EOS) for the core of neutron stars (NSs) within the Bayesian statistical approach, we infer the EOS parameters of super-dense neutron-rich nuclear matter from three sets of imagined mass-radius correlation data representing typical predictions by various nuclear many-body theories, i.e, the radius stays the same, decreases or increases with increasing NS mass within $\pm 15\%$ between 1.4 M$_{\odot}$ and 2.0 M$_{\odot}$. The corresponding average density increases quickly, slowly or slightly decreases as the NS mass increases from 1.4 M$_{\odot}$ to 2.0 M$_{\odot}$. Using the posterior probability distribution functions (PDFs) of EOS parameters inferred from GW170817 and NICER radius data for canonical NSs as references, we investigate how future radius measurements of massive NS will improve our knowledge about the EOS of super-dense neutron-rich nuclear matter, especially its symmetry energy term, compared to what people have already learned from analyzing the GW170817 and NICER data. While the EOS of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding high-density symmetry energies at densities above about $2\rho_0$ are very different, indicating that the radii of massive NSs carry reliable information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS.

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

Abstract: With the advent of nuclear interactions based on chiral effective field theory, it is becoming possible to accurately describe atomic nuclei and infinite nuclear matter as found in neutron stars. A key challenge is the simultaneous quantification of uncertainties associated to the nuclear interaction and many-body approaches. By performing benchmark calculations of pure neutron matter with realistic interactions and several many-body approaches, this manuscript presents a first step in this direction.

Bayesian Inference of Dense Matter Equation of State within Relativistic Mean Field Models Using Astrophysical Measurements

Abstract: We present a Bayesian analysis to constrain the equation of state of dense nucleonic matter by exploiting the available data from symmetric nuclear matter at saturation and from observations of compact X-ray sources and from the gravitational wave event GW170817. For the first time, such analysis is performed by using a class of models, the relativistic mean field models, which allow to consistently construct an equation of state in a wide range of densities, isospin asymmetries and temperatures. The selected class of models contains five nuclear physics empirical parameters at saturation for which we construct the joint posterior distributions. By exploring different types of priors, we find that the equations of state with the largest evidence are the ones featuring a strong reduction of the effective mass of the nucleons in dense matter which can be interpreted as an indication of a phase transition to a chiral symmetry restored phase. Those equations of state in turn predict $R_{1.4} \sim 12$ km. Finally, we present a preliminary investigation on the effect of including $\Lambda$ hyperons showing that they appear in stars more massive than about $1.6 M_{\odot}$ and lead to radii larger than about $R_{1.4} \sim 14$ km. Within the model here explored, the formation of such particles provide a poor agreement with the constraints from GW170817.

A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions

Abstract: With the aim of understanding the phase structure of nuclear matter created in high-energy nuclear collisions at finite baryon density, a beam energy scan program has been carried out at Relativistic Heavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticality and heavy flavor productions will be discussed. The goal here is to establish the connection between current available data and future heavy-ion collision experiments in a high baryon density region.

Effects of dark matter on the nuclear and neutron star matter

Abstract: We study the dark matter effects on the nuclear matter parameters characterising the equation of states of super dense neutron-rich nucleonic-matter. The observables of the nuclear matter, i.e. incompressibility, symmetry energy and its higher-order derivatives in the presence dark matter for symmetric and asymmetric nuclear matter are analysed with the help of an extended relativistic mean-field model. The calculations are also extended to beta-stable matter to explore the properties of the neutron star. We analyse the dark matter effects on symmetric nuclear matter, pure neutron matter and neutron star using NL3, G3 and IOPB-I forces. The binding energy per particle and pressure are calculated with and without considering the dark matter interaction with the nuclear matter systems. The influences of dark matter are also analysed on the symmetry energy and its different coefficients. The incompressibility and the skewness parameters are affected considerably due to the presence of dark matter in the nuclear matter medium. We extend the calculations to the neutron star and find its mass, radius and the moment of inertia for static and rotating neutron star with and without dark matter contribution. The mass of the rotating neutron star is considerably changing due to rapid rotation with the frequency in the mass-shedding limit. The effects of dark matter are found to be important for some of the nuclear matter parameters, which are crucial for the properties of astrophysical objects.

Atomic Nuclei From Quantum Monte Carlo Calculations With Chiral EFT Interactions

Abstract: Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schr\"odinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These \textit{ab-initio} methods have been used to accurately compute properties of light nuclei -- including their spectra, moments, and transitions -- and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chiral effective field theory.

Speed of sound constraints from tidal deformability of neutron stars

Abstract: The upper bound of the speed of sound in dense nuclear matter is one of the most interesting but still unsolved problems in nuclear physics. Theoretical studies in connection with recent observational data of isolated neutron stars as well as binary neutron stars systems offer an excellent opportunity to shed light on this problem. In the present work, we suggest a method to directly relate the measured tidal deformability (polarizability) of binary neutron stars system (before merger) to the maximum neutron star mass scenario and possible upper bound on the speed of sound. This method is based on the simple but efficient idea that while the upper limit of the effective tidal deformability favors soft equations of state, the recent high measured values of neutron star mass favor stiff ones. In the present work, first, using a simple well established model we parametrize the stiffness of the equation of state with the help of the speed of sound. Second, in comparison with the recent observations by LIGO/VIRGO collaboration of two events, GW170817 and GW190425, we suggest possible robust constraints. Moreover, we evaluate and postulate, in the framework of the present method, what kind of future measurements could help us to improve the stringent of the constraints on the neutron star equation of state.

Anisotropic neutron stars modelling: constraints in Krori-Barua spacetime

Abstract: Dense nuclear matter is expected to be anisotropic due to effects such as solidification, superfluidity, strong magnetic fields, hyperons, pion-condensation. Therefore an anisotropic neutron star core seems more realistic than an ideally isotropic one. We model anisotropic neutron stars working in the Krori–Barua (KB) ansatz without preassuming an equation of state. We show that the physics of general KB solutions is encapsulated in the compactness. Imposing physical and stability requirements yields a maximum allowed compactness $$2GM/Rc^2 < 0.71$$ for a KB-spacetime. We further input observational data from numerous pulsars and calculate the boundary density. We focus especially on data from the LIGO/Virgo collaboration as well as recent independent measurements of mass and radius of miilisecond pulsars with white dwarf companions by the Neutron Star Interior Composition Explorer (NICER). For these data the KB-spacetime gives the same boundary density which surprisingly equals the nuclear saturation density within the data precision. Since this value designates the boundary of a neutron core, the KB-spacetime applies naturally to neutron stars. For this boundary condition we calculate a maximum mass of 4.1 solar masses.

Effects of the equation of state on the bulk properties of maximally rotating neutron stars

Abstract: Neutron stars are among the densest known objects in the universe and an ideal laboratory for the strange physics of supercondensed matter. While the simultaneous measurements of mass and radius of nonrotating neutron stars may impose constraints on the properties of the dense nuclear matter, the observation and study of maximally rotating ones, close to the mass-shedding limit, may lead to significantly further constraints. Theoretical predictions allow neutron stars to rotate extremely fast (even more than $2000\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$). However, until this moment, the fastest observed rotating pulsar has a frequency of $716\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$, much lower compared to the theoretical predictions. There are many suggestions for the mechanism which lead to this situation. In any case, the theoretical study of uniformly rotating neutron stars, along with accurate measurements, may offer rich information concerning the high-density part of the equation of state. In addition, neutron stars through their evolution may provide us with a criterion to determine the final fate of a rotating compact star. Sensitivity of bulk neutron stars properties on the equation of state at the mass-shedding limit are the main subject of the present study.

Are nuclear matter properties correlated to neutron star observables

Abstract: We investigate properties of nuclear matter and examine possible correlations with neutron star observables for a set of microscopic nuclear equations of state derived within the Brueckner–Hartree–Fock formalism employing compatible three-body forces. We find good candidates for a realistic nuclear EOS up to high density and confirm strong correlations between neutron star radius, tidal deformability, and the pressure of betastable matter. No correlations are found with the saturation properties of nuclear matter.

Gravitomagnetic tidal resonance in neutron-star binary inspirals

Abstract: A compact binary system implicating at least one rotating neutron star undergoes gravitomagnetic tidal resonances as it inspirals toward its final merger. These have a dynamical impact on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star. Four distinct modes are involved, and the resonances occur within the frequency band of interferometric gravitational-wave detectors when the star spins at a frequency that lies within this band. The resonances are driven by the gravitomagnetic tidal field created by the companion star; this is described by a post-Newtonian vector potential, which is produced by the mass currents associated with the orbital motion. These resonances were identified previously by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)], but these authors accounted only for the response of a single mode, the r-mode, a special case of inertial modes. All four relevant modes are included in the analysis presented in this paper. The total accumulated gravitational-wave phase shift is shown to range from approximately $10^{-2}$ radians when the spin and orbital angular momenta are aligned, to approximately $10^{-1}$ radians when they are anti-aligned. Such phase shifts will become measurable in the coming decades with the deployment of the next generation of gravitational-wave detectors (Cosmic Explorer, Einstein Telescope); they might even come to light within this decade, thanks to planned improvements in the current detectors. With good constraints on the binary masses and spins gathered from the inspiral waveform, the phase shifts deliver information regarding the internal structure of the rotating neutron star, and therefore on the equation of state of nuclear matter.

Neutron Star Merger Remnants.

Abstract: Binary neutron star mergers observations are a unique way to constrain fundamental physics and astrophysics at the extreme. The interpretation of gravitational-wave events and their electromagnetic counterparts crucially relies on general-relativistic models of the merger remnants. Quantitative models can be obtained only by means of numerical relativity simulations in 3+1 dimensions including detailed input physics for the nuclear matter, electromagnetic and weak interactions. This review summarizes the current understanding of merger remnants focusing on some of the aspects that are relevant for multimessenger observations.

Hyperon-nucleon three-body forces and strangeness in neutron stars

Abstract: Three-body forces acting on a $\Lambda$ hyperon in a nuclear medium are investigated, with special focus on the so-called hyperon puzzle in neutron stars. The hyperon-nucleon two-body interaction deduced from SU(3) chiral effective field theory is employed at next-to-leading order. Hyperon-nucleon three-body forces are approximated using saturation by decuplet baryons and are transcribed to density-dependent effective two-body interactions. These together are taken as input in a Brueckner-Bethe-Goldstone equation with explicit treatment of the $\Lambda N\leftrightarrow\Sigma N$ and $\Lambda NN\leftrightarrow\Sigma NN$ coupled channels. Single-particle potentials of a $\Lambda$ hyperon in symmetric nuclear matter and neutron matter are calculated. With parameters of the $\Lambda NN$ three-body force constrained by hypernuclear phenomenology, extrapolations to high baryon density are performed. By comparison of the $\Lambda$ and neutron chemical potentials at densities characteristic of the core of neutron stars it is found that the combined repulsive effects of two- and three-body correlations makes the appearance of $\Lambda$ hyperons in neutron stars energetically unfavourable, thus offering a possible solution to a longstanding question.