Understanding the equation of state (EOS) of cold nuclear matter, namely, the relation between the pressure and energy density, is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova, all depend critically on the equation of state of hadronic matter. In this contribution I will concentrate on the special role that nuclear physics plays in constraining the EOS of cold baryonic matter and its impact on the properties of neutron stars.
Using a set of model equations of state satisfying the latest constraints from both terrestrial nuclear experiments and astrophysical observations as well as state-of-the-art nuclear many-body calculations of the pure neutron matter equation of state, the tidal polarizability of canonical neutron stars in coalescing binaries is found to be a very sensitive probe of the high-density behavior of nuclear symmetry energy which is among the most uncertain properties of dense neutron-rich nucleonic matter. Moreover, it changes less than $\pm 10%$ by varying various properties of symmetric nuclear ma…
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We fi…
The eigen-frequencies of the axial w-modes of oscillating neutron stars are studied using the continued fraction method with an Equation of State (EOS) partially constrained by the recent terrestrial nuclear laboratory data. It is shown that the density dependence of the nuclear symmetry energy $E_{sym}(ρ)$ affects significantly both the frequencies and the damping times of these modes. Besides confirming the previously found universal behavior of the mass-scaled eigen-frequencies as functions of the compactness of neutron stars, we explored several alternative universal scaling functions. Mor…
We explore the unique and fascinating structure of neutron stars. Although neutron stars are of interest in many areas of Physics, our aim is to provide an intellectual bridge between Nuclear Physics and Astrophysics. We argue against the naive perception of a neutron star as a uniform assembly of neutrons packed to enormous densities. Rather, by focusing on the many exotic phases that are speculated to exist in a neutron star, we show how the reality is different and far more interesting.
Significant progress has been made in recent years in constraining nuclear symmetry energy at and below the saturation density of nuclear matter using data from both terrestrial nuclear experiments and astrophysical observations. However, many interesting questions remain to be studied especially at supra-saturation densities. In this lecture note, after a brief summary of the currently available constraints on nuclear symmetry energy near the saturation density we first discuss the relationship between the symmetry energy and the isopin and momentum dependence of the single-nucleon potential …
An attempt is made to interpret, in the framework of QCD, the likeness between the shapes of the neutron-neutron strong and electrostatic interactions at the distances $\sim 1÷3$ fm.
Heavy-ion reactions especially those induced by radioactive beams provide useful information about the density dependence of the nuclear symmetry energy, thus the Equation of State of neutron-rich nuclear matter, relevant for many astrophysical studies. The latest developments in constraining the symmetry energy at both sub- and supra-saturation densities from analyses of the isopsin diffusion and the $π^-/π^+$ ratio in heavy-ion collisions using the IBUU04 transport model are discussed. Astrophysical ramifications of the partially constrained symmetry energy on properties of neutron star crus…
In the past few years, new observations of neutron stars and neutron-star mergers have provided a wealth of data that allow one to constrain the equation of state of nuclear matter at densities above nuclear saturation density. However, most observations were based on neutron stars with masses of about 1.4 solar masses, probing densities up to $\sim$ 3-4 times the nuclear saturation density. Even higher densities are probed inside massive neutron stars such as PSR J0740+6620. Very recently, new radio observations provided an update to the mass estimate for PSR J0740+6620 and X-ray observations…
The neutron-proton effective mass splitting in neutron-rich nucleonic matter reflects the space-time nonlocality of the isovector nuclear interaction. It affects the neutron/proton ratio during the earlier evolution of the Universe, cooling of protoneutron stars, structure of rare isotopes and dynamics of heavy-ion collisions. While there is still no consensus on whether the neutron-proton effective mass splitting is negative, zero or positive and how it depends on the density as well as the isospin-asymmetry of the medium, significant progress has been made in recent yeas in addressing these …
I study the effect of nuclear equation of state on the r-mode instability of a rotating neutron star. I consider the case where the crust of the neutron star is perfectly rigid and I employ the related theory introduced by Lindblom {\it et al.} \cite{Lidblom-2000}. The gravitational and the viscous time scales, the critical angular velocity and the critical temperature are evaluated by employing a phenomenological nuclear model for the neutron star matter. The predicted equations of state for the $β$-stable nuclear matter are parameterized by varying the slope $L$ of the symmetry energy at sat…
Nuclear astrophysics and californium fission neutron spectrum averaged cross sections and their uncertainties for ENDF materials have been calculated. Absolute values were deduced with Maxwellian and Mannhart spectra, while uncertainties are based on ENDF/B-VII.1, JEFF-3.1.2, JENDL-4.0 and Low-Fidelity covariances. These quantities are compared with available data, independent benchmarks, EXFOR library, and analyzed for a wide range of cases. Recommendations for neutron cross section covariances are given and implications are discussed.
Microscopic calculations of neutron matter based on nuclear interactions derived from chiral effective field theory, combined with the recent observation of a 1.97 +- 0.04 M_sun neutron star, constrain the equation of state of neutron-rich matter at sub- and supranuclear densities. We discuss in detail the allowed equations of state and the impact of our results on the structure of neutron stars, the crust-core transition density, and the nuclear symmetry energy. In particular, we show that the predicted range for neutron star radii is robust. For use in astrophysical simulations, we provide d…
We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. This includes the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron dripline. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. We first review our unde…
In this contribution nuclear constraints on the equation of state for a neutron star are discussed. A combined fit to nuclear masses and charge radii leads to improved values for the symmetry energy and its derivative at nuclear saturation density, $S_{\rm{v}}= 31$ MeV and $L=68\pm 8$ MeV. As an application the sensitivity of some properties of rotating supramassive neutron stars on the EoS is discussed.
The ratio of pre-equilibrium neutrons to protons from collisions of neutron-rich nuclei is studied as a function of their kinetic energies. This ratio is found to be sensitive to the density dependence of the nuclear symmetry energy, but is independent of the compressibility of symmetric nuclear matter and the in-medium nucleon-nucleon cross sections. The experimental measurement of this ratio thus provides a novel means for determining the nuclear equation of state of asymmetric nuclear matter.
The screening potential in the $^1S_0$ and $^3S_1$ pairing channels in neutron and nuclear matter in different approximations is discussed. It is found that the vertex corrections to the potential are much stronger in nuclear matter than in neutron matter.
The nuclear binding energy is studied using a finite temperature density functional theory. A Skyrme interaction is used in this work. Volume, surface, and symmetry energy contributions to the binding energy are investigated. The case of neutron skin is considered in detail. The neutron skin modifies the mass $A$ dependence of various terms and $I$ dependence of the skin thickness is proportional to $I$ for the case of same central density.
The neutron-proton differential flow is shown to be a very useful probe of the isospin-dependence of the nuclear equation of state (EOS). This novel approach utilizes constructively both the isospin fractionation and the nuclear collective flow as well as their sensitivities to the isospin-dependence of the nuclear EOS. It also avoids effectively uncertainties associated with other dynamical ingredients of heavy-ion reactions at intermediate energies.
Within a transport model it is shown that the neutron/proton ratio of squeezed-out nucleons perpendicular to the reaction plane, especially at high transverse momenta, in heavy-ion reactions induced by high energy neutron-rich nuclei can be a useful tool for studying the high density behavior of the nuclear symmetry energy.
Recent neutron star observations set new constraints for the equation of state of baryonic matter. A chiral effective field theory approach is used for the description of neutron-dominated nuclear matter present in the outer core of neutron stars. Possible hybrid stars with quark matter in the inner core are discussed using a three-flavor Nambu--Jona-Lasinio model.
In this work, the reliability of the Landau expression for the nuclear level density calculations is tested, for the first-time, to describe nuclear level densities of some light, intermediate mass and heavy nuclei at excitations corresponding to discrete and s-wave neutron resonance energies. The chi-2 minimizing method is used in treatment of the experimental data for the two suggested energy range of discrete energies given by Nuclear Data Sheet [1] and by the systematic for nuclear level density parametrization in [2]. Our comparison with the related data in the discrete energy range has s…
It is shown that the hole in the centre of $ ^{3}H $, $ ^{3}He $ and $ ^{4}He $, the neutron halos in nuclei, the $ α- $ and other clustering effects in nuclei and the nuclear molecules all basically arise due to the same underlying effect. We shall show that all these ground state properties of nuclei are manifestations of quark effects. The role of triton clustering in very neutron rich nuclei is emphasized. All these require the concept of hidden colour states which arise from confinement ideas of QCD for the multi-quark systems. This provides comprehensive understanding of diverse nuclear …
We calculate the equation of state of neutron matter with realistic two- and three-nucleon interactions using quantum Monte Carlo techniques, and illustrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and higher densities relevant to neutron stars. Our model also makes an experimentally testable prediction for the correlation between the nuclear symmetry energy and its density dependence -- determined solely by the strength of the short-range terms in the three neutron force. The same force provides a sig…
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction $^{132}$Sn+$^{124}$Sn at a beam energy of 400 MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transv…
The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the s…
Precision mass spectrometry of neutron-rich nuclei is of great relevance for astrophysics. Masses of exotic nuclides impose constraints on models for the nuclear interaction and thus affect the description of the equation of state of nuclear matter, which can be extended to describe neutron-star matter. With knowledge of the masses of nuclides near shell closures, one can also derive the neutron-star crustal composition. The Penning-trap mass spectrometer ISOLTRAP at CERN-ISOLDE has recently achieved a breakthrough measuring the mass of 82Zn, which allowed constraining neutron-star crust compo…
A precise determination of the neutron skin thickness of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (the neutron skin thickness is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on 208Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of the neutron skin thickness of 208Pb from the parity-violating asymmetry probed in the experiment. We demonstrate a high linear correlation between the parity-violatin…
The nuclear neutron-proton contact is introduced, generalizing Tan's work, and evaluated from medium energy nuclear photodisintegration experiments. To this end we reformulate the quasi-deuteron model of nuclear photodisintegration and establish the bridge between the Levinger constant and the contact. Using experimental evaluations of Levinger's constant we extract the value of the neutron-proton contact in finite nuclei and in symmetric nuclear matter. Assuming isospin symmetry we propose to evaluate the neutron-neutron contact through measurement of photonuclear spin correlated neutron-prot…
We investigate the correlation between nuclear neutron radii and the radius of neutron stars. We use a well-established hadronic SU(3) model based on chiral symmetry that naturally includes non-linear vector meson and scalar meson - vector meson couplings. The relative strengths of the couplings modify the nuclear isospin-dependent interactions. We study the dependence of nuclear and neutron star radii on the coupling strengths. The relevance of the results for parity-violating electron-nucleus scattering and the URCA process in neutron stars is discussed.
Radii of charge and neutron distributions are fundamental nuclear properties. They depend on both nuclear interaction parameters related to the equation of state of infinite nuclear matter and on quantal shell effects, which are strongly impacted by the presence of nuclear surface. In this work, by studying the dependence of charge and neutron radii, and neutron skin, on nuclear matter parameters, we assess different mechanisms that drive nuclear sizes. We apply nuclear density functional theory using a family of Skyrme functionals obtained by means of different optimization protocols targetin…
We describe a relation between the symmetry energy coefficients c_sym(rho) of nuclear matter and a_sym(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of c_sym(rho). Here we take advantage of this relation to explore the prospects for constraining c_sym(rho) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.
A direct method is developed to reconstruct the equation of state for high-density nuclear matter from the relationship between any two properties of neutron stars, such as masses, radii, moments of inertia, baryonic masses, binding energies, gravitational redshifts, and their combinations.
Realistic calculations of nuclear disappearance lifetimes induced by neutron-antineutron oscillations are reported for oxygen and iron, using antineutron nuclear potentials derived from a recent comprehensive analysis of antiproton atomic X-ray and radiochemical data. A lower limit of 3.3 x 10E8 s on the neutron-antineutron oscillation time is derived from the Super-Kamiokande I new lower limit of 1.77 x 10E32 yr on the neutron lifetime in oxygen. Antineutron scattering lengths in carbon and nickel, needed in trap experiments using ultracold neutrons, are calculated from updated antinucleon op…
We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrang…
We investigate how the neutron drip line is related to the density dependence of the symmetry energy, by using a macroscopic nuclear model that allows us to calculate nuclear masses in a way dependent on the equation of state of asymmetric nuclear matter. The neutron drip line obtained from these masses is shown to appreciably shift to a neutron-rich side in a nuclear chart as the density derivative of the symmetry energy increases. Such shift is clearly seen for light nuclei, a feature coming mainly from the surface property of neutron-rich nuclei.
Recent progress in quantum Monte Carlo with modern nucleon-nucleon interactions have enabled the successful description of properties of light nuclei and neutron-rich matter. As a demonstration, we show that the agreement between theoretical calculations of the charge form factor of 12C and the experimental data is excellent. Applying similar methods to isospin-asymmetric systems allows one to describe neutrons confined in an external potential and homogeneous neutron-rich matter. Of particular interest is the nuclear symmetry energy, the energy cost of creating an isospin asymmetry. Combining…
The remaining uncertainties of isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although the neutron-skin thickness data or the isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations between other parameters are built. Using combined data of both the neutron-skin thickness and the isovector giant dipole resonance helps to constrain significantly all isovector interaction parameters, thus serves as a useful way in the future analysis.
Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretica…
Neutron stars -- compact objects with masses similar to that of our Sun but radii comparable to the size of a city -- contain the densest form of matter in the universe that can be probed in terrestrial laboratories as well as in earth- and space-based observatories. The historical detection of gravitational waves from a binary neutron star merger has opened the brand new era of multimessenger astronomy and has propelled neutron stars to the center of a variety of disciplines, such as astrophysics, general relativity, nuclear physics, and particle physics. The main input required to study the …
Properties and structure of neutron stars are determined by the equation of state (EOS) of neutron-rich stellar matter. While the collective flow and particle production in relativistic heavy-ion collisions have constrained tightly the EOS of symmetric nuclear matter up to about five times the normal nuclear matter density, the more recent experimental data on isospin-diffusion and isoscaling in heavy-ion collisions at intermediate energies have constrained considerably the density dependence of the nuclear symmetry energy at subsaturation densities. Although there are still many uncertainties…
Motivated by the newly observed $^{39}$Na in experiments, systematic calculations of global nuclear binding energies with seven Skyrme forces are performed. We demonstrate the strong correlation between the two-neutron separation energies ($S_{2n}$) of $^{39}$Na and the total number of bound nuclei of the whole nuclear landscape. Furthermore, with calculated nuclear masses, we perform astrophysical rapid-neutron capture process ($r$-process) simulations by using nuclear reaction code TALYS and nuclear reaction network code SkyNet. $r$-process abundances from ejecta of neutron star mergers and …
The formation of $α$-particle clusters on the surface of heavy nuclei is described in a generalized relativistic mean-field model with explicit cluster degrees of freedom. The effects on the size of the neutron skin of Sn nuclei and ${}^{208}$Pb are investigated as a function of the mass number and the isospin-dependent part of the effective interaction, respectively. The correlation of the neutron skin thickness with the difference of the neutron and proton numbers and with the slope of the nuclear symmetry energy is modified as compared to the mean-field calculation without alpha-cluster cor…
We present an equation of state (EoS) for neutron stars using the relativistic mean-field model with isoscalar- and isovector-meson mixing. Taking into account the results of the neutron skin thickness, $R_{\rm skin}$, of $^{208}$Pb reported by the PREX collaboration, the dimensionless tidal deformability of a canonical neutron star observed from GW170817, and a $2.6$ $M_{\odot}$ compact star implied by the secondary component of GW190814, a new effective interaction is constructed so as to reproduce the saturation condition of nuclear matter and the ground-state properties of finite, closed-s…
We explore constraints on the equation of state (EOS) of neutron-rich matter based on microscopic calculations up to nuclear densities and observations of neutron stars. In a previous work we showed that predictions based on modern nuclear interactions derived within chiral effective field theory and the observation of two-solar-mass neutron stars result in a robust uncertainty range for neutron star radii and the EOS over a wide range of densities. In this work we extend this study, employing both the piecewise polytrope extension from Hebeler et al. as well as the speed of sound model of Gre…
Extrapolations from nuclei to neutron stars hinge on the symmetry term in nuclear binding formulas. The term describes reduction in the binding associated with neutron-proton (np) imbalance. Regrettably, binding formulas in the literature commonly lack an intrinsic consistency with regard to the symmetry term. Our elementary considerations determine the universal macroscopic limit for the term and predict its weakening in light nuclei due to emergence of the nuclear asymmetry-skin. Experimental systematic of isobaric-analogue states allows for a determination of the volume and surface coeffici…
We discuss the one-body potentials for protons and neutrons obtained from Dirac-Brueckner-Hartree-Fock calculations of neutron-rich matter, in particular their dependence upon the degree of proton/neutron asymmetry. The closely related symmetry potential is compared with empirical information from the isovector component of the nuclear optical potential.
The inner crust of neutron stars, formed of a crystal lattice of uclear clusters immersed in a sea of unbound neutrons, may be the nique example of periodic nuclear systems. We have calculated the neutron specific heat in the shallow part of the crust using the band theory of solids with Skyrme nucleon-nucleon interactions. We have also tested the validity of various approximations. We have found that the neutron specific heat is well described by that of a Fermi gas, while the motion of the unbound neutrons is strongly affected by the nuclear lattice. These apparently contradictory results ar…
The symmetry energy for nuclear matter and its relation to the neutron skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.
Neutron stars are the most dense objects in the observable Universe and conventionally one uses nuclear theory to obtain the equation of state (EOS) of dense hadronic matter and the global properties of these stars. In this work, we review various aspects of nuclear matter within an effective Chiral model and interlink fundamental quantities both from nuclear saturation as well as vacuum properties and correlate it with the star properties.
The determination of the equation of state (EOS) for nuclear matter has been one of the biggest problems in nuclear astrophysics, because the EOS is essential for determining the properties of neutron stars. To constrain the density-dependence of the nuclear symmetry energy, several nuclear experiments, e.g., reported by the S$π$RIT and PREX-II collaborations, have recently been performed. However, since their uncertainties are still large, additional constraints such as astronomical observations must be crucial. In addition, it is interesting to see the effect of their reported value on neutr…
In this work, masses and radii of neutron stars are considered to investigate the effect of nuclear symmetry energy to the astrophysical observables. A relativistic mean field model with density-dependent meson-baryon coupling constants is employed in describing the equation of state of dense nuclear matter, and the density dependencies of the symmetry energies are quoted from the recent phenomenological formulae obtained from the heavy ion data at subnuclear saturation densities. Since hyperons can take part in the $β$-equilibrium of the dense matter inside neutron stars, we include hyperons …
The pervasive role of the nuclear symmetry energy in establishing some nuclear static and dynamical properties, and in governing some attributes of neutron star properties is highlighted.
In neutron star crust, non-uniform structure of nuclear matter is expected, which is called the "pasta" structure. From the recent studies of giant flares in magnetars, these structures might be related to some observables and physical quantities of the neutron star crust. To investigate the above quantities, we numerically explore the pasta structures with a fully threedimensional geometry and study the properties of low-density nuclear matter, based on the relativistic mean-field model and the Thomas-Fermi approximation. We observe typical pasta structures for fixed proton number-fraction an…
The spin structure of parity violating and time reversal invariance violating effects in neutron scattering is discussed. The explicit relations between these effects are presented in terms of functions nuclear spins and neutron partial widths of p-wave resonances.
We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determine…
Neutron star radii are primarily determined by the pressure of isospin asymmetric matter which is proportional to the slope of the nuclear symmetry energy. Available terrestrial laboratory data on the isospin diffusion in heavy-ion reactions at intermediate energies constrain the slope of the symmetry energy. Using this constraint, we show that the radius (radiation radius) of a 1.4 solar mass neutron star is between 11.5 (14.4) and 13.6 (16.3) km.
X-ray observations of the neutron star in the Cas A supernova remnant over the past decade suggest the star is undergoing a rapid drop in surface temperature of $\approx$ $2-5.5\%$. One explanation suggests the rapid cooling is triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). Using consistent neutron star crust and core equations of state (EOSs) and compositions, we explore the sensitivity of this interpretation to the density dependence of the symmetry energy $L$ of the EOS used, …
Understanding the equation of state of dense QCD matter remains a major challenge in both nuclear physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave observatories will offer even more detailed observations of neutron stars. Utilizing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feas…
