Showing papers on "Nuclear matter published in 2016"

Masses, Radii, and Equation of State of Neutron Stars

Abstract: We summarize our current knowledge of neutron star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the last few years, leading to a large number of mass measurements. These discoveries show that the neutron star mass distribution is much wider than previously thought, with 3 known pulsars now firmly in the 1.9-2.0 Msun mass range. For radii, large, high quality datasets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 9.9-11.2 km range and shrinking their uncertainties due to a better understanding of the sources of systematic errors. The combination of the massive neutron star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk properties of cold nuclear matter at densities higher than that of the atomic nucleus, a major unsolved problem in modern physics.

Neutron star radii and crusts: Uncertainties and unified equations of state

Abstract: The uncertainties in neutron star radii and crust properties due to our limited knowledge of the equation of state are quantitatively analyzed. We first demonstrate the importance of a unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core equation of state based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\ensuremath{\sim}30$ % for the crust thickness and 4% for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified equations of state for purely nucleonic matter is obtained based on twenty-four Skyrme interactions and nine relativistic mean-field nuclear parametrizations. In addition, for relativistic models fifteen equations of state including a transition to hyperonic matter at high density are presented. All these equations of state have in common the property of describing a $2{M}_{\ensuremath{\bigodot}}$ star and of being causal within stable neutron stars. Spans of $\ensuremath{\sim}3$ and $\ensuremath{\sim}4$ km are obtained for the radius of, respectively, $1.0{M}_{\ensuremath{\bigodot}}$ and $2.0{M}_{\ensuremath{\bigodot}}$ stars. Applying a set of nine further constraints from experiment and ab initio calculations the uncertainty is reduced to $\ensuremath{\sim}1$ and 2 km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the equation of state near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope $L$. Indeed, this parameter exhibits a linear correlation with the stellar radius, which is particularly clear for small mass stars around $1.0{M}_{\ensuremath{\bigodot}}$. The other equation-of-state parameters do not show clear correlations with the radius, within the present uncertainties. Potential constraints on $L$, the neutron star radius, and the equation of state from observations of thermal states of neutron stars are also discussed. The unified equations of state are made available in the Supplemental Materials and via the CompOSE database.

Maximum mass, moment of inertia and compactness of relativistic stars

Abstract: A number of recent works have highlighted that it is possible to express the properties of general-relativistic stellar equilibrium configurations in terms of functions that do not depend on the specific equation of state employed to describe matter at nuclear densities. These functions are normally referred to as "universal relations" and have been found to apply, within limits, both to static or stationary isolated stars, as well as to fully dynamical and merging binary systems. Further extending the idea that universal relations can be valid also away from stability, we show that a universal relation is exhibited also by equilibrium solutions that are not stable. In particular, the mass of rotating configurations on the turning-point line shows a universal behaviour when expressed in terms of the normalised Keplerian angular momentum. In turn, this allows us to compute the maximum mass allowed by uniform rotation, M_{max}, simply in terms of the maximum mass of the nonrotating configuration, M_{TOV}, finding that M_{max} ~ (1.203 +- 0.022) M_{TOV} for all the equations of state we have considered. We further show that a universal relation can be found between the dimensionless moment of inertia and the stellar compactness. Although this relation is not surprising as it involves two quantities that have been shown to exhibit universal behaviour with other stellar properties, our parameterisation represents a refinement over a similar relation by Lattimer and Schutz (2005), where a different normalisation was used, and could provide an accurate tool to constrain the equation of state of nuclear matter when measurements of the moment of inertia become available.

Symmetry Parameter Constraints From A Lower Bound On The Neutron-Matter Energy

Abstract: We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter $S_0$. In addition, for assumed values of $S_0$ above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter $L$, which describes the lowest-order density dependence of the symmetry energy. A lower bound on the neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust-core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.

Effects of neutron-star dynamic tides on gravitational waveforms within the effective-one-body approach

Abstract: Extracting the unique information on ultradense nuclear matter from the gravitational waves emitted by merging neutron-star binaries requires robust theoretical models of the signal. We develop a novel effective-one-body waveform model that includes, for the first time, dynamic (instead of only adiabatic) tides of the neutron star as well as the merger signal for neutron-star–black-hole binaries. We demonstrate the importance of the dynamic tides by comparing our model against new numerical-relativity simulations of nonspinning neutron-star–black-hole binaries spanning more than 24 gravitational-wave cycles, and to other existing numerical simulations for double neutron-star systems. Furthermore, we derive an effective description that makes explicit the dependence of matter effects on two key parameters: tidal deformability and fundamental oscillation frequency.

Gravitational-wave signal from binary neutron stars: A systematic analysis of the spectral properties

Abstract: A number of works have shown that important information on the equation of state of matter at nuclear density can be extracted from the gravitational waves emitted by merging neutron-star binaries. We present a comprehensive analysis of the gravitational-wave signal emitted during the inspiral, merger and post-merger of 56 neutron-star binaries. This sample of binaries, arguably the largest studied to date with realistic equations of state, spans across six different nuclear-physics equations of state and ten masses, allowing us to sharpen a number of results recently obtained on the spectral properties of the gravitational-wave signal. Overall we find that: (i) for binaries with masses differing no more than $20\%$, the frequency at gravitational-wave amplitude's maximum is related quasi-universally with the tidal deformability of the two stars; (ii) the spectral properties vary during the post-merger phase, with a transient phase lasting a few millisecond after the merger and followed by a quasi-stationary phase; (iii) when distinguishing the spectral peaks between these two phases, a number of ambiguities in the identification of the peaks disappear, leaving a simple and robust picture; (iv) using properly identified frequencies, quasi-universal relations are found between the spectral features and the properties of the neutron stars; (v) for the most salient peaks analytic fitting functions can be obtained in terms of the stellar tidal deformability or compactness. Altogether, these results support the idea that the equation of state of nuclear matter can be constrained tightly when a signal in gravitational waves from binary neutron stars is detected.

Asymmetric nuclear matter based on chiral two- and three-nucleon interactions

Abstract: We calculate the properties of isospin-asymmetric nuclear matter based on chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions. To this end, we develop an improved normal-ordering framework that allows us to include general 3N interactions starting from a plane-wave partial-wave-decomposed form. We present results for the energy per particle for general isospin asymmetries based on a set of different Hamiltonians, study their saturation properties, the incompressibility, symmetry energy, and also provide an analytic parametrization for the energy per particle as a function of density and isospin asymmetry.

The Nuclear Symmetry Energy

Abstract: The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.

Observational constraints on neutron star masses and radii

Abstract: Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond pulsars, burst oscillations with millisecond periods, and accretion-powered millisecond pulsars; and modeling the gravitational radiation waveforms of coalescing double neutron star and neutron star - black hole binary systems. We describe the strengths and weaknesses of these approaches, most of which currently have substantial systematic errors, and discuss the prospects for decreasing the systematic errors in each method.

Equation of state for nucleonic and hyperonic neutron stars with mass and radius constraints

Abstract: We obtain a new equation of state for the nucleonic and hyperonic inner core of neutron stars that fulfills the 2$M_{\odot}$ observations as well as the recent determinations of stellar radii below 13 km. The nucleonic equation of state is obtained from a new parametrization of the FSU2 relativistic mean-field functional that satisfies these latest astrophysical constraints and, at the same time, reproduces the properties of nuclear matter and finite nuclei while fulfilling the restrictions on high-density matter deduced from heavy-ion collisions. On the one hand, the equation of state of neutron star matter is softened around saturation density, which increases the compactness of canonical neutron stars leading to stellar radii below 13 km. On the other hand, the equation of state is stiff enough at higher densities to fulfill the 2$M_{\odot}$ limit. By a slight modification of the parametrization, we also find that the constraints of 2$M_{\odot}$ neutron stars with radii around 13 km are satisfied when hyperons are considered. The inclusion of the high magnetic fields present in magnetars further stiffens the equation of state. Hyperonic magnetars with magnetic fields in the surface of $ \sim 10^{15}$ G and with values of $\sim 10^{18}$ G in the interior can reach maximum masses of 2$M_{\odot}$ with radii in the 12-13 km range.

Neutron star radii, universal relations, and the role of prior distributions

Abstract: We investigate constraints on neutron star structure arising from the assumptions that neutron stars have crusts, that recent calculations of pure neutron matter limit the equation of state of neutron star matter near the nuclear saturation density, that the high-density equation of state is limited by causality and the largest high-accuracy neutron star mass measurement, and that general relativity is the correct theory of gravity. We explore the role of prior assumptions by considering two classes of equation of state models. In a first, the intermediate- and high-density behavior of the equation of state is parameterized by piecewise polytropes. In the second class, the high-density behavior of the equation of state is parameterized by piecewise continuous line segments. The smallest density at which high-density matter appears is varied in order to allow for strong phase transitions above the nuclear saturation density. We critically examine correlations among the pressure of matter, radii, maximum masses, the binding energy, the moment of inertia, and the tidal deformability, paying special attention to the sensitivity of these correlations to prior assumptions about the equation of state. It is possible to constrain the radii of $ 1.4 M_{\odot}$ neutron stars to be larger than 10km, even without consideration of additional astrophysical observations, for example, those from photospheric radius expansion bursts or quiescent low-mass X-ray binaries. We are able to improve the accuracy of known correlations between the moment of inertia and compactness as well as the binding energy and compactness. We also demonstrate the existence of a correlation between the neutron star binding energy and the moment of inertia.

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XVI: Inclusion of self-energy effects in pairing

Abstract: Extending our earlier work, a new family of three Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-30, HFB-31, and HFB-32, is presented, along with their underlying interactions, BSk30, BSk31, and BSk32, respectively. The principle new feature is a purely phenomenological pairing term that depends on the density gradient. This enables us to have a bulk pairing term that is fitted to realistic nuclear-matter calculations in which for the first time the self-energy corrections are included, while the behavior of the nucleon effective masses in asymmetric homogeneous nuclear matter is significantly improved. Furthermore, in the particle-hole channel all the highly realistic constraints of our earlier work are retained. In particular, the unconventional Skyrme forces containing ${t}_{4}$ and ${t}_{5}$ terms are still constrained to fit realistic equations of state of neutron matter stiff enough to support the massive neutron stars PSR J1614--2230 and PSR J0348+0432. All unphysical long-wavelength spin and spin-isospin instabilities of nuclear matter, including the unphysical transition to a polarized state in neutron-star matter, are eliminated. Our three interactions are characterized by values of the symmetry coefficient $J$ of 30, 31, and 32 MeV, respectively. The best fit to the database of 2353 nuclear masses is found for model HFB-31 $(J=31\phantom{\rule{0.16em}{0ex}}\mathrm{MeV})$ with a model error of 0.561 MeV. This model also fits the charge-radius data with an root-mean-square error of 0.027 fm.

Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT

Abstract: We compute from chiral two- and three-nucleon interactions the energy per particle of symmetric nuclear matter and pure neutron matter at third-order in perturbation theory including self-consistent second-order single-particle energies. Particular attention is paid to the third-order particle-hole ring-diagram, which is often neglected in microscopic calculations of the equation of state. We provide semi-analytic expressions for the direct terms from central and tensor model-type interactions that are useful as theoretical benchmarks. We investigate uncertainties arising from the order-by-order convergence in both many-body perturbation theory and the chiral expansion. Including also variations in the resolution scale at which nuclear forces are resolved, we provide new error bands on the equation of state, the isospin-asymmetry energy, and its slope parameter. We find in particular that the inclusion of third-order diagrams reduces the theoretical uncertainty at low densities, while in general the largest error arises from omitted higher-order terms in the chiral expansion of the nuclear forces.

Holographic Quark Matter and Neutron Stars.

Abstract: We use a top-down holographic model for strongly interacting quark matter to study the properties of neutron stars. When the corresponding equation of state (EOS) is matched with state-of-the-art results for dense nuclear matter, we consistently observe a first-order phase transition at densities between 2 and 7 times the nuclear saturation density. Solving the Tolman-Oppenheimer-Volkov equations with the resulting hybrid EOSs, we find maximal stellar masses in excess of two solar masses, albeit somewhat smaller than those obtained with simple extrapolations of the nuclear matter EOSs. Our calculation predicts that no quark matter exists inside neutron stars.

The Quarkyonic Star

Abstract: We discuss theoretical scenarios on crossover between nuclear matter (NM) and quark matter (QM). We classify various possibilities into three major scenarios according to the onset of diquark degrees of freedom that characterizes color-superconducting (CSC) states. In the conventional scenario NM occurs at the liquid-gas (or liquid-vacuum at zero temperature) phase transition and QM occurs next, after which CSC eventually appears. With the effect of strong correlation, the BEC-BCS scenario implies that CSC occurs next to NM and QM comes last in the BCS regime. We adopt the quarkyonic scenario in which NM, QM, and CSC are theoretically indistinguishable and thus these names refer to not distinct states but relevant descriptions of the same physical system. Based on this idea we propose a natural scheme to interpolate NM near normal nuclear density and CSC with vector coupling at high baryon density. We finally discuss the mass-radius relation of the neutron star and constraints on parameters in the proposed scheme. Subject headings: Neutron star, Equation of state, Nuclear matter, Quark matter, Color superconductor

Variations on the excluded-volume mechanism

Abstract: The conventional excluded-volume mechanism in the theoretical description of matter properties is generalized by introducing more general functional dependencies of the available volume fraction. The requirement of thermodynamic consistency governs the appearance of rearrangement contributions to thermodynamic quantities and to particle potentials. The main features of the method are studied in three examples: the dissolution of deuterons in warm and dense nuclear matter, the stiffening or softening of the nuclear matter equation of state in a relativistic mean-field model, and the effects of medium-dependent effective degeneracy factors in a Fermi gas model for quark matter.

Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter II

Abstract: Exploiting certain robust topological inputs from the skyrmion description of compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict the equation of state that is consistent with the properties of nuclear matter at the equilibrium density, supports the maximum mass of massive compact star $\sim 2 M_\odot$ and surprisingly gives the sound velocity close to the "conformal velocity" $1/\sqrt{3}$ at densities $\gtrsim 3 n_0$. At the core of this result is the observation that parity-doubling occurs in the nucleon structure as density goes above $\sim 2n_0$ with a chiral-singlet mass $m_0 \sim (0.6-0.9) m_N$, hinting at a possible up-to-date unsuspected source of proton mass and an emergence at high density of scale symmetry and flavor local symmetry, both hidden in the QCD vacuum.

Characteristics of hybrid compact stars with a sharp hadron-quark interface

Abstract: We describe two aspects of the physics of hybrid stars that have a sharp interface between a core of quark matter and a mantle of nuclear matter. Firstly, we analyze the mass-radius relation. We describe a generic “Constant-Speed-of-Sound” (CSS) parameterization of the quark matter equation of state (EoS), in which the speed of sound is independent of density. In terms of the three parameters of the CSS EoS we obtain the phase diagram of possible forms of the hybrid star mass-radius relation, and we show how observational constraints on the maximum mass and typical radius of neutron stars can be expressed as constraints on the CSS parameters. Secondly, we propose a mechanism for the damping of density oscillations, including r-modes, in hybrid stars with a sharp interface. The dissipation arises from the periodic conversion between quark matter and nuclear matter induced by the pressure oscillations in the star. We find the damping grows nonlinearly with the amplitude of the oscillation and is powerful enough to saturate an r-mode at very low saturation amplitude, of order \( 10^{-10}\) , which is compatible with currently available observations of neutron star spin frequencies and temperatures.

Hyperons in nuclear matter from SU(3) chiral effective field theory

Abstract: Brueckner theory is used to investigate the properties of hyperons in nuclear matter. The hyperon-nucleon interaction is taken from chiral effective field theory at next-to-leading order with SU(3) symmetric low-energy constants. Furthermore, the underlying nucleon-nucleon interaction is also derived within chiral effective field theory. We present the single-particle potentials of $ \Lambda$ and $ \Sigma$ hyperons in symmetric and asymmetric nuclear matter computed with the continuous choice for intermediate spectra. The results are in good agreement with the empirical information. In particular, our calculation gives a repulsive $ \Sigma$ -nuclear potential and a weak $ \Lambda$ -nuclear spin-orbit force.

Chiral EFT based nuclear forces: achievements and challenges

Abstract: During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory and three-nucleon forces up to fifth order. Applications of some of these forces have been conducted in nuclear few- and many-body systems—with a certain degree of success. But in spite of these achievements, we are still faced with great challenges. Among them is the issue of a proper uncertainty quantification of predictions obtained when applying these forces in ab initio calculations of nuclear structure and reactions. A related problem is the order by order convergence of the chiral expansion. We start this review with a pedagogical introduction and then present the current status of the field of chiral nuclear forces. This is followed by a discussion of representative examples for the application of chiral two- and three-body forces in the nuclear many-body system including convergence issues.

Full jet evolution in quark-gluon plasma and nuclear modification of jet production and jet shape in Pb + Pb collisions at 2.76 A TeV at the CERN Large Hadron Collider

Abstract: We study the evolution of the full jet shower in quark-gluon plasma by solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in full jets. In our jet evolution equations, we include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with a realistic ($2+1$)-dimensional viscous hydrodynamic simulation for the spacetime profiles of the hot and dense nuclear medium produced in heavy-ion collisions, we apply our formalism to calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and the jet shape function (at partonic level) in $\text{Pb}+\text{Pb}$ collisions at $2.76A$ TeV. The roles of various jet-medium interaction mechanisms on the full jet modification are studied. We find that the nuclear modification of jet shape is sensitive to the interplay of different interaction mechanisms as well as the energies of the full jets.

Heavy Hadrons in Nuclear Matter

Abstract: Current studies on heavy hadrons in nuclear medium are reviewed with a summary of the basic theoretical concepts of QCD, namely chiral symmetry, heavy quark spin symmetry, and the effective Lagrangian approach. The nuclear matter is an interesting place to study the properties of heavy hadrons from many different points of view. We emphasize the importance of the following topics: (i) charm/bottom hadron-nucleon interaction, (ii) structure of charm/bottom nuclei, and (iii) QCD vacuum properties and hadron modifications in nuclear medium. We pick up three different groups of heavy hadrons, quarkonia ($J/\psi$, $\Upsilon$), heavy-light mesons ($D$/$\bar{D}$, $\bar{B}$/$B$) and heavy baryons ($\Lambda_{c}$, $\Lambda_{b}$). The modifications of those hadrons in nuclear matter provide us with important information to investigate the essential properties of heavy hadrons. We also give the discussions about the heavy hadrons, not only in nuclear matter with infinite volume, but also in atomic nuclei with finite baryon numbers, to serve future experiments.

Strong correlations of neutron star radii with the slopes of nuclear matter incompressibility and symmetry energy at saturation

Abstract: We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing $2{M}_{\ensuremath{\bigodot}}$ neutron stars. Unified EoSs for the inner-crust--core region have been built for all the phenomenological models, both relativistic and nonrelativistic. Our investigation shows the existence of a strong correlation of the neutron star radii with the linear combination of the slopes of the nuclear matter incompressibility and the symmetry energy coefficients at the saturation density. Such correlations are found to be almost independent of the neutron star mass in the range $0.6\text{--}1.8\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$. This correlation can be linked to the empirical relation existing between the star radius and the pressure at a nucleonic density between one and two times saturation density, and the dependence of the pressure on the nuclear matter incompressibility, its slope, and the symmetry energy slope. The slopes of the nuclear matter incompressibility and the symmetry energy coefficients as estimated from the finite nuclei data yield the radius of a $1.4{M}_{\ensuremath{\bigodot}}$ neutron star in the range $11.09\text{--}12.86$ km.

Low Density Phases in a Uniformly Charged Liquid

Abstract: This paper is concerned with the macroscopic behavior of global energy minimizers in the three-dimensional sharp interface unscreened Ohta–Kawasaki model of diblock copolymer melts. This model is also referred to as the nuclear liquid drop model in the studies of the structure of highly compressed nuclear matter found in the crust of neutron stars, and, more broadly, is a paradigm for energy-driven pattern forming systems in which spatial order arises as a result of the competition of short-range attractive and long-range repulsive forces. Here we investigate the large volume behavior of minimizers in the low volume fraction regime, in which one expects the formation of a periodic lattice of small droplets of the minority phase in a sea of the majority phase. Under periodic boundary conditions, we prove that the considered energy \({\Gamma}\)-converges to an energy functional of the limit “homogenized” measure associated with the minority phase consisting of a local linear term and a non-local quadratic term mediated by the Coulomb kernel. As a consequence, asymptotically the mass of the minority phase in a minimizer spreads uniformly across the domain. Similarly, the energy spreads uniformly across the domain as well, with the limit energy density minimizing the energy of a single droplet per unit volume. Finally, we prove that in the macroscopic limit the connected components of the minimizers have volumes and diameters that are bounded above and below by universal constants, and that most of them converge to the minimizers of the energy divided by volume for the whole space problem.

Stellar properties and nuclear matter constraints

Abstract: We analyze the stellar properties of the relativistic mean-field (RMF) parametrizations shown to be consistent with the recently studied constraints related to nuclear matter, pure neutron matter, symmetry energy, and its derivatives [Phys. Rev. C 90, 055203 (2014)]. Our results show that only two RMF parametrizations do not allow the emergence of the direct Urca process, important aspect regarding the evolution of a neutron star. Moreover, among all approved RMF models, fourteen of them produce neutron stars with maximum masses inside the range $1.93\ensuremath{\le}M/{M}_{\ensuremath{\bigodot}}\ensuremath{\le}2.05$, with ${M}_{\ensuremath{\bigodot}}$ being the solar mass. Only three models yield maximum masses above this range and a discussion on the inclusion of hyperons is presented. Finally, we verified that the models satisfying the neutron star maximum mass constraint do not observe the squared sound velocity bound; namely, ${v}_{s}^{2}l1/3$, corroborating recent findings. However, the recently proposed $\ensuremath{\sigma}$-cut scheme can make the RMF models consistent with both constraints, depending on the isoscalar-vector interaction of each parametrization.

Finite Nuclei in the Quark-Meson Coupling Model.

Abstract: We report the first use of the effective quark-meson coupling (QMC) energy density functional (EDF), derived from a quark model of hadron structure, to study a broad range of ground state properties of even-even nuclei across the periodic table in the nonrelativistic Hartree-Fock+BCS framework. The novelty of the QMC model is that the nuclear medium effects are treated through modification of the internal structure of the nucleon. The density dependence is microscopically derived and the spin-orbit term arises naturally. The QMC EDF depends on a single set of four adjustable parameters having a clear physics basis. When applied to diverse ground state data the QMC EDF already produces, in its present simple form, overall agreement with experiment of a quality comparable to a representative Skyrme EDF. There exist, however, multiple Skyrme parameter sets, frequently tailored to describe selected nuclear phenomena. The QMC EDF set of fewer parameters, derived in this work, is not open to such variation, chosen set being applied, without adjustment, to both the properties of finite nuclei and nuclear matter.