Pure Neutron Matter Research Articles

Density-dependent effective baryon–baryon interaction from chiral three-baryon forces

A density-dependent effective potential for the baryon–baryon interaction in the presence of the (hyper)nuclear medium is constructed, based on the leading (irreducible) three-baryon forces derived within SU(3) chiral effective field theory. We evaluate the contributions from three classes: contact terms, one-pion exchange and two-pion exchange. In the strangeness-zero sector we recover the known result for the in-medium nucleon–nucleon interaction. Explicit expressions for the ΛN in-medium potential in (asymmetric) nuclear matter are presented. Our results are suitable for implementation into calculations of (hyper)nuclear matter. In order to estimate the low-energy constants of the leading three-baryon forces we introduce the decuplet baryons as explicit degrees of freedom and construct the relevant terms in the minimal non-relativistic Lagrangian. With these, the constants are estimated through decuplet saturation. Utilizing this approximation we provide numerical results for the effect of the three-body force in symmetric nuclear matter and pure neutron matter on the ΛN interaction. A moderate repulsion that increases with density is found in comparison to the free ΛN interaction.

Di-neutrons in neutron matter within a Brueckner-Hartree-Fock approach

We investigate the appearance of di-neutron bound states in pure neutron matter within the Brueckner-Hartree-Fock approach at zero temperature. We consider Argonne $v_{18}$ and Paris bare interactions as well as chiral two- and three-nucleon forces. Self-consistent single-particle potentials are calculated controlling explicitly singularities in the $g$ matrix associated with bound states. Di-neutrons are loosely bound, with binding energies below $1$ MeV, but are unambiguously present for Fermi momenta below $1$ fm$^{-1}$ for all interactions. Within the same framework we are able to calculate and characterize di-neutron bound states, obtaining mean radii as high as $\sim 110$ fm. The resulting equations of state and mass-radius relations for pure neutron stars are analyzed including di-neutron contributions.

Di-nucleon structures in homogeneous nuclear matter based on two- and three-nucleon interactions

We investigate homogeneous nuclear matter within the Brueckner-Hartree-Fock (BHF) approach in the limits of isospin-symmetric nuclear matter (SNM) as well as pure neutron matter at zero temperature. The study is based on realistic representations of the internucleon interaction as given by Argonne v18, Paris, Nijmegen I and II potentials, in addition to chiral N$^{3}$LO interactions, including three-nucleon forces up to N$^{2}$LO. Particular attention is paid to the presence of di-nucleon bound states structures in $^1\textrm{S}_0$ and $^3\textrm{SD}_1$ channels, whose explicit account becomes crucial for the stability of self-consistent solutions at low densities. A characterization of these solutions and associated bound states is discussed. We confirm that coexisting BHF single-particle solutions in SNM, at Fermi momenta in the range $0.13-0.3$~fm$^{-1}$, is a robust feature under the choice of realistic internucleon potentials.

Microscopically constrained mean-field models from chiral nuclear thermodynamics

We explore the use of mean field models to approximate microscopic nuclear equations of state derived from chiral effective field theory across the densities and temperatures relevant for simu- lating astrophysical phenomena such as core-collapse supernovae and binary neutron star mergers. We consider both relativistic mean field theory with scalar and vector meson exchange as well as energy density functionals based on Skyrme phenomenology and compare to thermodynamic equa- tions of state derived from chiral two- and three-nucleon forces in many-body perturbation theory. Quantum Monte Carlo simulations of symmetric nuclear matter and pure neutron matter are used to determine the density regimes in which perturbation theory with chiral nuclear forces is valid. Within the theoretical uncertainties associated with the many-body methods, we find that select mean field models describe well microscopic nuclear thermodynamics. As an additional consistency requirement, we study as well the single-particle properties of nucleons in a hot/dense environment, which affect e.g., charged-current weak reactions in neutron-rich matter. The identified mean field models can be used across a larger range of densities and temperatures in astrophysical simulations than more computationally expensive microscopic models.

Hot and dense matter beyond relativistic mean field theory

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $\Gamma_{th}=1+(P_{th}/\epsilon_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $\Gamma_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.

Nuclear matter saturation with chiral three-nucleon interactions fitted to light nuclei properties

Abstract The energy per particle of symmetric nuclear matter and pure neutron matter is calculated using the many-body Brueckner–Hartree–Fock approach and employing the Chiral Next-to-next-to-next-to leading order (N3LO) nucleon–nucleon (NN) potential, supplemented with various parametrizations of the Chiral Next-to-next-to leading order (N2LO) three-nucleon interaction. Such combination is able to reproduce several observables of the physics of light nuclei for suitable choices of the parameters entering in the three-nucleon interaction. We find that some of these parametrizations provide a satisfactory saturation point of symmetric nuclear matter and values of the symmetry energy and its slope parameter L in very good agreement with those extracted from various nuclear experimental data. Thus, our results represent a significant step toward a unified description of few- and many-body nuclear systems starting from two- and three-nucleon interactions based on the symmetries of QCD.

Medium polarization in asymmetric nuclear matter

The influence of the core polarization on the effective nuclear interaction of asymmetric nuclear matter is calculated in the framework of the induced interaction theory. The strong isospin dependence of the density and spin density fluctuations is studied along with the interplay between the neutron and proton core polarizations. Moving from symmetric nuclear matter to pure neutron matter the crossover of the induced interaction from attractive to repulsive in the spin singlet state is determined as a function of the isospin imbalance.The density range in which it occurs is also determined. For the spin triplet state the induced interaction turns out to be always repulsive. The implications of the results for the neutron star superfluid phases are shortly discussed.

Deformation properties with a finite-range simple effective interaction

Deformed and spherical even–even nuclei are studied using a finite-range simple effective interaction within the Hartree–Fock–Bogoliubov mean-field approach. Different parameter sets of the interaction, corresponding to different incompressibility, are constructed by varying the exponent γ of the density in the traditional density-dependent term. Ten of the 12 parameters of these interactions are determined from properties of asymmetric nuclear matter and spin-polarized pure neutron matter. The two remaining parameters are fitted to reproduce the experimental binding energies known in 620 even–even nuclei using several variants of the rotational energy correction. The rms deviations for the binding energy depend on the value of γ and the way the rotational energy correction is treated but they can be as low as 1.56 MeV, a value competitive with other renowned effective interactions of Skyrme and Gogny type. Charge radii are compared to the experimental values of 313 even–even nuclei and the rms deviation is again comparable and even superior to the one of popular Skyrme and Gogny forces. Emphasis is given to the deformation properties predicted with these interactions by analyzing the potential energy surfaces for several well deformed nuclei and the fission barriers of some nuclei. Comparison of the results with the experimental information, where available, as well as with the results of the Gogny D1S force, shows satisfactory agreement.

Transport properties of the Fermi hard-sphere system

The transport properties of neutron star matter play an important role in many astrophysical processes. We report the results of a calculation of the shear viscosity and thermal conductivity coefficients of the hard-sphere fermion system of degeneracy $\nu$=2, that can be regarded as a model of pure neutron matter. Our approach is based on the effective interaction obtained from the formalism of correlated basis functions and the cluster expansion technique. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second order contributions to the self-energy that are not taken into account in nuclear matter studies available in the literature.

Stellar properties and nuclear matter constraints

We have analyzed 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 [Dutra et al., 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 $1.93\leqslant M/M_\odot\leqslant 2.05$, with $M_\odot$ 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 have verified that the models satisfying the neutron star maximum mass constraint do not observe the squared sound velocity bound, namely, $v_s^2 < 1/3$, corroborating recent findings. However, the recently proposed $\sigma$-cut scheme can make the RMF models consistent with both constraints depending on the isoscalar-vector interaction of each parametrization.

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

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 $1.4~\mathrm{M}_{\odot}$ neutron stars to a be larger than 10 km, 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.

Reducible chiral four-body interactions in nuclear matter

The method of unitary transformations generates five classes of leading-order reducible chiral four-nucleon interactions which involve pion-exchanges and a spin-spin contact-term. Their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter are evaluated in detail. For most of the closed four-loop diagrams the occurring integrals over four Fermi-spheres can be reduced to easily manageable one- or two-parameter integrals. One observes substantial cancelations among the different contributions arising from 2-ring and 1-ring diagrams. Altogether, the net attraction generated by the chiral four-nucleon interaction does not exceed values of $-1.3$\,MeV for densities $\rho<2\rho_0$.

Latest results of Skyrme-Hartree-Fock-Bogoliubov mass formulas

The latest developments made in deriving accurate mass predictions within the microscopic Skyrme Hartree-Fock-Bogolyubov (HFB) approach are described. Using the HFB method, we have refitted our BSk20 and BSk21 models, on which were based the HFB-20 and HFB-21 mass tables, to the 2353 measured masses of nuclei with N and Z ≥ 8 given in the newly available 2012 Atomic Mass Evaluation. In addition, we have now investigated the sensitivity to the symmetry coefficient J and the stiffness of the neutron matter equation of state. We present here in all 5 new Skyrme interactions, along with their corresponding mass tables. The root-mean square deviation obtained with our preferred model (HFB-24) with respect to essentially all the 2353 available mass data falls to 0.549 MeV, the best value ever found within the mean-field framework. Since our Skyrme force is also constrained by the properties of pure neutron matter this new model is particularly well-suited for application to astrophysical problems involving a neutron-rich environment, such as the elucidation of the r-process of nucleosynthesis, and the description of supernova cores and neutron-star crusts.

Electric dipole polarizability inPb208as a probe of the symmetry energy and neutron matter aroundρ0/3

It is currently a big challenge to accurately determine the symmetry energy $E_{\text{sym}}(\rho)$ and the pure neutron matter equation of state $E_{\text{PNM}}(\rho)$, even their values around saturation density $\rho_0 $. We find that the electric dipole polarizability $\alpha _ {\text{D}}$ in $^{208}$Pb can be determined uniquely by the magnitude of the $E_{\text{sym}}(\rho)$ or almost equivalently the $E_{\text{PNM}}(\rho)$ at subsaturation densities around $\rho_0/3 $, shedding a light upon the genuine correlation between the $\alpha _ {\text{D}}$ and the $E_{\text{sym}}(\rho)$. By analyzing the experimental data of the $\alpha _ {\text{D}}$ in $^{208}$Pb from RCNP using a number of non-relativistic and relativistic mean-field models, we obtain very stringent constraints on $E_{\text{sym}}(\rho)$ and $E_{\text{PNM}}(\rho)$ around $\rho_0/3 $. The obtained constraints are found to be in good agreement with the results extracted in other analyses. In particular, our results provide for the first time the experimental constraints on $E_{\text{PNM}}(\rho)$ around $\rho_0/3 $, which are in harmony with the recent determination of $E_{\text{PNM}}(\rho)$ from microscopic theoretical studies and potentially useful in constraining the largely uncertain many-nucleon interactions in microscopic calculations of neutron matter.

Nuclear and neutron matters at low density

In this study, symmetric and asymmetric nuclear matter, as well as pure neutron matter in the low-density regime, where the density ranges 0.01 fm−3ρ 0.13 fm−3, have been investigated. Two different realistic and accurate two-body forces are considered. These include Argonne V18 and the CD-Bonn, which give quite different equations of state. The binding energy per nucleon as a function of the density is calculated using the Brueckner-Hartree-Fock approximation. Both the conventional (gap) and continuous choice of single-particle energies are utilized. For the sake of comparison, the equation of state within the self-consistent Green’s function approach is calculated using the CD-Bonn potential. The contribution of the hole-hole terms leads to a repulsive contribution to the energy per nucleon which increases with the nuclear density. Significantly, very good agreement between the experimental symmetry energy values and those calculated in the self-consistent Green’s function and BHF approaches especially at low density, has been accomplished. Finally, The results are compared with those from various many-body approaches, such as variational and relativistic mean field approaches.

Isospin quartic term in the kinetic energy of neutron-rich nucleonic matter

The energy of a free gas of neutrons and protons is well known to be approximately isospin parabolic with a negligibly small quartic term of only $0.45$ MeV at the saturation density of nuclear matter $\rho_0=0.16/\rm{fm}^3$. Using an isospin-dependent single-nucleon momentum distribution including a high (low) momentum tail (depletion) with its shape parameters constrained by recent high-energy electron scattering and medium-energy nuclear photodisintegration experiments as well as the state-of-the-art calculations of the deuteron wave function and the equation of state of pure neutron matter near the unitary limit within several modern microscopic many-body theories, we show for the first time that the kinetic energy of interacting nucleons in neutron-rich nucleonic matter has a significant quartic term of $7.18\pm2.52\,\rm{MeV}$. Such a large quartic term has significant ramifications in determining the equation of state of neutron-rich nucleonic matter using both terrestrial and astrophysical observables.

Comparative study of three-nucleon force models in nuclear matter

We calculate the energy per particle of symmetric nuclear matter and pure neutron matter using the microscopic many-body Brueckner-Hartree-Fock (BHF) approach and employing the Argonne V18 (AV18) nucleon-nucleon (NN) potential supplemented with two different three-nucleon force models recently constructed to reproduce the binding energy of $^{3}\mathrm{H},\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}$, and $^{4}\mathrm{He}$ nuclei as well as the neutron-deuteron doublet scattering length. We find that none of these new three-nucleon force models is able to reproduce simultaneously the empirical saturation point of symmetric nuclear matter and the properties of three- and four-nucleon systems.

Efficacy of crustal superfluid neutrons in pulsar glitch models

In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{\rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results of low-density pure neutron matter calculations. When entrainment is included at the level suggested by recent microscopic calculations and the core is fully coupled to the crust, the model is only able to account for the Vela glitch activity for a 1.4$M_{\odot}$ star if the equation of state is particularly stiff $L>100$ MeV. However, an uncertainty of about 10\% in the crust-core transition density and pressure allows for the Vela glitch activity to be marginally accounted for in the range $L\approx30-60$MeV consistent with a range of experimental results. Alternatively, only a small amount of core neutrons need be involved. If less than 50\% of the core neutrons are coupled to the crust during the glitch, we can also account for the Vela glitch activity using crustal neutrons alone for EOSs consistent with the inferred range of $L$. We also explore the possibility of Vela being a high-mass neutron star, and of crustal entrainment being reduced or enhanced relative to its currently predicted values.

From asymmetric nuclear matter to neutron stars: A functional renormalization group study

A previous study of nuclear matter in a chiral nucleon-meson model is extended to isospin-asymmetric matter. Fluctuations beyond mean-field approximation are treated in the framework of the functional renormalization group. The nuclear liquid-gas phase transition is investigated in detail as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of both symmetric nuclear matter and pure neutron matter are found to be in good agreement with realistic many-body computations. We also study the density dependence of the pion mass in the medium. The question of chiral symmetry restoration in neutron matter is addressed; we find a stabilization of the phase with spontaneously broken chiral symmetry once fluctuations are included. Finally, neutron star matter including beta equilibrium is discussed. The model satisfies the constraints imposed by the existence of two-solar-mass neutron stars.

Thermal properties of asymmetric nuclear matter

The thermal properties of asymmetric nuclear matter are investigated in a relativistic mean-field approach. We start from free-space $NN$ interactions and derive in-medium self-energies by the Dirac-Brueckner theory. By the density-dependent relativistic hadron procedure we derive in a self-consistent approach density-dependent meson-baryon vertices. At the mean-field level, we include isoscalar and isovector-scalar and vector interactions. The nuclear equation of state is investigated for a large range of total baryon densities up to the neutron star regime, the full range of asymmetries $\ensuremath{\xi}=Z/A$ from symmetric nuclear matter to pure neutron matter, and temperatures up to $T\ensuremath{\sim}100$ MeV. The isovector-scalar self-energies are found to modify strongly the thermal properties of asymmetric nuclear matter. A striking result is the change of phase transitions when isovector-scalar self-energies are included.