Brueckner Hartree Fock Research Articles

Relativistic Brueckner–Hartree–Fock Calculations for Cold and Hot Neutron Stars

This study investigates the properties of symmetric and asymmetric nuclear matter using the relativistic Brueckner–Hartree–Fock formalism, examining both zero and finite temperatures up to 70 MeV. Employing the full Dirac space, we incorporate three Bonn potentials (A, B, and C), which account for meson masses, coupling strengths, cutoff parameters, and form factors. The calculated properties of asymmetric nuclear matter form the basis for constructing equation-of-state (EOS) models tailored for neutron stars. These models, in turn, enable the computation of bulk properties for nonrotating, uniformly rotating, and differentially rotating neutron stars. Notably, the EOS models studied in this paper are sufficiently versatile to accommodate the mass of the most massive neutron star ever detected, PSR J0952–0607, estimated to be 2.35 ± 0.17 M ⊙. Furthermore, they yield masses and radii for PSR J0030+451 that align with the confidence intervals established for this pulsar.

Nuclear Matter Equation of State in the Brueckner–Hartree–Fock Approach and Standard Skyrme Energy Density Functionals

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin–isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon–nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy density functional, and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Dark matter effects on the properties of neutron stars: Optical radii

We study the effects of dark matter on the properties of neutron stars by employing a DM-admixed model. The Brueckner–Hartree–Fock theory with realistic three-body forces and a generic bosonic self-interacting dark matter model describe the equations of state for nuclear matter and DM, respectively. We study the complete set of stable ‘dark’ neutron stars and in particular the observable radii of these objects. A rich variety of stellar configurations is found and discussed in detail.

The isovector density-dependence of the M3Y nucleon-nucleon interactions and related soft and hard equations of state

Towards a precise equation of state (EOS) of nuclear matter (NM) based on a realistic interaction, we use non-relativistic Brueckner-Hartree-Fock (BHF) scheme to deduce the isovector (IV) density dependence (DD) of M3Y-Paris and Reid nucleon-nucleon interactions, via comparison with previous BHF calculations of nucleon optical potential. The single particle rearrangement correction is taken into account. With analytical parameterization of the isoscalar DD, the IV DD is parameterized (IVF1) for a broad range of EOSs, from soft EOS of saturation incompressibility K0 = 150 MeV to stiff one with K0 = 300 MeV. These Paris (Reid) EOSs indicate symmetry energy coefficient of 30.06±0.02 MeV (31.76±0.06 MeV), with corresponding density-slope sticks around L = 49.7 MeV (51.9 MeV). We found that the IVF1 DD indicates larger (smaller) saturation binding-energy (density) of asymmetric NM, and more high-density repulsion increasing with density and isospin asymmetry, as well as higher pressure, than those based on the IVF0 DD that scaled in terms of the isoscalar DD. Also, the IVF1 confirms the mostly indicated hard symmetry energy at supra-saturation density, on the contrary of the IVF0 that indicates soft one. Increasing the stiffness of the EOS increases the NM energy, though it decreases the symmetry energy. The more neutron-rich NM gets less bound, over less bound-density range. Only the fine ranges of Paris (K0 = 240 - 250 MeV) and Reid (K0 = 230 - 240 MeV) EOSs maintain simultaneous consistency with earlier experimental constraints and accurate calculations on NM energy, symmetry energy, and pressure.

Spontaneous scalarization in proto-neutron stars

Proto-neutron stars are born when a highly evolved and massive star collapses under gravity. In this paper, we investigate the spontaneous scalarization in proto-neutron stars. Based on the scalar tensor theory of gravity as well as the physical conditions in proto-neutron star, we examine the structure of proto-neutron star. To describe the fluid in proto-neutron star, we utilize SU(2) chiral sigma model and the finite temperature extension of the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Here, we apply the equation of state of proto-neutron stars considering different cases i.e. hot pure neutron matter and hot beta -stable neutron star matter without neutrino trapping as well as with neutrino trapping. The effects of temperature and entropy of proto-neutron stars on the star structure are also studied. Our results confirm that the spontaneous scalarization is affected by different physical conditions in proto-neutron stars.

Quasielastic (p, n) reactions described by a microscopic optical model based on the Gogny force

In this work, we want to study quasielastic (p, n) exchange reactions using a semi-microscopic optical model derived from a previous work, Lopez Moraña and Viñas (2021 J. Phys. G48 035104) based on a nuclear matter approach where the real and imaginary parts are given by the first and second order terms, respectively, of the mass operator obtained by a Brueckner–Hartree–Fock calculation using a G-matrix built up with an effective Gogny interaction. The study of these quasielastic reactions is performed within a Distorted Wave Born Approximation to evaluate the wave functions in the entrance and exit channels, which in turn are used to compute the transition matrix elements. This model, which is free of adjustable parameters, provides a reasonably good agreement with the considered experimental data, namely differential cross sections, analyzing powers and total cross sections, of different reactions spanned along the periodic table at several energies.

Study of6,8He+p elastic scattering using the BHF formalism with three-body forces

In the present work, we have analyzed the elastic scattering data of6He+p at 25.6, 38.6, 40.9, and 71 MeV/A and8He+p at 15.6, 25.6, 32.5, 66, and 72 MeV/A, using the microscopic local optical potential calculated within the framework of the Brueckner–Hartree–Fock (BHF) formalism. The calculation requires mainly two inputs: (1) the nucleon–nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. In the present work, realistic internucleon (NN) potential from Argonne v18 (AV18) and the Urbana IX (UVIX) model of three-body forces with several nucleon density distributions are used for generating the nucleon–nucleus optical potential. We have used the exact method for calculating both the direct and the exchange parts of the spin–orbit potential. We confirm the earlier results that the spin–orbit potential for these neutron-rich nuclei is diffused and extended. Our results show that the different density distributions reproduce rather well the experimental differential cross sections for both isotopes, while the phenomenological density with a two-neutron halo gives satisfactory results for6He-p analyzing power data. None of the densities used for8He can reproduce the experimentally analyzed power data. Our analysis reveals that the calculated microscopic optical potentials, with and without three-body forces using the BHF approach, provide satisfactory agreement with the elastic scattering data for6,8He+p.

Nuclear Matter and Neutron Stars from Relativistic Brueckner–Hartree–Fock Theory

The momentum and isospin dependence of the single-particle potential for the in-medium nucleon are the key quantities in the Relativistic Brueckner–Hartree–Fock (RBHF) theory. It depends on how to extract the scalar and the vector components of the single-particle potential inside nuclear matter. In contrast to the RBHF calculations in the Dirac space with the positive-energy states (PESs) only, the single-particle potential can be determined in a unique way by the RBHF theory together with the negative-energy states, i.e., the RBHF theory in the full Dirac space. The saturation properties of symmetric and asymmetric nuclear matter in the full Dirac space are systematically investigated based on the realistic Bonn nucleon–nucleon potentials. In order to further specify the importance of the calculations in the full Dirac space, the neutron star properties are investigated. The direct URCA process in neutron star cooling will happen at density ρ DURCA = 0.43, 0.48, 0.52 fm−3 with proton fractions of Y p,DURCA = 0.13. The radii of a 1.4M ⊙ neutron star are predicated as km, and their tidal deformabilities are for potential Bonn A, B, C. Compared with the results obtained in the Dirac space with PESs only, the full-Dirac-space RBHF calculation predicts the softest symmetry energy, which would be more favored by the gravitational wave detection of GW170817. Furthermore, the results from the full-Dirac-space RBHF theory are consistent with the recent astronomical observations of massive neutron stars and simultaneous mass–radius measurement.

Isoentropic equations of state of beta -stable hadronic matter with a quark phase transition

We construct isoentropic equations of state (EOSs) of beta -stable dense hadronic matter considering the possibility that a quark deconfinement phase transition can take place. These conditions can be actually realized in different astrophysical contexts like core-collapse supernovae (CCSNe), during the early stages of the evolution of a newly formed neutron star (protoneutron star, PNS) or in the postmerger compact object formed in binary neutron star (BNS) mergers. We consider four different EOSs to describe the hadronic phase: three EOSs from relativistic mean field theory and one EOS recently derived from microscopic calculations in the framework of the Brueckner–Hartree–Fock approach. We combine these hadronic EOSs with a quark matter EOS obtained from a modified MIT-Bag model which takes into account some perturbative corrections in the grand canonical potential due to the quark–quark interaction. The two phases are then joined up through a Gibbs construction. For each model we study thermal and neutrino trapping effects on the matter composition and consequently on the EOS. We finally determine the PNS static structure integrating the Tolman–Oppenheimer–Volkoff equations. We find that the thermal contribution and particularly the effect of neutrino trapping play an important role on the full EOS. The latter can get softer or stiffer according to the strangeness content in the hadronic phase. These effects are thus crucial to provide a proper description of the dynamical evolution of both the postmerger compact object formed in a BNS merger or the PNS formed in a CCSN.

A microscopic study of spin-polarized neutron matter

In this work, the static fluctuation approximation (SFA) is used to investigate the thermodynamic properties of spin-polarized neutron matter. The energy per particle, pressure, entropy per particle, specific heat capacity, and effective magnetic field are studied as functions of density, temperature, and polarization fraction. The Argonne v18 nucleon–nucleon potential is used here. It is found that the energy per particle, pressure, entropy per particle, and effective magnetic field increase as the density or temperature increases. Also, the energy per particle and pressure are linearly dependent on the quadratic spin polarization δ2. The system becomes more ordered as δ increases. Our calculations are found to be in good agreement with previously published results obtained with different many-body techniques, such as the lowest order constrained variational (LOCV) method, the Brueckner–Hartree–Fock (BHF) approach, and the Dirac–Brueckner–Hartree–Fock (DBHF) technique.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now, 2.14−0.09+0.10M⊙ for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5M⊙ deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility.

Microscopic equation of state of hot nuclear matter for numerical relativity simulations

Context. A precise understanding of the equation of state (EOS) of dense and hot matter is key to modeling relativistic astrophysical environments, including core-collapse supernovae (CCSNe), protoneutron star (PNSs) evolution, and compact binary mergers. Aims. In this paper, we extend the microscopic zero-temperature BL (Bombaci and Logoteta) nuclear EOS to finite temperature and arbitrary nuclear composition. We employ this new EOS to describe hot β-stable nuclear matter and to compute various structural properties of nonrotating PNS. We also apply the EOS to perform dynamical simulations of a spherically symmetric CCSN. Methods. The EOS is derived using the finite temperature extension of the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Neutron star properties are computed by solving the Tolman–Oppenheimer–Volkoff structure equations numerically. The sperically symmetric CCSN simulations are performed using the AGILE-IDSA code. Results. Our EOS models are able to reproduce typical features of both PNS and spherically symmetric CCSN simulations. In addition, our EOS model is consistent with present measured neutron star masses and particularly with the masses: M = 2.01 ± 0.04 M⊙ and M = 2.14−0.18+0.20 M⊙ of the neutron stars in PSR J0348+0432 and PSR J0740+6620 respectively. Finally, we suggest a feasible mechanism to produce low-mass black holes (M ∼ 2 M⊙) that could have far-reaching consequences for interpreting the gravitational wave event GW190814 as a BH–BH merger.

Nucleon-nucleus optical potential computed with the Gogny interaction

The ability of the Gogny forces of the D1 family to describe the nucleon-nucleus scattering is studied. To this end, we use an optical model (OM) potential built up using a semi-microscopic nuclear matter (NM) approach. The real and imaginary parts of the OM are provided by the first and second-order terms, respectively, of the Taylor expansion of the mass operator calculated within the Brueckner–Hartree–Fock (BHF) method using the reaction G-matrix built up with the effective Gogny force instead of a microscopic interaction. The optical potential in finite nuclei is obtained through the local density approximation (LDA) using the neutron and proton densities provided by a quasi-local Hartree–Fock (HF) calculation with the same Gogny force for the sake of consistency. A reasonable good agreement is found between the theoretical differential cross-sections and the analyzing powers (AP) of the elastic neutron and proton scattering along the periodic table from Ca to Pb calculated with the Gogny forces and the corresponding values predicted by the global phenomenological potential of Koning and Delaroche. To investigate the limits of the approximations used in this work, comparisons with the results of nucleon-nucleus elastic scattering in 40Ca and 48Ca obtained using the nuclear structure model (NSM) are also performed.

Isospin-density-dependent pairing from infinite nuclear matter to finite nuclei

The effective isospin-density dependent pairing interaction (P1) [S. S. Zhang, U. Lombardo and E. G. Zhao, Sci. Chin. Phys. Mech. Astro. {\bf 54}, 236 (2011)] extracted from neutron pairing gaps for $^1$S$_0$ in asymmetric nuclear matter calculations [S. S. Zhang, L. G. Cao, U. Lombardo, et al. Phys. Rev. C {\bf 81}, 044313 (2010)] is employed to study the bulk properties of Ca, Ni, Zr and Sn isotopes. The odd-even mass (OEM) staggering is calculated by the Skyrme Hartree-Fock plus BCS method (SHF + BCS) with the SkP interaction. For comparison, we study two other types of isovector effective pairing interactions. One is also extracted from pairing gaps of infinite nuclear matter by the Brueckner-Hartree-Fock (BHF) method but for free spectrum (P2). The other is obtained by fitting the empirical OEM (P3). An isoscalar effective pairing interaction (P4) is also adopted which is determined by fitting the empirical OEM. We find that interaction P1 can better describe the OEM staggering of Ni, Zr and Sn isotopes by $14.3 \%, 41 \%, 30.4 \%$ compared with interaction P2, in terms of root mean square deviations to the empirical OEM, respectively. On the other hand, the performance of P1 and P2 is comparable for Ca isotopes. For Ca and Ni isotopes, P1 behaves similarly as P3, but for Zr isotopes P1 is better than P3 by $\sim 34 \%$. Among the four pairing interactions studied, P4 performs the worst. Therefore, one may conclude that for neutron pairings in finite nuclei, the isovector pairings are preferred than the isoscalar one. It is quite interesting to note that the pairing interaction P1 extracted from nuclear matter calculations can describe pairing gaps of finite nuclei as well as or even better than the interaction P3 directly fitted to finite nuclei.

Spinodal instabilities of spin-polarized asymmetric nuclear matter

We analyze the spinodal instabilities of spin polarized asymmetric nuclear matter at zero temperature for several configurations of the neutron and proton spins. The calculations are performed with the Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential plus a three-nucleon force of Urbana type. An analytical parametrization of the energy density, which reproduces with good accuracy the BHF results, is employed to determine the spinodal instability region. We find that, independently of the of the orientation of the neutron and proton spins, the spinodal instability region shinks when the system is polarized, being its size smaller smaller when neutron and proton spins are antiparallel than when they are oriented in a parallel way. We find also that the spinodal instability is always dominated by total density fluctuation independently of the degree of polarization of the system, and that restoration of the isospin symmetry in the liquid phase, {\it i.e.,} the so-called isospin distillation or fragmentation effect, becomes less efficient with the polarization of the system.

Properties of nuclear matter in relativistic Brueckner–Hartree–Fock model with high-precision charge-dependent potentials

Properties of nuclear matter are investigated in the framework of relativistic Brueckner–Hartree–Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as a pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon–nucleon (NN) interactions, G matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleon are around −10.72 MeV to −16.83 MeV at saturation densities, 0.139 fm−3 to 0.192 fm−3 with these three potentials, respectively. It clearly demonstrates that the pseudovector coupling between pion and nucleon can generate reasonable saturation properties comparing with pseudoscalar coupling. Furthermore, these saturation properties have strong correlations with the tensor components of NN potentials, i.e., the D-state probabilities of deuteron, PD to form a relativistic Coester band. The equations of state of pure neutron matter from pvCD-Bonn potentials are almost identical, since the prominent difference of pvCD Bonn potentials are the components of tensor force, which provides very weak contributions in the case of total isospin T = 1. In addition, the charge symmetry breaking (CSB) and charge independence breaking (CIB) effects are also discussed in nuclear matter from the partial wave contributions with these high-precision charge-dependent potentials. In general, the magnitudes of CSB from the differences between nn and pp potentials are about 0.05 MeV, while those of CIB are around 0.35 MeV from the differences between np and pp potentials.

Asymmetric nuclear matter and realistic potentials

The equation of state for asymmetric nuclear matter is presented within the Brueckner–Hartree–Fock (BHF) approach by using recent high-quality soft nucleon–nucleon potentials from next-to-leading order (NLO) up to fifth order (N4LO) of the chiral expansion for the wide range of densities and asymmetry parameter, which are very interesting these days in the heavy-ion collisions and neutron stars. For comparison purposes, the same calculations are performed for Brueckner–Hartree–Fock approach plus two-body density-dependent Skyrme potential which is equivalent to three-body forces. Also the results are compared with the other theoretical models, especially the Brueckner–Hartree–Fock plus three-body forces and the Dirac–Brueckner–Hartree–Fock approaches. Our equation-of-state models are able to reproduce the empirical symmetry energy $$\hbox {E}_\mathrm{{sym}}$$ and its slope parameter L at the empirical saturation density $$\rho _{0}$$ and are compatible with experimental data from collisions between heavy nuclei. The symmetry energy of about 30 MeV is obtained at the saturation nuclear matter density. There is very good agreement between the experimental symmetry energy value and those calculated in the Brueckner–Hartree–Fock approach.

The Effect of Various Three-Body Forces on Nuclear Matter and Neutron Stars Properties

The binding energy per nucleon for nuclear matter, i.e., equation of state (EOS), within the Brueckner–Hartree–Fock (BHF) approach with the consideration of various three-body forces (3BFs) like the phenomenological 3BF and by adding a contact term to the BHF calculations are considered at variance densities. The 3BF contribution turns out to be nonnegligible contribution and to have a substantial saturation effect. The calculations are done utilizing the CD-Bonn and Argonne V18 nucleon–nucleon (NN) potentials. These NN potentials give great fitting to the deuteron properties and are phase-shift equivalent. The resultant EOS is compatible with the phenomenological analysis on the saturation point. It is demonstrated that the 3BF influences significantly on the nuclear matter EOS at high densities. Moreover, it is necessary for reproducing the empirical saturation properties for symmetric nuclear matter. The pressure has been also calculated and the suggested approaches reproduce fairly well agreement with the empirical data. We also examined the maximum neutron star masses which are close to two solar masses, which is again compatible with recent observational data. Comparison with other microscopic EOS is presented and discussed.

Properties of Neutron Stars Described by a Relativistic Ab Initio Model

Abstract Properties of neutron stars are investigated by an available relativistic ab initio method, the relativistic Brueckner–Hartree–Fock (RBHF) model, with the latest high-precision, relativistic charge-dependent potentials, pvCD-Bonn A, B, C. The neutron star matter is solved within the beta equilibrium and charge neutrality conditions in the framework of the RBHF model. Compared to the conventional treatment, where the chemical potential of leptons was approximately represented by the symmetry energy of nuclear matter, the equation of state of neutron star matter in the present self-consistent calculation with pvCD-Bonn B has a striking difference above the baryon number density n b = 0.55 fm−3. However, these differences influence the global properties of neutron stars only about 1% to 2%. Then, three two-body potentials pvCD-Bonn A, B, C, with different tensor components, are systematically applied in the RBHF model to calculate the properties of neutron stars. It is found that the maximum masses of neutron stars are around 2.21–2.30 M ⊙, and the corresponding radii are R = 11.18–11.72 km. The radii of a 1.4 M ⊙ neutron star are predicated as R 1.4 = 12.34–12.91 km, and their dimensionless tidal deformabilities are Λ1.4 = 485–626. Furthermore, the direct URCA process in neutron star cooling will happen from n b = 0.414 to 0.530 fm−3 with the proton fractions Y p = 0.136–0.138. All of the results obtained from the RBHF model only with two-body pvCD-Bonn potentials completely satisfy various constraints from recent astronomical observations of massive neutron stars, gravitational wave detection (GW170817), and simultaneous mass–radius measurement.