Brueckner Hartree Fock Approach Research Articles

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.

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.

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.

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.

Cooling of hybrid neutron stars with microscopic equations of state

ABSTRACT We model the cooling of hybrid neutron stars combining a microscopic nuclear equation of state in the Brueckner–Hartree–Fock approach with different quark models. We then analyse the neutron star cooling curves predicted by the different models and single out the preferred ones. We find that the possibility of neutron p-wave pairing can be excluded in our scenario.

Accretion-induced prompt black hole formation in asymmetric neutron star mergers, dynamical ejecta, and kilonova signals

ABSTRACT We present new numerical relativity results of neutron star (NS) mergers with chirp mass 1.188 M⊙ and mass ratios q = 1.67 and q = 1.8 using finite-temperature equations of state (EOS), approximate neutrino transport, and a subgrid model for magnetohydrodynamics-induced turbulent viscosity. The EOS are compatible with nuclear and astrophysical constraints and include a new microphysical model derived from ab initio calculations based on the Brueckner–Hartree–Fock approach. We report for the first time evidence for accretion-induced prompt collapse in high-mass-ratio mergers, in which the tidal disruption of the companion and its accretion on to the primary star determine prompt black hole (BH) formation. As a result of the tidal disruption, an accretion disc of neutron-rich and cold matter forms with baryon masses ∼0.15 M⊙, and it is significantly heavier than the remnant discs in equal-masses prompt-collapse mergers. Massive dynamical ejecta of the order of ∼0.01 M⊙ also originate from the tidal disruption. They are neutron-rich and expand from the orbital plane with a crescent-like geometry. Consequently, bright, red, and temporally extended kilonova emission is predicted from these mergers. Our results show that prompt BH mergers can power bright electromagnetic counterparts for high-mass-ratio binaries, and that the binary mass ratio can be, in principle, constrained from multimessenger observations.

A hybrid model of Skyrme- and Brueckner-type interactions for neutron star matter

Abstract We suggest a hybrid model for neutron star matter to discuss the hyperon puzzle inherent in the 2.0 M$_{\odot}$ of the neutron star. For the nucleon–nucleon ($NN$) interaction, we employ the Skyrme–Hartree–Fock approach based on various Skyrme interaction parameter sets, and take the Brueckner–Hartree–Fock approach for the interactions related to hyperons. For the many-body interactions including hyperons, we make use of the multi-pomeron-exchange model, whose parameters have been adjusted to the data deduced from various hypernuclei properties. For clear understanding of the physics in the hybrid model, we discuss fractional functions of related particles, symmetry energies, and chemical potentials in dense matter. Finally, we investigate the equations of state and mass–radius relation of neutron stars, and show that the hybrid model can properly describe the 2.0 M$_{\odot}$ neutron star mass data with the many-body interaction employed in the hybrid model. Recent tidal deformability data from the gravitational wave observation are also compared to our calculations, especially in terms of the neutron skin of $^{208}$Pb and nuclear incompressibility.

A nuclear matter calculation with the tensor-optimized Fermi sphere method with central interaction

Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4$^\prime$$NN$ potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function $F$, where $F$ can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian $\mathcal{H}$ and $F$. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ fm$^{-3}$ in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.

Global α - nucleus optical model based on an Dirac Brueckner Hartree Fock approach

The global α-nucleus optical model is studied based on the nucleon self-energies in an Dirac-Brueckner-Hartree-Fock (DBHF) approach. The newly developed nucleon-nucleus optical model CTOM derived from DBHF, is used as the basis to consistently generate the real and imaginary potentials of the α-nucleus optical potential by double-folding model. The same range correction a of the improved local density approximation (ILDA) in CTOM is adopted, which is also suitable to modify the nucleon interaction range in α-nucleus systems. To get better description of experimental data, the re-normalization factors (NR,NI) are introduced in α-nucleus scattering calculations, and the individual optimized (NR,NI) for all nuclei and energies are searched out under the guidance of χ2 criterion. We systematically explore the energy dependence of NR and NI by considering the α elastic scattering from 12C to 208Pb at incident energies below 120MeV/nucleon and a simple exponential function is extracted. With this global α-nucleus optical potential, a reasonable description of all available experimental data for α scattering from nuclei is achieved.

Tensor optimized Fermi sphere method for nuclear matter—Power series correlated wave function and a cluster expansion

A new formalism, called “tensor optimized Fermi sphere (TOFS) method”, is developed to treat the nuclear matter using a bare interaction among nucleons. In this method, the correlated nuclear matter wave function is taken to be a power series type, ΨN=[∑n=0N(1∕n!)Fn]Φ0 and an exponential type, Ψex=exp(F)Φ0, with the uncorrelated Fermi-gas wave function Φ0, where the correlation operator F can induce central, spin–isospin, tensor, etc. correlations, and Ψex corresponds to a limiting case of ΨN (N→∞). In the TOFS formalism based on Hermitian form, it is shown that the energy per particle in nuclear matter with Ψex can be expressed in terms of a linked-cluster expansion. On the basis of these results, we present the formula of the energy per particle in nuclear matter with ΨN. We call the Nth-order TOFS calculation for evaluating the energy with ΨN, where the correlation functions are optimally determined in the variation of the energy. The TOFS theory is applied for the study of symmetric nuclear matter using a central NN potential with short-range repulsion. The calculated results are fairly consistent to those of other theories such as the Brueckner–Hartree–Fock approach etc.

Proton spectral functions in finite nuclei based on the extended Brueckner–Hartree–Fock approach

We have calculated the proton spectral functions in finite nuclei based on the local density approximation where the properties of finite nuclei and nuclear matter are calculated by the Skyrme–Hartree–Fock method and the extended Brueckner–Hartree–Fock approach, respectively. The scaled spectral function from our calculation is in good agreement with experimental results at small momenta while the difference between them becomes apparent at high momenta. Besides, a target dependence of the scaled proton spectral function is also obtained in our calculation as was observed in experiment. A further investigation indicates that the proportion of the high density region of the proton has a significant contribution to this target-dependent behavior since the spectral function in asymmetric nuclear matter increases significantly as a function of density.

Temperature Effects on the Equation of State and Symmetry Energy at Low and High Densities

Thermal properties of symmetric nuclear matter and pure neutron matter are studied in a selfconsistent Green’s function and Brueckner–Hartree–Fock approaches with the inclusion of the contact interaction using CDBONN potential. Also we investigate the temperature dependence of the symmetry energy. The symmetry energy at fixed density is found to generally decrease with temperature. The temperature effects on the nuclear matter symmetry energy are found to be stronger at lower densities while become much weaker at higher densities. The results of several microscopic approaches are compared. Also the results are compared with recent experimental data. There is good agreement between the experimental symmetry energy and those calculated in the Brueckner–Hartree–Fock approach.

Nuclear matter calculations with chiral interactions

Using two-nucleon and three-nucleon interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit Δ isobar contributions, we calculate the energy per particle of symmetric nuclear matter and pure neutron matter employing the microscopic Brueckner–Hartree–Fock approach. Specifically, we present nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with Δ isobar intermediate states (N3LOΔ) recently developed by Piarulli et al. [1] supplemented with a local N2LO three-nucleon interaction with explicit Δ isobar degrees of freedom. We show that for this combination of two- and three-nucleon interactions it is possible to obtain a good saturation point of symmetric nuclear matter. We also calculate the nuclear symmetry energy and compare our results with the available empirical constraints on this quantity.

Analysis of 11Be + p elastic scattering using a BHF approach

The elastic scattering of the halo nucleus 11Be on the proton at various incident energies has been analysed using the microscopic optical potential (OP) calculated within the first order non-relativistic Brueckner–Hartree–Fock (BHF) approach. Argonne v-18 inter-nucleon potential is employed to calculate the microscopic OP. The nuclear density distribution has been obtained using a semi-phenomenological model. The density used shows extended neutron distribution indicating a possible halo structure. We have also compared our results with an empirical analysis using CH89 global OP. The analysis reveals that the BHF approach provides good agreement with the experimental data for all incident energies considered in this paper.

Neutron star structure with chiral interactions

We use two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit ∆ isobar contributions to calculate the energy per particle of symmetric nuclear matter and pure neutron matter employing the microscopic Brueckner–Hartree–Fock approach. In particular, we present nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with ∆ isobar intermediate states (N3LO∆) recently developed by Piarulli et al. [1]. We compute the β-equilibrium equation of state and determine the neutron star mass-radius and mass-central density sequences. We find that the adopted interactions are able to provide satisfactory properties of nuclear matter at saturation density as well as to fulfill the limit of two-solar mass for the maximum mass configuration as required by recent observations.

Relativistic effects and three-nucleon forces in nuclear matter and nuclei

We review a large body of predictions obtained within the framework of relativistic meson theory together with the Dirac–Brueckner–Hartree–Fock approach to nuclear matter and finite nuclei. The success of this method has been largely related to its ability to take into account important three-body effects. Therefore, the overarching theme of this paper is the interpretation of the so-called “Dirac effects” as an effective three-nucleon force. We address the equation of state (EoS) of isospin symmetric and asymmetric nucleonic matter and related issues, ranging from proton and neutron density distributions to momentum distributions and short-range correlations. A central part of the discussion is devoted to the optical model potential for nucleon–nucleus scattering. We also take the opportunity to explore similarities and differences with predictions based on the increasingly popular chiral effective field theory.

The Thermal Properties of Asymmetric Nuclear Matter within the Extended Brueckner–Hartree–Fock Approach

The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole–hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole–hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner–Hartree–Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the press...

Microscopic optical model potential based on a Dirac Brueckner Hartree Fock approach and the relevant uncertainty analysis

A relativistic microscopic optical model potential, named CTOM , for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n , p + A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

Asymmetric nuclear matter and neutron star properties within the extended Brueckner theory

Microscopically, the equation of state (EOS) and other properties of asymmetric nuclear matter at zero temperature have been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF) and the extended BHF approaches by using the self-consistent Green’s function approach or by including a phenomenological three-body force. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. We can calculate the total mass and radius for neutron stars using various equations of state at high densities in $ \beta$ -equilibrium without hyperons. A comparison with other microscopic predictions based on non-relativistic and density-dependent relativistic mean-field calculations has been done. It is found that relativistic EOS yields however larger mass and radius for neutron star than predictions based on non-relativistic approaches. Also the three-body force plays a crucial role to deduce the theoretical value of the maximum mass of neutron stars in agreement with recent measurements of the neutron star mass.

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.