Brueckner Hartree Fock Approximation Research Articles

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.

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.

Quark degrees of freedom and nuclear matter saturation

It has been found in previous works [M. Baldo and K. Fukukawa, Phys. Rev. Lett. 113, 241501 (2014); K. Fukukawa, M. Baldo, G. F. Burgio, L. Lo Monaco and H.-J. Schulze, Phys. Rev. 92, 065802 (2015)] that the nucleon–nucleon potential of [Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki Phys. Rev. C 64, 054001 (2001); Y. Fujiwara et al., Phys. Rev. C 65, 014002 (2001)] gives an accurate saturation point in symmetric nuclear matter once the three hole-line contributions are included in the Brueckner–Bethe–Goldstone expansion without the addition of three-body forces in the nuclear Hamiltonian. The potential is based on a quark model of nucleons and on the quark–quark interaction together with quark exchange processes. These features introduce an intrinsic nonlocality of the nucleon–nucleon interaction. In order to clarify the role of the quark degrees of freedom and of the nonlocality in the saturation, we perform a comparative study of this potential and the traditional meson exchange models, exemplified in the CD-Bonn potential. We find that at the Brueckner–Hartree–Fock approximation, which corresponds to the two hole-line level of approximation, the dominant modification of the nucleon–nucleon interaction with respect to CD-Bonn is incorporated in the s-wave channels, where the quark degrees of freedom should be more relevant, in particular for the short range quark exchange processes. However, when the three hole-line contribution is included, we find that the higher partial waves play a relevant role, mainly in the term that describes the effect of the medium on the off-shell propagation of the nucleon.

Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions

Aims. We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods. The EOS is derived using the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Neutron star properties are next computed solving numerically the Tolman–Oppenheimer–Volkov structure equations. Results. Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to ~4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of 1S0 proton–proton and 3PF2 neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.

Study of Nuclear Binding Energy per Nucleon of Nuclear Matter Based on Three-Body Forces

We study the properties of symmetric nuclear matter and pure neutron matter at zero temperature within the framework of the Brueckner theory using tabulated values of effective masses and depth of the single-particle energies. These tabulated values are chosen according to the work of Hassaneen et al, 2011. The Brueckner–Hartree–Fock approximation plus a density-dependent contact term as a three-body force are used to achieve the empirical saturation property of symmetric nuclear matter. The three-body force provides a strong enhancement of pressure and incompressibility in good agreement with relativistic approaches. Realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts are used in the present calculations. Good agreement is obtained in comparison with the experimental data.

Ground-state properties of closed-shell nucleus 56Ni with realistic nucleon–nucleon interactions

We have calculated the ground-state energy of the doubly magic nucleus 56Ni within the framework of the Green’s function using the CD-Bonn and N3LO nucleon–nucleon potentials. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. Both the continuous and conventional choices of single particle energies are used. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. In this study, comparison of the calculated ground-state energies, obtained by using the Brueckner–Hartree–Fock approach using continuous choice and different nucleon–nucleon potentials, with the experimental value is accomplished. The results show good agreement between the calculated values and the experimental one for the 56Ni nucleus. The sensitivity of our results to the choice of the model space is examined.

A study of the ground-state energy of 4He with nucleon–nucleon potentials

Ground-state properties are evaluated for the finite nucleus 4He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N 3LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones.

Nuclear binding energy and symmetry energy of nuclear matter with modern nucleon–nucleon potentials

The binding energy of nuclear matter at zero temperature in the Brueckner–Hartree–Fock approximation with modern nucleon–nucleon potentials is studied. Both the standard and continuous choices of single particle energies are used. These modern nucleon–nucleon potentials fit the deuteron properties and are phase shifts equivalent. Comparison with other calculations is made. In addition we present results for the symmetry energy obtained with different potentials, which is of great importance in astrophysical calculation.

Microscopic Three-Body Force Effect on Nucleon-Nucleon Cross Sections in Symmetric Nuclear Matter

We provide a microscopic calculation of neutron-proton and proton-proton cross sections in symmetric nuclear matter at various densities, using the Brueckner–Hartree–Fock approximation scheme with the Argonne V14 potential including the contribution of microscopic three-body force. We investigate separately the effects of three-body force on the effective mass and on the scattering amplitude. In the present calculation, the rearrangement contribution of three-body force is considered, which will reduce the neutron and proton effective mass, and depress the amplitude of cross section. The effect of three body force is shown to be repulsive, especially in high densities and large momenta, which will suppress the cross section markedly.

The Nuclear Symmetry Energy in Self-Consistent Green-Function Calculations

In this paper we have reported the study of symmetry energy within the self-consistent Green-function approach. For the sake of comparison, the same calculations are performed using Brueckner–Hartree–Fock approximation. The symmetry energy is calculated for different densities and discussed in comparison with other predictions. The self-consistent Green's function leads to slightly larger energies as compared to the Brueckner–Hartree–Fock approach. This effect increases with density and thereby leads to smaller symmetry energies. The calculation of the symmetry energy in the Brueckner–Hartree–Fock approach shows a monotonic increase as a function of baryonic density. We extract the symmetry energy coefficient at density ρ= 0.16 fm -3 to be about 28.3 MeV for self-consistent Green-function approach using CD-Bonn potential, which is in good agreement with the empirical value of 30 ±4 MeV. The dependence of the equation of state on the neutron excess parameter is clearly linear as function of α 2 for self-co...

Equation of state for neutron-rich matter with self-consistent Green function approach

The properties of asymmetric nuclear matter have been investigated in the framework of the self-consistent Green function approach at zero temperature. Results of the total energy per nucleon as a function of the density and asymmetry parameter are presented for two modern realistic nucleon–nucleon interactions: Nijmegen II and CD-Bonn. For comparison purposes, the same calculations are performed for Brueckner–Hartree–Fock approximation. Also we have compared our results with the predictions of other theoretical models especially the Dirac–Brueckner–Hartree–Fock approach. The self-consistent Green's function approach leads to a stiffer equation of state as compared to the Brueckner–Hartree–Fock approximation. This effect increases with density.

Bulk properties of nuclear matter from extended Brueckner theory

The bulk properties of nuclear matter are studied within the Brueckner–Hartree–Fock (BHF) and extended Brueckner–Hartree–Fock (EBHF) approaches using different realistic nucleon–nucleon interactions. Nuclear matter saturation points, incompressibility, chemical potential and speed of sound are calculated and analysed as functions of the density, for nuclear matter. We found that both the BHF and the EBHF approaches fail to reproduce the empirical saturation point of nuclear matter. Also, we found that the EBHF approach leads to a slightly smaller chemical potential compared to the BHF approximation. This effect becomes more pronounced as the density is increased further.

MICROSCOPIC CALCULATIONS IN NEUTRON MATTER

The properties of neutron matter are investigated in the framework of the extended Brueckner–Hartree–Fock approximation at zero temperature. Self-consistent calculations using different realistic interactions are reported for pure neutron matter. In this contribution, all the self-energies are calculated self-consistently. Using the self-energy, k-mass is evaluated using realistic NN interactions. Furthermore, the effect of hole–hole contributions is examined. We found that the hole–hole ladder brought about a non-negligible contribution.

Correlations and spectral functions in asymmetric nuclear matter

The self-energy of nucleons in asymmetric nuclear matter is evaluated employing different realistic models for the nucleon-nucleon interaction. Starting from the Brueckner Hartree Fock approximation without the usual angle-average in the two-nucleon propagator the effects of the hole-hole contributions are investigated within the self-consistent Green's function approach. Special attention is paid to the isospin-dependence of correlations, which can be deduced from the spectral functions of nucleons in asymmetric matter. The strong components of the proton - neutron interaction lead in neutron-rich matter to a larger depletion for the occupation probability of proton states below the Fermi momentum.

Neutron Star Properties with Relativistic Equations of State

We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner–Hartree–Fock approximation for electrically charge neutral neutron star matter in beta–equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree– or Hartree–Fock approximation. The special features of the different approximations and compositions are discussed in detail. Besides standard neutron star properties special emphasis is put on the limiting periods of neutron stars, for which the Kepler criterion and gravitation–reaction instabilities are considered. Furthermore the cooling behaviour of neutron stars is investigated, too. For comparison we also give the outcome for some nonrelativistic equations of state.

Spin-orbit splitting in nuclei near closed shells: (I). Contribution of the two-body spin-orbit interaction

We have studied the spin-orbit (s.o.) splitting arising from the effective two-body s.o. interaction in the Brueckner-Hartree-Fock (BHF) approximation, considering all of the most commonly used realistic nucleon-nucleon (NN) interactions and three different nuclear models. We conclude that the s.o. interaction alone cannot account for the observed s.o. splitting in nuclei. We derive the one-body s.o. potential arising from the effective NN s.o. interaction in the BHF approximation. The derivation applies to the interaction of a nucleon with a spin-saturated (s.s.) core of nucleons. The expression we obtain is more than a factor of two stronger than some similar expressions obtained by previous investigators. The enhancement results from the exchange term, which had previously been ignored. We discuss, and obtain expressions for, the effective s.o. interaction arising, in the local-density approximation, from the most commonly used realistic NN potentials, namely the Reid soft core (RSC), Reid hard core (RHC), Hamada-Johnston (HJ), Yale, and Gammel-Thaler (GT) potentials. We find that they yield two distinct sets of values for the strength, − 1 2 πS 30 , of the one-body potential: the RSC, RHC, and HJ potentials give − 1 2 πS 30 ≈ 59 MeV · fm 5 while the Yale and GT potentials give − 1 2 πS 30 ≈ 73 MeV · fm 5 . We have calculated the s.o. splitting for three different nuclear models: (a) the spherical harmonic oscillator (h.o.) shell model, (b) a hybrid model which uses a Fermi distribution to describe the nucleons in the s.s. core and h.o. orbitals to describe the single-particle levels, and (c) the self-consistent Brueckner model of Negele. For each of these, quantitative results for the splitting are obtained for the five modern NN potentials listed above. Significant differences between the three models are found, models (b) and (c) giving better agreement with experiment than (a) for the heavier nuclei. We have also used the h.o. model to verify the numerical accuracy of our approach. We find that the effective s.o. interaction gives splittings which are roughly compatible with experiment for the normally unoccupied levels of the entirely s.s. nuclei 16O and 40Ca. For all the other levels of the nuclei studied, it appears that the s.o. interaction alone lacks sufficient strength to account for the entire s.o. splitting.

Perturbation theory of a many-fermion system: (II). Expansions in reaction matrices

Currently, the most satisfactory version of Brueckner theory from the formal point of view is the generalized-time-ordered series of Brandow. In this formalism the Brueckner-Hartree-Fock (BHF) self-energy for normally empty (“particle”) states does not factorize, and for this reason it is not included in the single-particle potential, U. This feature of the theory leads to differences: (i) between single-particle and separation energies, and (ii) between U and the real part of the optical potential. In article I the time-dependent Green function formulation was used to achieve more extensive factorization, with the consequence that U could be defined to include the leading terms of the on-energy-shell BHF potential for “particles”. In the present paper this earlier expansion is written in terms of Brueckner reaction matrices, and the low orders of the resulting series are investigated. For this task, it has been found more convenient to employ the Fourier-transformed formalism of energy-dependent Green functions, G (ω). First, diagram rules for expansions in the bare interaction, V, and an arbitrary U are given in sufficient generality to apply to finite systems, for which U and f(ω) are not diagonal matrices. The binding energy is expressed in terms of closed, propagator-renormalized, ω-dependent, ground state diagrams including over-counting corrections. Then U is chosen, in correspondence with article I and a paper of Klein, in terms of the real part of the proper self-energy. In the framework employed here U may be defined conveniently to be hermitian. A prescription, stated with remarkable simplicity in the G(ω) formalism, is obtained for converting an expansion in V to one in a general transition or reaction matrix. Our U is the quasiparticle separation-energy potential, containing on-energy-shell self-energies of all topologies. For example, when the reaction matrix is that of Brueckner, the first-order (BHF) and secondorder (“rearrangement energy”) insertions are shown to be included in U both for “particles” and holes. Truncation schemes based on a stationary property of the propagator-renormalized series are explored. The simplest is a renormalized BHF approximation similar to that for Brandow's expansion but differing from it by (a) containing the RBHF potential for “particle” states, which implies a smaller energy gap and greater diffuseness at the Fermi surface; and (b) propagator renormalization (“line weighting”) factors which contain single-particle density matrices (“true occupation probabilities”) as in Brandow's expansion, plus “folded” terms. The present formulation allows a close connection between “virtual” and “valence” single-particle states, while staying close to the computationally successful framework of the Brueckner theory and avoiding complex energies.