Nuclear and Neutron Matter Properties Using BHF Approximation (original) (raw)
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The Hot and Cold Properties of Nuclear Matter
The properties of nuclear matter at zero and finite temperatures in the frame of the Brueckner theory realistic nucleon-nucleon potentials are studied. 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 calculat ion. Properties of asymmetric nuclear matter are derived fro m various many-body approaches. This includes phenomenological ones like the Skyrme Hartree-Fock and relat ivistic mean field approaches, which are adjusted to fit properties of nuclei, as well as mo re microscopic attempts like the BHF appro ximation, a Self-Consistent Greens Function (SCGF) method and the so-called V lowk approach, which are based on realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts. These microscopic approaches are supplemented by a density-dependent contact interaction to achieve the empirical saturation property of symmet ric nuclear matter. Special attention is paid to behavior o f the isovector and the isoscalar co mponent of the effective mass in neutron-rich matter. The nuclear sy mmetry potential at fixed nuclear density is also calculated and its value decreases with increasing the nucleon energy. In particu lar, the nuclear symmet ry potential at saturation density changes fro m positive to negative values at nucleon kinetic energy of about 200 MeV. The hot properties of nuclear matter are also calculated using T 2 -approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data especially at low densities.
The Properties of Nuclear Matter at Zero and Finite Temperatures
Ядерная физика, 2014
The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T 2 -approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.
Bulk Properties of Symmetric Nuclear and Pure Neutron Matter
Journal of Modern Physics, 2013
We study the equation of state (EOS) of symmetric nuclear and neutron matter within the framework of the Brueckner-Hartree-Fock (BHF) approach which is extended by including a density-dependent contact interaction to achieve the empirical saturation property of symmetric nuclear matter. This method is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. Realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts are used in the present calculations.
The Effect of Various Three-Body Forces on Nuclear Matter and Neutron Stars Properties
Moscow University Physics Bulletin, 2020
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 nucleonnucleon (NN) potentials. These NN potentials give great fitting to the deuteron properties and are phaseshift 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.
Physical Review, 1958
The properties of nuclear matter have been determined by the solution of the nuclear many-body problem, using the reaction matrix theory of Brueckner. The nonlinear integral equations characteristic of the theory have been solved with the aid of the fast electronic computer IBM 704. The two-body interaction assumed is the phenomenological potential of Gammel, Christian, and Thaler. It is found that the binding energy of nuclear matter, neglecting Coulomb forces, is 14.6 Mev per particle at a density corresponding to a radius parameter ro-1. 00&(10 " cm. The Coulomb repulsion in a heavy nucleus is shown to drop the density by approximately 15%. The tensor force is shown to give approximately 6-Mev binding energy. The results are found to be very sensitive to the self-consistency requirements of the theory, the binding energy shifting from 14.6 Mev to 34.4 Mev if the velocity dependence of the single-particle potential is neglected. The actual solutions were made self-consistent by an iteration procedure which converged in five or six iterations, the final results being self-consistent to one part in 10' or 10'. The effective mass for nucleon motion in the Fermi sea is found to vary from 0.56M for slow particles to 0.66M for particles near the Fermi surface. This velocity dependence of the potential is closely related to the symmetry energy which also depends, however, on the shifting in the spin populations as the neutronproton ratio is changed from unity. The symmetry energy computed is 10 to 15/z larger than that deduced from experiment. I. INTRODUCTION ' 'N previous papers, ' ' one of us (K. A. B.) and others~h ave developed a method for determining the properties of extended nuclear matter. This theory was first used to make an approximate study of the equilibrium density and binding energy of nuclear matter' ' and to develop a theory of high-energy nuclear reactions,ẽ nergy-level fine structure, and conlguration mixing, ' and neutron reactions with nuclei at low energy. " Later studies, " " particularly that by Bethe, ' have made further analyses of the theoretical foundation of the method and also examined the problems which arise in applying the method to finite systems. Thus in this paper, it is not necessary to review the'foundations of the method. The purpose of this paper is to give the details" of *Work performed under the auspices of the U. S. Atomic Energy Commission.
The Equation of State of Nuclear Matter and Neutron Stars Properties
Journal of Modern Physics, 2014
The equation of state (EOS) of symmetric nuclear and pure neutron matter has been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF). For more comparison, the extended BHF approaches using the self-consistent Green's function approach or by including a three-body force will be done. The EOS will be studied for different approaches at zero temperature. We can calculate the total mass and radius of neutron stars using various equations of state. A comparison with relativistic BHF calculations will be done. Relativistic effects are known to be important at high densities, giving an increased repulsion. This leads to a stiffer EOS compared to the EOS derived with a non-relativistic approach.
Nuclear Physics A, 1996
Realistic versions of the M3Y effective nucleon-nucleon interaction have been used to calculate the basic properties of asymmetric nuclear matter within a non-relativistic Hartree-Fock scheme. Special attention was devoted to the dependence of the binding energy, pressure and incompressibility upon the neutron-proton asymmetry. Our results reproduce reasonably well the empirical value of the symmetry energy and the softening of the equation of state for neutron-rich nuclear matter, as suggested in several supernova studies. The same effective interaction has been further used to calculate the interaction potential between neutron-rich nuclei within an extended version of the double-folding model, where the knock-on exchange and the isospin dependence of the nucleon-nucleon interaction are treated explicitly. The symmetry (isospin-dependent) term of the central nucleus-nucleus potential was found to be negligible compared to the isoscalar term. An exploratory study of the elastic 8He, nLi+14C scattering was performed using the new folded potentials, and possible signatures of the 8He,nLi neutron halos in these processes have been discussed.
Properties of pure neutron matter at low and high densities
Pramana, 2021
We report a new microscopic equation of state (EoS) of pure neutron matter (PNM) at zero temperature using the recent realistic two-body interaction derived in the framework of chiral perturbation theory (ChPT). The EoS is derived using the Brueckner-Bethe-Goldstone quantum many-body theory in the Brueckner-Hartree-Fock approach. We have calculated the EoS of PNM at low and high densities using LO, NLO, N 2 LO, N 3 LO, N 4 LO potentials at three different values of the momentum-space cutoff = 450, 500 and 550 MeV. It is found that the EoS is not much affected by the cutoff variations at low densities. Also the binding energy of PNM has been computed within the framework of the Brueckner-Hartree-Fock (BHF) approach plus two-body density-dependent Skyrme potential which is equivalent to three-body forces. The effect of the two-body density-dependent Skyrme potential is to produce a stiffer EoS. This is actually needed to improve the saturation point of symmetric nuclear matter obtained using the two-body N N interaction. The results of several microscopic approaches are compared. It is found that the EoS is sensitive to the momentum-space cutoff . Also the partial wave contributions to potential energy at the empirical saturation density ρ = 0.16 fm −3 for different potentials are listed from 1 S 0 to 3 F 3 states. It is found that all contributions are nearly cutoff independent except the ones from 3 P 1 , 3 P 2 , 3 H 4 and 3 F 4 states, which are increasing with the cutoff . Actually, the size of these contributions is strongly dependent on the central and tensor components in the N N potential. The larger cutoff corresponds to harder interactions and gives more repulsive contribution to the N N potential at short distance. It leads to smaller binding energy.
Nuclear and neutron matter calculations with different model spaces
Nuclear Physics A, 1997
In this work we investigate the so-called model-space Brueckner-Hartree-Fock (MBHF) approach for nuclear matter as well as for neutron matter and the extension of this which includes the particle-particle and hole-hole (PPHH) diagrams. A central ingredient in the model-space approach for nuclear matter is the boundary momentum k M beyond which the single-particle potential energy is set equal to zero. This is also the boundary of the model space within which the PPHH diagrams are calculated. It has been rather uncertain which value should be used for k M. We have carried out model-space nuclear matter and neutron matter calculations with and without PPHH diagrams for various choices of k M and using several modern nucleon-nucleon potentials. Our results exhibit a saturation region where the nuclear and neutron matter matter energies are quite stable as k M varies. The location of this region may serve to determine an "optimum" choice for k M. However, we find that the strength of the tensor force has a significant influence on binding energy variation with k M. The implications for nuclear and neutron matter calculations are discussed.
Field theoretical model for nuclear and neutron matter: Thermal effects
Physical Review C, 1989
We analyze a field-theoretical Lagrangian model for the many-body problem of baryonic matter. The Lagrangian describes the baryonic interaction through the exchange of o, T , o, and p mesons, and contains various models studied in the literature as particular cases. The model is solved in the relativistic Hartree approximation using the technique of the covariant Wigner function. The vacuum fluctuation effects are considered and renormalized through a counterterm procedure. The equation of state is obtained in this renormalized Hartree approximation at finite temperature and in the presence of homogeneous and isotropic meson condensates. In a first particular case (the Serot model) the parameters of the model are determined in order to explain the nuclear saturation and symmetry energy of symmetric nuclear matter at nuclear density and to account for the expected low-density behavior of dense matter after the neutron drip in a phenomenological way. In this case the incompressibility of nuclear matter at the nuclear density is 460 MeV. A second determination of the parameters of the general model leads to a a model with an explicit symmetry-breaking term and is coupled to the o and p mesons in a renormalizable way. The equation of state thus obtained explains accurately all the properties of nuclear matter at nuclear density. In particular, we obtain a nuclear incompressibility of 225 MeV. The analysis of the resulting energy density as a function of the meson condensates shows that the presence of homogeneous and isotropic pion condensates or abnormal states of Lee-Wick type in neutron matter at T=O is energetically forbidden in this approximation.