Self-Consistent Green Function Method in Nuclear Matter

Symmetric nuclear matter is studied within the Brueckner-Hartree-Fock (BHF) approach and is extending to the self-consistent Green’s function (SCGF) approach. Both approximations are based on realistic nucleon-nucleon interaction; that is, CD-Bonn potential is chosen. The single-particle energy and the equation of state (EOS) are studied. The Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove theorem. In comparison to the BHF approach, the binding energy is reduced and the EOS is stiffer. Both the SCGF and BHF approaches do not reproduce the correct saturation point. A simple contact interaction should be added to SCGF and BHF approaches to reproduce the empirical saturation point.

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The Ground-State Calculations for Some Nuclei by Mesonic Potential of Nucleon-Nucleon Interaction

Advances in High Energy Physics ◽

10.1155/2020/3271975 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

K. M. Hanna ◽

S. H. M. Sewailem ◽

R. Hussien ◽

L. I. Abou-Salem ◽

Asmaa G. Shalaby

Keyword(s):

Ground State ◽

Degrees Of Freedom ◽

Vector Fields ◽

Theoretical Models ◽

Nucleon Nucleon ◽

Particle Energy ◽

Exchange Potential ◽

Hartree Fock ◽

Scalar And Vector Fields ◽

Nucleon Nucleon Interaction

The interaction of nucleon-nucleon (NN) has certain physical characteristics, indicated by nucleon, and meson degrees of freedom. The main purpose of this work is calculating the ground-state energies of 12H and 24He through the two-body system with the exchange of mesons (π, σ, and ω) that mediated between two nucleons. This paper investigates the NN interaction based on the quasirelativistic decoupled Dirac equation and self-consistent Hartree-Fock formulation. We construct a one-boson exchange potential (OBEP) model, where each nucleon is treated as a Dirac particle and acts as a source of pseudoscalar, scalar, and vector fields. The potential in the present work is analytically derived with two static functions of meson, the single-particle energy-dependent (SPED) and generalized Yukawa (GY) functions; the parameters used in meson functions are just published ones (mass, coupling constant, and cutoff parameters). The theoretical results are compared to other theoretical models and their corresponding experimental data; one can see that the SPED function gives more satisfied agreement than the GY function in the case of the considered nuclei.

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CORRELATIONS AND THE RELATIVISTIC STRUCTURE OF THE NUCLEON SELF-ENERGY

International Journal of Modern Physics E ◽

10.1142/s0218301399000148 ◽

1999 ◽

Vol 08 (02) ◽

pp. 179-196 ◽

Cited By ~ 2

Author(s):

H. MÜTHER ◽

S. ULRYCH ◽

H. TOKI

Keyword(s):

Nuclear Matter ◽

Particle Energy ◽

The Self ◽

Momentum Dependence ◽

Hartree Fock ◽

Self Energy ◽

The Matrix ◽

Lorentz Scalar ◽

Bonn Potential ◽

Non Locality

A key point of Dirac-Brueckner-Hartree-Fock calculations for nuclear matter is to decompose the self-energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small components in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.

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NUCLEON-NUCLEON CROSS SECTIONS IN ISOSPIN ASYMMETRIC NUCLEAR MATTER

International Journal of Modern Physics E ◽

10.1142/s0218301310016211 ◽

2010 ◽

Vol 19 (08n09) ◽

pp. 1788-1793

Author(s):

HONGFEI ZHANG ◽

JIANMIN DONG ◽

WEI ZUO ◽

UMBERTO LOMBARDO

Keyword(s):

Nuclear Matter ◽

Cross Sections ◽

Nucleon Nucleon ◽

Density Region ◽

Proton Proton ◽

Asymmetric Nuclear Matter ◽

Hartree Fock ◽

Nucleon Nucleon Interaction ◽

Three Body ◽

Neutron Cross Sections

The in medium nucleon-nucleon (NN) cross sections in isospin asymmetric nuclear matter at various densities are investigated in the framework of Brueckner-Hartree-Fock theory with the Bonn B two-body nucleon-nucleon interaction supplemented with a new version microscopic three-body force (TBF). The TBF depresses the amplitude of cross sections at high density region. At low densities, the proton-proton and neutron-neutron cross sections decrease while the proton-neutron one increases as the asymmetry increases. But the sensitivity of the NN cross sections to the isospin asymmetry are reduced with the increasing density.

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A SKYRME PARAMETRIZATION BASED ON NUCLEAR MATTER BHF CALCULATIONS

Modern Physics Letters A ◽

10.1142/s0217732300001663 ◽

2000 ◽

Vol 15 (20) ◽

pp. 1287-1299 ◽

Cited By ~ 24

Author(s):

M. RASHDAN

Keyword(s):

Nuclear Matter ◽

Density Functional ◽

Nucleon Nucleon ◽

Energy Density Functional ◽

Hartree Fock ◽

Saturation Properties ◽

Nucleon Nucleon Interaction ◽

Three Body ◽

Finite Nuclei

Using a modified energy density functional of nuclear matter derived by solving the Bethe–Goldstone equation with a realistic nucleon–nucleon interaction and by including corrections due to relativistic and three-body effects, an effective Skyrme parameter set is derived. These corrections are found to be important in order to well describe the saturation properties of nuclear matter. The obtained Skyrme parameter set, which we denoted by SKRA, is found to better account for nuclear correlations and satisfactory describes finite nuclei, when used in the Skyrme–Hartree–Fock theory. The SKRA interaction can also be considered as an important step toward removing the ambiguities in the determination of Skyrme parameters.

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EQUATION OF STATE OF ASYMMETRIC NUCLEAR MATTER WITH GOGNY AND COULOMB INTERACTIONS

Modern Physics Letters A ◽

10.1142/s0217732390001190 ◽

1990 ◽

Vol 05 (14) ◽

pp. 1071-1080 ◽

Cited By ~ 7

Author(s):

S. W. HUANG ◽

M. Z. FU ◽

S. S. WU ◽

S. D. YANG

Keyword(s):

Equation Of State ◽

Nuclear Matter ◽

Coulomb Interaction ◽

Chemical Potential ◽

Compression Modulus ◽

Nucleon Nucleon ◽

Effective Density ◽

Coulomb Interactions ◽

Asymmetric Nuclear Matter ◽

Nucleon Nucleon Interaction

The equation of state of the asymmetric nuclear matter is calculated with the Gogny D1 effective density-dependent nucleon-nucleon interaction and the Coulomb interaction in the framework of the finite-temperature HF method with the rearrangement term. The dependence of the thermodynamical properties such as the critical temperature of the liquid-gas phase transition, the chemical potential, the compression modulus and the entropy on the Coulomb interaction in nuclear matter is treated by using a shielded two-body Coulomb potential and this method has been found to be a reasonable and effective approach.

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