Journal of Nuclear and Particle Physics 2013, 3(4): 77-96
DOI: 10.5923/j.jnpp.20130304.05
The Hot and Cold Properties of Nuclear Matter
Khaled Hassaneen
1,2,*
, Hesham Mansour
3
1
Department of Physics, Faculty of Science, Sohag University, Sohag, Egypt
2
Department of Physics, Faculty of Science, Taif University, Taif, Saudi Arabia
3
Department of Physics, Faculty of Science, Cairo University, Gizza, Egypt
Abstract 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 calculation. Properties of
asymmetric nuclear matter are derived from various many-body approaches. This includes phenomenological ones like the
Skyrme Hartree-Fock and relativistic mean field approaches, which are adjusted to fit properties of nuclei, as well as more
microscopic attempts like the BHF approximation, 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 symmetric nuclear matter. Special attention is paid to behavior of the isovector and the isoscalar component of the
effective mass in neutron-rich matter. The nuclear symmetry potential at fixed nuclear density is also calculated and its value
decreases with increasing the nucleon energy. In particular, the nuclear symmetry potential at saturation density changes from
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.
Keywords Brueckner-Hartree-Fock Approximation, Self-Consistent Greens Function (SCGF) Method, Three-body
Forces, Symmetry Energy, Symmetry Potential, Effective Mass, T
2
–approximation Method
1. Introduction
One of the most fundamental problems in nuclear
many-body theory is the attempt to evaluate the nuclear
matter binding energy and saturation properties, starting
from a realistic Nucleon-Nucleon (NN) interaction with no
free parameters. In fact a lot of work has been done trying to
solve this problem using different approaches and methods
which are discussed in details by Müther and Polls[1]. An
important ingredient of all these approaches is the
consideration of the two-nucleon correlations which are
induced by the strong short-range components of the NN
interaction. In lowest-order Brueckner theory, the familiar
Brueckner-Hartree-Fock (BHF) approach, is adopted to
calculate the energy, the so-called G-matrix for evaluating
the energy in the Hartree-Fock approach. In the G-matrix one
accounts for the particle-particle correlations which means
the scattering of two nucleons from states which are
occupied in the Slatter determinant describing the ground
state, into unoccupied particle states above the Fermi
surface[2-4].
* Corresponding author:
khs_94@yahoo.com (Khaled Hassaneen)
Published online at http://journal.sapub.org/jnpp
Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved
The potentials we will employ here are the recent models
of the Nijmegen group[5], the Argonne V18 potential[6] and
the charge-dependent Bonn potential (CD-Bonn)[7]. The
recent versions of The Nijmegen group are Nijm-I, Nijm-II
and Reid93 potentials. Although all these potentials predict
almost identical phase shifts, their mathematical structure is
quite different.
Most of the microscopic calculations have been addressed
to study symmetric matter[2] and pure neutron matter[8,9].
The study of asymmetric nuclear matter is technically more
involved and only few Brueckner-Hartree-Fock (BHF)
calculations are available[4,10,11]. The BHF approximation
includes the self-consistent procedure of determining the
single-particle auxiliary potential, as first devised by
Brueckner and Gammel[12], which is an essential ingredient
of the method. Different approaches have been used to study
the EoS of asymmetric nuclear matter including
Dirac-Brueckner-Hartree-Fock (DBHF) calculations[13-16],
Brueckner-Hartree-Fock (BHF) approximation to
Brueckner-Bethe-Goldstone (BBG) calculations[17,18] and
variational methods[19,20]. Besides these microscopic
approaches, effective theories such as Relativistic Mean
Field (RMF) theory[21,22] and non-relativistic effective
interactions[23,24] have also been used extensively to study
the EoS and mean field properties of the asymmetric nuclear
matter.