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.