Nuclear matter equation of state and three-body forces
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NUCLEI Theory
Nuclear Matter Equation of State and Three-Body Forces* H. M. M. Mansour and A. M. A. Algamoudi Physics Department, Faculty of Science, Cairo University, Egypt Received April 29, 2011; in final form, October 24, 2011
Abstract—The energy per particle, symmetry energy, pressure, and free energy are calculated for symmetric nuclear matter using BHF approach with modern nucleon–nucleon CD-Bonn, Nijm1, Argonne v18 , and Reid 93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent to a density-dependent two-nucleon interaction a la Skyrme force. Good agreement is obtained in comparison with previous theoretical estimates and experimental data. DOI: 10.1134/S1063778812040114
1. INTRODUCTION On a microscopic basis the equation of state (EOS) of symmetric nuclear matter has been extensively studied within the variational approach [1–3] as well as relativistic [4–10] and nonrelativistic [11, 12] Brueckner–Hartree–Fock (BHF) theories. The predictions of nonrelativistic microscopic approaches (including both the BHF and variational approaches) based on pure two-body nucleon–nucleon (N N ) forces (2BF) do not give the empirical saturation point of symmetric nuclear matter (Coester band [13]). In order to improve the nuclear saturation, two lines have been followed. One is the development of the relativistic mean field (RMF) theory [14] and Dirac–Brueckner–Hartree–Fock (DBHF) approach [5, 15–19]. The DBHF has been successful in describing the saturation properties of symmetric nuclear matter (SNM), however, still there are some problems remaining unsettled, such as the negative energy state problem, the ambiguities related to the decomposition of the effective reaction matrix into covariant amplitudes due to various approximations introduced for reducing the four-dimensional Bethe–Salpeter equation to the corresponding threedimensional one. In the second line the medium effects are taken into account by phenomenological or microscopic three-body forces (3BF) within nonrelativistic contexts. Calculations with phenomenological 3BF have been performed both in the framework of the variational approach [1, 2] and the BHF approximation [20–23]. The basic input quantity in the BHF calculation is the N N interaction in free space. In the previous work [24] using BHF we adopted some ∗
The text was submitted by the authors in English.
of the modern potentials, namely: the recent models of the Nijmegen group [25], the Argonne v18 potential [26], and the charge-dependent Bonn potential (CD-Bonn) [27]. The recent versions of the Nijmegen group are Nijm1, Nijm 2, and Reid 93 potentials. In the present work we add the corrections of the threebody forces using an equivalent density-dependent two-body forces of Skyrme type. Hot systems are also considered for small temperatures. In the next section we give a brief description of the method of calculation. Section 3 is devoted to the presentation of our main results. 2. THEORY Here, we start with a short review of the theoretical
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