Medium polarization and pairing in asymmetric nuclear matter
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NUCLEI Theory
Medium Polarization and Pairing in Asymmetric Nuclear Matter∗ J. M. Dong1) , U. Lombardo2)** , H. F. Zhang3) , and W. Zuo1) Received June 6, 2016
Abstract—The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner– Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of 1 S0 proton–proton and 3 P F2 neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (antiscreening) interaction going from pure neutron matter to symmetric nuclear matter is discussed. DOI: 10.1134/S1063778817010069
1. BRUECKNER–HARTREE–FOCK APPROXIMATION
stars (NS) [5] according to recent observations [6]. Moreover, a correct estimate of the saturation point is important, since in beta-stable (asymmetric) nuclear matter the transition threshold to mixed nucleon– quark phase can appear close to that point [7].
The Brueckner–Bethe–Goldstone (BBG) theory proved to be one of the most advanced microscopic theories of nuclear matter after the achievements of the last few decades. The last two main steps were first the numerical demonstration that the holeline expansion rapidly converges at low density [1], and second, that theory can be extended to higher baryon densities after including the three-body force (3BF) [2]. The latter in fact allows the theory not only to reproduce quite well the empirical saturation properties of nuclear matter with realistic nucleonnucleon interactions [3, 4], but also to open a window to the investigation of high-density nuclear matter systems, such as compact astrophysical objects. In their interior in fact the baryon density can reach values from two to three times the saturation density, where processes like the excitation of nucleon– antinucleon pairs and nucleonic resonances (together with the production of other hadrons) are expected to sizeably influence the nuclear interaction. These processes can be incorporated in the interaction as medium virtual excitations. Their global effect at high density is strongly repulsive, leading to a remarkable increase of the maximum mass of neutron
1.1. Hole Line Expansion of the Energy The general formalism of the Brueckner–Bethe– Goldstone (BBG) theory for cold asymmetric nuclear matter can be found in [8, 9] and the extension to finite temperature can be found in [10]. The basic ingredient of the Brueckner approach is the reaction G matrix. In the case of asymmetric nuclear matter, the reaction matrix depends on the isospin components of the two interacting nucleons. Therefore, the reaction matrices of proton–proton and neutron–neutron interaction are different from each other. They satisfy the generalized BBG equation: Gτ τ [ρ, β, T, ω] |k1 k2 Qτ τ k1 k2 | =υ+υ ω − eτ (k1 ) − eτ
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