Fermi Liquid parameters for dense nuclear matter in Effective Chiral Model
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Abstract:
We calculate relativistic Fermi liquid parameters (RFLPs) for the description of the properties of dense nuclear matter (DNM) using Effective Chiral Model. Analytical expressions of Fermi liquid parameters (FLPs) are presented both for the direct and exchange contributions. We present a comparative study of perturbative calculation with mean field (MF) results. Moreover we go beyond the MF so as to estimate the pionic contribution to the FLPs. Finally, we use these parameters to estimate some of the bulk quantities like incompressibility, sound velocity, symmetry energy etc. for DNM interacting via exchange of $σ$, $ω$ and $π$ meson. In addition, we also calculate the energy densities and the binding energy curve for the nuclear matter. Results for the latter have been found to be consistent with two loop calculations reported recently within the same model.Keywords:
Fermi energy
We derive the equation of state (EOS) of nuclear matter within a generalised Nambu–Jona–Lasinio (NJL) model which saturates at normal nuclear density, ρ 0 . Chiral symmetry is restored at ~ 6–7 ρ 0 . At low densities the model includes clustering and reproduces the properties of nuclear matter namely binding energy and incompressibility. At high densities (ρ>3–4.5 ρ 0 ) quark matter is more stable than nuclear matter. The confinement-deconfinement phase transition is studied.
Deconfinement
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The equation of state (EOS) of nuclear matter is investigated in a semi-classical mean-field (MF) approach. Starting from the phase-space NN-interaction of Myers and Swiatecki [Nucl. Phys. A 601 (1996) 141], the EOS of nuclear matter by the Thomas–Fermi approximation is derived. A self-consistent semi-classical approach is presented by employing the Landau Fermi-Liquid theory (LFT). In our statistical approach, the phase-space occupation number can be expressed in terms of an extended effective mass which is affected by both temperature and nucleonic density. Accordingly, an explicit expression of the nucleonic chemical potential inside the nucleonic occupation number can be obtained. Special attention is also devoted to the density dependence of the nuclear symmetry free energy at different temperatures. The results of this model are compared with other theoretical predictions.
Thomas–Fermi model
Landau theory
Mean field theory
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Nuclear force
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The role of chiral (pion) dynamics in nuclear matter is reviewed. Contributions to the energy per particle from one- and two-pion exchange are calculated systematically, and it is demonstrated that already at order $k^4_f$ in the Fermi momentum, two-pion exchange produces realistic nuclear binding together with very reasonable values for the compressibility and the asymmetry energy. Further implications of these results are discussed.
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Recent work of Cohen, Furnstahl, and Griegel has advanced our understanding of the behavior of quark and gluon condensates in nuclear matter. We make use of their analysis to discuss the role of chiral condensates as they appear in relativistic Brueckner-Hartree-Fock theory. We find some support for assumptions we used to discuss the properties of nuclear matter in our earlier work. We also find that a rather consistent picture emerges from these studies, when we relate the parameters of the boson-exchange model of nuclear forces to an underlying field-theoretic description of nuclear matter.
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Pseudogap
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We show that the traditional classification of quantum inpurity models based on thermodynamics is insufficient to probe the nature of their low-energy dynamics. We propose an analysis based on scattering theory, dividing Fermi liquids into regular Fermi liquids and singular Fermi liquids. In both cases electrons at the Fermi energy scatter elastically off the impurity, but in the case of regular Fermi liquids the scattering has analytical properties in the vicinity of the Fermi energy, while for singular Fermi liquids it does not, resulting in a breakdown of Nozi\`eres' Fermi-liquid picture and singular thermodynamic behavior. Using the Bethe ansatz and numerical renormalization group, we show that the ordinary Kondo model is a regular Fermi liquid whereas the underscreened Kondo model is a a singular Fermi liquid. Conventional regular Fermi liquid behavior is reestablished in an external magnetic field $H$, but with a density of states which diverges as $1∕H$. Our results may be relevant for the recently observed field-tuned quantum criticality in heavy electron materials.
Fermi energy
Kondo model
Bethe ansatz
Pseudogap
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