Nuclear Potentials Relevant to the Symmetry Energy in Chiral Models

Niu Li,Wei-Zhou Jiang,Si-Na Wei

doi:10.3390/sym14030474

Niu Li, Wei-Zhou Jiang + Show 1 more

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https://doi.org/10.3390/sym14030474

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Abstract

We employ the extended Nambu-Jona-Lasinio (NJL), linear-σ models, and the density-dependent model with chiral limits to work out the mean fields and relevant properties of nuclear matter. To have the constraint from the data, we re-examine the Dirac optical potentials and symmetry potential based on the relativistic impulse approximation (RIA). Unlike the extended NJL and the density-dependent models with the chiral limit in terms of the vanishing scalar density, the extended linear-σ model with a sluggish changing scalar field loses the chiral limit at the high-density end. The various scalar fields can characterize the different Schrödinger-equivalent potentials and kinetic symmetry energy in the whole density region and the symmetry potential in the intermediate density region. The drop in the scalar field due to the chiral restoration results in a clear rise of the kinetic symmetry energy. The chiral limit in the models gives rise to the softening of the symmetry potential and thereof the symmetry energy at high densities.

Highlights

Besides the development of the various many-body theories based on the boson exchanges in the quantum field theory, e.g., see Ref. [1], the gauge invariance is regarded to be important to construct the model for strong interacting systems
We single out three models from these categories that feature the partial restoration of the chiral symmetry in nuclear matter to expose the role of the chiral symmetry in the nuclear and symmetry potentials relevant to the symmetry energy in the relativistic impulse approximation (RIA)
Together with the usual relativistic mean-field (RMF) model and the density-dependent model with the chiral limit, we have made a comparative study on the nuclear potentials that are relevant to the symmetry energy

Summary

Introduction

Besides the development of the various many-body theories based on the boson exchanges in the quantum field theory, e.g., see Ref. [1], the gauge invariance is regarded to be important to construct the model for strong interacting systems. The typical models are the linear-σ [3,4] and Nambu–Jona–Lasinio (NJL) [5] models where the order parameters for the chiral symmetry are the scalar condensate or the scalar field σ In these models, the potentials are characteristic of the field term of the fourth power that ensures a double-well potential, and the chiral parter is the so-called Nambu–Goldstone boson, the pion that is the fundamental and unique boson in the effective field theory [6]. It is interesting to note that Schwinger has the view that the gauge boson does not necessarily have zero mass for the special vacuum [7], and soon later Anderson adds that the gauge boson and Nambu–Golstone boson can cancel each other to leave the finite mass boson only [8] These are, the looming prelude for the Higgs mechanism. Since no dynamics of the scalar field is given by the chiral EFT [25], we do not include the chiral EFT in our work that involves the energy region beyond the validity of the chiral EFT

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