Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

Abstract

We derive a microscopic relativistic point-coupling model of nuclear many-body dynamics constrained by in-medium QCD sum rules and chiral symmetry. The effective Lagrangian is characterized by density dependent coupling strengths, determined by chiral one-and two-pion exchange and by QCD sum rule constraints for the large isoscalar nucleon self-energies that arise through changes of the quark condensate and the quark density at finite baryon density. This approach is tested in the analysis of the equations of state for symmetric and asymmetric nuclear matter, and of bulk and single-nucleon properties of finite nuclei. In comparison with purely phenomenological mean-field approaches, the built-in QCD constraints and the explicit treatment of pion exchange restrict the freedom in adjusting parameters and functional forms of density dependent couplings. It is shown that chiral (two-pion exchange) fluctuations play a prominent role for nuclear binding and saturation, whereas strong scalar and vector fields of about equal magnitude and opposite sign, induced by changes of the QCD vacuum in the presence of baryonic matter, generate the large effective spin-orbit potential in finite nuclei.

Relativistic nuclear energy density functional constrained by low-energy QCD

“…In Refs. [11,12] we have shown that a very good description of nuclear matter and finite nuclei from oxygen to calcium can be based on the following minimal Lagrangian density:…”

“…To first order in the scalar and baryon densities, these self-energies can be expressed as follows [12,35,36,37,38,39]: …”

“…This is illustrated in Fig. 3 where for the set of spherical nuclei that were used in the fit (see Tab. 2), we compare the deviations between calculated and experimental binding energies and charge radii, respectively, for the FKVW interaction with explicit inclusion of ∆(1232) excitations, and for the previous version of the interaction [12] which did not include the ∆(1232) degree of freedom. The latter displays a systematic underbinding with the increase of the neutronproton asymmetry in heavier nuclei, and the deviations exceed 5% already for Sn isotopes.…”

“…(63) - (67)) are listed in Table 6. [57,58] for the density-dependent point-coupling interaction FKVW with explicit inclusion of ∆(1232) excitations (diamonds) used in the present work, and for the previous version [12] which did not include the ∆(1232) degree of freedom (cirles). [57], and the calculated charge isotope shifts in comparison with data [61], for the chain of even-A P b isotopes.…”

“…A first version (not yet including explicitly the ∆(1232)) of this microscopic approach has been tested in the analysis of bulk and single-nucleon properties of finite nuclei [11,12]. It was shown that chiral (two-pion exchange) fluctuations play a prominent role in nuclear binding and in the saturation mechanism, while additional strong scalar and vector mean fields of about equal magnitude and opposite sign, induced by changes of the QCD vacuum in the presence of baryonic matter, generate the large effective spin-orbit potential in finite nuclei.…”