In Search of a Pristine Signal for (Scale-)Chiral Symmetry in Nuclei

I describe the long-standing search for a "smoking-gun" signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown's last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ($\rho$,$\omega$) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau-Migdal fixed point interaction $G_0^\prime$, the nuclear tensor forces and Brown-Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, "run the show and make all forces equal."Comment: To appear in G.E. Brown Memorial Volum

Topology Change and Tensor Forces for the EoS of Dense Baryonic Matter

When skyrmions representing nucleons are put on crystal lattice and compressed to simulate high density, there is a transition above the normal nuclear matter density $n_0$ from a matter consisting of skyrmions with integer baryon charge to a state of half-skyrmions with half-integer baryon charge. We exploit this observation in an effective field theory formalism to access dense baryonic system. We find that the topology change involved implies a changeover from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate in the nucleon "melted off." The $\sim 80$ of the nucleon mass that remains, invariant under chiral transformation, points to the origin of the (bulk of) proton mass that is not encoded in the standard mechanism of spontaneously broken chiral symmetry. The topology change engenders a drastic modification of the nuclear tensor forces, thereby nontrivially affecting the EoS, in particular, the symmetry energy, for compact star matter. It brings in stiffening of the EoS needed to accommodate a neutron star of $\sim 2$ solar mass. The strong effect on the EoS in general and in the tensor force structure in particular will also have impact on processes that could be measured at RIB-type accelerators.Comment: 16 pages, 4 figures: Note dedicated to Gerry Brown, prepared for contribution to "EPJA Special Volume on Nuclear Symmetry Energy.

Correlations in Hot Asymmetric Nuclear Matter

The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases while the occupation of the neutron states is enhanced as compared to the symmetric case. The self-consistent Green's function approach leads to slightly smaller energies as compared to the Brueckner Hartree Fock approach. This effect increases with density and thereby modifies the saturation density and leads to smaller symmetry energies.Comment: 7 pages, 7 figure

Shell Structure and ρ\rho-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory

A new effective interaction PKA1 with $\rho$-tensor couplings for the density-dependent relativistic Hartree-Fock (DDRHF) theory is presented. It is obtained by fitting selected empirical ground state and shell structure properties. It provides satisfactory descriptions of nuclear matter and the ground state properties of finite nuclei at the same quantitative level as recent DDRHF and RMF models. Significant improvement on the single-particle spectra is also found due to the inclusion of $\rho$-tensor couplings. As a result, PKA1 cures a common disease of the existing DDRHF and RMF Lagrangians, namely the artificial shells at 58 and 92, and recovers the realistic sub-shell closure at 64. Moreover, the proper spin-orbit splittings and well-conserved pseudo-spin symmetry are obtained with the new effective interaction PKA1. Due to the extra binding introduced by the $\rho$-tensor correlations, the balance between the nuclear attractions and the repulsions is changed and this constitutes the physical reason for the improvement of the nuclear shell structure.Comment: 20 pages, 11 figures, 6 table