On the Isovector Channels in Relativistic Point Coupling Models within the Hartree and Hartree-Fock Approximations

Abstract

We investigate the consequences of Fierz transformations acting upon the contact interactions for nucleon fields occurring in relativistic point coupling models in Hartree approximation, which yield the same models but in Hartree-Fock approximation instead. We find for four-fermion interactions occurring in two existing relativistic point coupling phenomenologies that whereas in Hartree the isovector-scalar strength, corresponding to delta-meson exchange, is unnaturally small, indicating a possible new symmetry, in Hartree-Fock it is instead comparable to the isovector-vector strength corresponding to rho-meson exchange, but the sum of the two isovector coupling constants appears to be preserved in both approaches. Furthermore, in Hartree-Fock approximation, both QCD-scaled isovector coupling constants are natural (dimensionless and of order 1) whereas in Hartree approximation only that of the isovector-vector channel is natural. This indicates that it is not necessary to search for a new symmetry and, moreover, that the role of the delta-meson should be reexamined.

10 pages; accepted for publication in Nuclear Physics A

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• Equation of state of isospin-asymmetric nuclear matter in relativistic mean-field models with chiral limits
• Nuclear symmetry potential in the relativistic impulse approximation
• Critical parameters of consistent relativistic mean-field models
• Correlations between the nuclear matter symmetry energy, its slope, and curvature from a nonrelativistic solvable approach and beyond
• Correlations between critical parameters and bulk properties of nuclear matter
• Correlations between bulk parameters in relativistic and nonrelativistic hadronic mean-field models
• Nuclei embedded in an electron gas
• The symmetry energy $\gamma$ parameter of relativistic mean-field models