Self-consistent random-phase approximation based on the relativistic Hartree-Fock theory: Role of ρ -tensor coupling

Abstract

The framework of the random-phase approximation (RPA) based on the relativistic Hartree-Fock (RHF) theory is extended to achieve a self-consistent calculation with the $\ensuremath{\rho}$-meson tensor coupling. The model self-consistency is verified by the check of the isobaric analog state, and it is found that the $\ensuremath{\rho}$-tensor and $\ensuremath{\rho}$-vector-tensor couplings play significant roles in maintaining the self-consistency. Using the RHF Lagrangian PKA1, the properties of the Gamow-Teller resonances (GTR) are investigated, in which the roles played by the particle-hole residual interaction of various meson-nucleon couplings are clarified in details. Furthermore, the effects of the tensor force, which is introduced naturally via the Fock terms, are analyzed by comparing the calculations with full Lagrangians and the ones artificially dropping the tensor force components. It is found that for the RHF Lagrangians $\mathrm{PKO}i$ $(i=1,2,3)$ and PKA1, the tensor forces play the role mainly via the RHF mean field rather than via the RPA residual interaction in determining the GTR. Moreover, the tensor-force effects are not as strong as those indicated by the Skyrme Hartree-Fock calculations.