Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei

Staring from the Lagrangian density that foots on the meson-propagated picture of nuclear force, the full Hamiltonian, that contains both mean field and pairing contributions, is derived by quantizing the Dirac spinor field in the Bogoliubov quasi-particle space, and the expectation with respect to the Bogoliubov ground state gives the full energy functional. As an extension of the D-RHF model, the degree of freedom associated with the $\rho$-tensor ($\rho$-T) coupling is implemented, and incorporating with the Bogoliubov scheme the finite-range Gogny force D1S is utilized as the pairing force. Moreover, qualitative analysis on the nature of the $\pi$-PV and $\rho$-T couplings are presented for better understanding their enhancements on the deformation effects. Space convergence related to the spherical DWS base is confirmed for the D-RHFB model by taking light nucleus $^{24}$Mg and mid-heavy one $^{156}$Sm as candidates. Compared to light nuclei, extraordinary more negative energy states are necessitated to keep the expansion completeness on the spherical DWS base for mid-heavy and heavy nuclei, due to the enhanced correlations between the expansion components with large $\kappa$-quantity as indicated by the nature of the $\pi$-PV and $\rho$-T couplings. Furthermore, because of the enhanced deformation effects by the $\pi$-PV and $\rho$-T couplings, the RHF Lagrangian PKA1 presents deeper bound ground state for $^{24}$Mg than the other selected Lagrangians, in addition to predicting a fairly deep bound local minimum with large oblate deformation.