近期龙文辉教授课题组发展了基于球对称Dirac Woods-Saxon基的轴对称形变相对论Hartree-Fock-Bogoliubov 模型，其中为理解形变效应，定性分析了ρ-张量耦合与π-赝矢量耦合顶角。以24Mg与156Sm为例，验证了程序的可靠性，并进一步发现ρ-张量耦合与π-赝矢量耦合强的形变效应对于24Mg的影响。该工作将形变、连续态、对关联、张量力与自旋轨道劈裂统一处理，实现了不稳定形变原子核的可靠描述，为将来大规模探索形变不稳定原子核以及形变超重原子核核结构奠定理论基础。
文章已被： 已被Physical Review C 接收，arXiv: 2202.00482
文章标题： Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei
文章链接： https://doi.org/10.48550/arXiv.2202.00482
摘要：
Background: At the forefront of nuclear science, unstable nuclei are of special significance, in which the deformation and pairing correlations play an essential role in determining the nuclear structure. Under the mean field approach, the pairing and deformation effects have been uniformly considered within the deformed non-relativistic Hartree-Fock-Bogoliubov model and deformed relativistic Hartree-Bogoliubov (D-RHB) model. However, due to the limitation of the Hartree approach, the important ingredient of nuclear force, such as the tensor force that contributes via the Fock diagram, is missing in the D-RHB model. Recently, the axially deformed relativistic Hartree-Fock (D-RHF) model was established for deformed nuclei, in which the π-pseudo-vector (π-PV) coupling can get the tensor force effects into account naturally. While limited by the BCS pairing, it cannot be safely applied to describe unstable nuclei.
Purpose: The aim of this work is to develop the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model for the reliable description of wide-range unstable nuclei, by utilizing the spherical Dirac Woods-Saxon (DWS) base.
Method: 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 ρ-tensor (ρ-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 π-PV and ρ-T couplings are presented for better understanding their enhancements on the deformation effects.
Results: Space convergence related to the spherical DWS base is confirmed for the D-RHFB model by taking light nucleus 24Mg and mid-heavy one 156Sm 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 κ-quantity as indicated by the nature of the π-PV and ρ-T couplings. Furthermore, because of the enhanced deformation effects by the π-PV and ρ-T couplings, the RHF Lagrangian PKA1 presents deeper bound ground state for 24Mg than the other selected Lagrangians, in addition to predicting a fairly deep bound local minimum with large oblate deformation.
Conclusions: Axially deformed relativistic Hartree-Fock-Bogoliubov model has been established with confirmed convergence checks. The effects of the π-PV and ρ-T couplings, coupled with nuclear deformation, are analyzed in both light and mid-heavy nuclear systems, which are expected to be manifested in wide-range unstable nuclei.
