Abstract
Following a recent letter [J.-Y. Guo, S.-W. Chen, Z.-M. Niu, D.-P. Li, and Q. Liu, Phys. Rev. Lett. 112, 062502 (2014)], we present more details for the relativistic symmetry research by using the similarity renormalization group. With the theoretical formalism expressed in detail, we explore the origin and breaking mechanism of relativistic symmetries for an axially deformed nucleus. By comparing the energy splitting between the (pseudo-) spin doublets, it is shown that the spin energy splitting arises almost completely from the spin-orbit coupling, while the pseudospin energy splitting arises from a combination of the nonrelativistic, dynamical, and spin-orbit terms. Furthermore, these splittings are correlated with nuclear deformation as well as with the quantum numbers of the doublets. The origin of relativistic symmetries is disclosed and the breaking mechanism of spin and pseudospin symmetries is clarified.
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