Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper (lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian. Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying (improving) the spin (pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the (pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.