Further investigation of relativistic symmetry with the similarity renormalization group

Abstract

Following a recent rapid communications[Phys.Rev.C85,021302(R) (2012)], we present more details on the investigation of the relativistic symmetry by use of the similarity renormalization group. By comparing the contributions of the different components in the diagonal Dirac Hamiltonian to the pseudospin splitting, we have found that two components of the dynamical term make similar influence on the pseudospin symmetry. The same case also appears in the spin-orbit interactions. Further, we have checked the influences of every term on the pseudospin splitting and their correlations with the potential parameters for all the available pseudospin partners. The result shows that the spin-orbit interactions always play a role in favor of the pseudospin symmetry, and whether the pseudospin symmetry is improved or destroyed by the dynamical term relating the shape of the potential as well as the quantum numbers of the state. The cause why the pseudospin symmetry becomes better for the levels closer to the continuum is disclosed.

Pseudospin symmetry in nuclear structure and its supersymmetric representation

“…For details see Refs. [130,131] for the spherical case and Ref. [132] for the axially deformed case.…”

“…In this Subsection, we will first introduce the basic idea of similarity renormalization group for the Dirac Hamiltonian [130,131,132], then present the perturbative nature of pseudospin symmetry by combining the supersymmetric quantum mechanics, the similarity renormalization group, and the perturbation calculations [136,137].…”

“…[130,131,132] bridged the gap between the perturbation calculations and the SUSY description of PSS by using the SRG technique. The idea of SRG [133,134,135] is to drive the Hamiltonian toward a band-diagonal form via the so-called flow equation and unitary transformations that suppress offdiagonal matrix elements.…”

“…Recent works by Guo and coauthors [130,131,132] bridged the gap between the perturbation calculations and the supersymmetric description of pseudospin symmetry by using the similarity renormalization group (SRG) [133,134,135] for transforming the Dirac Hamiltonian into a diagonal form. The effective Hamiltonian expanded in a series of 1/M is Hermitian, which makes the perturbation calculations feasible.…”

Resonant states and pseudospin symmetry in the Dirac-Morse potential

“…In Ref. [66], the similarity renormalization group is used as the critical tool for understanding the origin of the PSS and the cause why the PSS becomes better for the levels closer to the continuum is disclosed in a quantitative way [67]. In combination with the supersymmetric quantum mechanics, the origin of the PSS and its breaking mechanism are detailedly analyzed at the nonrelativistic limit [68].…”