Investigation of pseudospin and spin symmetries in relativistic mean field theory combined with a similarity renormalization group approach

Abstract

Similarity renormalization group (SRG) is combined with the relativistic mean-field (RMF) theory, the Schr\"odinger-like Hamiltonian describing the motion of nucleon is obtained. The Hamiltonian with the scalar and vector potential from the self-consistent RMF calculations is used to explore the pseudospin and spin symmetries and their evolution with mass number for Sn isotopes. The contribution of every term to the pseudospin (spin) energy splitting is extracted. The spin energy splitting comes almost entirely from spin-orbit coupling, whereas the pseudospin energy splitting is also dominated by nonrelativistic and dynamical terms. The magnitude of the splitting is related to the radial, angular, and isospin quantum numbers of the doublet. The isospin dependence of pseudospin (spin) symmetry comes from the nonrelativistic term (the spin-orbit coupling). The pseudospin symmetry of neutron is superior to that of proton from the weakening of nonrelativistic and dynamical breaking. These results are helpful to understand the origin and breaking mechanism of pseudospin and spin symmetries.