Relativistic effect of spin and pseudospin symmetries

Abstract

Dirac Hamiltonian is scaled in the atomic units $\hslash =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength . The evolutions of the spin and pseudospin symmetries towards the non-relativistic limit are investigated by solving the Dirac equation with the parameter $\lambda$. With $\lambda$ transformation from the original Compton wavelength to 0, the spin splittings decrease monotonously in all spin doublets, and the pseudospin splittings increase in several pseudospin doublets, no change, or even reduce in several other pseudospin doublets. The various energy splitting behaviors of both the spin and pseudospin doublets with $\lambda$ are well explained by the perturbation calculations of Dirac Hamiltonian in the present units. It indicates that the origin of spin symmetry is entirely due to the relativistic effect, while the origin of pseudospin symmetry cannot be uniquely attributed to the relativistic effect.

15 pages, 7 figures, accepted by PRC

References in corpus (3)

• Perturbative interpretation of relativistic symmetries in nuclei
• Exploration of relativistic symmetry by the similarity renormalization group
• Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian

Cited by in corpus (10)

• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects
• Relativistic interpretation on the nature of nuclear tensor force
• Further investigation of the relativistic symmetry by similarity renormalization group
• Resonant states and pseudospin symmetry in the Dirac Morse potential
• κ state solutions for the fermionic massive spin-1/2 particles interacting with double ring-shaped Kratzer and oscillator potentials
• Approximate -state Solutions to the Dirac Mobius Square-Yukawa and Mobius Square-quasi Yukawa Problems under Pseudospin and Spin Symmetry limits with Coulomb-like Tensor Interaction
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential