Relativistic effect of spin and pseudospin symmetries

TL;DR

This paper investigates how spin and pseudospin symmetries evolve as the Dirac Hamiltonian approaches the non-relativistic limit by varying the Compton wavelength, revealing their different relativistic origins.

Contribution

It provides a detailed analysis of the relativistic effects on spin and pseudospin symmetries using perturbation theory and the Dirac equation with a variable parameter.

Findings

Spin splittings decrease monotonously with decreasing mbda.

Pseudospin splittings vary, increasing, decreasing, or remaining unchanged across different doublets.

Spin symmetry is purely relativistic in origin, pseudospin symmetry is not solely due to relativistic effects.

Abstract

Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us to take the non-relativistic limit by setting the Compton wavelength $% \lambda \rightarrow 0 $. 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.