Significance of tensor force in pseudo-spin symmetry

TL;DR

This paper investigates how the tensor force influences pseudo-spin symmetry (PSS) in nuclei, revealing its dependence on proton and neutron numbers and highlighting its importance beyond relativistic models.

Contribution

It demonstrates the significant role of the tensor force in the Z- and N-dependence of PSS using non-relativistic Hartree-Fock calculations with realistic tensor interactions.

Findings

Tensor force affects the Z- and N-dependence of PSS.

Variation in energy levels from $^{40}$Ca to $^{34}$Si aligns with tensor-force effects.

Results suggest tensor force's importance in PSS discussions.

Abstract

We point out that the pseudo-spin symmetry (PSS) of nuclei significantly depends on the proton ($Z$) and neutron numbers ($N$), sometimes giving rise to the characteristic structures. By using the non-relativistic spherical Hartree-Fock calculation with a realistic tensor force, we show that the tensor force may be deeply relevant to the $Z$- and $N$-dependence of the PSS. While the PSS has often been discussed in the context of the relativistic symmetry, the tensor-force effects on the PSS sometimes look analogous to the $Z$-and $N$-dependence of the PSS in the relativistic mean-field (RMF) calculations without explicit tensor force. The observed variation of the $p0d_{3/2}$-$p1s_{1/2}$ levels from $^{40}$Ca to $^{34}$Si is consistent with the tensor-force-driven $Z$-dependence of the PSS, but not necessarily with the RMF result. Even though it is too early to be conclusive, this result elucidates the significance of the tensor force when discussing the PSS.