Background: Pseudospin symmetry (PSS) in proton resonant states remains largely unexplored due to the long-range Coulomb interaction and the inherent difficulties in modeling resonant phenomena.

Purpose: We aim to clarify the interplay between the Coulomb field and nuclear shell effects in governing PSS breaking, by systematically studying the Po isotopic chain ($A=190–220$) across the $N=126$ neutron shell closure.

Method: We employ the relativistic mean-field theory with complex momentum representation (RMF-CMR), incorporating the Landé subtraction to handle the Coulomb singularity in momentum space, which enables a unified description of both bound and resonant proton states.

Results: Our calculations reveal that resonance energies and widths decrease monotonically with neutron number, with PSS becoming progressively restored near the continuum threshold. We identify a robust correlation between the energy splitting and a newly defined momentum-space wave function splitting, $\mathrm{\Delta }G$. By systematically varying the Coulomb strength, we observe that most pseudospin doublets exhibit enhanced breaking with increasing Coulomb repulsion (e.g., the $3\tilde{p}$ splitting increases by a factor of $\sim 2.8$), whereas the inverted $1\tilde{i}$ doublet shows the opposite behavior, evolving toward degeneracy—both trends arising from the same underlying mechanism, namely that the energies of the $j_{<}$ states increase faster than those of the $j_{>}$ states as the Coulomb strength is increased. Crucially, at the magic number $N=126$, both energy and wave function splittings exhibit a local suppression, providing direct evidence that shell stabilization counteracts Coulomb-induced symmetry breaking.

Conclusions: PSS breaking in proton resonances is governed by a delicate competition among the $\mathrm{\Sigma }$ potential, Coulomb repulsion, and shell closure. By focusing on the role of shell stabilization across a magic neutron number—an aspect not addressed in previous studies—our results establish a quantitative picture of how Coulomb repulsion and shell effects compete in governing PSS breaking in proton resonances. The predicted local minimum in PSS splitting near ${}^{210}\mathrm{Po}$ offers a clear signature for experimental verification via transfer reactions. The RMF-CMR method is demonstrated as a powerful tool for future investigations of deformed and paired systems near the proton drip line.

Close

PrevNext

View figure in article

• Nuclear forces
• Nuclear structure & decays
• 190 ≤ A ≤ 219
• Nuclear density functional theory