• Accepted Paper

Competing roles of Coulomb repulsion and shell closure in pseudospin symmetry breaking of proton resonant states

Jin He, Quan Liu, and Jian-You Guo

Phys. Rev. C - Accepted 10 September, 2026

DOI: https://doi.org/10.1103/x57v-tlvg

Abstract

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. 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=190220) across the N=126 neutron shell closure. We employ the relativistic mean-field theory with complex momentum representation (RMF-CMR), incorporating the Land'e subtraction to handle the Coulomb singularity in momentum space, which enables a unified description of both bound and resonant proton states. 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 wavefunction splitting, ΔG. By systematically varying the Coulomb strength, we observe that most pseudospin doublets exhibit enhanced breaking with increasing Coulomb repulsion (e.g., the 3p̃ splitting increases by a factor of 2.8), whereas the inverted 1ĩ 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 wavefunction splittings exhibit a local suppression, providing direct evidence that shell stabilization counteracts Coulomb-induced symmetry breaking. PSS breaking in proton resonances is governed by a delicate competition among the Σ 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 210Po 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.

Export citation

Export citation

Choose format for download:

Download Citation

If the author has provided any supplemental materials with this article they will be available upon publication of the version of record.

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation