Constraints on $\hat{I}›N$ Effective Interactions from Mirror Hypernuclei in a Deformed Relativistic Hartree-Bogoliubov Model

Abstract

We investigate the ground-state properties of four mirror hypernuclei pairs--${}_{\hat{I}}^{10}›$Be-${}_{\hat{I}}^{10}›$B, ${}_{\hat{I}}^{12}›$B-${}_{\hat{I}}^{12}›$C, ${}_{\hat{I}}^{16}›$N-${}_{\hat{I}}^{16}›$O, and ${}_{\hat{I}}^{40}›$K-${}_{\hat{I}}^{40}›$Ca--within the deformed relativistic Hartree-Bogoliubov framework, analyzing their connection to $\hat{I}›N$ effective interactions. Systematic calculations with eight distinct effective interactions reveal linear correlations between mirror hypernuclei in $\hat{I}›$ separation energies and charge radii. The charge symmetry breaking effects, quantified through $\hat{I}›$ separation energy differences, exhibit a positive correlation with the SU(3) flavor symmetry violation. We emphasize that constraints derived from $A=10$ and $A=12$ hypernuclear pairs must explicitly incorporate rotational energy correction effects. Precision measurements of the (near) spherical $A=16$ and $A=40$ mirror systems are proposed as critical benchmarks for refining the isospin part of the hyperon-nucleon interactions.

10 pages, 5 figures