Constraints on $ΛN$ Effective Interactions from Mirror Hypernuclei in a Deformed Relativistic Hartree-Bogoliubov Model

Abstract

We investigate the ground-state properties of four mirror hypernuclei pairs--$^{10}_Λ$Be-$^{10}_Λ$B, $^{12}_Λ$B-$^{12}_Λ$C, $^{16}_Λ$N-$^{16}_Λ$O, and $^{40}_Λ$K-$^{40}_Λ$Ca--within the deformed relativistic Hartree-Bogoliubov framework, analyzing their connection to $ΛN$ effective interactions. Systematic calculations with eight distinct effective interactions reveal linear correlations between mirror hypernuclei in $Λ$ separation energies and charge radii. The charge symmetry breaking effects, quantified through $Λ$ 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.