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

TL;DR

This study uses a deformed relativistic Hartree-Bogoliubov model to analyze mirror hypernuclei, revealing correlations between hypernuclear properties and $ ext{Λ}N$ interactions, and emphasizing the importance of precise measurements for refining these interactions.

Contribution

It provides systematic analysis of mirror hypernuclei with multiple effective interactions, highlighting the role of charge symmetry breaking and rotational corrections in constraining hyperon-nucleon interactions.

Findings

Linear correlations between $ ext{Λ}$ separation energies and charge radii.

Charge symmetry breaking effects correlate with SU(3) flavor symmetry violation.

Proposes precise measurements of $A=16$ and $A=40$ systems as benchmarks.

Abstract

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