Charge symmetry breaking effect in mirror Λ hypernuclei with Skyrme-Hartree-Fock model

TL;DR

This paper investigates charge symmetry breaking (CSB) in mirror Λ hypernuclei across A ≈ 7–40 using a deformed Skyrme-Hartree-Fock model with BCS pairing, augmented by a ΛN CSB term. The ΛN CSB interaction is implemented as a contact term with strength v0, contributing to the Λ and nucleon mean fields and the CSB energy density, and its value is fitted to six empirical CSB data sets. The study finds that including CSB substantially enhances the single-Λ binding-energy differences ΔB_Λ between mirror pairs, bringing many results into good agreement with experimental data, especially for A=7–12, while deformation effects are pronounced in light to mid-mass nuclei (A=8,9) and minor in heavier, near-spherical systems (A=16,32). Extracted CSB strengths are around $v_0 ≈ 27.4$–$27.8$ MeV fm$^3$, and the framework makes predictions for A=32 and A=40 that can be tested experimentally, offering a unified view of CSB in hypernuclei and its mass/shape dependence.

Abstract

We study the charge symmetry breaking (CSB) effect in mirror hypernuclei using the deformed Skyrme Hartree-Fock (DSHF)+ Bardeen-Cooper-Schrieffer (BCS) model together with the CSB term and pairing interaction. Our model provides good account for the observations of CSB effect in mirror hypernuclei in the mass region of A = 7~16. We investigate the effect of deformation on the single-Lambda binding energy differences and we found that, in mirror hypernuclei with mass numbers A = 8 and A = 9, deformation has a noticeable impact on the energy difference.

Figures (2)

• Figure 1: The differences $\Delta B_{\Lambda}$ of the single-$\Lambda$ binding energies between the mirror hypernuclei ($^{7}_{\Lambda}$He, $^{7}_{\Lambda}$Be), ($^{8}_{\Lambda}$Li, $^{8}_{\Lambda}$Be), ($^{9}_{\Lambda}$Li, $^{9}_{\Lambda}$B), ($^{10}_{\Lambda}$Be, $^{10}_{\Lambda}$B), ($^{12}_{\Lambda}$B, $^{12}_{\Lambda}$C), ($^{16}_{\Lambda}$N, $^{16}_{\Lambda}$O), ($^{32}_{\Lambda}$P, $^{32}_{\Lambda}$S), and ($^{40}_{\Lambda}$Ca, $^{40}_{\Lambda}$K) obtained by the DSHF+BCS approach with and without the $\Lambda N$ CSB interaction. The red filled (open) circles represent the calculated results with (without) $\Lambda N$ CSB interaction in the DSHF+BCS approach, while blue open squares correspond to the binding energy differences of four pairs of mirror hypernuclei calculated by the RMF model sun2025charge with CSB interaction, respectively. The upper (lower) panel shows results with $NN$ interaction SLy4 (SLy5). The experimental data are denoted by black inverted triangles, with vertical black lines indicating the experimental uncertainties (Exp-1). Data are from Refs. botta2017bindinggogami2016highhasegawa1996spectroscopictang2014experimentsdavis200550pile1991study. In the cases of mirror hypernuclei with $A = 9$jurivc1973newdavis200550 and $A = 10$cantwell1974bindinggogami2016highdavis200550, two sets of experimental data are available; the second set is represented by orange upright triangles and orange error bars (Exp-2).
• Figure 2: The differences $\Delta B_{\Lambda}$ of the single-$\Lambda$ binding energies between the mirror hypernuclei calculated by the DSHF+BCS approach including the $\Lambda N$ CSB interaction, with and without nuclear deformation. The calculation results are obtained by using the $NN$ interaction SLy4 and $\Lambda N$ interaction SLL4. The red filled circles (blue filled squares) represent the calculated results with (without) nuclear deformation from the DSHF+BCS approach, while blue open squares correspond to the binding energy differences calculated by the RMF model sun2025charge with CSB interaction, respectively. The upper (lower) panel shows results with $NN$ interaction SLy4 (SLy5). The experimental data are denoted by black inverted triangles, with vertical black lines indicating the experimental uncertainties (Exp-1). Data are from Refs. botta2017bindinggogami2016highhasegawa1996spectroscopictang2014experimentsdavis200550pile1991study. In the cases of mirror hypernuclei with $A = 9$jurivc1973newdavis200550 and $A = 10$cantwell1974bindinggogami2016highdavis200550, two sets of experimental data are available; the second set is represented by orange upright triangles and orange error bars (Exp-2).