Charge symmetry breaking effects of $ω$-$ρ^0$ mixing in relativistic mean-field model

TL;DR

This work addresses charge-symmetry breaking in nuclear forces by implementing $\omega$-$\rho^0$ meson mixing within a covariant density-functional framework and by incorporating detailed electromagnetic corrections. The authors develop a relativistic Hartree-Bogoliubov model with density-dependent meson couplings and a CSB mixing term controlled by $\Delta m_{\text{v}}^2$, calibrating the parameters against $T=1/2$ mirror-nucleus mass differences and magic-nucleus observables to obtain the DD-ME-CSB set. They demonstrate that $\omega$-$\rho^0$ mixing provides the dominant CSB contribution to mirror energy differences beyond the Coulomb term, and they establish a gradient-expansion link to a Skyrme-type CSB functional, aligning relativistic and nonrelativistic CSB descriptions. The results offer a consistent RMF-based account of CSB effects with implications for the nuclear equation of state and avenues for extending CSB to hypernuclei and $N$-$\Lambda$ interactions.

Abstract

We present a relativistic mean-field model that incorporates charge symmetry breaking (CSB) of nuclear force via $ ω$-$ ρ^0 $ meson mixing, along with corrections to the electromagnetic interaction including the nucleon form factors, first-order vacuum polarization, and Coulomb exchange and pairing terms. The model parameters are refitted using the mass differences of $ T = 1/2 $ mirror nuclei and ground-state properties of magic nuclei, yielding DD-ME-CSB parameter set. The DD-ME-CSB parameter set reproduces the mass differences of mirror nuclei reasonably well up to $ T = 2 $, demonstrating the importance of $ ω$-$ ρ^0 $ mixing. A connection of the present model to a Skyrme-type CSB interaction is also established through a gradient expansion of the energy density functional.

Figures (6)

• Figure 1: Comparison of nuclear matter equations of state (EoS) for DD-ME-CSB and DD-ME2. The solid and dashed curves show the EoS of symmetric and pure neutron matters, respectively, for DD-ME-CSB while open circles and crosses show those for DD-ME2.
• Figure 2: Deviations from the experimental data of (a) binding energies and (b) charge radii for doubly- and semi-magic nuclei. The results of DD-ME-CSB parameter set are compared to those obtained with DD-ME2 ddme2, FSUGold2 fsugold2 and FRDM frdm12. Note that ${}^{4}_{}\mathrm{He}$ and ${}^{12}_{}\mathrm{C}$ are not included in the fit.
• Figure 3: Deviations of the mass differences of mirror nuclei from the measured values of (a) $T = 1/2$, (b) $T = 1$, and (c) $T = 2$ systems for parameter sets DD-ME-CSB and DD-ME-CSB (00--15), plotted as functions of the $\Delta m_{{\text{\textmd{v}}}}^2$ values.
• Figure 4: Decomposition of the mass difference of mirror nuclei subtracted by its Coulomb part, $\Delta B - \Delta B_{{\text{\textmd{C}}}}$, into the contributions from the $\omega$-$\rho^0$ mixing and the sum of kinetic and charge-symmetry-conserving (CSC) potential energies for DD-ME-CSB00 ($\Delta m_{{\text{\textmd{v}}}}^2 = 0$) and DD-ME-CSB models. For comparison, the experimental values of $\Delta B$ subtracted by the calculated Coulomb contributions are also plotted by crosses. The experimental uncertainties are smaller than the vertical size of the crosses for all the cases.
• Figure 5: Deviations from the experimental data of (a) binding energies and (b) charge radii for doubly- or semi-magic nuclei. The results of the DD-ME-CSB parameter set are compared to those obtained with DD-ME-CSB (00--15). Note that ${}^{4}_{}\mathrm{He}$ and ${}^{12}_{}\mathrm{C}$ are not included in the fit.