Charge symmetry breaking effects of \(\omega \)-\(\rho ^0\) mixing in relativistic mean-field model

Abstract

We present a relativistic mean-field model that incorporates charge symmetry breaking (CSB) of nuclear force via the \( \omega \)-\( \rho ^0 \) 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 \( \omega \)-\( \rho ^0 \) 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.