$π$-$η$ mixing and charge symmetry violating NN potential in matter

We construct density dependent Class $III$ charge symmetry violating (CSV) potential due to mixing of $π$-$η$ meson with off-shell corrections. The density dependence enters through the non-vanishing $π$-$η$ mixing driven by both the neutron-proton mass difference and their asymmetric density distribution. The contribution of density dependent CSV potential is found to be appreciably larger than the contribution of vacuum CSV potential.

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