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Effects of level inversion on the Coulomb displacement energies of the Ar-K isobaric analog state pairs

The Coulomb displacement energies of the neutron-rich Ar-K isobaric analog state pairs with mass number $A=35-47$ are calculated within the relativistic mean field model and the effects of level inversion on the Coulomb displacement energies of the Ar-K isobaric analog state pairs are studied. The calculations are carried out in two cases, with and without consideration of the possible $2s_{1/2}$ and $1d_{3/2}$ proton level inversion of the neutron-rich Ar isotopes. Results show that the $2s_{1/2}$ and $1d_{3/2}$ level inversion of the neutron-rich Ar isotopes may reduce the Coulomb displacement energy by 0.06$\sim$0.17 MeV for the Ar-K isobaric analog state pairs. The results may provide a reference for experimental investigations of nuclear level inversion and a new test of the relativistic mean field model.