Evolution of nuclear shell structure due to the pion exchange potential

The evolution of nuclear shell structure is investigated for the first time within density-dependent relativistic Hartree-Fock theory and the role of $\pi $-exchange potential is studied in detail. The energy differences between the neutron orbits $\{\nu 1h_{9/2}, \nu 1i_{13/2}\}$ in the $N=82$ isotones and between the proton ones $\{\pi 1g_{7/2}, \pi 1h_{11/2}\}$ in the $Z=50$ isotopes are extracted as a function of neutron excess $N - Z$. A kink around $Z=58$ for the $N=82$ isotones is found as an effect of pion correlations. It is shown that the inclusion of π-coupling plays a central role to provide substantial isospin dependence of the energy differences. In particular, the tensor part of the π-coupling has an important effect on the characteristic isospin dependence observed in recent experiments.