Effects of finite nucleon size, vacuum polarization, and electromagnetic spin-orbit interaction on nuclear binding energies and radii in spherical nuclei

The electromagnetic effects of the finite size of the nucleon are implemented self-consistently on top of the Skyrme Hartree-Fock calculation, where the electric form factors of both protons and neutrons are considered. Furthermore, the vacuum polarization and the electromagnetic spin-orbit interaction are taken into account. The self-consistent finite-size effects give a different Coulomb potential from the conventional one and affect the neutrons as well. The contribution of the finite-size effects to the total energy reaches $ 7 , $\mathrm{M}\mathrm{e}\mathrm{V}$ $in$ {}^{208} $\mathrm{P}\mathrm{b}$ $. The vacuum polarization and the electromagnetic spin-orbit interaction are also non-negligible, especially in the heavy nuclei. These effects provide a comparable contribution of the total energy to that of the isospin symmetry-breaking terms of the nuclear interaction. The mirror nuclei mass difference in ${}^{48}\mathrm{C}\mathrm{a}$–${}^{48}\mathrm{N}\mathrm{i}$ is also studied, and its value is improved by approximately one order of magnitude.