Systematic study of Coulomb displacement energy based on the Coulomb energy empirical formula and mass model

In this study, starting from the nuclear binding energy, we studied the empirical formula of the Coulomb energy systematically. Beginning with the simplest empirical formula, we added the Coulomb exchange term, pairing correlation, and shell correction, to calculate the Coulomb energy more precisely. In addition, we investigated the Coulomb displacement energy of widely used mass models. The discrepancies between the calculation results and experimental data might be caused by the missing of the isospin breaking terms of strong interactions in theory. By investigating these discrepancies, we found that the results obtained by microscopic theories presented a distinctive systematical behavior. Thus, these theories can be improved by including isospin breaking terms. However, in the results obtained by phenomenological models, the systematical behavior is unclear. This occurs because it is difficult for the information of the microscopic nuclear structure to be absorbed into the parameters of phenomenological models.