An effective Coulomb interaction in nuclear energy density functionals

It is well-known that the charge-violating interaction is usually underestimated in nuclear many-body approaches. In the framework of the Skyrme–Hartree–Fock (SHF) method, the effective two-body charge-symmetry breaking (CSB) and charge-independent breaking (CIB) interactions in nuclear medium based on Brueckner theory are included, then we constrain the effective Coulomb interaction in turn with the help of experimental Coulomb displacement energy (CDE), i.e., the binding-energy difference between mirror nuclei. Accordingly, we introduce a new (effective) Coulomb coupling constant e 0 2 = e 2 ( 1 + a exc Z − 2 / 3 ) to replace the original one e 2 between protons (note that the original coupling constant just applies to point-like charge), where Z is proton number. This effective coupling constant e 0 2 is phenomenologically embodying the effects of many complicated corrections beyond mean-field method or even nuclear structure physics such as core polarization, nucleon finite size and vacuum polarization. With e 0 2 = e 2 ( 1 + 0.45 Z − 2 / 3 ) for SLy4 interaction, the experimental CDE for T = 1 / 2 , 1 , 3 / 2 , 2 isobaric multiplets, together with the excitation energy of isobaric analog states for heavy nuclei such as 208Pb, can be rather well reproduced, indicating the validity of such a treatment. Moreover, the c coefficients in the isobaric multiplet mass equation for isobaric quartets are computed, and the results based on Coulomb force turns out to be around 10%–15% lower than the experimental ones persistently, just as the Nolen–Schiffer anomaly. Yet, the introduction of both the CIB effect and the e 0 2 systematically improves the agreement with experimental data substantially.