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Magnetic-dipole (M1) excitations of $^{18}$O and $^{42}$Ca nuclei areinvestigated within a relativistic nuclear energy density functional framework.In our last work \cite{2019OP}, these nuclei are found to have unique M1excitation and its sum rule, because of their characteristic structure: thesystem consists of the shell-closure core plus two neutrons. For a moresystematic investigation of the M1 mode, we have implemented a framework basedon the relativistic nuclear energy density functional (RNEDF). For benchmark,we have performed the RNEDF calculations combined with the random-phaseapproximation (RPA). We evaluate the M1 excitation of $^{18}$O and $^{42}$Ca,whose sum-rule value (SRV) of the M1 transitions can be useful to test thecomputational implementation \cite{2019OP}. We also apply this RNEDF method to$^{208}$Pb, whose M1 property has been precisely measured\cite{1979Holt,1987Koehler,1988Laszewski,2016Birkhan}. Up to the level of theM1 sum rule, our result is in agreement with the experiments, except thediscrepancy related with the quenching factors for $g$ coefficients.

Relativistic energy-density functional approach to magnetic-dipole excitation and its sum rule