Relativistic random-phase-approximation description of M1 excitations with the inclusion of π mesons

Abstract

Based on the covariant density functional theory, the magnetic dipole ($M1$) resonance is described in the framework of relativistic random-phase approximation with density-dependent meson-nucleon coupling. The isovector-pseudovector interaction channel, represented by the exchange of $\ensuremath{\pi}$ meson, is included in the residual interaction to describe unnatural parity transitions. The strength distributions of $M1$ resonances are studied in doubly magic nuclei $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$, in comparison with their analog Gamow-Teller (GT) excitations. It is found that the $\ensuremath{\pi}$ meson and its zero-range counterterm are responsible for almost all of the energy shift caused by residual interaction, which is similar to the case of GT excitation. However, the strength of the counterterm suggested by the GT study is not suitable to simultaneously reproduce the experimental $M1$ peak energies from $^{48}\mathrm{Ca}$ to $^{208}\mathrm{Pb}$. To improve the descriptions of $M1$, effects caused by adjusting the strength of pionic counterterm and introducing the density dependence of the $\ensuremath{\pi}$ meson channel are explored. Finally, from the analyses of dominant transition configurations of GT and $M1$ resonance, we find that the proper spin-orbit splitting is the key to simultaneously reproduce the $M1$ strength distributions from light to heavy nuclei.