Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon

Abstract

Using the relativistic point-coupling model with the density functional PC-PK1, the magnetic moments of the nuclei ${}^{207}$Pb, ${}^{209}$Pb, ${}^{207}$Tl, and ${}^{209}$Bi with a $jj$ closed-shell core ${}^{208}$Pb are studied on the basis of relativistic mean field theory. The corresponding time-odd fields, the one-pion exchange currents, and the first- and second-order corrections are taken into account. The present relativistic calculations are in reasonable agreement with the data. The relative deviation between theory and experiment for these four nuclei is $6.1%$ for the relativistic calculations and somewhat smaller than the value of $13.2%$ found in earlier nonrelativistic investigations. It turns out that the pion meson is important for the description of magnetic moments, first by means of one-pion exchange currents and second by the residual interaction provided by the pion exchange.