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

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Using the relativistic point-coupling model with density functional PC-PK1, the magnetic moments of the nuclei ²⁰⁷Pb, ²⁰⁹Pb, ²⁰⁷Tl and ²⁰⁹Bi with a jj closed-shell core ²⁰⁸Pb are studied on the basis of relativistic mean field (RMF) 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 results reproduce the data well. 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 non-relativistic investigations. It turns out that the π 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 π exchange.