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Electric and Magnetic Moments and Transition Probabilities in $^{208}$Pb $\pm 1$ Nuclei

We present moments and transition probabilities in the neighboring odd-mass nuclei of $^{208}$Pb calculated fully self-consistently from the s.p. properties of $^{208}$Pb with polarization corrections from its excitations, both given from previous Skyrme-Hartree-Fock and RPA calculations. The electric results agree nicely with the data with two very interesting exceptions. In the magnetic case we obtain similar results. We discuss also polarization contributions to the $l$-forbidden $M1$ transitions, which are, however, much too small compared to the data. With a modified external field operator which accounts effectively for mesonic and many-body effects the description of the data can be substantially improved.