Nuclear magnetization distribution and hyperfine splitting in Bi$^{82+}$ ion

Hyperfine splitting in Bi$^{82+}$ and Pb$^{81+}$ ions was calculated using continuum RPA approach with effective residual forces. To fix the parameters of the theory the nuclear magnetic dipole moments of two one- particle and two one-hole nuclei around $^{208}$Pb were calculated using the same approach. The contribution from velocity dependent two-body spin- orbit residual interaction was calculated explicitly. Additionally, the octupole moment of $^{209}$Bi and the hfs in muonic bismuth atom were calculated as well in the same approach. All the calculated observables, except the electronic hfs in $^{209}$Bi, are in good agreement with the data. We argue for more accurate measurement of the octupole moment and the muonic hfs for $^{209}$Bi.