Shell-model study of Pb, Bi, Po, At, Rn, and Fr isotopes with masses from 210 to 217

Large-scale shell-model calculations are performed for even-even, odd-mass, and doubly odd nuclei of Pb, Bi, Po, At, Rn, and Fr isotopes in the neutron rich region ($Ng126$) assuming $^{208}\mathrm{Pb}$ as a doubly magic core. Seven orbitals above the magic number 126, the $1{g}_{9/2}$, $0{i}_{11/2}$, $0{j}_{15/2}$, $2{d}_{5/2}$, $3{s}_{1/2}$, $1{g}_{7/2}$, and $2{d}_{3/2}$ orbitals, are considered for neutrons and all the six orbitals between the magic numbers 82 and 126, the $0{h}_{9/2}$, $1{f}_{7/2}$, $0{i}_{13/2}$, $2{p}_{3/2}$, $1{f}_{5/2}$, and $2{p}_{1/2}$ orbitals, are considered for protons. For a phenomenological effective two-body interaction, one set of the monopole-pairing, quadrupole-quadrupole, and multipole-pairing interactions is adopted for all the nuclei considered. The calculated energies and electromagnetic properties are compared with the experimental data. Many isomeric states are analyzed in terms of the shell-model configurations. The spins and parities of some experimentally ambiguous states are suggested.