Systematic shell-model study of Rn isotopes with $A=$ 207 to 216 and isomeric states

In the present work, we have performed systematic large-scale shell-model calculations for Rn isotopes with $A=$ 207 to 216. For the $^{207-212}$Rn isotopes, we have performed calculations with KHH7B interaction, while for $^{213-216}$Rn isotopes with KHPE and KHH7B interactions. Calculations have been carried out with the KHH7B in a model space consisting of the proton orbitals $d_{5/2}, h_{11/2}, d_{3/2}$ and $s_{1/2}$ below the $Z$ = 82 shell gap, and the $h_{9/2}, f_{7/2}$, and $i_{13/2}$ above it, and for neutron, the $i_{13/2}, p_{3/2}, f_{5/2},$ and $p_{1/2}$ orbitals are below $N$ = 126 shell gap, and the $g_{9/2}, i_{11/2}, j_{15/2}$ orbitals are above it. The calculations for KHPE interaction are performed in the full Z = 82--126 proton-neutron model space with proton orbitals $h_{9/2}, f_{7/2}, f_{5/2}, p_{3/2}, p_{1/2}$, and $i_{13/2}$, and neutron orbitals $i_{11/2},g_{9/2}, g_{7/2}, d_{5/2}, d_{3/2}, s_{1/2}$, and $j_{15/2}$. The calculated energies and electromagnetic properties have been compared with the available experimental data. We have also analyzed several isomeric states from the calculated shell-model configurations and half-lives. In the case of even Rn isotopes, the ${8_1}^+$ isomeric state is due to seniority $v$ =2, the ${14_1}^+$ and ${17_1}^-$ isomeric states are due to seniority $v$ =4. For the odd Rn isotopes, the ${13/2_1}^+$ isomeric state is due to seniority $v$ =1, the ${35/2_1}^+$, ${43/2_1}^-$ and ${49/2_1}^+$ isomeric states are due to seniority $v$ = 5. We have also suggested spins and parities of several unconfirmed states from the recent experimental data.