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Systematic shell model study for $N=82$ and $N=126$ isotones and nuclear isomers

In the present work, we have done a systematic shell model study of $N=82$ and $N=126$ isotones. For the $N=82$ isotones, we have performed calculations using SN100PN interaction, while for $N=126$ isotones, we have used KHPE interaction. Similarities between these two isotonic chains have been reported, using the strong resemblance between the high-$j$ orbitals. Apart from the nuclear spectroscopic properties, we have also explained different isomeric states in these two regions. In the $N$ =82 region, we have mainly discussed the properties of the $6^+$ and $17/2^+$ isomers, while in the $N=126$ region for $8^+$, $11^-$, $21/2^-$ and $29/2^+$ isomers. We have reported $B(E2)$, $B(E3)$, $g$-factor, and quadrupole moments of the isomeric states for comparison in these two isotonic chains.