In this work, we present a systematic study of low-lying states and electromagnetic properties of the semimagic $N=82$ isotonic chain with proton number $Z$ = 51–77, using the full configuration interaction shell model with a newly developed high-quality effective interaction. The calculations are performed in a large model space that includes all proton orbitals between $Z=50$ and 82: $0g_{7/2}, 1d_{5/2}, 1d_{3/2}, 2s_{1/2}$, and $0h_{11/2}$. The effective interaction is derived through the principal component analysis approach, starting from 160 two-body matrix elements and five single-particle energies and considering up to 30 degrees of freedom. Those are optimized by fitting to 204 available experimental energy levels. The resulting root-mean-square deviation is as low as 102 keV. The new interaction successfully reproduces the binding energies, low-lying spectra, electric quadrupole transition probabilities $B\left(E2\right)$, and magnetic dipole moments across both even-even and odd-mass isotones. The nuclear structure of low-lying states is analyzed in detail. Additionally, predictions are made for several more proton-rich nuclei beyond current experimental reach, including ${}^{155}\mathrm{Ta}, {}^{156}\mathrm{W}, {}^{157}\mathrm{Re}, {}^{158}\mathrm{Os}$, and ${}^{159}\mathrm{Ir}$.

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• Binding energy & masses
• Electromagnetic transitions
• Energy levels
• Nuclear shapes and moments
• Nuclear spin & parity
• Nuclear structure & decays
• Nucleon-nucleon interactions
• Shell model
• 150 ≤ A ≤ 189
• 90 ≤ A ≤ 149