We employ a specific U(5)-O(6) Hamiltonian of the interacting boson model (IBM) to describe even-even nuclei near the O(6) limit. Our analysis identifies a zero generalized boson pairing mode, where the generalized pairing energy vanishes exactly. Within this zero mode, excitation energies remain invariant under variations in the control parameters. Exact solutions for this zero mode are derived from the zeros of the corresponding Jacobi polynomials, while solutions for the nonzero mode are obtained from the more complex extended Heine-Stieltjes polynomials. We fit some low-lying positive-parity energy levels and associated $B$($E2$) values for ${}^{194,196}\mathrm{Pt}$. The results demonstrate that ${}^{194}\mathrm{Pt}$ lies closer to the O(6) limit as evidenced by the available experimental $B$($E2$) values.

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• Collective levels
• Nuclear many-body theory
• Nuclear structure & decays
• 190 ≤ A ≤ 219
• Models based on symmetries