Within the interacting boson model (IBM), a geometric analysis of transitional nuclei is carried out through angular momentum projection of the intrinsic coherent state. The results indicate that $K$-mixing effects in the calculations are typically negligible, validating the use of $K$-fixed projection for semiclassical analyses of the spin dependence of quadrupole deformation in the IBM. Further analysis indicates that in a rotating transitional system, quadrupole deformation is stretched with increasing angular momentum, providing a geometrically intuitive perspective on the commonly observed Jacobi-type transitions, as exemplified by the case studies of ${}^{160}\mathrm{Gd}$ and ${}^{162}\mathrm{Dy}$. The method is additionally applied to the yrast states of ${}^{170}\mathrm{Os}$ to probe quadrupole deformation changes linked to the observed low-spin $B\left(E2\right)$ anomaly behavior, demonstrating the capability of IBM-based angular momentum projection in interpreting exotic collective phenomena.

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• Nuclear structure & decays
• Collective models
• Models based on symmetries