Background: The study of the structure of odd-mass nuclei in regions characterized by the interplay of multiple particle-hole configurations represents a major challenge in nuclear structure physics. The odd-mass niobium isotopes ($Z=41$), located near the $N=60$ region, are of particular interest due to the occurrence of shape coexistence and quantum phase transitions.

Purpose: This work aims to investigate the structure of the ${}^{93-103}\mathrm{Nb}$ isotopes using the intrinsic-frame formalism of the interacting boson-fermion model with configuration mixing (IBFM-CM). The goal is to determine the nuclear shapes and explore the phenomena of shape coexistence, configuration crossing, and quantum phase transitions.

Method: We employ the intrinsic formalism of the IBFM-CM, which includes both 0p-0h (regular) and 2p-2h (intruder) configurations interacting with the unpaired nucleon. This approach provides a self-consistent framework to study energy surfaces, shape coexistence, and intruder bands for both positive- and negative-parity states. A realistic Hamiltonian for niobium, determined in previous studies, is adopted.

Results: The formalism is applied to the ${}^{93-103}\mathrm{Nb}$ isotopes for both positive- and negative-parity bands. A detailed analysis of the mean-field energy surfaces has been performed, including axial energy curves, triaxial energy surfaces in the $\beta \text{−}\gamma$ plane, and the corresponding equilibrium deformation parameters. The results reveal clear evidence of configuration coexistence and crossing along the isotopic chain.

Conclusions: We have applied the recently developed intrinsic-state formalism of the IBFM-CM using a realistic Hamiltonian for a chain of niobium isotopes. The existence of crossing configurations has been demonstrated around $N=60$, corresponding to a quantum phase transition previously identified in the Sr and Zr isotopic chains. Furthermore, we find that the presence of an unpaired nucleon in Nb influences the abruptness of the quantum phase transition, underscoring the sensitivity of the structural evolution to single-particle degrees of freedom.

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• Nuclear shapes and moments
• Nuclear structure & decays
• 90 ≤ A ≤ 149
• Models based on symmetries