Microscopic modeling of low-energy spectroscopy in medium-heavy and heavy odd-$A$ nuclei is an outstanding open problem in nuclear physics. We propose a novel spectra-generating collective model for odd-$A$ nuclei constructed by means of the nuclear energy density functional theory and the interacting boson-fermion model. The bosonic Hamiltonian for an even-even nucleus, which is treated as a core, and the strength parameters for the interactions between the core and an odd nucleon are completely determined by using as microscopic inputs the potential energy curves and deformed single-particle spectra obtained from the self-consistent mean-field calculations. In applications to odd-$A$ Eu, Sm, La, and Ba isotopes, we demonstrate the validity of the proposed method in reproducing reasonably the observed low-energy spectra and shape phase transitions in the general cases of the quadrupole collective states, that is, nearly spherical, strongly deformed, and $\gamma$-soft shapes, in the presence of an odd nucleon in a single-$j$ orbit.

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• Collective levels
• Electromagnetic transitions
• Energy levels
• Nuclear structure & decays
• 150 ≤ A ≤ 189
• 90 ≤ A ≤ 149
• Models based on symmetries
• Nuclear density functional theory