https://doi.org/10.1140/epjp/s13360-022-03328-9
Regular Article
Prolate–oblate quantum phase transition in odd nuclei for 
and 5/2 orbits within the 
limit of the IBFM
1
Department of Physics, Shiraz University, 71946, Shiraz, Iran
2
Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, 35131, Padova, Italy
3
INFN-Sezione di Padova, Via Marzolo 8, 35131, Padova, Italy
Received:
3
August
2022
Accepted:
25
September
2022
Published online:
21
October
2022
We study an exactly solvable algebraic Hamiltonian for odd systems that allows to span the whole range between prolate and oblate spectra, while maintaining the 
dynamical symmetry, thanks to the mixing of quadratic and cubic Casimir operators of . We choose a 
fermionic basis that is coupled to coherent states for the boson part. With this, we diagonalize the Boson–Fermion Hamiltonian obtaining potential energy surfaces for each component. We find a very rich variety of behaviours: the various orbitals do not display the same shape, some are prolate, while others are oblate, and they make the transition following different paths.
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