UBF (5) to SUBF (3) shape phase transition in odd nuclei for j=1/2, 3/2, and 5/2 orbits: The role of the odd particle at the critical point

We investigate the phase transition in odd nuclei within the Interacting Boson Fermion Model in correspondence with the transition from spherical to stable axially deformed shape. The odd particle is assumed to be moving in the single-particle orbitals with angular momenta j = 1/2, 3/2, 5/2 with a boson-fermion Hamiltonian that leads to the occurrence of the SUBF (3) boson-fermion symmetry when the boson part approaches the SU(3) condition. Both energy spectra and electromagnetic transitions show characteristic patterns similar to those displayed by the even nuclei at the corresponding critical point. The role of the additional particle in characterizing the properties of the critical points in finite quantal systems is investigated by resorting to the formalism based on the intrinsic frame.