The concept of supersymmetry and phase transitions are brought together through a study of the consistent-$Q$ Hamiltonian of the interacting Boson-Fermion model, constructed with a vibrational one-body term and a quadrupole-quadrupole interaction, and which is applicable to odd-$A$ nuclei with dominant $j=\frac{1}{2}$, $\frac{3}{2}$, and $\frac{5}{2}$ single-particle orbits. A conservation condition for the pseudo-orbital angular momentum is discussed.

• Received 25 September 2003

DOI:https://doi.org/10.1103/PhysRevC.70.011305