Shape phase transition in odd nuclei in a multi-j model: The U-B(6)circle times U-F(12) case

The phase transition in odd nuclei when the underlying even-even core nuclei experience a transition from spherical to deformed gamma-unstable shapes is investigated. The odd particle is assumed to be moving in the three single-particle orbitals j=1/2,3/2, and 5/2 . At the critical point in the phase transition, an analytic solution to the corresponding Bohr Hamiltonian, called E(5/12), is worked out. Energy spectra and electromagnetic transitions and moments are presented. The same problem is also attacked in the framework of the interacting boson-fermion model (IBFM). Two different Hamiltonians are used. The first one is constructed ad hoc so as to mimic the situation in the E(5/12) model. The second one leads to the occurrence of the O(B)(6)circle times U(F)(12) symmetry when the boson part approaches the O(6) condition. The entire transition line is studied with this Hamiltonian and, in particular, the critical point. Both IBFM calculations at the critical point are consistent with the E(5/12) results.