Critical-point symmetries in Boson-Fermion systems: The case of shape transitions in odd nuclei in a multiorbit model

Abstract

We investigate phase transitions in boson-fermion systems. We propose an analytically solvable model [E(5/12)] to describe odd nuclei at the critical point in the transition from the spherical to γ-unstable behavior. In the model, a boson core described within the Bohr Hamiltonian interacts with an unpaired particle assumed to be moving in the three single-particle orbitals j=1/2, 3/2, 5/2. Energy spectra and electromagnetic transitions at the critical point compare well with the results obtained within the interacting boson-fermion model, with a boson-fermion Hamiltonian that describes the same physical situation.