Exact solution of the particle-rotor model,angular momentum spread and transition rates

The particle-plus-rotor model with valence particles in an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ shell is solved exactly including single-particle splitting and pairing forces. Backbending and the spread of angular momentum of the valence shell is studied in detail for the two lowest bands and quadrupole transition rates are calculated.