The U(612) supersymmetric limit of the interacting Boson-Fermion Model

The $\text{U(}\text{6}\text{12}\text{)}$ dynamical supersymmetry of the Interacting Boson-Fermion Model, appropriate for nuclei where the odd nucleon can occupy the single-particle orbits $\text{J =}\text{1}\text{2}\text{,}\text{3}\text{2}\text{,}\text{and}\text{5}\text{2}$ is analyzed. The subgroup structure of $\text{U(}\text{6}\text{12}\text{)}$ is discussed and the generators and Casimir operators of these subgroups are given. In each of the three dynamical symmetries of $\text{U(}\text{6}\text{12}\text{)}$ the energy formulas, reduction rules, and wave functions are obtained and closed expressions for E2 transition rates and one-nucleon transfer intensities are derived. Examples of $\text{U(}\text{6}\text{12}\text{)}$ symmetries are presented.