Study of dynamical supersymmetries in nuclear physics

The Interacting Boson Model has been very successful in describing the low-lying collective quadrupole states of even-even nuclei. It is an algebraic approach to the spectra of such nuclei. Similarly, the Interacting Boson-Fermion Model is an algebraic approach to the spectra of odd-even nuclei. In this dissertation a unified algebraic approach to the spectra of both even-even and odd-even nuclei in the context of dynamical supersymmetries is presented. In this unified approach, the spectra of a number of nuclei (some even-even, some odd-even), belonging to the same representation of a unification group will be related by the symmetry operations of this group. Since these representations contain both bosonic and fermionic states, this group must be a supergroup. The representation theory of supergroups has been studied to some extent. In this dissertation, first the representation theory of supergroups is further developed, then it is applied to the nuclear spectra. In particular, predictions for excitation energies, electromagnetic transition rates and transfer reaction intensities are given and compared with experimental data