Supersymmetry Methods, in nuclei, dynamical

Supersymmetry in nuclear physics is from the unitary type and thus different to the one used in particle physics [1 2 3 4]. It is related to the interacting boson approximation, which allows to construct an algebraic model describing the low-lying excitations of even-even nuclei. Based on the pairing property between nucleons occupying the same orbits, the interacting boson model replaces nucleon pairs by N s and d bosons. The number of bosons is given by half the number of valence nucleons. The model space is then spanned by the irreducible representation [N] of U(6). An attractive feature of this model [5,6] is that it has three dynamical symmetries, called after the first subgroup U(5), SU(3) and O(6), which were found to correspond to three classes of nuclei observed in nature. To describe nuclei with an odd number of neutrons or protons, a system with N bosons and one fermion is considered in the model. Generally the odd nucleon can occupy several single particle orbits j _...