Group O(4) in the Nuclear IBA Model

Abstract

The group O(4) is established as a link in the group chains of the interacting-boson model (IBA) of nuclear structure. It is obtained as a subgroup of O(5) by excluding the m = 0 component of the d boson. Since only the third component of the angular momentum is then conserved, O(4) symmetry is limited to intrinsic states. No O(3) can be sandwiched between this O(4) and the physical O(2). Branching rules are derived for groups U(4), O(4) and O(2). The dynamic-symmetry contributions of O(4) and U(4) to the energy are given. The structure $O\left( 4 \right) \approx O\left( 3 \right) \times O\left( 3 \right) \supset O\left( 3 \right)$is established