The consequences of the spontaneous breaking of rotational symmetry are investigated in a field theory model for deformed nuclei, based on simple separable interactions. The crucial role of the Ward-Takahashi identities in describing the rotational states is emphasized. We show explicitly how the rotor picture emerges from the isoscalar Goldstone modes and how the two-rotor model emerges from the isovector scissors modes. As an application of the formalism, we discuss the $M1$ sum rules in deformed nuclei and make the connection to empirical information.

• Received 9 June 2011

DOI:https://doi.org/10.1103/PhysRevC.84.014327