Nuclear Rotation, Nambu-Goldstone Mode and Higgs Mechanism

Abstract

We discuss an interesting analogy between the Bohr model of nuclear collective rotation and the Higgs mechanism in spontaneously broken gauge theory. The rotation invariant Lagrangian of the Bohr model, which is also regarded as a d= 1 field theory with an internal 0(3) symmetry, allows a spontaneously deformed and thus resulting in the appearance of zero energy N ambu-Goldstone modes. Our approach to the nuclear collective rotation is to formulate the theory to be form-invariant under an arbitrary time-dependent rotation. We treat a class of manifestly rotation invariant potentials, which lead to the spontaneous breakdown of the rotation symmetry. The vector variables of angular velocity introduced as an analogue of time-dependent gauge fields then absorb those N ambu-Goldstone modes and give rise to massive rotational spectra with a finite moment of inertia. This may be regarded as an analogue of the Higgs mechanism, although not identical with it. We also comment on the nuclear collective rotation from a viewpoint of the quantization of the deformed soliton solution in the Bohr model.