Intrinsic Lie group and nuclear collective rotation about intrinsic axes

Abstract

For any Lie group G, is so called intrinsic Lie group G is introduced, G and G being commutative and anti-isomorphic. It is shown that in the parameter space of a Lie group G, the corresponding intrinsic Lie group G is just the second parameter group. The general relations between the first and second parameter groups are derived in a simple way. For the group SO(3), there is the intrinsic Lie group SO(3). The infinitesimal generators of SO(3) are precisely the components of the angular momentum in the intrinsic coordinate system. Therefore the intrinsic Lie group SO(3) provides an appropriate mathematical formalism for the description of collective rotations of nuclei about their intrinsic axes.