On the collective octupole degrees of freedom

The collective octupole degrees of freedom are considered. The spherical components of a real, electric octupole tensor are treated as collective octupole laboratory coordinates. Decomposition of the octupole irreducible representation of orthogonal group O(3) onto three irreducible representations of the cubic Oh group is presented. Intrinsic cubic coordinates are introduced. The two Oh-symmetric intrinsic coordinate frames are defined. Relations between the laboratory coordinates and the intrinsic cubic ones are discussed in the two cases of intrinsic frame. Operator of the angular momentum and Hamiltonian for the octupole motion are given and expressed in terms of both sets of the intrinsic coordinates. Differences between description of the octupole and the quadrupole degrees of freedom are concluded.