The Algebraic Image of the Asymmetric Top.

The algebraic realization of the quantum mechanical rotor by the SU(3) (---\u3e) SO(3) algebra is investigated. It is shown that a hamiltonian built from rotationally invariant functions of SU(3) generators reproduces the eigenvalues of the rotor hamiltonian. The equivalence of both models is established also for the quadrupole transition rates and the D(,2) symmetry of the rotor. The relation between the SU(3) (---\u3e) SO(3) algebra and the nuclear shell model allows therefore a microscopic interpretation of rotational motion as a many-particle effect