Nuclear Collective Rotation in the Random Phase Approximation

The collective rotation in deformed nuclei is described in the random phase approximation (RPA). The RPA Hamiltonian can be separated into a rotational and an intrinsic part. The phase angle conjugate to the angular momentum is introduced to describe the rotational motion. The collective rotational mode corresponds to the zero-frequency eigenmode of the RPA Hamiltonian. As a result, the spurious states arising from vibrations of the symmetry axis about its assumed direction have zero energy. The formula for the moment of inertia of the ground state rotational band of even-even nuclei agrees with that given by Thouless or Thouless and Valatin. We also treat the case in which the Hartree-Fock ground state has non-vanishing eigenvalue of Jz, as in odd-A nuclei: our rotational Hamiltonian is compared with that originally given by Bohr and Mottelson. In such a case, a method is proposed to extend the cranking model formula for the moment of inertia