A Quantum Mechanical Treatment of Nuclear Collective Motion

 In this work, we deal with a quantum mechanical  treatment of  nuclear collective motion. To carry out this study, we invoke the nuclear Born--Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we deal with non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells.  Moreover, we look at a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using a mean-field approximation to describe the intrinsic structure, we show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia. We then show that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high-lying rotational states. Finally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model, which is known to successfully reproduce vast amounts of experimental data ranging from low-lying rotational states to high angular momentum states.