Group-theoretical treatment of the Nilsson model

The properties of the infinitesimal operators of theSU3-group are used to investigate the group-theoretical structure of the eigenstates of the Nilsson Hamiltonian. This group-theoretical method is applied to the (N=2) oscillator shell. It turns out that the exact solutions can be understood by purely algebraic arguments to a large extent, especially for positive deformations. It is shown that this fact can advantageously be used for a general discussion of nuclear properties as well as for an algebraic calculation of potential-energy surfaces as a function of the deformation parameter. Furthermore, the coupling between different oscillator shells is also discussed within our group-theoretical frame.