Comparison of the Nilsson and Skyrme Hartree-Fock results for the properties of highly deformed states in nuclei

Abstract

A Comparison of the Nilsson model and the Skyrme Hartree-Fock model for studying highly deformed states in nuclei is made. The states constructed are the 4-particle, 4-hole and 8-particle, 8-hole states in 40Ca and the linear alpha chain states in 12C and 16O. The deformations obtained in the two approaches are remarkably similar. The change in the radius of the np-nh state in 40Ca relative to the ground state is smaller in the Skyrme Hartree-Fock model than in the Nilsson model, indicating monopole shrinkage in the former approach, hence volume non-conservation. Whereas the energies of the 4 p−4 h states are nearly the same in the two approaches, the 8 p−8 h is at too high an energy in the Nilsson model. For the linear chain states in 12C and 16O, the Skyrme 3 Hartree-Fock approach gets the energies of the projected J π = 0 + states a factor of two too high while the results of the Nilsson model are in surprisingly good agreement with experiments. The quadrupole moment in momentum space ( Q p ) for the ground state and the metastable highly deformed states is discussed.