@article{884d1b990fea46f291700ab30882439d,

title = "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 4p-4h states are nearly the same in the two approaches, the 8p-8h 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 Jπ = 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 (Qp) for the ground state and the metastable highly deformed states is discussed.",

author = "L. Zamick and Zheng, {D. C.} and Lee, {S. J.} and Caballero, {J. A.} and {Moya de Guerra}, E.",

note = "Funding Information: superimposed on the large deformations, e.g., a monopole shrinkage for the Xp-8h state in {\textquoteleft}%a. Whether or not these monopoie shifts are correctly given by the Skyrme 3 Hartree-Fock remains to be seen. The quadrupole moments in momentum space Q,, vanish for all the states considered here in the deformed oscillator model (where Q,=O is equivalent to Motteison condition) and are either zero or very small in hte Nilsson model In the Hartree-Fock calculations Q, is very small for most states but not for the linear chain states. The Skyrme Hartree-Fock calculations overestimate the energies of the linear chain states by almost a factor of two. For other deformed states such as 4p-4h and Sp-8h states in 40Ca, however, the results are quite good with this model. On a more positive note, even when the energies are off, the shapes of the intrinsic states come out very good in both the Nilsson and Skyrme Hartree-Fock models. The calculations largely confirm results of the picturesque alpha clustering model for states in “{\textquoteleft}C and 160--linear chain states really should exist and they do! This work has been supported by a NATO Collaborative Research Grant 0702/87 and by U.S. DOE Grant DE-FG05-86ER-40299 and by DGICYT (Spain) Contract PB870311. One of us (J.A.C.) thanks MEC (Spain) for a Fulbright Scholarship. We thank David Brink for useful discussions.",

year = "1991",

month = dec,

doi = "10.1016/0003-4916(91)90121-N",

language = "English (US)",

volume = "212",

pages = "402--418",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "2",

}