The Tilted Axis Cranking (TAC) model [1] has turned out to be an appropriate theoretical tool for the description of the magnetic dipole bands. This model is a natural generalization of the cranking model for situations where the axis of rotation does not coincide with a principal axis of the density distribution of the rotating nucleus, and thus the signature is not a good quantum number. Since introduced, TAC has proven to be a reliable approximation for the energies and intraband transitions in both normally and weakly deformed nuclei. Hitherto the TAC calculations were based on the Nilsson Hamiltonian with the standard set of parameters [2]. This parameter set is known to have problems, for instance, in the A = 130 region where a better set has been suggested in [3]. On the other hand the Woods-Saxon potential with the universal parameter set [4] works very well around A = 130 and also in other mass regions. It is expected that this potential, which has a realistic radial profile instead of the artificial l²- term of the Nilsson model, is more reliable when exploring mass regions where the Nilsson parameters have not been locally optimized. In addition, the l²- dependence of the Nilsson potential is known to be problematic when the mean field is cranked at high angular velocity. In order to avoid the mentioned problems we developed an hybrid model which consists in adapting the Nilsson potential as close as possible to the Woods-Saxon one. Instead of the parameterizing the single particle levels of the spherical modified oscillator in the standard way by means of an ls- and an l²-term, the hybrid model directly takes the energies of the spherical Woods-Saxon potential. The deformed part of the hybrid potential is an anisotropic harmonic oscillator. This compromise keeps the simplicity of the Nilsson potential, because coupling between the oscillator shell can be approximately taken into account by means of stretched coordinates [2], and it amounts to a minor modification of the existing TAC code. On the other hand, it has turned out to be quite a good approximation of the realistic flat bottom potential as long as the deformation is moderate. Another motivation for the hybrid potential is the considerably lower computation time (about a factor of 10) as compared with the full Woods-Saxon potential, which is important for the TAC calculations, which demand to achieve selfconsistency in two extra dimensions (the orientation angles).
Technically, the necessary replacements are rather simple, because the existing TAC code uses states of good l,j,m as a basis. The spherical Nilsson energies e^(nil)_N,l,j are replaced by the spherical Woods - Saxon energies e^(ws)_N,l,j. It turns out to be unproblematic to associate the quantum numbers of the two different potentials. For a given combination l,j the third quantum number N is found by counting from the state with the lowest energy. The fact that the spherical Woods-Saxon code uses a harmonic oscillator basis permitted a check of the algorithm. The major component of the Woods-Saxon wavefunction agrees with the state found by our counting algorithm. In the high-lying part of the single-particle spectrum (three shells above the valence shell or higher) there are occasional ambiguities in assigning the states. Small errors of this kind are not expected to have any consequences at moderate or small deformation. These states do not couple strongly to the states near the Fermi surface.

¹ Faculty of Physics, Sofia University, 1164 Sofia, Bulgaria
² on leave of absence at the Faculty of Physics, University of Notre Dame, IN 46556, USA

References

[1]	S. Frauendorf, Rev. Mod. Phys., in press
[2]	S.G. Nilsson and I. Ragnarsson, Shapes and Shells in Nuclear Structure,
	Cambridge University Press, 1995
[3]	Jing-ye Zhang, N. Xu, D. B. Fossan, Y. Liang, R. Ma, and E. S.Paul,
	Phys. Rev. C 39, 714 (1989) and Phys. Rev. C 42, 1394 (1990)
[4]	S.Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, and T. Werner,
	Comput. Phys.Commun. 46, 379 (1987)

 IKH 06/20/01 © F. Dönau