A Rigorous Application of the Collective Model to Some Rare Earth Nuclei

Abstract

The collective model of an odd neutron in an axially symmetric deformed Woods–Saxon potential, coupled to a rotating core, and containing the full RPC and pairing corrections has been used to predict the full low lying rotational band spectrum of the nuclei with N = 91 to 97. Only three adjustable parameters were used in each nucleus to fit the complete spectrum. It was possible in several nuclei to obtain the correct level sequence and in most to confirm level assignments, and the adjusted parameters were in good agreement with accepted values. However, the accuracy of this method is insufficient, in most nuclei, to provide reliable predictions for as yet unidentified bands. The lack of good overall agreements in the low lying spectra of these nuclei confirms that the core shape parameters do change from one band to another.

Calculation of the properties of the rotational bands ofGd155,157

“…We believe that the reason for this distortion is the Coriolis interaction which is included naturally in the core Hamiltonian (H, ). The standard approach to this difficulty is to attenuate the Coriolis interaction [12,13]. Since there is no justification for this ad hoc procedure, the best approach is to include other forms of interaction which will counteract this effect.…”

“…In Refs. [12,13] a deformed Woods-Saxon potential is considered. Again, pairing is taken into account by means of a BCS transformation.…”

“…Again, pairing is taken into account by means of a BCS transformation. Another extension of the original model takes into account mixing between different major shells [12,13]. In Fig.…”

“…The first one [ Fig. 13(b)] is from [12]. In this paper the model Hamiltonian includes a quadrupole and hexadecapole deformed core.…”

“…In later applications one finds extensions of the original model (we shall use calculations for 155,157 Gd as references throughout the discussion). The Nilsson potential can be replaced by a more realistic deformed Woods-Saxon potential [6], pair correlations can be taken into account by a quasi-particle transformation of BCS type [6,7,8,9], and mixing between different major shells (states with principal quantum number N differing by two) [10,11,12,13,8,9] can be included. Finally one can allow for phonon excitations of the core [6,7,14,15], in contrast with the standard core-particle coupling model (CPC model) where the core is assumed to be a rigid rotor.…”