U(15)⊃ Su(6) Description of the Sdg Boson Model

Abstract

The most prominent feature of the interacting boson model1 proposed by Arima and Iachello is that it can describe vibrational, rotational and γ-unstable nuclei in one model space, spanned by s- and d-bosons, in terms of the subgroup-reduction chains, U(6)⊃SU(5)⊃O(5)⊃O(3), U(6)⊃SU(3)⊃0(3) and U(6)⊃O(6)⊃O(5)⊃O(3). To describe detailed properties of various nuclei, however, the model space is sometimes too small, and one introduces other bosons, g-boson for example. The sdg boson model has been studied2 in the U(15)⊃SU(3)⊃O(3) reduction chain to improve the sd description of deformed nuclei. It is interesting to investigate how the introduction of the g-boson changes other reduction chains. In this paper a counterpart of the U(6)⊃0(6)⊃0(5)⊃0(3) reduction chain will be considered. One of its obvious extension to the sdg model space is the U(15)⊃O(15)⊃0(14)⊃O(3) chain. However, the U(15)⊃SU(6)⊃Sp(6)⊃0(3) chain is found to be another sdg extension. Essential features of the 0(6) description are easily seen to be carried over into the 0(15) one, but details of the SU(6) description are not well known. Their investigation is the main purpose of this paper.