Comparative study of theSp (2,R) and theSp(6,R) models and an application to theBa chain of isotopes

We investigate the Sp(2, R) model for light and heavy nuclei and compare it to recent applications of the Sp(6, R) model. The same Hamiltonian is used and the basis states will have good angular momentum. We not only confirm that the restricted space of the Sp(6, R) model gives the dominant contribution but also that there is no practical difference from the Sp(6, R) model calculations. The Sp(2, R) model is then applied to the chain of Ba-isotopes which show, according to a recent application of the geometrical model, a dominant prolate behavior with an important γ-unstable component. They represent limiting cases where the Sp(2, R) model can be put to an extreme test. Work supported by CONACyt (No. E120-550/95).