Deformation of nuclei as a function of angular momentum in the U(6) ⊃ SU(3) model

In the framework of a hybrid rotational model, proposed recently by Moshinsky as a consequence of a comparison between the Gneuss and Greiner extension of the Bohr and Mottelson model and the interacting boson model, we study the shape of nuclei by calculating the average of the expectation value of the square of the deformation parameter β with respect to the rotational states with the same angular momentum belonging to a given irreducible representation of SU(3). This work generalises to three dimensions the corresponding analysis carried out in two dimensions by Chacón, Moshinsky, and Vanagas. We use the canonical chain for U(3), i.e., the chain U(6) ? U(3) ? U(2) ? U(1), to obtain an analytical formula for the quantity studied. We bring out the overall stretching effect of the angular momentum on the shape of nuclei. The influence of other parameters, such as the boson number and the irreducible representation of SU(3), is also studied.