Approches algébriques sdg-IBM et sdg-IBFM et applications en spectroscopie nucléaire

Abstract

This thesis concerns the study of hexadecapole properties in the atomic nuclei in the framework of the sdg-interacting boson model (sdg-IBM). We first study the configuration mixing in the sdg-IBM. Our aim was to determine the contribution of each type of the three bosons to the nuclear states. Particular emphasis was then given to electric monopole transitions. A consistent and general correlation between E0 transitions and nuclear radii was established. To test its robustness, this relation was applied systematically to even-even isotopes in the rare earth region from Ce to W at first in the context of the sdg-IBM then by introducing the g boson. This study has shown that the effect of the hexadecapole deformation, although small on nuclear radii, is important on E0 transitions. Moreover, the study of the geometric shapes associated with each of the dynamical symmetries of the sdg-IBM model has shown that they correspond two by two to the three limits of the sd-IBM. The development of the classical limit of the most general sdg-IBM hamiltonian is a good prospect for establishing the phase diagram of the model. Finally, an extension of the sdg-IBM model to the odd mass nuclei was also developed. The UB(15) ⊗ UF(n) algebra was constructed. This algebra exhibits a very rich sub-structure given rise to a considerable amount of dynamical symmetries to the sdg-IBFM model.