A Semimicroscopic Algebraic Cluster Model for Heavy Nuclei

Abstract

An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU (3) model ( SU (3)). The Hamiltonian and the spectroscopic factor operator of the model are presented and a procedure of constructing the model space. Because a huge number of SU (3) irreducible representations (irrep) appear, one has to be careful in designing a practical, consistent path to reduce the Hilbert space. The concept of forbiddenness, taking into account excitations of the clusters, is introduced and applied. The applications are to two systems with a low forbiddenness, namely to 236 U → 210 Pb + 26 Ne and 224 Ra → 210 Pb + 14 C, and to 236 U → 146 Xe + 90 Sr, which appears in the fission of 236 U , which requires a large forbiddenness. Energies, electromagnetic transitions and spectroscopic factors are calculated.