A Semimicroscopic Algebraic Cluster Model for Heavy Nuclei

TL;DR

This paper extends the Semimicroscopic Algebraic Cluster Model using pseudo-SU(3) to better describe heavy nuclei, incorporating forbiddenness and applying it to specific nuclear fission systems to calculate energies and transition properties.

Contribution

It introduces a new extension of the SACM based on pseudo-SU(3), including a method to handle large Hilbert spaces and forbiddenness in heavy nuclei modeling.

Findings

Accurately calculated energies and electromagnetic transitions for selected heavy nuclei.

Demonstrated the model's effectiveness in systems with low and high forbiddenness.

Provided a practical approach to reduce the Hilbert space in complex nuclear models.

Abstract

An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is proposed, based on the pseudo-SU(3) model. 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 236U -> 210Pb + 26Ne and 224Ra -> 210Pb + 14C, and to 236U -> 146Xe + 90Sr, which appears in the fission of 236U, which requires a large forbiddenness. Energies, electromagnetic transitions and spectroscopic factors are calculated.