Eur. Phys. J. A (2021) 57: 146
https://doi.org/10.1140/epja/s10050-021-00460-5

Regular Article –Theoretical Physics

A semimicroscopic algebraic cluster model for heavy nuclei

I: One heavy and one light cluster

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., A.P. 70-543, 04510, Mexico City, DF, Mexico
² Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe Universität, Ruth-Moufang-Str. 1, 60438, Frankfurt am Main, Germany

^a hess@nucleares.unam.mx

Received: 29 January 2021
Accepted: 7 April 2021
Published online: 24 April 2021

Abstract

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