The Algebraic Cluster Model (⁸Be, ¹²C) and the Cluster Shell Model (¹³C, ⁷Be, ¹⁹F, ⁸Be)

LNS at Avery Point, Univ. of Connecticut, Dept. of Physics, 1084 Shennecossett Rd, Groton, CT 06340, USA

^* email: moshe.gai@uconn.edu, web: https://astro.uconn.edu

Published online: 28 October 2024

Abstract

Bijker and Iachello’s algebraic cluster model (ACM) and its extension to the cluster shell model (CSM), provides a new theoretical platform for the study of alpha-clustering in light nuclei. It led to the discovery of the D_3h symmetry in ¹²C and ²⁰Ne, with the discovery in ¹²C of a new g.s. rotational band with the spin sequence of, 0⁺, 2⁺, 3^-, 4⁺/4^- and 5^-, including the predicted 4⁺ and 4^- parity doublet. Applications of the CSM shell model to particle molecular orbits in ⁹Be and ¹³C (C₂’ and D_3h’ particle symmetries, respectively), lead us to conjecture molecular hole states in ⁷Be and ¹⁹F. We observe in these nuclei the predicted phenomenological structure. And we further consider conjectured p-h states in ⁸Be with the predicted phenomenological p-h structure of rotational band at high excitations of approximately 20 MeV. A search for these rotational band in ⁸Be was performed at ISOLDE.