Symplectic symmetry and clustering in atomic nuclei

Abstract

A new symplectic-based shell-model approach to clustering in atomic nuclei is proposed by considering the simple system ${}^{20}$Ne. Its relation to the collective excitations of this system is mentioned as well. The construction of the Pauli allowed Hilbert space of the cluster states with maximal permutational symmetry is given for the ${}^{16}$O+${}^4$He $\to$ ${}^{20}$Ne channel in the case of one-component many-particle nuclear system. The equivalence of the obtained cluster model space to that of the semi-microscopic algebraic cluster model is demonstrated.

Comments: 5 pages; This is a slightly modified version of the published paper [Int. J. At. Nucl. Phys. 6(1), 027 (2021)], which also concerns shortly the mutual interrelations between the shell model, $Sp(6,R)$ symplectic model and cluster model states, and ,in addition, suggests how to account properly the point group symmetries in the present symplecic-based shell-model approach to clustering