Eur. Phys. J. A (2018) 54: 232
https://doi.org/10.1140/epja/i2018-12671-6

Regular Article - Theoretical Physics

Breaking and restoration of rotational symmetry in the low energy spectrum of light -conjugate nuclei on the lattice I: ⁸Be and ¹²C

¹ Helmholtz Institut für Strahlen- und Kernphysik, Universität Bonn, Nußallee 14-16, 53115, Bonn, Germany
² Bethe Center for Theoretical Physics, Universität Bonn, Nußallee 12, 53115, Bonn, Germany
³ Department of Engineering, Karamanoğlu Mehmetbey University, 70200, Karaman, Turkey
⁴ Insitute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425, Jülich, Germany
⁵ Ivane Javakhishvili Tbilisi State University, 0186, Tbilisi, Georgia

^* e-mail: stellin@hiskp.uni-bonn.de

Received: 13 September 2018
Accepted: 3 December 2018
Published online: 24 December 2018

Abstract

The breaking of rotational symmetry on the lattice for bound eigenstates of the two lightest alpha conjugate nuclei is explored. Moreover, a macroscopic alpha-cluster model is used for investigating the general problems associated with the representation of a physical many-body problem on a cubic lattice. In view of the descent from the 3D rotation group to the cubic group symmetry, the role of the squared total angular momentum operator in the classification of the lattice eigenstates in terms of SO(3) irreps is discussed. In particular, the behaviour of the average values of the latter operator, the Hamiltonian and the inter-particle distance as a function of lattice spacing and size is studied by considering the , , and (artificial) bound states of ⁸Be and the lowest , and multiplets of ¹²C.