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The breaking of rotational symmetry on the lattice for bound eigenstates ofthe two lightest alpha conjugate nuclei is explored. Moreover, a macroscopicalpha-cluster model is used for investigating the general problems associatedwith the representation of a physical many-body problem on a cubic lattice. Inview of the descent from the 3D rotation group to the cubic group symmetry, therole of the squared total angular momentum operator in the classification ofthe lattice eigenstates in terms of SO(3) irreps is discussed. In particular,the behaviour of the average values of the latter operator, the Hamiltonian andthe inter-particle distance as a function of lattice spacing and size isstudied by considering the $0^+$, $2^+$, $4^+$ and $6^+$ (artificial) boundstates of $^{8}\mathrm{Be}$ and the lowest $0^+$, $2^+$ and $3^-$ multiplets of$^{12}\mathrm{C}$.

european physical journal. a, hadrons and nuclei

Breaking and restoration of rotational symmetry in the low-energy  spectrum of light alpha-conjugate nuclei on the lattice I: $^{8}\mathrm{Be}$  and $^{12}\mathrm{C}$