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

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 $0^{+}$, $2^{+}$, $4^{+}$ and $6^{+}$ (artificial) bound states of ${}^8\mathrm{Be}$ and the lowest $0^{+}$, $2^{+}$ and $3^{-}$ multiplets of ${}^{12}\mathrm{C}$.

arXiv commentSubmitted to the European Physical Journal A, ID: EPJA-104750

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Cited by in corpus (6)

• Transition densities and form factors in the triangular $\alpha$-cluster model of ${}^{12}$C with application to ${}^{12}$C+$\alpha$ scattering
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• The triton lifetime from nuclear lattice effective field theory
• Adiabatic projection method with Euclidean time subspace projection
• Magnetic dipole moments as a strong signature for $\alpha$-clustering in even-even self-conjugate nuclei
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations