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

  • Gianluca StellinEmail author
  • Serdar Elhatisari
  • Ulf-G. Meißner
Regular Article - Theoretical Physics

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 8Be and the lowest \( 0^+\), \( 2^+\) and \( 3^-\) multiplets of 12C.

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Copyright information

© SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Gianluca Stellin
    • 1
    • 2
    Email author
  • Serdar Elhatisari
    • 1
    • 2
    • 3
  • Ulf-G. Meißner
    • 1
    • 2
    • 4
    • 5
  1. 1.Helmholtz Institut für Strahlen- und KernphysikUniversität BonnBonnGermany
  2. 2.Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  3. 3.Department of EngineeringKaramanoğlu Mehmetbey UniversityKaramanTurkey
  4. 4.Insitute for Advanced SimulationInstitut für Kernphysik and Jülich Center for Hadron PhysicsJülichGermany
  5. 5.Ivane Javakhishvili Tbilisi State UniversityTbilisiGeorgia

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