Single-particle levels in cluster potentials

We calculate single-particle levels in potentials with Z2 (dumbbell), D3h (triangle) and Td (tetrahedral) symmetry, appropriate to the α-cluster structure of 8Be, 12C and 16O respectively. We suggest that these can be used to study, within the framework of a cluster shell model (CSM), kα+x nucleon structures, with k=2,3,4 and x=1,2,…, in particular the single particle (x=1) structures 9Be, 9B; 13C, 13N; 17O, 17F.