[en] In earlier work, representations of r nucleons were constructed by taking the rth Kronecker product of self-representations of the complete homogeneous Lorentz group L₀, where these were in the form of a four-component Dirac spinor with components corresponding to the internal symmetries of spin, parity, and charge. When permutations that include every possible exchange of spin, charge, and coordinate, are factored out, the 4/sup r/ coordinates of flat Minskowski space are contracted by an isometry v such that energy levels correspond to troughs or saddle points in the new nuclear manifold M. This is a symmetric space, and using the critical point theory of Morse for the neighborhood of an energy level, it is found that the symmetry s associated with v separates M into just the sets of rotational and vibrational levels. Furthermore, by employing only one parameter, corresponding to the range of energies encounterd, good agreement is found with the experimental levels and state labels of ¹⁰B, ¹⁰Be, ¹⁰C, ¹²C, and ¹⁶O. The supermultiplet theory of Wigner is a necessary condition for the existence of the states