Nuclear structure on a Grassmann manifold
Abstract
Products of particlelike representations of the homogeneous Lorentz group are used to construct the degrees of spin angular momentum of a composite system of protons and neutrons. If a canonical labeling system is adopted for each state, a shell structure emerges. Furthermore the use of the Dirac ring ensures that the spin is characterized by halfangles in accord with the neutronrotation experiment. It is possible to construct a ClebschGordan decomposition to reduce a state of complex angular momentum into simpler states which can be identified with α and β particles, multipole operators, etc. Finally, groundstate energy levels are calculated for all the eveneven nuclei by using a differentiable manifold that is spingraded and gaugeinvariant by construction. It is shown that this manifold is Grassmann.
 Publication:

Foundations of Physics
 Pub Date:
 October 1987
 DOI:
 10.1007/BF00938009
 Bibcode:
 1987FoPh...17..993D