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 half-angles in accord with the neutron-rotation experiment. It is possible to construct a Clebsch-Gordan 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, ground-state energy levels are calculated for all the even-even nuclei by using a differentiable manifold that is spin-graded and gauge-invariant by construction. It is shown that this manifold is Grassmann.
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de Wet, J.A. Nuclear structure on a Grassmann manifold. Found Phys 17, 993–1018 (1987). https://doi.org/10.1007/BF00938009
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DOI: https://doi.org/10.1007/BF00938009