Abstract
Cartan's geometric theory of partial differential equations is applied to a system of Schrödinger equations. It is shown that the choice of a Riemann manifold which is a torus is equivalent to using a many-body neutron and proton potential commonly used in nuclear theory. The theory is applied to spinless, ground-state systems using the Dirichlet principle to minimise the energy, to obtain the neutron-proton ratios, Coulomb and binding energies of nuclei. A shell structure naturally manifests itself from the choice of the manifold.
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Ramanna, R., Jyothi, S. On the geometric foundations of nuclear shell structure. Int J Theor Phys 2, 381–403 (1969). https://doi.org/10.1007/BF00670704
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DOI: https://doi.org/10.1007/BF00670704