On the geometric foundations of nuclear shell structure

Ramanna, R. ; Jyothi, S. (1969) On the geometric foundations of nuclear shell structure International Journal of Theoretical Physics, 2 (4). pp. 381-403. ISSN 0020-7748

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Official URL: http://www.springerlink.com/content/g7644863461462...

Related URL: http://dx.doi.org/10.1007/BF00670704


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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