Wormhole Model for Neon-20

Abstract

A quantum mechanical model for the Neon-20 nucleus is developed that allows for the splitting of a bipyramidal structure of five alpha-partices into an alpha-particle and an Oxygen-16 nucleus. The geometry of the configuration space is assumed to be a 3-dimensional spatial wormhole, and on the wormhole background there is an attractive short-range potential. This leads to a radial Schr\"odinger equation of the Heun form, which simplifies for threshold bound states to an associated Legendre equation that has explicit solutions. The energies of the true bound states for all spin/parities are numerically calculated, and match those of the well-established $K^\pi=0^+$, $K^\pi=0^-$, and certain higher rotational bands of Neon-20.