  Based on a theory of extra dimensional confinement of quantum particles [E.
R. Hedin, Physics Essays 25, 2 (2012)], a simple model of a nucleon-nucleon
(NN) central potential is derived which quantitatively reproduces the radial
profile of other models, without adjusting any free parameters. It is
postulated that a higher-dimensional simple harmonic oscillator confining
potential localizes particles into 3d space, but allows for an evanescent
penetration of the particles into two higher spatial dimensions. Producing an
effect identical with the relativistic quantum phenomenon of zitterbewegung,
the higher-dimensional oscillations of amplitude h/(2{\pi}mc) can be
alternatively viewed as a localized curvature of 3d space back and forth into
the higher dimensions. The overall spatial curvature is proportional to the
particle`s extra dimensional ground state wave function in the higher
dimensional harmonic confining potential well. Minimizing the overlapping
curvature (proportional to the energy) of two particles in proximity to each
other, subject to the constraint that for the two particles to occupy the same
spatial location one of them must be excited into the first excited state of
the harmonic potential well, gives the desired NN potential. Specifying only
the nucleon masses, the resulting potential well and repulsive core reproduces
the radial profile of several published NN central potential models. In
addition, the predicted height of the repulsive core, when used to estimate the
maximum neutron star mass, matches well with the best estimates from
relativistic theory incorporating standard nuclear matter equations of state.
Nucleon spin, Coulomb interactions, and internal nucleon structure are not
considered in the theory as presented in this article.
