A higher-dimensional model of the nucleon-nucleon central potential

Abstract

Based on a theory of extra dimensional confinement of quantum particles [E. R. Hedin, Physics Essays, 2012, 25(2): 177], 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 three-dimensional (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 ħ/(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 1st 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.