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

TL;DR

This paper introduces a higher-dimensional harmonic oscillator model to derive a nucleon-nucleon central potential, successfully reproducing empirical profiles and providing insights into nuclear interactions and neutron star mass limits.

Contribution

It presents a novel higher-dimensional confinement model that quantitatively reproduces NN potentials without free parameters, linking extra dimensions to nuclear force characteristics.

Findings

Reproduces radial profiles of established NN potentials

Predicts the height of the repulsive core accurately

Estimates maximum neutron star mass consistent with relativistic theories

Abstract

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.