The theory and experimental validation of nuclear electrons’ Heisenberg uncertainty

Abstract The nuclear electron concept does not violate Noether’s theorem, does not require the emission of heavy particles that were never observed in any β -decay, and does not require fractional elementary charges. Each of these advantages is a major argument in favor of the nuclear electron concept. However, it remained unclear up to now how to reconcile the Heisenberg uncertainty principle with an fm-scale nuclear radius in the context of the experimentally indicated 1.5 MeV nuclear electron. The main objective of this study is therefore to examine the Heisenberg uncertainty of a proton-bound nuclear electron. The secondary objective is to calculate the nuclear photo-electric effect, as it was historically postulated that this effect would photo-dissociate nuclear electrons, but without any proper calculation being actually carried out. After understanding how Heisenberg uncertainty applies to the nuclear electron, we use it to predict the most probable kinetic energy of a β -decaying nuclear electron. Our calculations are validated by experiments. Lastly, we predict and validate the existence of a giant nuclear halo in certain β -decaying heavy isotopes.