An Electromagnetic Model for Proton-Neutron Binding in Deuterium Based on a Modified Lockyer Framework

This study investigates a modified version of Thomas Lockyer’s model, which calculates the proton-to-electron and neutron-to-electron mass ratios with high precision (relative errors of −0.00000026 for the proton and +0.00000335 for the neutron). In Lockyer’s framework, the proton is conceptualized as a positron with increasing energy layers nested inside it like Russian dolls, and the neutron as a proton with an additional electron and a doubled first energy layer. We modify this by modeling the neutron as a proton with an electron orbiting at a radius of approximately 0.935 fm, calculated to reproduce the neutron’s mass. The proton- neutron binding in the deuterium nucleus is hypothesized to result from the sharing of this electron between the proton and the neutron’s internal proton, mimicking a covalent-like electromagnetic interaction. This hypothesis tests Lockyer’s model, which excludes quarks and gluons central to quantum chromodynamics (QCD), proposing instead that the strong force could arise from electron sharing, analogous to molecular bonding. Using CODATA 2022 values, we calculate a binding energy of 2.097461571 MeV, remarkably close to the experimental deuterium binding energy of 2.224589 MeV (94.29% of the true value). This suggests that Lockyer’s framework, despite its departure from QCD, captures significant aspects of nuclear binding.