We have seen that Real Quantum Mechanics RealQM as new formulation of Schrödinger's equation for a multi-electron system in the form of a classical continuum model in 3 space dimensions, gives results in accordance with observations for atoms and molecules, with more information on this blog with tags RealQM and Real Quantum Chemistry.
Let us now apply RealQM to atomic kernels consisting of a collection of $Z$ positively charged protons and $N$ zero charge neutrons with $N=Z$ in typical most stable configurations. We here start with $N=Z=2$ preceded by a single neutron.
Recall that a neutron is composed of a proton and an electron, with a binding energy of 0.782343 MeV which is released when a neutron decays into a free proton and free electron.
Switch proton and electron and you get a neutron! Same thing, just 1 million times smaller.
Recall next that a Hydrogen atom takes the form of a small positively charged proton surrounded by a large negatively charged electron (cloud) with a binding energy of 0.5 eV.
Let us now view a neutron to take the form of a very small negatively charged electron surrounded by a small proton cloud. In other words, we just switch the roles in a Hydrogen atom into a small neutron as in the above figure. In both cases a small central charge is surrounded by a larger cloud of opposite charge, both described by the same Schrödinger equation the only difference being the spatial scale. The neutron would then be kept together by the same electromagnetic Coulomb force between charges of opposite sign as in the Hydrogen atom!
Does it work? Well, changing the spatial scale in Schrödinger's equation with some factor changes the the binding energy by the same factor. The observed energy scale factor from 0.78 MeV to 0.5 eV is about $10^6$, while the spatial scale factor is believed to be about $10^5$, thus roughly the same range. Does this rule out the idea of a neutron as a small "inverted" Hydrogen atom? Maybe not since the effective quantum mechanical size of a neutron is difficult to measure.
Let us do the same thing starting with a Helium 2- ion (two extra electrons) as a 4Helium atom with a kernel consisting of two protons and two neutrons surrounded by a 1st shell with two electrons and 2nd shell with two extra electrons. You can view RealQM applied to this case running this code describing two protons surrounded by four electrons in two layers (here the two kernel neutrons play no role). Switching roles as above we thus view a Helium kernel of two protons and two neutrons to consist of two very compressed electrons surrounded by a two-shell cloud of four protons.
The observed binding energy of a Helium kernel is about 28 MeV while Real QM with a scale factor of $10^6$ gives about 6 MeV.
We thus pose the question if it is possible to view the force keeping an atomic kernel together as an electromagnetic Coulomb force between compressed electrons surrounded by proton clouds without need to introduce the strong force of the Standard Model. The electrons would then act as a "glue" to bind the protons together by Coulomb force in the same way an Helium ion is held together by Coulomb attraction between protons and electrons.
An important feature of RealQM is that compression of an electron without corresponding increase of kinetic energy is possible since in RealQM electrons and proton charge densities meet with a homogenous Neumann condition (and not a homogeneous Dirichlet condition, which would increase kinetic energy with compression). Similarly, the kinetic energy of the proton is not an element of the Schrödinger equation for Hydrogen.
Here is the idea again: