Real Quantum Mechanics for Atomic Kernels

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 consider here a single neutron and $N=Z=1$ with one electron, $N=Z=2$ with a negative charge of two as well as a dineutron. 

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 100.000 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 13.6 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 binding energy by the same factor. The observed energy scale factor from 0.78 MeV to 13.6 eV is about $10^5$, while the spatial scale factor is believed to also be about $0.5\times 10^5$. Bingo?

The binding energy of a deuterium kernel consisting of one proton and one neutron is 2.23 MeV plus 0.78 MeV for decay of a neutron altogether about 3 MeV, which we similarly compare with the binding energy 14.5 eV of a H- ion consisting of one proton surrounded by two electrons, with a factor of about $2\times 10^5$.

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), which gives a binding energy of 115 eV. 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 binding energy of a 4Helium kernel is about 28 MeV, thus with an energy scale factor of about $2.5\times 10^5$.  Note that here that the two electrons  are assumed to be compressed to a -2 point charge without self-repulsion like a +2 proton point charge. 

We view a dineutron with estimated binding energy of 3 MeV, as a 2-electron kernel surrounded by 2-proton shell, which we compare with 2Helium atom with binding energy of about 78 eV, thus with a scale factor of about $0.4\times 10^5$. 

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 a Helium ion is held together by Coulomb attraction between a positive point charge and surrounding electron densities. 

Here is the man idea again with a Hydrogen atom switched to a neutron kernel: 

What then about a nucleon with $N=Z>2$ with $N$ electrons surrounded by $2N$ protons? Will Coulomb attraction be sufficient to keep such a nucleon together?  Is it necessary to include some form of strong force?