The Neutron as Key to a Periodic Table for Nuclei

In recent posts I have tested an idea to view a system comprised of 1 proton + 1 electron in two different ways held together by Coulomb attraction:

• Hydrogen atom H of size $10^{-10] m with point-like proton kernel surrounded by electron density.   (H)
• Neutron N of size $10^{-15}$ m (inside atomic nucleus) as point-like electron kernel surrounded by proton density with a change of spatial scale of $10^5$. (N) 

The observed spatial scale between H and N is thus $10^5$. A transition from H to N would correspond to "shrinking" by a factor $10^{10}$ of the electron density around a proton into forming a kernel of a proton density, thus a a very strong shrinking. 

The observed binding energy of 13.6 eV for H and 0.8 MeV for N correspond to a spatial scale $D=0.6\times 10^5\approx 10^5$, in accordance with the $\frac{1}{r}$ spatial scaling of a Coulomb potential. 

Both systems can be described by a RealQM Schrödinger equation in non-overlapping wave functions $\psi_e(x)$ and $\psi_p(x)$ for electron and proton densities, as minimisers of total energy $E$ given by: 

• $E(\psi_e,\psi_p, m_e, m_p)=\frac{1}{2m_e}\int\vert\nabla\psi_e(x)\vert^2dx+\frac{1}{2m_p}\int\vert\nabla\psi_p(x)\vert^2dx-\int\int\frac{\psi_e^2(x)\psi_p^2(y)}{\vert x-y\vert} dxdy$   (S)

as the sum of separate kinetic energies for electron and proton and common Coulomb potential energy, where $\frac{1}{m_e}$ and $\frac{1}{m_p}$ set spatial scales of electron and proton.    

The standard case H is represented by minimisation of E without proton kinetic energy (formally $m_p=\infty$) and central point-like proton into a binding energy of $13.6$ eV.    

The non-standard case N is represented by minimisation of E without electron kinetic energy (formally $m_e=\infty$) and central point-like electron, which agrees with observation with $\frac{m_p}{m_e}=D$. 

We understand that since the above Schrödinger model does not involve gravitation, only Coulomb attraction between charges of different sign, the physical meaning of the factors $m_e$ and $m_p$ in the kinetic energies, do not connect to mass but rather to (inverse) spatial scale. What determines the roles of protons and electrons is their spatial scale. 

The conception that the mass of proton is about 2000 times that of an electron is thus not in conflict with $D\approx 10^5$ in the above Schrödinger model.   

The basic idea is to view the formation of a neutron inside a nucleus as a form of "capturing" by a proton density of an electron into the center of the proton density in a process at high temperature/pressure driven by Coulomb attraction under release of 1 MeV. The idea of electron capturing by a nucleus was an important element of nuclear physics even before the advent of the Standard Model in the 1960s.

Further capturing of electrons can create nuclei as a negative kernel surrounded by non-overlapping positive proton densities organised into shells, as a direct analog to an atom with a positive kernel surrounded by non-overlapping negative electron densities organised into shells. 

Recall that in the Standard Model the strong force appears as an ad hoc invention of remarkable fanciness.  If you ask a professional physicist what keeps a nucleus together thus overpowering Coulombic repulsion between protons, you get the answer that it is a form of "glue" of unknown physical nature named "strong force" transmitted by "gluons" of 8 different "colors" serving as "force carriers" between 6 different "quarks", where a proton is turned into a neutron when one of its two "up-quarks" turns into a "down-quark". If you ask how this can be you get the help that since very much energy is released when H fuses to Helium in the Sun a very strong force must be involved and this is the ”strong force” thus proven to exist. But gravitation is missing in the Standard Model because no “graviton” as force carrier is believed to exist, which is a trauma of modern physics since 50 years without hope.

In RealQM a nucleus has a negative kernel surrounded by positive proton densities held together by Coulomb attraction, as an analog to an atom with a positive kernel surrounded by negative electron densities. The observed "periodic table for nuclei" starting with 2, 8, 20,...appears as an analog to the periodic table for atoms starting 2, 8, 18... 

In the Standard Model a nucleus consists of a collection of protons and neutrons, with each proton and neutron consisting of three quarks held together by gluons, without explanation of the observed periodic table for nuclei.  

The great triumph of modern physics was to model the atom in terms of Coulombic attraction/repulsion between + and - charges using a basic element of classical deterministic physics in a new setting of statistics. RealQM shows that the new setting is not needed. Both atom and atomic nucleus can be modeled within classical deterministic mathematical continuum physics. This should be met with relief by students of physics struggling with weird concepts of modern physics.

The next step is to understand the formation of the nucleus of Deuterium D consisting of 1 proton and 1 neutron, or in RealQM 2 proton densities surrounding 1 electron kernel. In the Standard Model D is held together by a residual strong force as a left-over of the strong force holding proton and neutron together, like a molecule held together by residuals of Coulomb forces holding atoms together.  RealQM makes this analog real for nuclei: Both atoms and nuclei are held together by Coulomb forces.