New Model of Atomic Nucleus

Modern physics involves four fundamental forces: 

1. Electromagnetic force described by Coulomb Law.
2. Weak nuclear force involved in radioactive decay. 
3. Strong nuclear force describing the force keeping an atomic nucleus together.
4. Gravitational force described by Newton's Law of Gravitation (or Einstein's general relativity).   

The Standard Model of atomic physics formed in the 1960s includes 1-3 but leaves out 4. The dream of a modern physicist is to unite at least 1-3 into one unified electromagnetic-nuclear force with the ultimate goal of including also 4. Little progress towards this goal has been made. 

In recent posts I have tested an idea to unify 1-3 into a single electromagnetic force captured by Coulombs Law. In this model we start with a Universe of high temperature consisting of free protons of charge +1 and equally many free electrons of charge -1. We assume that about half of the protons and electrons fuse to form neutrons and that as temperature drops the rest combine to Hydrogen atoms. Both neutron and H-atom then consists of a proton-electron pair, but the physics is vastly different. A seemingly natural way to understand the difference is to switch roles: 

• H-atom = proton kernel surrounded by electron cloud.
• Neutron = electron kernel surrounded by proton cloud.    

In both cases we have a particle-like kernel surrounded by a cloud of opposite charge, which can be described by the same Schrödinger's equation with only a change of scale, showing to be about $10^5$ according to observation: The size of a Hydrogen atom is a about $10^5$ times that of a neutron, with a corresponding scaling of binding energy: The observed binding energy of a neutron is a bout 1 MeV and that of an H-atom about 10 eV with again a factor of roughly $10^5$.  

The non-standard element here is that a neutron consists of a kernel as a very compressed electron surrounded by a proton cloud. In the Standard model a neutron is composed of three quarks as a more complicated model. 

We now have a Universe consisting of an equal number of neutrons and H-atoms and it is possible to envision a next step where an H-atom combines with a neutron to form a deuterium atom with a nucleus composed of a proton and a neutron, and in a next step we could expect two deuterium nuclei to fuse into a 4Helium nucleus consisting of 2 protons and 2 neutrons. The binding energy per nucleon is 1.1 MeV for deuterium and 7 MeV for 4Helium and so the fusion delivers massive energy. 

Inspired by the idea of a neutron as an electron kernel surrounded by a proton cloud, we can think of the 4Helium nucleus to consist of 4 protons altogether of charge +4 surrounding an electron kernel of charge -2, with a net charge of +2. 

Switching roles we then compare with an atom with a +2 proton nucleus surrounded by 4 electrons thus a Helium atom with 2 extra electrons forming He2-. This is a stable atom with an observed binding energy of about 80 eV, which with a change of scale/role forms a 4Helium nucleus with binding energy in the range of 27 MeV with here a factor of about $3\times 10^5$. 

To obtain a large binding energy of a 4Helium nucleus as 2 compressed electrons surrounded by a 4-proton cloud, it is necessary to discard the repulsion energy between the electrons, which would appear as the energy released in the fusion of deuterium. We then have the same situation for a nucleus as for an atom with in both cases no repulsion between same charges in the kernel.

It is thus possible to explain how that not only an atom is held together by attractive Coulomb forces between charges of different sign, but in an analogous way also an atomic nucleus by switching the roles of proton and electron. 

What remains to explain is how electron-electron repulsion can be cancelled in a nucleus with electron kernel. If that can be achieved we would have a unified model built on electromagnetic Coulomb forces without need of inventing weak and strong nuclear forces as in the Standard Model asking for quarks.

Further fusion into nuclei with the same number of protons and neutrons can be similarly envisioned in agreement with observations.

The key role of the strong force is to overcome the repulsion between protons in a nucleus. In the above model this is achieved by Coulomb force through the presence of neutrons and electron kernels.  

It is possible to envision a model based on protons and electrons interacting by electromagnetic Coulomb forces which describes both atoms and atomic nuclei. A key element is a kernel of a nucleus consisting of compressed electrons without repulsion, like a negative point charge bigger than one. 

You are now invited to choose one of the following models of a neutron:

• A proton cloud surrounding an electron kernel.
• Two down quarks of charge -1/3 combined with an up quark of charge +2/3, all of different colors.  

In any case, the formation of neutrons is essential, assuming we start from protons and electrons. 

Recall that electric charge density $\rho$ is connected to electric field $E$ by Poisson's equation $\Delta E=\rho$ opening the possibility of creation of equal amount of positive (protons) and negative charge density (electrons) from a fluctuation around zero of $E$, as out of nothing.  

If nuclear physics can be understood as geared by Coulomb force, then a unification with gravitational physics geared by Newton's Law is natural.  

The binding energy of a nucleus with $Z$ protons and $Z$ neutrons scales with $Z^2$ and so with $Z$ per nucleon, which is roughly what is observed for $2\le Z\le 56$.