Atomic Nucleus Secret Revealed?: Revision

We continue the exploration of RealNucleus as a RealQM model of an atomic nucleus consisting of 

• a kernel as an inner shell of non-overlapping $-1$ charge densities of total charge density $-Z$ 
• an outer shell of non-overlapping $+1$ charge densities of total charge $+2Z$
• interacting by Coulomb potentials.  

The key question is:

• Is such nucleus stable in the sense of having a negative total energy as the sum of kinetic and potential energy? 

Let us start with $Z=1$, thus with a -1 kernel surrounded by two +1 charges. The atom analog obtained by switching the sign of the charges is a proton surrounded by two electrons, which is an $H$ atom with an extra electrons.  This is the $H^-$ ion, which is known to be stable. RealNucleus confirms by computing the total energy 

Next, we consider $Z=2$, thus 4He with a kernel inner shell of a -2 charge density surrounded by an outer shell of four +1 charges. We use this code to find an energy from the outer shell of about -6 MeV per nucleon when the radius of the inner shell is small (less than 1 percent) compared to the radius of the outer shell. We thus get a clear signal of stability of the outer shell. 

 

The inner shell charge is subject to a constant potential from the outer shell, which is compatible with a constant charge density without kinetic energy.  What remains is the potential energy from overlap of two constant -1 charge densities. Can the inner shell be stable despite the repulsion present from charge density overlap and so the whole kernel be stable? We shall seek an answer using the spherical symmetry of the overlapping -1 charge densities hoping to find some form of cancellation compatible with stability. 

The bottom line is that the RealNucleus model shows existence of a +Z nucleus formed by 2Z protons surrounding a constant negative kernel charge density -Z, which is not subject to de-stabilising self-repulsion as key open problem. The constant inner charge density will act on the outer shell protons as a -Z central charge with the radius of the inner shell acting as model parameter. Charge densities from inner and outer shells can meet without continuity, in contrast to electron densities in RealQM meeting with continuity.