Real Quantum Mechanics for Atomic Nuclei

The Nobel Prize in Physics 1963 was awarded to  Maria Goeppert Mayer (1/4) and Hans Jensen (1/4) for a shell model of atomic nuclei with the protons and neutrons forming a nucleus arranged in shells in a attractive spherically symmetric potential. 

The model was inspired by the standard quantum mechanics (stdQM) model of an atom as a positive pointlike nucleus/kernel surrounded by electrons arranged in shells with shell $n$ containing $2*n^2$ when full, for $n=1,2,3...$. The shell model for atoms was motivated by the Pauli Exclusion Principle reflecting that electrons can have two forms of spin (up and down) and that two electrons with the same quantum identification including spin cannot occupy the same position. 

Real Quantum Mechanics RealQM offers a model of an atom as a system of non-overlapping electron densities interacting by Coulomb potentials, where an electron is identified by space occupancy only. RealQM gives a new explanation of the sequence $2*n^2$ as a natural solution of a packing problem where the size of an electron scales with the effective attraction from the kernel under shielding from electrons in inner shells. 

RealQM can be extended to a nucleus consisting of $Z$ protons and $N$ neutrons with in the basic case $N=Z$ appearing as a pointlike negative kernel of charge $-Z$ surrounded by $2*Z$ protons of total charge total $+2*Z$ again arranged in shells as a resolution of a packing problem (assuming a neutron contributes one proton and one electron). A nucleus is here held together by Coulomb potentials assuming that the negative kernel is not subject to internal repulsion, then without need of strong/weak nuclear force as a most remarkable feature. 

Deuterium consisting of one proton and one neutron would then switching signs correspond to an  $H^-$ ion consisting of one proton and two electrons. 

$4Helium$ consisting of two protons and two neutrons would then correspond to a $He2-$ ion. 

You are invited to test RealQM Nuclear Simulator to compute the energy of different ways of filling shells. You find some examples below if you hesitate to use the Simulator yourself. 

The shell model of the 1963 Nobel Prize is today complemented by the Standard Model where the protons and neutrons of a nucleus consist of triples of quarks.  Does that mean the shell model is obsolete or even worse incorrect? After all, it was considered to be (more or less) correct in 1963. Is there a shell model in the Standard Model?

Here are nuclear binding energie per nucleon computed by RealQM Nuclear Simulator:

• $Z=N=1$: 1 MeV (Deuterium)
• $Z=N=2$: 4 MeV  ($4Helium$)
• $Z=N=4$: 8 MeV

which roughly fits with observation.