Stability of Matter with RealQM 2

A basic task of theoretical physics is to prove stability of matter in the sense that the total energy $E$ of the ground state of an atom is bounded below, which signifies that the electrons surrounding the atomic kernel do not collapse into the kernel with energy going to minus infinity. 

In Standard Quantum Mechanics StdQM this is viewed to be difficult to prove with a first 100-page proof by Dyson and Lenard in 1967 followed by a somewhat shorter proof by Lieb and Thirring in 1975 showing a lower bound scaling with $-Z^{\frac{7}{3}}$ for an atom with kernel charge $Z>1$. 

For $Z=1$ the proof is straight-forward as recalled in the previous post.  

In RealQM the proof for $Z>1$ is essentially the same as for $Z=1$ and so gives a lower bound scaling with $-Z^2$, which is to be expected by a simple dimensional analysis, and also is observed. 

In RealQM an atom has a shell structure with stability established successively from innermost shell with the kernel to the next shell with reduced kernel charge and so on. Further, the stability of molecules in the sense of non-collapse naturally follows from stability of atoms.    

The fact that stability of matter is so far-fetched in StdQM ($-Z^{\frac{7}{3}}$) and so direct in RealQM ($-Z^2$) gives evidence that RealQM may be closer to real physics than StdQM. 

The Lieb-Thirring proof extends to many kernels with total charge Z, while we here think of just one atom or molecule. 

Stability of large collections of atoms or molecules ($Z=10^{23}$) is studied in thermodynamics, then without quantum mechanics because it does not make sense,