RealQM Shell Structure Design Principle

The atomic shell structure of RealQM comes out from optimal electron packing where electrons with non-overlapping supports filling a shell, have a certain size determined by the effective kernel potential reduced by the total charge in shells closer to the kernel. 

RealQM thus shows an approximate electronic shell structure for an atom with kernel charge $Z$ the have shell radius $r_m\sim m^3/Z$ and shell thickness $d_m\sim m^2/Z$, where $m$ is shell number with $2m^2$ electrons in a filled shell.

This conforms with charge density $\rho_m(r)\sim\frac{Z}{r^2}$, thus with a constant shell charge per unit of distance $r$ to the kernel in spherical symmetry, which gives a total energy $E\sim log(Z)Z^2$ in accordance with observations for $Z<30$ outside first shell, and also for larger $Z$ outside second shell. This also conforms to $d_m\sim \frac{1}{Z_{eff}}$ as the effective potential for $r>r_m$.

The shell structure is determined from optimal electron packing under consecutive filling of shells, as a possible physical design principle.