New Quantum Mechanics 7: Atoms 1-10

This post presents computations with the model of New Quantum Mechanics 5 for ground states of atoms with N= 2 - 10 electrons in spherical symmetry with 2 electrons in an inner spherical shell and N-2 electrons in an outer shell with the radius of the free boundary as the interface of the shells adjusted to maintain continuity of charge density. The electrons in each shell are smeared to spherical symmetry and the repulsive electron potential is reduced by the factor n-1/n with n the number of electrons in a shell to account for lack of self repulsion.

The ground state is computed by parabolic relaxation in the charge density formulation of New Quantum Mechanics 1 with restoration of total charge after each relaxation and shows good agreement with table data as shown in the figures below.

The graphs show as functions of radius, charge density per unit volume in color, charge density per unit radius in black, kernel potential in green and total electron potential in cadmium red. The homogeneous Neumann condition at the interface of charge density per unit volume is clearly visible.

The shell structure with 2 electrons in the inner shell and N-2 in the outer shell is imposed based on a principle of "electron size" depending on the strength of effective kernel potential, which gives the familiar pattern of  2-8-18-32 of electrons in successively filled shells as a consequence of shell volume of nearly constant thickness scaling quadratically with shell number. This replaces the ad hoc unphysical Pauli exclusion principle with a simple physical principle of size and no overlap.

The electron size principle allows the first shell to house at most 2 electrons, the second shell 8 electrons, the third 18 electrons,  et cet.

In the next post similar results for Atoms 11-86 will be presented and it will be noted that a characteristic of a filled shell structure 2-8-18-32- is comparable total energy in each shell, as can be seen for Neon below.

The numbers below show table data of total energy in the first line and computed in second line, while the groups show total energy, kinetic energy, kernel potential energy and electron potential energy in each shell.