The sign change in the expression for force density implies that the force between \(\psi\) at a distance \(a_\psi\), and the center is attractive. Beyond \(a_\psi\) the force is repulsive but very small. (cf the post "Flux It,")
It does not matter where the mass of the electron is, at the center or at \(a_\psi\).
There is no need for a nucleus!
A number of electrons can be in parallel orbits and they are mutually attracted to each other by magnetic forces.
Electronic atoms have no nucleus! Mass/anti-mass atoms may have a nucleus. (cf. post "Anti-Mass, Don't Gather Here Please")