It has been shown that fine energy levels of an atom can be calculated using this model.
This type of energy corresponds very precisely to the spatial density of the electron.
For example, for p1/2 and p3/2:
For d3/2 and d5/2:
For f5/2 and f7/2:
etc.
And the results are here.
For hydrogen H I - 77 percent of calculations below the level of measurability with today's technology
For helium He II - 55 percent of calculations below the level of measurability with today's technology
For lithium Li III - 45 percent of calculations below the level of measurability with today's technology