Why is the quantum defect less dependent on n than l in alkali atoms?

[kuecken]

Why does the quantum defect depend only weakly on the principal quantum number n?

The dependence on l is strong. Because this will change the probability distribution of the electron to be closer to the nucleus and thus the shielding of the other electrons a lot.

A change in n, however, will not change the angular wavefunction, it will only change the radial one. Is it because the change in radial wavefunction is not very big between different n? If we change from an s orbital of n=4 to one of n=3, the probability density to be at the nucleus is nonzero in both cases.

Any better ideas would be great.
Thank you

 

[DrClaude]

Penetration is the principal effect responsible for the quantum defect, as this is what results in an electron experiencing somthing else than a Coulomb-like central potential. The conclusion would then be that penetration is much less dependent on $n$ then on $l$. This makes sense since $l > 0$ results in an effecitve centrifugal barrier and the electron is kept away from the nucleaus and core electrons.