# Is the effective nuclear charge only defined for valence electrons?

I've just been taught about the effective nuclear charge and screening effect in school. I'd like to ask and confirm if the effective nuclear charge is only defined for valence electrons. If not then why don't we consider the repulsion from the electrons further away from the nucleus than the test electron, which by common sense should add to the attractive force by nucleus?

• In chemistry you often worry only about the outermost electrons. In atomic physics they worry about more of them (e.g. levels leading to x-ray generation). As you have noticed, trying to pack all the effects into one parameter (effective nuclear charge) doesn't work so well for all of the electrons. May 12 at 12:41

$$Z=Z_{eff}+\sigma$$, where $$\sigma$$ is shielding constant calculated according to Slater's rule. Since Slater's rule can be applied to any electron regardless of whether or not it's a valence electron, $$Z_{eff}$$ and $$Z$$ can be defined for any electron too, $$Z$$ in particular remaining constant. In his paper, which I have attached below, Slater states that the approximations to the wave functions that he gives have been obtained empirically, and do not involve any of the outer electrons.
Original paper by JC Slater ($$1930$$): https://web.archive.org/web/20120323031605/http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/04/008.pdf