# Why is Mosely screening in heavy atom K-shell 1 unit?

The Wikipedia article on Moseley's law seems to show that the screening of heavy atoms is by 1 electron charge exactly (in the limit of large Z, experimental precision, within nonrelativistic limits, and).

But why is this exactly one unit? The other K-shell electron is not screening exactly one unit, and this seems to be a conspiracy of other electrons. I suspect it is because of an unappreciated hole-picture of deep holes in heavy atoms (electrons missing in deep shells), and I will describe this theory briefly.

If you remove an electron from close to the nucleus, the electron-hole behaves as an object with positive charge and negative mass (this is why it orbits the nucleus that it is repelled by). The state is not a vacuum quite, because of the presence of other electrons, but the rigidity of the Fermi liquid near the nucleus of a heavy atom means that the hole behaves as a single particle. This single-particle behavior is in the potential background of the nucleus and the other electrons, and it is possible that the result can give an exact 1 unit screening. I developed the formalism a little bit to see what the form should be, but I did not see any reason for 1 unit screening. Perhaps there is none, but it looks to be more than a coincidence.

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I am confident that your explanation is at least on the right track. At any rate, even the Wikipedia article does say that $(Z-1)$ arises because of differences in the electron-electron interactions between the initial and final states and holes could be very useful to quantify this difference. It must be possible to justify the number 1 in some way. –  Luboš Motl Apr 13 '12 at 10:06
Ron, what about charge conservation? In truth there are Z-1 electrons going around and the hole must take its apparent charge from the Z of the nucleus to have charge conservation of the system from afar. Charge number is quantized after all in units of e.This might leave the nucleus at Z-1. –  anna v Apr 13 '12 at 10:38
@annav: This doesn't work--- the Z-1 is only for K-shell, and I don't see a reason this is linked to the number of electrons. I also am not sure this is nonrelativistically exact--- I just saw a convergence in the values at large Z by eye. –  Ron Maimon Apr 13 '12 at 19:32
Are you saying that by "remove" you mean the electron is on a higher energy shell but still attached to the atom? If it is off the atom then the atom is ionized and will have a charge +1 . –  anna v Apr 14 '12 at 3:10
look at "binding energy" here : en.wikipedia.org/wiki/Ionization_energy . –  anna v Apr 14 '12 at 3:14