If something becomes an ion, is its zeff changed?

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Bipolarity
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If some atom loses or gains an electron, is its effective nuclear charge changed? I would think that it would change, considering that having lost an electron the shielding effect weakens, making the zeff larger, but people are saying there is no effect? Is there some explanation?

THanks!

BiP
 
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A simple counter example may also help. Consider He. In neutral He, the effective charge is somewhere between 1 and 2, while in He^+ it is exactly 2.