Do external electronic shells influence internal ones?

Question

There is a well-known electron shielding effect: negatively-charged internal electronic shell screens external shells from positive nuclei, thus increasing their radii.

Thus, 2S orbital radius of Li atom (ground state) should be greater than radius of excited Li2+ cation with single 2S electron.

But is there a reverse influence: from external electronic shells to internal ones? For example, are radii of 1S orbital in Li and Li+ equal, or not?

I am sure there is not a big difference anyway, but this is theoretically interesting. Probably it can be proved by comparision of internal shell ionisation energies of Li and Li+ but I am not sure where to look for appropriate experimental data.

I have some intuitive considerations, while they did not lead me to certain answer:

• Concept of Faraday cage looks to be irrelevant, because electron shells are not literally material conductive shells, but they are filled space regions.
• Shells interpenetrate, thus external shell can a bit force out internal shell from nucleus by increasing electron density in space adjacent to nucleus.
• Classically, internal one of two concentric elastic charged spheres should shrink. If we imagine big spheres, their small areas should interact repulsively as parallel plates. But considered spheres are actually not "big".

Answer 1

Not only do "outer" electrons impart some shielding to "inner" ones, but an analytical technique is based on that fact.

In X-ray photoelectron spectroscopy, binding energies of electrons just below the outer shell are measured. These binding energies are typically hundreds of electron volts, roughly 280-300 eV for carbon as a typical example. An important feature is that this binding energy is measurably not fixed for a given element, rather it varies according to how the atom is chemically bound. As an example, the 1s electrons in carbon lie at about 285 eV binding energy in hydrocarbons, but shifted by as much as 8 eV by bonding to fluorine (see here), which is more electronegative and draws electrons away from the carbon 2s and 2p shells. Similarly, the 1s electrons in oxygen range from about 529 to 534 eV in various oxides, with the higher values tending to occur in nonmetal oxides (see here).