How do the orbitals distort when adding more protons?

How do the orbitals distort as you move along the series of chemical elements with greater protons. I cant imagine, the first 1s orbital remains a similar shape at Kr 36 protons as compared to He 2. And is the addition of protons responsible for the orbital energy imbalance occurring at the transition metals at Sc>


[![enter image description here](https://i.stack.imgur.com/TtDdd.png)](https://i.stack.imgur.com/TtDdd.png)




The simplest approximation you can make is to describe each orbital by a one-electron wavefunction [like the ones we find in the hydrogen atom](https://en.wikipedia.org/wiki/Hydrogen-like_atom). For those wavefunctions, the radial distribution is described by an exponential factor of $exp(-Zr/n)$ (with $n$ the principal quantum number) and a polynomial with mixed powers of $Z$ and $r$. If you increase $Z$, this function becomes "narrower" along the $r$ axis. Thus, increasing the number of protons in the nucleus contracts the orbitals. We can intuitively explain this due to the increased electrostatic attraction between the nucleus and the electrons.


This is ignoring all effects from actually having multiple electrons in your atom, where inner electrons can "shield" outer ones from feeling the full nuclear charge. In those cases, the outer electron shells are affected less by that contraction. In general however, it's difficult to say exactly what a multi-electron wavefunction will do because we don't have a closed analytical expression for them like we do for the one-electron case.


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