Graduate Experimental values for screening constants? (Slater rules)

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In multiple-electron atoms, the effective nuclear charge experienced by an electron is reduced due to electron shielding, represented by the equation Z_eff = Z - s, where s is the screening constant. Slater's rules are commonly used to calculate this screening constant, but finding reliable experimental values remains a challenge. A 1936 translation of Arnold Sommerfeld's work suggests experimental values, though they are not explicitly stated. Additionally, a 1967 study provides Hartree-Fock calculations of screening constants without experimental references, highlighting discrepancies in results. The discussion also mentions alternative methods for estimating effective charge, including x-ray spectroscopy, which requires knowledge of binding energies in electron shells.
jarekduda
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In multiple-electron atoms the effective charge of nucleus for a given electron, is reduced by the presence of other electrons (including those from more external shells, against the shell theorem):
Z_eff = Z - s
where the screening constant s depends on Z and the concerning orbital. It is usually calculated by semi-empirical so called Slater's rules: https://en.wikipedia.org/wiki/Slater's_rules

I have tried to find some experimental values.
On page 286 of 1936 English translation of Arnold Sommerfeld's "Atomic structure and spectral lines" there is a clear figure (on the left below) with dots suggesting experimental values (but I couldn't find it being explicitly written).
Wikipedia article cites 1967 "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons" by Clementi, Raimondi, Reinhardt ( http://scitation.aip.org/content/aip/journal/jcp/47/4/10.1063/1.1712084 ) which contains Hartee-Fock calculations of screening constants (figure on the right) - unfortunately it doesn't seem to refer to any experiment (?)

https://dl.dropboxusercontent.com/u/12405967/sceen.jpg

These two figures have some essential differences (including order!) - could anybody refer to some better experimental results?
 
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there is another method for estimating the effective z...see
Screening Constant by Unit Nuclear Charge Calculations of Energies and Fine
Structure Splitting for Li-Like Ions
I. Sakho
Department of Physics, UFR of Sciences and Technologies,
University Assane Seck of Ziguinchor, Ziguinchor, Senegal
psroc.org/cjp/download.php?type=paper...

another experimental method is through x-ray spectra..
see
In order to calculate the energies corresponding to
thecharacteristic lines, the energy levels in the atom
(bindingenergies in the electron shells) have to be known.
These canbe treated in a similar way to hydrogen by replacing the realcharge of the nucleus Z by the effective charge
http://www.ld-didactic.de/literatur/hb/e/p6/p6354_e.pdf
 
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