Experimental values for screening constants? (Slater rules)

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The discussion centers on the calculation of effective nuclear charge (Z_eff) in multiple-electron atoms, specifically using Slater's rules to determine the screening constant (s). The user references Arnold Sommerfeld's 1936 work for experimental values and a 1967 paper by Clementi et al. that provides Hartree-Fock calculations but lacks experimental validation. The differences in figures from these sources raise questions about the accuracy of the screening constants, prompting a request for better experimental data and alternative methods, including x-ray spectra analysis.

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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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