This site contains tables of critical screening parameters for several potentials: Yukawa, Hulthén, pseudoHulthén (Hulthén extended), Exponential Cosine Screened Coulomb. This has been recently (March 2026) published in the open access journal Atoms from MDPI. Here is the citation
A second paper is to be submitted shortly. Associated data tables are posted below.
These tables (also published as supplementary data by the journal Atoms) contain critical parameters, computed to 60 digits accuracy (by an adaptation of the Phase Method - http://gbxafs.iit.edu/phase-method) listing as mu_c = 1/D_c, in units of 1/au) for Debye screening lengths up to D=1000 au, and for angular momentum l=0…20.
They are in order sequentially, and are straight ASCII text files. The number of states varies for each potential and angular momentum because that’s how it goes.
To make full use of their accuracy, if you need it, take care not to have your program unthinkingly convert them to machine precision which is only accurate to about 16 digits.
Also posted below are critical screening lengths, accurate to 30 significant digits, for all states up to D=10^5 au and for l=0…12 for Yukawa/Debye, Hulthén, and ECSC potentials. These show the strange sawtooth structure explained in the second paper. D_c is 1/mu_c and more convenient to work with.
If you have questions or are interested in other potentials or parameter ranges, please email bunker@illinoistech.edu
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