Please note: Illinois Institute of Technology domain iit.edu has been changed to illinoistech.edu. bunker@illinoistech.edu is the preferred email address now.
This site contains tables of critical screening parameters for several potentials: Yukawa, Hulthén, pseudoHulthén (Hulthén extended), ECSC Exponential Cosine Screened Coulomb. The title of the first paper is “Numerical Computation of Critical Binding Parameters of Screened Coulomb Potentials”. It was (March 2026) published in the open access journal Atoms, from MDPI.
Here is the first paper on the publisher’s web site
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.
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Our second paper is now in print June 28, 2026, in the open access journal Atoms from MDPI Its title is “An Anomalous Structure in the Critical Screening Parameters of the ECSC Potential”. It explains the anomalous structure found in the first paper, and also explains another mystery unexplained for >50 years, and makes some more general predictions.
Here is the second paper on the publisher’s web site
Also posted below (and as supplementary data at the publisher) 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 that is explained in the second paper. D_c is 1/mu_c and more convenient to work with.
Download the supplementary data tables numbered S1-S39 as in the Atoms (MDPI) convention
Download the same with explicit file names zip file here
If you have questions or are interested in other potentials or parameter ranges, please email bunker@illinoistech.edu
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