Research · Research notebook
Beyond Slater — research notebook
Reframing an early effective-nuclear-charge project as a modern, falsifiable study of interpretable semi-empirical screening models.
Question
Under declared data definitions and validation splits, which low-parameter phenomenological screening models predict a derived effective-charge target better than a Slater-style baseline, and do they keep doing so out of sample?
The goal is not to name a new screening rule early. It is to ask which simple models remain useful after modern atomic data, relativistic effects and stronger validation are taken seriously.
Why this question
Slater's 1930 shielding rules are the historical anchor: a handful of constants that approximate how inner electrons screen the nuclear charge. An earlier project of mine tried to improve on them. This notebook restarts that project with a stricter method.
Definitions and scope
A re-audit of the project's own earlier pipeline found that the legacy target labelled “experimental effective nuclear charge” was actually a hydrogenic inversion of binding energy, followed in places by target imputation, and that the old headline fit was evaluated in-sample. Those choices are now treated as model assumptions rather than ground truth.
This page therefore does not claim that any earlier fit was validated. The target variable, the unit of analysis, and the included regimes will be fixed and published before any result is.
Candidate model families
All candidates are planned; none has been tested under the protocol below.
- constrained occupancy screening;
- low-order relativistic residual terms of the fine-structure kind;
- direct energy, quantum-defect, or Dirac mappings;
- radius-matched definitions;
- compact Yukawa screening functions.
Evidence and methods
Validation is designed around forward-Z, leave-period, leave-shell-family and source/definition-transfer splits, with element-level leakage guards and no target imputation. Baselines, metrics, uncertainty treatment, and success criteria will be stated on this page before any result is reported.
Findings
No result reported yet.
Uncertainty and open questions
- Data: source definitions and uncertainties differ between atomic-data compilations; observed, interpolated, and theoretical values must be kept apart.
- Model: any effective charge depends on the inversion that defines it, so results may not transfer between definitions.
- Generalization: a model that works across one period or shell family may fail on the next; the splits above exist to expose that.
A negative result is an acceptable result and will be recorded here rather than removed.
Evidence register
| ID | Type | Public source | Role |
|---|---|---|---|
| E1 | primary literature | J. C. Slater, “Atomic Shielding Constants”, Physical Review 36, 57 (1930), doi:10.1103/PhysRev.36.57 | historical baseline; not evidence for any new model |
| E2 | reference database | NIST Atomic Spectra Database, doi:10.18434/T4W30F | candidate atomic-data source; exact inputs and version will be pinned when results are published |
Change log
- 2026-09-25: restructured into question, scope, planned candidates, and protocol; separated project status from conclusion status.
- 2026-08-20: first public note.