The Rules of the Terms: Hund's Three Sentences and the One Atom They Cannot See
Year: 2026
Type: preprint
Abstract: Between 1925 and 1927 Friedrich Hund stated three rules that select the ground term of an atom's configuration — maximum spin, then maximum orbital angular momentum, then the total angular momentum by shell filling — and a century of spectroscopy has run on them. This paper evaluates the rules' warrant at their founding address, converting census attack CC-163 whole. The rules were offered as empirical regularities of the term orderings, with no derivation from the atomic Hamiltonian in the founding papers; the bench therefore audits them as what they are — a selection rule resting on inspection — enumerating every microstate of each declared configuration exactly, reading the rule-selected term off mechanically, and scoring it against the declared observed ground terms across forty atoms. The audit: 39 of 40 rows hit, a rate of 97.500000\%, with the machinery check exact (enumeration and the closed-form extremal reading agree on all 33 configuration cells). The one failure is named and its mechanism is the deficit's own: cerium, where the rules select ^3H_4 and the record's ground term is ^1G_4 — a rival from a different spin sector lying below the selected term, an inversion an ordering that carries no energies cannot see. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.
Author: Aldred, William Alexander
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225463739