The Isobaric Ladder — the un-fitted coefficient meets Wigner's b

The deposit's mass ledger has exactly one coefficient that was never fitted: the Coulomb term MeV, derived from the packed sphere's radius. In total masses that derived coefficient is one voice among four fitted ones. But inside a single mass number A, the fitted volume, skin and pairing terms largely cancel in differences — so mass differences within an isobaric multiplet read the derived coefficient almost alone. That makes Wigner's isobaric multiplet mass equation the cleanest isolation of the deposit's one derived number that the mass table offers. The test: fourteen triplets ( to 58, members , , Z+1 around ), the IMME coefficient solved exactly from the three masses — identically for the measured masses and the ledger masses. Result: the derived coefficient lands to ~16% with nothing tuned — and the residual is flat and one-signed, which is the signature of a missing term. The missing term turned out to be standard physics: adding the parameter-free Fermi-gas Coulomb exchange term (Bethe–Bacher 1936) takes the miss to ~4%. The leftover, MeV one-signed, is recorded as open — and one tempting label for it is explicitly fenced off. [earned for b; null-fenced for the leftover's interpretation; prior art credited] This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23848093
Primary Topic
Nuclear physics research studies
Type
preprint
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preprint

The Isobaric Ladder — the un-fitted coefficient meets Wigner's b

James Norman Ibbotson
Zenodo (CERN European Organization for Nuclear Research)
Nuclear physics research studies
preprint

The Isobaric Ladder — the un-fitted coefficient meets Wigner's b

James Norman Ibbotson
preprint en

Abstract

The deposit's mass ledger has exactly one coefficient that was never fitted: the Coulomb term MeV, derived from the packed sphere's radius. In total masses that derived coefficient is one voice among four fitted ones. But inside a single mass number A, the fitted volume, skin and pairing terms largely cancel in differences — so mass differences within an isobaric multiplet read the derived coefficient almost alone. That makes Wigner's isobaric multiplet mass equation the cleanest isolation of the deposit's one derived number that the mass table offers. The test: fourteen triplets ( to 58, members , , Z+1 around ), the IMME coefficient solved exactly from the three masses — identically for the measured masses and the ledger masses. Result: the derived coefficient lands to ~16% with nothing tuned — and the residual is flat and one-signed, which is the signature of a missing term. The missing term turned out to be standard physics: adding the parameter-free Fermi-gas Coulomb exchange term (Bethe–Bacher 1936) takes the miss to ~4%. The leftover, MeV one-signed, is recorded as open — and one tempting label for it is explicitly fenced off. [earned for b; null-fenced for the leftover's interpretation; prior art credited] This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.

Zenodo (CERN European Organization for Nuclear Research)
Nuclear physics research studies
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