The Resonance Read Alone: Breit and Wigner's Isolation and the Drift Inside Every Level Table

In 1936 Gregory Breit and Eugene Wigner gave resonance physics its shape: near an isolated level of the compound nucleus, the capture cross-section follows the single-level formula, a Lorentzian whose two parameters are the level's energy E_0 and width \Gamma — a derivation, given the isolation, and the working instrument of the field ever since. The isolation is the paper's step: one level, constant widths, no interference with neighbouring levels or with the non-resonant background, postulated in the very system whose levels are dense. This paper evaluates it in the formula's own currency — parameter drift. The bench's control reads a genuinely isolated declared level back exactly (fitted E_0 drift 0.000000, fitted \Gamma drift 0.000000). A second declared level at one width's separation merges the curve into a single peak whose single-level reading returns a width of 2.264597 against the declared 1.000000; at half a width, the fitted energy drifts by +0.162500; and a declared flat background amplitude of 0.300000 displaces even a truly isolated level's fitted energy by +0.073500 through interference the formula has no term to express. The formula given the isolation stands entire. What is counted here is the derivation status of the isolation itself: 1 isolation approximation, 0 derivations in 1936 that compound-nucleus resonances are isolated where the formula is used. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24015219
Primary Topic
Nuclear physics research studies
Type
preprint
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preprint

The Resonance Read Alone: Breit and Wigner's Isolation and the Drift Inside Every Level Table

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Nuclear physics research studies
preprint

The Resonance Read Alone: Breit and Wigner's Isolation and the Drift Inside Every Level Table

William Alexander Aldred
preprint en

Abstract

In 1936 Gregory Breit and Eugene Wigner gave resonance physics its shape: near an isolated level of the compound nucleus, the capture cross-section follows the single-level formula, a Lorentzian whose two parameters are the level's energy E_0 and width \Gamma — a derivation, given the isolation, and the working instrument of the field ever since. The isolation is the paper's step: one level, constant widths, no interference with neighbouring levels or with the non-resonant background, postulated in the very system whose levels are dense. This paper evaluates it in the formula's own currency — parameter drift. The bench's control reads a genuinely isolated declared level back exactly (fitted E_0 drift 0.000000, fitted \Gamma drift 0.000000). A second declared level at one width's separation merges the curve into a single peak whose single-level reading returns a width of 2.264597 against the declared 1.000000; at half a width, the fitted energy drifts by +0.162500; and a declared flat background amplitude of 0.300000 displaces even a truly isolated level's fitted energy by +0.073500 through interference the formula has no term to express. The formula given the isolation stands entire. What is counted here is the derivation status of the isolation itself: 1 isolation approximation, 0 derivations in 1936 that compound-nucleus resonances are isolated where the formula is used. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.

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