arXiv: 2607.15250

康普頓與貝特-費曼產額公式的等效性

Equivalence of the Compton and Bethe-Feynman Yield Formulas

July 16, 2026

作者: Edwin Lyman

physics.soc-phphysics.soc-ph

摘要

貝特-費曼公式已被證實有助於估算簡易裂變武器的爆炸當量。然而，公開文獻中對該公式的推導採用了近似方法，其有效性並不顯然，且其中存在明顯矛盾。本文證明，貝特-費曼公式可直接從阿瑟·H·康普頓在1941年國家科學院鈾委員會報告中所提出的更早期當量估算方法中提取出來。康普頓詳盡的推導過程，為理解貝特-費曼公式的物理基礎提供了更為直觀的認識。

English

The Bethe-Feynman formula has proven useful for estimating the explosive yields of simple fission weapons. However, derivations of the Bethe-Feynman formula found in the open literature utilize approximations whose validity is not obvious, and which contain an apparent contradiction. Here we show that the Bethe-Feynman formula can be extracted in a straightforward manner from the results of an earlier approach for estimating yield by Arthur H. Compton, as presented in the 1941 National Academy of Sciences Uranium Committee report. Compton's detailed derivation provides a more intuitive understanding of the physical basis for the Bethe-Feynman formula.