Comparison between historic nuclear explosion yield formulas

TL;DR

This paper compares historic nuclear explosion yield formulas, revealing that the Bethe-Feynman formula from 1943 closely aligns with earlier formulas by Frisch and Peierls after adjustments, with differences mainly due to scaling factors.

Contribution

It provides a comparative analysis of historic nuclear yield formulas, clarifying their relationships and historical context.

Findings

Bethe-Feynman formula closely matches earlier formulas after adjustments.

Earlier formulas differ mainly by a scaling factor.

No evidence Bethe and Feynman knew of the Frisch-Peierls formula.

Abstract

During the Manhattan project a simple formula was developed by Bethe and Feynman in 1943 to estimate the yield of a fission-only nuclear explosion of a uniformly-dense bare-sphere of supercritical fissile material. We have not found any evidence that Bethe and Feynman knew of the first yield formula obtained by Frisch and Peierls contained within their famous March 1940 memorandum. Similarly, we have not found any technical documents that compare the Bethe-Feynman formula to the earlier works of Frisch and Peierls, or Serber. After adjusting for differences in the labeling of critical radii, we find that earlier formulas only differ by a scaling factor.