Bethe–Feynman formula

The Bethe–Feynman efficiency formula, a simple method for calculating the yield of a fission bomb,^[1] was first derived in 1943 after development in 1942. Aspects of the formula are speculated to be secret restricted data.^[2]

Related formula

• a = internal energy per gram
• b = growth rate
• c = sphere radius

${\displaystyle a\approx (bc)^{2}f}$

A numerical coefficient would then be included to create the Bethe–Feynman formula—increasing accuracy by more than an order of magnitude.^[3]

${\displaystyle E_{f}f=\left({\frac {E_{2}}{\gamma -1}}\right)\cdot \alpha _{max}^{2}\cdot R_{crit}^{2}\cdot \left({\frac {\delta }{1-\delta }}\right)\cdot \left({\frac {2+3\delta }{2}}\right)}$

where γ is the thermodynamic exponent of a photon gas, E₂ is the prompt energy density of the fuel, α is V_n (neutron velocity) / λ_mfptot (total reaction mean free path), R_crit is the critical radius and 𝛿 is the excess supercritical radius (R_core - R_crit) / R_crit.

See also

• Richard Feynman
• Hans Bethe
• Robert Serber

References

1. "4.1 Elements of Fission Weapon Design".
2. Meeting and working with Richard Feynman at Los Alamos, Web of Stories, story by Hans Bethe recorded in December 1996, last accessed 2015/04/20.
3. Hans Volland (1995). Handbook of atmospheric electrodynamics, Volume 2. CRC Press. ISBN 0-8493-2520-X.