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

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

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

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

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_mfp_tot (Total reaction mean free path), R_crit is the critical radius and 𝛿 is the excess supercritical radius (R_core - R_crit) / R_crit.

References

^ "4.1 Elements of Fission Weapon Design".
^ 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.
^ Hans Volland (1995). Handbook of atmospheric electrodynamics, Volume 2. CRC Press. ISBN 0-8493-2520-X.