Bethe–Feynman formula

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

• 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.

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

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.

• Richard Feynman
• Hans Bethe
• Robert Serber