Theorem: Gamow-peak saddle E_0 = 2^(1/3) b^(2/3) (k_BT)^(2/3) / 2 (unique positive real root)

Theorem (Gamow-peak saddle canonical): solving the stationarity condition f'(E_0) = 0 for f(E) = -E/k_BT - b/sqrt(E) gives E_0 = 2^(1/3) * b^(2/3) * (k_BT)^(2/3) / 2 - the unique positive real solution of the cubic equation 2 E_0^(3/2) = b…