The average kinetic energy per relativistic electron/positron is of the order of \(u_{e} / n_{e} \sim k T\). The Coulomb energy per electron/positron is of the order of \(u_{c} \approx e^{2} /\left(4 \pi \epsilon_{0} a\right)\) where \(a \approx\left(1 / n_{e} \right)^{1 / 3}\) is of the order of the average distance between the charged particles. Using \(n_{e} \sim(k T / \hbar c)^{3}\) we get \(u_{c} / u_{e} \sim e^{2} /\left(4 \pi \epsilon_{0} \hbar c \right) \approx 1 / 137\). This is the justification for treating the relativistic electrons and positrons as noninteracting.