Hydrogen-helium free-free composition factor ($n_e{\sum }_i{Z}_i^2{n}_i=2n_e^2/(1+x_H)$)

For fully ionized hydrogen and helium with hydrogen mass fraction $x_H$, $n_e=(1+x_H)\rho /(2m_p)$ and ${\sum }_i{Z}_i^2{n}_i=\rho /m_p$. With the same unit Gaunt factor for both species, thermal bremsstrahlung at fixed electron number density is multiplied by $2/(1+x_H)$ relative to pure ionized hydrogen. The factor is one for pure hydrogen and two for pure helium.