Ion-density convention in the Debye screening length

The Debye length depends on the density of every mobile ionic species, weighted by squared charge. For dilute ions at a common temperature in a uniform medium, ${\lambda }_D^{-2}={\sum }_i{n}_i{z}_i^2{e}^2/(ϵk_{B}T)$, where $n_i$ is the bulk number density of species $i$.

For a symmetric monovalent electrolyte with density $n$ of each sign, the sum gives $2n{e}^2/(ϵk_{B}T)$. If the symbol $n$ instead denotes the total ion density, the prefactor is $n{e}^2/(ϵk_{B}T)$. The physics is identical; silently changing the meaning of density creates a spurious factor of $\sqrt{2}$ in the screening length.