In the discussion of "Landau Straggling", the following expression comes up for the energy loss $\xi$ in Landau's original paper:
$$\xi = x\frac{2\pi N e^4\varrho\sum Z}{mv^2\sum A}$$
Here $N$ is avogadro's number, $e$ is the electron charge, $\varrho$ is the density, $m$ the electron's mass and $v$ a velocity. Moreover $x$ is a measure of length and $Z$ and $A$ are the usual atomic and mass numbers.
The point here is not to get into the physics, but rather to look at the dimensional analysis: $$\rm [\xi]=[MeV]$$ But the units of the RHS are: $$ \rm[cm][statC^4][gm\cdot cm^{-3}][gm^{-1}][s^2\cdot cm^{-2}]=[MeV\cdot gm] \neq[MeV]\quad\bf!!$$ I'd ignore this as a typo, but all of the literature on the topic seems to follow the same discrepancy in units, so there must be something I'm missing.
I'd be tempted to say that $\varrho$ might be a number density, but Landau (and others) explicitly states this is mass per volume.
What am I missing? Where is the missing gram unit?
Edit: This snippet from Leroy (2009) on the topic has the same exact problem and may be simpler to understand:
![enter image description here][1]
So where is the missing gram?
The value of $n_A$, in units of $\rm cm^{-3},$ is given by $$ n_A=\dfrac{N_\rho}{A}, \tag{1.39} $$ where $N$ is the Avagadro constant (see Appendix $\text{A.2}$), $\rho$ is the absorber density, in $\rm g/cm^3$, and $A$ is the atomic weight [also known as relative atomic mass].
