Correcting units from this physics paper?

Hi all,

I've struggled to resolve a units issue in this 1973 paper by Hora:
https://www.academia.edu/23774741/E...tihydrogen_by_lasers_of_very_high_intensities
From the paper:

"
The number [itex]N_p[/itex] of pairs produced in a plasma volume [itex]V[/itex] during a time [itex]\tau[/itex] and a density [itex]n_e[/itex] of electrons is
[tex]N_p=\frac{e^8n_e^2}{\pi\hbar^2m_0^2c^5}V\tau\ln^3\frac{\epsilon_{kin}}{m_0c^2}.[/tex]
"

However, the units do not seem to work out as the LHS is dimensionless.

For what it's worth, I found that Equation (25) is missing one factor of [itex]E_v[/itex]:
[tex]\gamma=\frac{e^2\hbar}{\omega m_0^3c^3}E_v\quad(\mathrm{Incorrect})\quad\Rightarrow\quad\gamma=\frac{e^2\hbar}{\omega m_0^3c^3}E_v^2\quad(\mathrm{Correct})[/tex]

However, I can't tell what factors are missing in this expression. Even in units where [itex]k=1/(4\pi\epsilon_0)=1[/itex], I end up with dimensions of [itex]\mathrm{length}^{-3}[/itex] where I'm expecting dimensionless units.

FWIW, going back to Equation (28):

[tex]\sigma=\frac{e^8}{\pi\hbar^2m_0^2c^6}\ln^3\frac{\epsilon_\mathrm{kin}}{m_0c^2}[/tex]

I get dimensions of [itex]\mathrm{length}^{-2}[/itex], not [itex]\mathrm{length}^2[/itex].

It looks like this is very close to working... please, can someone help me "debug" the units here?

Thanks in advance,
HZ

To fllow you what physical dimension e has in your estimation ?