Solving Delta Ray Problem - N=epsilon(1/E1 - 1/Emax)

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Im trying to find the number of delta rays though a material and am having some trouble with the units, can anyone help?

The number of delta rays through a material is given by N=epsilon(1/E1 - 1/Emax), where epsilon=[2*Pi*A^2*e^4*ne*x]/[m*c^2], where A is unitless, [ne]=cm^-3, and the denominator is in MeV's. I think I want epsilon in MeV's because N should be unitless, so it would cancel out the MeV from the rest of the equation.

My problem is the factor of e. I know it can't be in coulombs, so I need to somehow convert it to the right units. From what I am seeing it needs to be in cm*MeV to have epsilon end up in MeV's.

I know Coulombs/(4*Pi*epsilon not) is Joules*Meters, but I am not sure how to use that correctly without introducing a factor of (4*Pi*epsilon not) that isn't part of the equation.
 

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I don't recognize what you are talking about. Are you talking about the Bethe Bloch energy loss equation dE/dx for charged particles in matter, and the ionization constant I ? I think that if you have dE/dx for a thickness dx, and the average energy loss per delta ray, the ratio would give the number of delta rays. There is an N that appears in dE/dx, which is atoms per cm3.