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

[jbb88]

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.

 

[Bob S]

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.

 

[sir-pinski]

It sounds like you are on the right track. The factor of e in the equation represents the elementary charge, which has units of coulombs. In order for the units to work out, you will need to convert the elementary charge to the appropriate units of Joules*Meters, which can be done by using the value of Coulombs/(4*Pi*epsilon not) as you mentioned. However, in order to avoid introducing an extra factor, you can use the value of epsilon not in terms of MeV, which is 8.85*10^-14 MeV^-1 cm^-1. This way, when you multiply the elementary charge by (4*Pi*epsilon not), the units will cancel out and you will be left with cm*MeV as desired for epsilon. I hope this helps and good luck with your calculations!