Obtaining range from bethe-bloch formula

[Cemil]

While studying particle physics, i saw that the range formula is the integration dE/(dE/dx) but as you know that there are no variable E in the formula. how could that integration be done?

well i think we can do it by ourselves and we must use a programming language and i think the trapezoidal rule would be useful to solve that.

But i could not find out how could that integration be done please help me. thank you

 

[Vanadium 50]

but as you know that there are no variable E in the formula.

But there is a velocity. From velocity you can get energy.

 

[Bob S]

Look at Equation (1) and Figure 1 in
http://beamdocs.fnal.gov/DocDB/0010/001068/001/A%20tutorial%20on%20beam%20loss%20monitoring.pdf
Eq (1) is the Bethe Bloch energy loss equation for protons. The independent variable is β. The integrated range is obtained by iteration of

dx = dE/[dE/dx]
E=E-dE
x=x+dx
etc.

Bob S