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I Dimensions of interaction/radiation length

  1. Dec 5, 2016 #1
    I've been given that in an electromagnetic calorimeter the radiation length of a material consisting of a single nucleus is:
    ##X_0 = \frac{716.4A}{Z(Z+1)\ln(287/\sqrt{74}}##

    Where ##X_0## is in g ##cm^{-2}##. How can it be in those units when everything in that expression is dimensionless? It's possible I'm meant to use density to calculate ##X_0## in the correct units somehow.

    Thanks for any help!
     
    Last edited: Dec 5, 2016
  2. jcsd
  3. Dec 5, 2016 #2
    Ok, change of question. Assuming ##X_0## is originally calculated in g##cm^{-2}##, can I use density to somehow calculate the value in cm instead? cm seems like a more sensible unit for a length. And dimensionally dividing a quantity in g##cm^{-2}## by g##cm^{-3}## gives cm, is there any justification for why ##\frac{X_0}{\rho}## would give ##X_0## in cm? Rather than some quantity completely different to radiation length?
     
    Last edited: Dec 5, 2016
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