Dimensions of interaction/radiation length

In summary, the conversation discusses the calculation of the radiation length (represented by the variable X_0) in an electromagnetic calorimeter. The formula for calculating X_0 involves the material's atomic number (Z), density (represented by the variable A), and natural logarithm. The question arises about the units of X_0, which is originally given in g ##cm^{-2}##, and whether it can be converted to cm using density. The possibility of using ##\frac{X_0}{\rho}## to obtain X_0 in cm is also mentioned.
  • #1
Kara386
208
2
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!
 
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  • #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?
 
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Related to Dimensions of interaction/radiation length

1. What is the definition of interaction length?

The interaction length is the average distance a particle can travel before undergoing an interaction with another particle. It is a measure of the probability of a particle interacting with matter.

2. How is the interaction length related to cross-section?

The interaction length is inversely proportional to the cross-section of a particle. This means that a larger cross-section will result in a shorter interaction length, as the particle is more likely to interact with matter.

3. How does the interaction length vary with energy?

The interaction length decreases with increasing energy of the particle. This is due to the fact that higher energy particles have a smaller cross-section, making them less likely to interact with matter.

4. What is the significance of the radiation length?

The radiation length is a measure of the distance a high-energy particle can travel before losing a significant amount of its energy through bremsstrahlung radiation. It is an important parameter in understanding the behavior of high-energy particles in matter.

5. How is the radiation length different from the interaction length?

The radiation length is a specific type of interaction length that only takes into account the energy loss through bremsstrahlung radiation. The interaction length, on the other hand, considers all possible interactions of a particle with matter.

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