Obtaining the CDSA range of Bethe-Bloch Equation

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In summary, the speaker is working on a junior project to measure the energy distribution of cosmic muons. They are using the Bethe-Bloch equation and have found that there is no working model for the range of 0.01 ≤ β ≤ 0.05. They are wondering if there is a way to find the values for R_0 and T_{min}, which are empirically determined. Another person responds that at beta=0.05, muons only have 130 keV left and the remaining stopping distance can be neglected.
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I'm currently working on my junior project (it's basically a senior project, but for some reason you're supposed to take it third year), which is to measure the energy distribution of cosmic muons. We're doing this by measuring the muon flux that reaches a scintillator paddle below a stack of lead and varying the size of the stack of lead. Of course we're using the Bethe-Bloch equation. Now I've found in both a book from the library and chapter 27 of the PDG's works that there is no working model for the [tex]0.01 \leq \beta \leq 0.05 [/tex] range, so in the equation
[tex]
R(T_0)=R_0(T_{min})+{\int_{T_{min}}}^T_0\left(\frac{dE}{dx}\right)^{-1}dE
[/tex]

The values for [tex]R_0[/tex] and [tex]T_{min}[/tex] are empirically determined. So is there anyway I can find these value? Any help at all? Thanks.

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Kristopher
 
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At beta=0.05 muons just have 130 keV left. You can neglect the remaining stopping distance, it is probably just something like 10 micrometers.
 

1. What is the Bethe-Bloch Equation?

The Bethe-Bloch Equation is a mathematical formula that describes the energy loss of a charged particle as it travels through a material. It is used in particle physics to study the interactions between particles and matter.

2. How is the CDSA range calculated using the Bethe-Bloch Equation?

The CDSA (Continuous Slowing Down Approximation) range is calculated by integrating the Bethe-Bloch Equation over the entire path length of the particle through the material. This gives the average energy loss of the particle and can be used to determine its range in the material.

3. Why is the Bethe-Bloch Equation important in particle physics?

The Bethe-Bloch Equation is important because it allows us to understand and predict the behavior of charged particles as they travel through matter. This is crucial in fields like nuclear medicine, where particles are used for imaging and therapy, as well as in high-energy physics experiments.

4. How is the Bethe-Bloch Equation derived?

The Bethe-Bloch Equation is derived from quantum mechanics and classical electrodynamics principles. It takes into account the interactions between the charged particle and the electrons in the material, as well as the properties of the material itself.

5. Are there any limitations to the Bethe-Bloch Equation?

Yes, there are some limitations to the Bethe-Bloch Equation. It is most accurate for high-energy particles, and becomes less accurate at lower energies. It also does not take into account the effects of multiple scattering, which can be important for particles with a large scattering angle.

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