Calculating range of muons in a detector?

In summary, the conversation discusses the approximation of NOvA detectors as being built from hundreds of "sandwiches" of PVC plastic and oil. The range of muon energies (200MeV, 500MeV, 1GeV, and 1.8GeV) in the detector is then discussed, with calculations being made using equations found in a source provided. There is some uncertainty around the use of Butane and "C-552 air-equivalent plastic" in the calculations and the assumption that particles are always minimally ionizing.
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Homework Statement


If one can approximate NOvA detectors being built out of hundreds of "sandwiches" or PVC plastic of 1cm thickness and a "plane" of oil of 5.6 cm, what is the range of muon of energy 200MeV, 500MeV, 1GeV, and 1.8GeV in the detector?

Homework Equations



\frac{dE}{dρ*x} = .15*(1.76) + .85*(2.2) = 2.14 MeV*cm2 / g
rho = .15*(1.76) + .85*(2.5) = 2.42 g/cm3
(using Butane as "oil" and "C-552 air-equivalent plastic" as CVC plastic)

The Attempt at a Solution


I got the values above from: http://pdg.lbl.gov/2014/AtomicNuclearProperties/adndt.pdf
I also use .15 and .85 because the detector is 15% plastic and 85% oil, if I use 1cm/(1cm + 5.6cm) and 5.6cm/(1cm+5.6cm)

From the equations above, I get

x = E / (ρ)*(2.14) = 200MeV / (2.4)(2.14) = 39.1 cm

Though I'm not sure its correct to use Butane as "oil" and "C-552 air-equivalent plastic" as CVC plastic

Am I doing this correctly?
 
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I have no idea what "C-552 air-equivalent plastic" is, but that should be fine.
The assumption that the particles are always minimally ionizing is more problematic, especially at 200 MeV.
 

Related to Calculating range of muons in a detector?

1. How do you calculate the range of muons in a detector?

The range of muons in a detector can be calculated using the Bethe-Bloch formula, which takes into account the energy, mass, and charge of the muon, as well as the density and thickness of the detector material. Other factors, such as the geometry and composition of the detector, may also need to be considered.

2. What is the purpose of calculating the range of muons in a detector?

The range of muons in a detector is an important factor in understanding the behavior and interactions of these particles. It can help in the design and optimization of detectors for various applications, such as particle physics experiments, medical imaging, and radiation monitoring.

3. How accurate are the calculations of muon range in a detector?

The accuracy of the calculations depends on the accuracy of the input parameters and the assumptions made in the model. In general, the range of muons in a detector can be predicted with a reasonable degree of accuracy, but the actual range may vary due to factors such as multiple scattering and energy loss in the detector material.

4. Can the range of muons in a detector be experimentally verified?

Yes, the range of muons in a detector can be experimentally verified through various techniques, such as measuring the energy spectrum of the muons before and after passing through the detector, or using imaging methods to visualize the path of the muons in the detector.

5. Are there any limitations to calculating the range of muons in a detector?

While the Bethe-Bloch formula is a widely used and reliable method for calculating the range of muons in a detector, it may not be applicable for all types of detectors and materials. Other factors, such as energy loss due to ionization and bremsstrahlung, may need to be taken into account for more accurate predictions in certain situations.

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