Bethe-Bloch Equation different materials

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Discussion Overview

The discussion centers around the application of the Bethe-Bloch equation to analyze the energy loss of muons as they pass through different materials, particularly in the context of a muon lifetime experiment. Participants are exploring the calculations related to kinetic energy and the parameters involved in the equation.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant is using the Bethe-Bloch equation to calculate the energy loss of muons and is questioning their results for maximum kinetic energy, suggesting they should be around 645 MeV but are obtaining values closer to 45 MeV.
  • There is a discussion about the parameters used in the kinetic energy equation, with one participant confirming the mass of the electron and muon, and questioning the use of units for the speed of light.
  • Another participant points out that if all quantities are in MeV, factors of c may not be necessary in the calculations.
  • Concerns are raised regarding the gamma factor needed to achieve the expected kinetic energy, with one participant noting that a gamma of approximately 25 is required to reach 645 MeV, while the quoted velocity corresponds to a gamma of about 7.
  • There is a discussion about the accuracy of muon velocities, with one participant stating that many muons produced in LHC collisions have velocities around 0.9999c, while another mentions the lack of monoenergetic muon sources at lower energies.
  • Participants discuss the energy levels of muons produced in LHC collisions, noting that the maximum muon energy from 450 GeV proton collisions on steel is around 30 GeV, with an average of approximately 1.5 GeV.

Areas of Agreement / Disagreement

Participants express differing views on the accuracy of muon velocities and the parameters used in the Bethe-Bloch equation. There is no consensus on the correct values or methods for calculating the kinetic energy of muons, and the discussion remains unresolved.

Contextual Notes

Participants highlight potential limitations in the accuracy of muon velocity measurements and the dependence on specific experimental conditions, which may affect the calculations being discussed.

stutiger99
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I am trying to use the Bethe-Bloch equation to investigate how a Muon loses its energy as it penetrates through different materials in the muon lifetime experiment. In order to do so I need 2 determine both the total energy and kinetic energy.
For kinetic energy maximum I have been using

Tmx = (2*m*p^2*c^4) / (m^2*c^4 + M^2*c^4 + 2*m*c^2*(p^2*c^2 + M^2*c^4)^0.5 )

Typical values for Tmax I should be getting I have been informed are around 645MeV however I keep getting values in the region of 45MeV so I have obviously went wrong somewhere. Am I correct in saying:
m = electron mass (0.511MeV)
p = momentum of muon (achieved via p= gamma*mass of muon*c)
M = mass of the muon (105.6584 MeV)

If it is correct is there a chanae I am wrong with units of c somewhere? Or is it even density realted?


Also the velocity of a muon, is it correct that it is 0.9901c (i.e Beta = v/c for special relativity) before striking the material?

Much help would be greatly appreciated.
 
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I don't understand your equation, but
if all masses, energies, and momenta are in MeV, you don't need any factors of c.
 
An equivalent of the equation is on wikipedia. It is slightly different but it can be simplified to what I have above for Tmax (N.B. this Tmax is the one used in the bethe-bloch equation.
 
To get 645 MeV with either equation, you need gamma ~ 25. The velocity you're quoting (0.9901c) corresponds to gamma ~ 7. That could be the problem. I don't know what the correct velocity is, it depends on your specific experiment.
 
stutiger99 said:
Also the velocity of a muon, is it correct that it is 0.9901c (i.e Beta = v/c for special relativity) before striking the material?

There aren't many muon sources with the velocity known to 4 digits of accuracy.
 
Vanadium 50 said:
There aren't many muon sources with the velocity known to 4 digits of accuracy.

Many muons produced in LHC collisions have energies greater than ~8 GeV and therefore have velocities of 0.9999c (to 4 digits of accuracy, rounded down).
 
hamster143 said:
Many muons produced in LHC collisions have energies greater than ~8 GeV and therefore have velocities of 0.9999c (to 4 digits of accuracy, rounded down).

Fine. You got me there.

Nonetheless, there are very few monoenergetic muon sources at the energies under discussion, which leads me to suspect something may be wrong here.
 
hamster143 said:
Many muons produced in LHC collisions have energies greater than ~8 GeV and therefore have velocities of 0.9999c (to 4 digits of accuracy, rounded down).

Have LHC started to colliding yet?

...trying to save Vanadium 50 ;-) ...
 
The LHC collided 450 GeV protons on steel. That gives a maximum muon energy of 30 GeV and an average muon energy of ~1.5 GeV.
 
  • #10
Vanadium 50 said:
The LHC collided 450 GeV protons on steel. That gives a maximum muon energy of 30 GeV and an average muon energy of ~1.5 GeV.

Ahh yeah that is true, during detector performance tests
 

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