Calculating Suitable Energies for a Muon Lifetime Experiment

In summary: But even if one does calculate the energy needed, what's the point? The experiment would be much more effective if they could detect more muons at lower energies. Has anyone else considered this?There is the possibility of using low-energy muons created in the atmosphere. However, they would only be useful if they could be detected on earth.
  • #1
genloz
76
1
Hi,

I'm starting a prac on muon lifetimes and we have been asked to calculate the range of energies suitable for the experiment...

Thinking about this, I was a bit stumped as to what we were supposed to be calculating... Is this a limitation of the detection equipment? Or do low energy muons never make it to earth? and high energy muons are too fast to detect?

These are the only other reasons I could come up with!

Any help would be greatly appreciated!

Thanks!
 
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  • #2
Well muons have a very short half-life, ~ 2.2 us, in the rest frame. Range (energy) is one issue, but also where the precursor reaction takes place, part of which is the avaible energy to the muon from pion decay.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/lepton.html#c3

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/muonatm.html

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cosmic.html#c2

http://teachers.web.cern.ch/teachers/archiv/HST2000/teaching/expt/muoncalc/lifecalc.htm

This might be of interest - http://web.mit.edu/8.13/www/JLExperiments/JLExp14.pdf
 
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  • #3
ok.. so high energy muons won't stop, but why aren't low energy muons useful?
 
  • #4
genloz said:
ok.. so high energy muons won't stop, but why aren't low energy muons useful?
I'm not sure what one means by useful - besides detecting muons, how is one trying to use them.

Range (from birth to decay) is function of energy. If the energy is too low, the muon doesn't cover much distance before it decays.

At higher energies, a muon could conceiveably travel through a detector. Way back when, I used a coincidence detector in physics lab to detect muons.

Has one considered the energy loss of the muon in comparison with that of a beta particle (or electron)?
 
  • #5
genloz said:
ok.. so high energy muons won't stop, but why aren't low energy muons useful?
Because they won't live to make it to your detector in sufficient numbers. Assume most muons are created at heights above 15km up. Using their known lifetimes (about 2.2 mu s) and an exponential decay law, calculate the minimum energy needed for say 1, in 10^5 muons created to survive the journey to the detector.
 

1. What is a muon lifetime experiment?

A muon lifetime experiment is a scientific experiment that measures the average lifespan of muons, which are subatomic particles that are similar to electrons but have a higher mass. This experiment typically involves accelerating muons to high energies and studying their decays.

2. How do scientists calculate suitable energies for a muon lifetime experiment?

Scientists use a variety of methods to calculate suitable energies for a muon lifetime experiment. This can include theoretical calculations based on known physical laws, as well as experimental data from previous studies. Additionally, computer simulations and models can be used to determine the best energy ranges for the experiment.

3. Why is it important to calculate suitable energies for a muon lifetime experiment?

Calculating suitable energies for a muon lifetime experiment is crucial for ensuring accurate and reliable results. The energy of the muons can greatly affect their behavior and their decay rates, so choosing the right energy range is essential for obtaining meaningful data and drawing valid conclusions from the experiment.

4. What factors are taken into consideration when calculating suitable energies for a muon lifetime experiment?

When calculating suitable energies for a muon lifetime experiment, scientists must take into account various factors such as the desired precision of the measurements, the capabilities of the experimental equipment, and the properties of the muons themselves. They also need to consider any potential sources of error and how to minimize their impact on the results.

5. How do scientists ensure the accuracy of the calculated energies for a muon lifetime experiment?

To ensure the accuracy of the calculated energies for a muon lifetime experiment, scientists may conduct multiple trials at different energy levels and compare the results. They may also collaborate with other researchers and consult with experts in the field to verify their calculations and make any necessary adjustments. Additionally, rigorous testing and calibration of the experimental equipment can help ensure precise and reliable measurements.

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