Calculating Suitable Energies for a Muon Lifetime Experiment

[genloz]

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!

 

[Astronuc]

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

 

[genloz]

ok.. so high energy muons won't stop, but why aren't low energy muons useful?

 

[Astronuc]

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)?

 

[Gokul43201]

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.