Muon Lifetime Exp: Urgent Qs on Scintillator-PMT Setup

In summary, the conversation discusses using a scintillator connected to PMTs to measure the lifetime of a muon. The concept of ΔxΔp = hbar is mentioned, as well as using the energy of the muon instead of measuring its time to calculate its average lifetime. It is explained that the experiment can still provide an accurate measurement of the muon's lifetime, regardless of how long it has been outside the scintillator, by assuming it follows exponential decay.
  • #1
martinhiggs
24
0

Homework Statement



In using the experiment where a scintillator is connected up to PMTs, and the data is then recorded on the computer... The muon has already lived outside the scintillator for a large amount of time before it decays in the scintillator, so how is it that the experiment still works in providing the actual lifetime of the muon??
 
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  • #2
just a quick guess but your measuring the energy or momentum using the scintillator yeh?

If so ΔxΔp = hbar

But cΔx = Δt
and cΔp = ΔE

So you get ΔEΔT = hbar
So ΔT = hbar/ΔE

Try using this concept to get the average lifetime of the muon, i don't think you can calculate the exact lifetime but the resolution using the energy it has instead of measuring the time...if that makes sense...
 
  • #3
venomxx said:
just a quick guess but your measuring the energy or momentum using the scintillator yeh?

My guess would be: a stopped muon starts your clock; whenever the corresponding decay positron gets registered, the clock is stopped. Neither energy nor impulse of the muon would be of interest in this case.

martinhiggs said:
The muon has already lived outside the scintillator for a large amount of time before it decays in the scintillator, so how is it that the experiment still works in providing the actual lifetime of the muon??

Your analysis will provide an average lifetime for muons in a muon ensemble. Basically, you assume that this is a similar scenario to nuclear decay, which follows:

[tex]N(t)=N(0)\cdot e^{(-\lambda t)}[/tex]

If your data shows exponential dependence of this kind, you are able to determine the mean lifetime [itex]\tau[/itex], as [itex]\tau=1/ \lambda[/itex]. It doesn't matter how long the muon has been outside your experiment*. This information wouldn't change the time constant of your exponential function. Further investigation would require you to consider the finite measurement time/resolution etc. (e.g., http://en.wikipedia.org/wiki/Maximum_likelihood" [Broken]).

*As long as you treat a stopped muon as if it was 'free'. This assumption is reasonable in this experiment for [itex]\mu^+[/itex]
 
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1. What is the purpose of this experiment?

The purpose of this experiment is to measure the lifetime of muons, which are subatomic particles that are constantly bombarding Earth's atmosphere. This measurement can provide valuable information about the behavior of elementary particles and their interactions with matter.

2. What is a scintillator and how does it work in this experiment?

A scintillator is a material that emits light when it is struck by a charged particle. In this experiment, the scintillator is used to detect the passage of muons. When a muon passes through the scintillator, it causes the material to emit light, which is then detected by a photomultiplier tube (PMT).

3. How does the PMT work in this experiment?

The PMT is a device that converts the light emitted by the scintillator into an electrical signal. It consists of a photocathode, which converts the light into electrons, and a series of dynodes, which amplify the signal. The amplified signal is then recorded and used to determine the passage of muons through the scintillator.

4. Why is this experiment urgent?

This experiment is urgent because the lifetime of muons is a constantly changing value. It is affected by various factors such as altitude, temperature, and atmospheric conditions. Therefore, it is important to conduct the experiment as soon as possible to obtain an accurate measurement of muon lifetime.

5. What are the potential applications of this experiment?

The measurement of muon lifetime has many potential applications in the field of particle physics. It can provide insight into the fundamental properties of subatomic particles and their interactions. It can also be used to test the validity of various theories and models in particle physics. Additionally, muon lifetime measurements can have practical applications in fields such as medical imaging and nuclear power.

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