Muon Lifetime Experiment

physguy09

I have been doing an experiment on muon lifetime, and am wondering if my count rate is correct.

A little about the experiment:
I have two scintillators (plastic) set up above a lead glass absorber, and a third scintillator(plastic), under the lead glass to veto muons that do not stop in the Pb-glass. If the Logic Unit (LU) detects coincidence, a start signal is sent to the Time-to-Amplitude converter. If the muon stops in the Pb-glass, a stop signal is sent. The area of the top portion of the lead glass (where the muon is incident) is roughly 225 cm².

So assuming this is correct, I figured I should be getting:
10,000 [tex]\frac{muons}{meter^2 minute}[/tex] * ([tex]\frac{1 meter^2}{10,000 cm^2}[/tex])*230 cm² = 230 muons/minute.

I have observed a count rate of about 50 muons/day, and this seems to be rather low. There are 10 floors above the location of my apparatus, so I know that there is some attenuation for that reason, but 50 muons/day is no where near the 331,000/day I should be getting.

Bob S

Most of the muons will penetrate 10's of meters of earth. Cosmic ray muons have been used to x-ray the pyramids in Egypt. Of those muons that do stop, up to half will be negative muons, which have lifetimes (in 1S atomic levels) measured as I recall from about 50 nanoseconds to 1 or 2 microseconds, depending on the specific atom.

physguy09

I understand that, so I guess a better question would be, if I was getting a descent count rate as I am only picking up about 50 muons/day on my Pb-glass. As of now I have a pretty descent lifetime measurement of
[tex]1.9\mu s[/tex].
The problem is just that I figured I would be getting more than 50 muons/day. Also I have noticed that the count rate appears to increase during the morning hours, as it does not change much during the day. I have concluded two things from this:

1) My electronics are screwy and I'm not only detecting muons (whether mu⁺ or mu^-),

2) The sun is the primary source of muons arriving in my detector.

Vanadium 50

Your calculation of 230 muons/minute seems not to calculate the number that stop in the glass.

hamster143

What percentage of cosmic muons would your scintillator detect? How many would pass through without setting off?

How thick is Pb glass and what is the mean free path of a cosmic muon in one?

Shouldn't the second scintillator be INSIDE Pb glass? If your muon stops inside it and decays, it's rather unlikely that the resulting electron will make it all the way back into the second scintillator.

physguy09

there is a PMT in the lead glass. The Pb glass is about 46 cm thick, and is composed of
SiO₂ (46%) Na₂(5%)K₂O (4%) PbO(45%).

The third scintillator is supposed to detect muons that do not stop in the Pb-glass, but i did not hook it up to a counter, might have been the best thing to do in order to see how many muons are actually picked up but go through. I figure most interactions occur with oxygen, as I remember from my particle physics course, but I cannot remember how to calculate the mean free path.

hamster143

Mean energy of cosmic muons at sea level is around 4 GeV. Based on my back-of-the-envelope calculation using energy loss figures for PDG (6-10 MeV/cm for your glass between 200 MeV and 10 GeV), if your apparatus were outside, your glass would have to be at least 10 times thicker to capture the bulk of muons that hit your detector. So, you're really capturing the long tail of the distribution.

On the other hand, 10 floors above you should have helped slow down the muons.

Is there a way to see how many events are captured by individual detectors? Can you move the apparatus to the nearest window?

Vanadium 50

Think of your scintillators as A, B and D, and the lead glass as C. You might think about what combination of A-D and the operators AND, OR and NOT would describe, a) a muon penetrating the apparatus, b) a muon stopping in the glass, and c) a muon decaying in the glass. From that, you can check that the rates are sensible or not.

physguy09

Unfortunately there aren't any windows in the lab. I guess the count rate might be fairly reasonable given that not all muons stop in the absorber, but i still can't figure out why the large difference in count rate throughout the day (During the day I'll only see about 10 new events, this is in a 9 hour span, should imply about 25-30 counts/day, but there seems to be a huge increase overnight as I see about 50 events difference between one day at 9am to the next day at 9am).

hamster143

That is a fair guess, though it's hard to draw conclusions with these kinds of numbers. It's possible that solar muons have lower energies than cosmic ray muons, which is why they stop in the absorber in greater numbers. It is also possible that you're detecting something other than muons.

Bob S

Cosmic ray muons at sea level are a combination of intergalactic mouns, and muons that are a result of very high energy protons striking the upper atmosphere and creating hadronic shower cascades, which include positive and negative pions that decay to muons before reaching the ground. Solar muon fluxes scale something like solar activity (sunspots, etc.). But it takes light 8 minutes to get here from the Sun, and the muon lifetime is only about 2 microseconds. So where do "solar muons" come from? They would have to come from solar protons. See
http://www.physics.adelaide.edu.au/astrophysics/muon/