Finding the Angle of Scattered Electrons???

 

Since the muons have very high energy, even by the time they reach our apparatus, one might expect the majority of any ejected electrons to be forward scattered, but there should be some at other angles as well. We will check to see if there is evidence of electrons scattered at various angles to the vertical flux of muons.

 

Then introduce the lead midway between the paddles and count for another long period of time. You should find a reduced rate due to the absorption by the lead of the electrons and muons travelling vertically downward.

To check for scattered electrons, mount a third paddle beside the lower paddle to detect electrons scattered out of the lead which make a small angle to the downward direction. You need to make sure the apparatus is set to count only upon receiving three (3) hits (“coincidence level” set at 3) and to do a custom run (5) after setting this. Again, 24 h is a suggestion of a reasonable time for data collection.

You might think that if you get any coincidences in this geometry there must be electrons scattered, but sometimes an experiment can teach us as much (or more) about our apparatus as the outside world we are trying to sample. It is presumably nearly simultaneous passage of a particle through the paddles which gets counted. It is possible, however, that multiple muons (or other charged energetic particles) could, by chance, pass through the detectors at very nearly the same time. Also remember that the photomultiplier tubes are converting and amplifying a very tiny amount of light into an appreciable voltage pulse using a fairly high voltage to do that. It is certainly possible that a fair amount of electrical noise exists in our apparatus and could result in spurious counts. You can check for noise by mounting this third paddle far away from the vertical arrangement such that it is very unlikely to be impacted by an ejected electron. If the results of this trial are indeed significantly lower than the previous trial, you may be encouraged that the hypothesis is true. You should make a long term measurement of the count rate in this configuration as a measurement of baseline noise level. This count rate, along with its uncertainty, should be subtracted from the count rates in the experiment (including uncertainties) before deciding about the validity of any count rate or count rate differences. 

Another check might be to mount the paddle detecting the supposed electrons beside the lower paddle as you had it, but to place a relatively thin sheet of aluminum (a few mm) or other material in front of this electron detecting paddle. That should cut down the number of electrons able to reach this paddle very significantly. Varying the material and its thickness could by quite interesting and constitute an experiment in itself.

You should check other scattering angles as well as the small angle. Since the paddles are quite large compared to the separation of elements in this setup, it will not be possible to set very precise angles, but surely you could try at something like 45° and 90°, and maybe 135° to check for the possibility of backscatter. Again, shielding the scattering detector should prove interesting and informative.

Remember that the uncertainty in each count rate in counts per hour needs to be figured if you wish to have any confidence in apparent differences. You might wish to convert each count to counts per hour by dividing the total counts by the total seconds and multiplying by 3600. To figure the uncertainty in each count rate you can take the square root of the number of counts and treat it the same way, dividing by the actual seconds and multiplying by 3600. You can be about 95% confident that two values are different if they differ by twice the square root of the sum of the squares of the calculated uncertainties.

Certainly it would be interesting to study the behavior as the amount of lead placed between the paddles is varied. Scattered electrons could easily b e self absorbed by thicker pieces of material.

It would also be interesting to change the orientation of the scattering material. The electrons scattered which we detect may be ones near the surface and if we orient the scattering material to present a large face to the scattering detector we may notice an enhanced detection of coincidences.

Also the actual material used as the scattering agent could be varied to see the effect.

[Note: This experiment, as several others, has not been carefully done, is open. You may have to vary the amount of lead, the geometry, the time of data collection, etc. It may not yield a clear result proving or disproving the hypothesis. That is the real attraction of these experiments.]