Does Muon Rate Depend on the Angle to the Vertical?

Introduction:

By this point, you have probably read or been told that muons result from cosmic rays coming from outer space.  When we talk about rays in physics, we think of straight up and down as being ninety degrees, and horizontal as being zero degrees.  Based on this, would you expect to see muon rate change with the angle of the detectors?  In what way?  That is to say, at what angle(s) would the rate be at a maximum?  A minimum?  Would the rate change evenly at all points between zero and ninety degrees (is the relationship linear)?

Procedure:

1.       Position two paddles for detection of vertically traveling muons.  (90º)

2.       Do a coincidence run.

3.       Keeping the paddles the same distance away from one another and their surfaces parallel to one another, rotate the setup to another angle.  Repeat steps 2 and 3 until you have enough data points to make a reasonable graph.  Be sure to include a run at 0º (paddles set to detect horizontally traveling muons).

Analysis:

Calculate muon rates and uncertainty in the rates.  Make a graph of rate versus angle that includes uncertainty bars on each point.

Extension:  Muon Rate for Various Angles With and Without a Lead Absorber

Muons coming from near horizontal directions have traveled a longer path through the atmosphere.  See the diagram below.   These muons may be more or less energetic than muons that have traveled vertically through the atmosphere to reach our apparatus.  This means that they may be harder or easier to block with a shielding material, such as lead.

 The dark ball represents the earth, the clear circle the atmosphere, and the arrows represent paths of muons.

To test your hypothesis, repeat your experimental procedure from before, but this time, place a bundle of lead between your paddles.   Be sure to do a control run (without lead), probably in the ninety degree position.

Analysis

If  your control run is significantly different from the first experiment, use this control value to normalize your data.  Graph the attenuated muon rate versus the angle from the vertical, including uncertainty bars.

Compare this graph to your first one.  Try to determine how the lead affected the flux at the various angles. You might wish to subtract the attenuated flux from the unattenuated flux and plot this difference as a function of angle. It might be helpful to figure the percentage reduction at each angle and plot this as a function of angle. Does the lead seem to be equally effective at each angle tested? Is the rate decreased by the same percentage in each case?