• Go to >
• SLAC Home |
• SLAC Today |
• For Staff |
• For Users
  
• Photon Science |
• Particle Physics and Astrophysics |
• Operations

Cosmic Ray Detector - Data Center Guided Tour Stop 3

Comparing muon count rates at different altitudes

Muons are created in the upper atmosphere by "primary" cosmic rays, mostly protons that come from deep space. Interactions of these cosmic ray protons with nuclei in the upper atmosphere create pions which then decay into muons. These highly energetic muons interact only weakly with the air and have a mean life time long enough for some to arrive at the Earth's surface.

In this section we will compare data rates taken at various altitudes. From the results, an estimate of the muon mean life time is possible.

Steve Kliewer, a teacher who participated in SLAC's Particles and Interactions Workshop, was interested in learning more about muons from cosmic rays. Steve and his colleague Jean Roberts proposed and received approval for a small cosmic ray experiment from NASA. They took one of SLAC's portable cosmic ray detectors up on the Kuiper Airborne Observatory, an airplane that was operated by NASA until 1999. They measured cosmic ray count rates at altitudes up to 41,000 feet. Steve also took the cosmic ray detector up Mauna Kea, an extinct 13,700 ft tall volcano on the big island of Hawaii. In the picture, you see him and Jean and a KAO staff member standing in front of the aircraft.

Note:

The cosmic ray detector Steve used was slightly different from the detector in SLAC's Visitor Center. The detector Steve used had different size panels with a different distance between them. Also, Steve measured cosmic rays only in the vertical direction.

Below is a combined table of Steve's measurements on board the airplane, as well as at various altitudes on the way to the top of Mauna Kea.

We can now draw Steve's data in the following graph:

The vertical scale in the plot shows the measured count rate in counts per minute, and the horizontal scale the altitude in feet. The vertical scale is logarithmic, i.e. the divisions are 1, 10, 100, and 1000 in equal distances.

What we clearly see is that muons disappear: the count rate of muons decreases as we move lower in altitude.

The graph has three curves plotted on it in the following form:

R = R₁ e^-(h₁-h)/H

for three values of H: 6,000 ft, 12,000 ft and 18,000 ft. On a logarithmic plot, such curves show up as straight lines. The data fit the red curve for H = 12,000 ft pretty well, given the expected errors. If you set H = 12000 ft (since it is the best fit), then when h₁ - h = 12000 ft the formula for R will read:

R = R₁e^{-(12000)/12000} = R₁e^-1 = R₁/e

So the rate R after having traveled 12000 feet from altitude h₁ is the rate at altitude R1 divided by e (e = 2.718...). Or, the rate has decreased to 1/e of the original rate.

A muon going at the speed of light will traverse 12,000 ft in about 12 microseconds. So we might conclude that if muons only disappear because they decay, then their "mean" life (defined by the time it takes for all but a fraction 1/e to still be there) is of the order of 12 microseconds. From other experiments we know, however, that the mean life of muons at rest is really only 2 microseconds!

The reason for this lies (mostly) in the fact that Einstein's theory of relativity says that clocks in fast-moving systems go slower. The muons are fast moving, but they measure their time with a clock that looks to us as if it is slow by a factor six. This relativistic effect is called time dilation.

Go to Tour Stop #4
(A model of cosmic ray production in the upper atmosphere)