A muon passing through the atmosphere is very likely to interact many times electromagnetically, but very unlikely to undergo a major nuclear interaction or be stopped outright.
The key point is that “interaction” can mean different things.
- Ordinary electromagnetic interactions — essentially certain
Because muons are charged, they continuously interact with atoms in the air by:
- ionizing molecules,
- exciting electrons,
- scattering slightly from nuclei.
A typical cosmic-ray muon loses about:
dE/dx ~= 2 MeV g^-1 cm^2
The whole atmosphere corresponds to about:
X_atm ~= 1030 g cm^-2
So a vertical muon typically loses on the order of a few GeV crossing the atmosphere. Since many cosmic muons are created with several GeV of energy, a large fraction survive to sea level.
So:
- probability of some interaction with air atoms: effectively 100%
- number of tiny interactions: billions
- Strong nuclear interactions — extremely rare
Muons are leptons, not hadrons, so they do not participate in the strong nuclear force the way protons or pions do.
A muon can occasionally interact directly with a nucleus, but the probability during one atmospheric transit is very small.
That is why muons are so penetrating:
- they can pass through kilometers of air,
- meters of rock,
- buildings and mountains.
- Being absorbed or stopped in the atmosphere
Whether a muon reaches the ground depends mostly on:
- its energy,
- its speed,
- relativistic time dilation.
At production altitude (~10-15 km), many muons would decay before reaching Earth if classical timing applied. But because they travel near light speed, relativistic effects greatly extend their observed lifetime.
Muon mean lifetime at rest:
tau_0 ~= 2.2 us
Without relativity, a muon traveling at nearly c would only go roughly:
d ~= c tau_0 ~= 660 m
Yet many reach the surface from >10 km altitude because of time dilation.
Roughly:
- about 10,000 muons per square meter per minute reach sea level,
- many more were produced higher in the atmosphere and decayed before arrival.
So the atmosphere is partially transparent to muons:
- constant weak interactions: guaranteed,
- catastrophic interaction: rare,
- survival to ground: common for energetic muons.