Many thousands of muons Mue hit the surface of the earth eac

Many thousands of muons (Mue) hit the surface of the earth each second. They ate created in the upper atmosphere due to high energy cosmic rays. Your task is to design an apparatus, to measure the velocity spread of the muons as they strike the earth. the average kinetic energy of the particles is 4GeV and they have a mass approximately 207 time that electron and have the same charge as an electron. A particle detector which can count individual particles that strike it is provided for you. It has a small detection surface of 1 mm^2. What is your design? What is the velocity selection width? (resolution) How are you going to control the selection of velocity to look at?

Solution

Design:

Proton ------>(upper atmosphere)------> muon ------> plastic scintilator ------> photon ------> photomultiplier tube ------> electron -----> DAQ

The following empirical formula gives a good approximation to the number at sea level as a function of zenith angle:

I()=Iv cos²()

Where Iv = 0.0083 cm^-2 s^-1 sr^-1 and is the zenith angle (Rossi 1948).

dN = I() d dA dt

is the number of muons incident on differential area dA during the time dt within the solid angle d from the direction normal to dA. Integrating this function over the appropriate solid angle, the total flux from all directions can be estimated.

v = D/(Td - Tu)
where D is the difference in the mean slant distance traveled by the muons from the top to the middle paddle
in the down and up positions. The time of flight between the two counters is given Td - Tu = D/v.