Detection of high-energy cosmic rays. Cosmic rays are rather difficult to detect

Question

Detection of high-energy cosmic rays. Cosmic rays are rather difficult to detect with semiconductor sensors for two main reasons. First, cosmic rays can have energies on the order of 10^18 eV or higher. Second, they are not a continuous flux, but rather individual events. But even at the lower end of their energy spectrum, cosmic rays are likely to penetrate through a sensor without generating carriers or generating too few for detection. In fact, detection is almost always indirect by detecting muons generated by cosmic rays as they collide with air or other matter. (Muons are high-energy charged particles with the charge of the electron but about 200 times heavier, and only exist for a period of a few microseconds.) Most muons have energies of about 4 GeV at the surface of the earth and about 6 GeV in the upper atmosphere, but some can have energies in excess of 100 GeV. Suppose one were to attempt to detect high-energy muons in the 100 GeV range using semiconductor sensors. Since semiconductor sensors would absorb little or no energy, it is essential to absorb the excess energy before the muons reach the sensor. This is done by placing the sensors deep under- ground, underwater, or by using thick layers of high-density materials in front of the sensor. Assuming that a germanium semiconducting sensor operates best below 10 MeV and the incoming muons have energy of 4 Gev: a. Calculate the depth at which the sensor should be placed underwater if the stopping power of water is 7.3 MeV middot cm^2g. Water has density of 1 g/cm^3. b. Calculate the thickness of a lead shield with a stopping power of 3.55 MeV middot cm^2/g and density of 11.34 g/cm^3.

Explanation / Answer

Stopping power is the retarding force that acts on a charged particle while passing through the medium. It is expressed as energy loss per unit path length.

a) stopping power of water   S = 7.3 Mev-cm2/g  

                                                  = 7.3 Mev/cm ( density of water = 1 g/cc, multiply with density we get linear stopping power)

The stopping power as given is const over the nergy range from 4Gev to 10 Mev,

S= dE/dx = 7.3 Mev/cm

dx = 4.0e+3/10 = 400 cm

The detctor shall be placed below a depth of 4 m or more under water to detect the muons

b) lead shield

stopping power S = 3.55 Mev-cm2/g = 3.55 *11.34 Mev/cm

                              = 40.26 Mev/cm

dx = 4.0e+3/40.26 = 99.35 cm

thickness of lead shielding required is 99.35 cm or more.

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