How did he calculate the probabilities?

[Urvabara]

www.particle.kth.se/SEASA/ph_exjobb.pdf (page 24/48)
"The smallest showers detectable with a reasonable probability over a larger area are $$10^{16}$$ eV showers. A lower shower counting rate for the setup can be deduced by only considering showers with this energy. A $$10^{16}$$ eV -shower is detected with a probability of 0.86 at 0 m distance, 0.12 at 100 m, and with zero probability at larger distances. This can be simplified to a probability $$P = \frac{0.86+0.12}{2} = 0.49$$ to detect a shower hitting within 100 m of the center, and zero probability outside this region. This collecting area is then 31415 m$$^{2}$$."

How did he calculate the probabilities 0.86, 0.12 and 0? Please explain, this is so important...

 

[Urvabara]

How did he calculate the probabilities 0.86, 0.12 and 0? Please explain, this is so important...

Never mind...

 

[sir-pinski]

The author calculated the probabilities based on the detection efficiency of the setup for a 10^{16} eV shower at different distances from the center. This information was likely obtained through experimental measurements or simulations.

At 0 m distance, the probability of detecting a 10^{16} eV shower is 0.86, meaning that if a shower hits directly at the center of the setup, there is a high chance of it being detected.

At 100 m distance, the probability decreases to 0.12, indicating that the detection efficiency decreases as the distance from the center increases. This could be due to factors such as energy loss or scattering of the particles in the shower.

Beyond 100 m, the probability drops to zero, meaning that there is no chance of detecting a 10^{16} eV shower at distances larger than 100 m from the center.

To simplify the calculation, the author took the average of the probabilities at 0 m and 100 m, which is (0.86+0.12)/2 = 0.49. This means that there is a 49% chance of detecting a 10^{16} eV shower within 100 m of the center.

Based on this probability, the author then calculated the collecting area of the setup to be 31415 m^{2}. This is the area within which a shower has a 49% chance of being detected.

In summary, the probabilities were calculated based on the detection efficiency of the setup at different distances from the center, and the average probability was used to determine the collecting area.