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What qualities of a radiator are important if I want to build a Cherenkov detector to detect muons? I don't know how to choose the most appropriate. Possibilities would include ice, water, maybe aerogel, anything I can easily get my hands on. I know water is most typically used, but is it worth exploring other options?

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The parameters that matter are

  • Index of refraction Which controls what speeds generate light ($v \gt \frac{c}{n}$), the opening angle of the cone of light generated, and the geometry for possible total internal reflection (TIR) of the light so generated (TIR can be necessary or a problem depending on the geometry you intend for your detector).

    Keep in mind that index of refraction is a frequency dependent quality. We are most interested in the value in the blue end of the optical and the near UV.

  • The path length through the material (yeah, length rather than areal density which dominated for other processes) which affects how much light is generated.

  • The transparency of the medium to the Cerenkov light. Especially if your geometry creates long optical paths in the radiator medium (designs where you take advantage of TIR to transmit the light out of the beam path can have this 'feature').

And the thing about this is that the values that you want are all a matter of design decisions for a particular case.

We can't give you hard and fast rules that apply to all designs. You really need to understand what your detector is designed to do.

But the easiest decision is usually the threshold velocity and that feeds into selecting the desired index of refraction range.

  • Most solids have $n \gtrsim 1.4$ which implies $v_\text{threshold} \ge 0.7c$
  • Most liquids have $n \gtrsim 1.2$ which implies $v_\text{threshold} \ge 0.8c$
  • Gasses and aerogels usually have low index of refraction meaning threshold velocities near $c$ and are often used for $0.9c < v_\text{threshold} < c$.
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