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• In a fixed-target experiment the target is usually a liquid or solid with a high density of individual target particles. In a colliding-beam experiment the “target” is one of the two beams, and the corresponding density is much lower. This means that colliding-beam experiments yield a much smaller number of events and are hence much harder to perform. Estimate the magnitude of this difference as follows: (a) Find the density of protons (number per unit volume) in a liquid hydrogen target. (The mass density of liquid hydrogen ≈ 0.07 g/cm3.) (b) Estimate the density of protons in a beam with the following characteristics: beam diameter ≈ 1 mm, beam current ≈ 1 A, speed of particles ≈ c. (c) Compare the “target” densities in the two types of experiment. (The rate of events depends on several other factors as well; nevertheless, low target density is one of the main problems to be overcome in colliding-beam experiments.)
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