(a) A 1 MeV fast electron passes across the 0.3 mm diameter of a plastic fiber s
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Question
(a) A 1 MeV fast electron passes across the 0.3 mm diameter of a plastic fiber scintillator. From the data given in Chapter 2, estimate the deposited energy. (b) Assuming a reasonable scintillation efficiency, calculate the corresponding number of scintillation photons created along the track. (c) The refractive index for the core and the cladding are 1.58 and 1.49, respectively, and the fiber has an attenuation length of 2 m. Estimate the number of scintillation photons arriving at one end of the fiber that is 1 m from the point of interaction.Explanation / Answer
(a). A 1 MeV electron passes across a 0.3 mm or 0.03cm scintillating plastic fiber. Using data from Chapter 2, the range is about 7 mm for (assuming a density of ~1 g /cm3). For minimum ionizing particles such as fast electrons, the specific energy loss is about 2 MeV/cm, considering the density of air is 1.293 g/cm3 at STP and that of plastic is about 1 g/cm3. Therefore, the energy loss in .03 cm is about 60 keV.
(b). Using data from Table 8.5, the estimated number of photons are ~10 photons/keV. Thus, the total number of scintillation photons is only ~600 photons.
(c). The fraction (F) of captured light which is passed to one end (without attenuation) is calculated using the ratio of the indices of refraction of the core and clad materials.
F = ½ (1-n1/n0)
Substituting, n1 = 1.49 and n0 = 1.58, we get F = 0.0285.
The light is attenuated exponentially along its travel direction, with an attenuation length of 2 m. We can estimate the number of photons emerging from one end after traveling 1 m using the equation
I/I0 = exp(-x/L)
where x = 1 m and L = 2 m, and multiplying the result of this by the fraction calculated above and the number of photons originally created.
scintillation photons arriving 1 m from the point of interacion = 600 F exp(-1/2) = 10.4
Thus, our total light output arriving at our light sensor is only ~10 photons! Clearly, low-noise, high-efficiency photon detectors are needed to recognize such a small signal.
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