9.2 Problems 4979.61 In an experiment using a Cerenkov counter, one measures the kinetic energy of
a given particle species asE(kin)=420 MeV and observes that the Cerenkov
angle in flint glass of refractive index (μ= 1 .88) isθ=arc cos(0.55). What
particles are being detected (calculate their mass inmeunits)
9.62 Calculate the number of Cerenkov photons produced by a particle travelling
atβ= 0 .95 in water (n= 1 .33) in the response range (3500–5500 A) per unit
path length.
9.63 Estimate the minimum length of a gas Cerenkov counter that could be used
in threshold mode to distinguish between charged pions and charged kaons
with momentum 15 GeV/c. Assume that a minimum of 175 photons need to
be radiated to ensure a high probability of detection. Assume also that the radi-
ation covers the whole visible spectrum between 400 and 700 nm and neglect
the variation with wavelength of the refractive index of the gas (n= 1 .0004)9.64 What type of material would you choose for a threshold Cerenkov counter
which is to be sensitive to 900 MeV/c pions but not to 900 MeV/c protons.
9.2.8 SolidStateDetector................................
9.65 A depletion-layer detector has an electrical capacitance determined by the
thickness of the insulating dielectric. Estimate the capacitance of a silicon
detector with the following characteristics: area 1.5cm^2 , dielectric constant
10, depletion layer 40μm. What potential will be developed across the capac-
itance by the absorption of a 5.0 MeV alpha particle which produces one ion
pair for each 3.5 eV dissipated?9.2.9 Emulsions ........................................
9.66 The range of protons in C 2 emulsion is given in the following table (Range in
microns, energy in MeV). Draw a graph of the Range – Energy-Relation for
Deuterons and^3 He particles.R 0 50 100 150 200 250 300 350 400 450 500
E 0 2.32 3.59 4.61 5.48 6.27 7.01 7.69 8.32 8.91 9.47
9.2.10 Motion of Charged Particles in Magnetic Field .......
9.67 For a relativistic particle of charge e moving in a circular orbit of radiusrin
a magnetic fieldBperpendicular to the orbital plane, show thatp= 0 .3Br,
where the momentumpis in GeV/c andBin Tesla andrin metres.