496 9 Particle Physics – I
combined capacitance of 45 PF. If an 8-mV output pulse is desired whenever a
55-keV beta particle is incident on the crystal, calculate the electron multipli-
cation required per stage. Assume perfect light collection and a photo-cathode
efficiency of 5% (assume 550 photons per beta particle)9.55 Figure 9.1 shows the gamma-ray spectrum of^22 Na in NaI scintillator. Indicate
with explanation the origin of the parts labeled as A, B, C, D and E, Given that
(^22) Na is a positron emitter and emits aγ-ray of 1.275 MeV.
Fig. 9.1
9.56 Assuming that the shape of the photpeak in the scintillation counter is described
by the normal distribution, show that the half width at half-maximum is
HWHM= 1. 177 σ
9.57 The peak response to the 661 keV gamma rays from^137 Cs occurs in energy
channel 298 and 316. Calculate the standard deviation of the energy, and the
coefficient of variation of the energy determination, assuming the pulse ana-
lyzer to be linear.
9.2.7 Cerenkov Counter ................................
9.58 Explain what is meant by Cerenkov radiation. How may a Cerenkov detector
distinguish between a kaon and a pion with the same energy? A pion of energy
20 GeV passes through a chamber containing CO 2 at STP. Calculate the angle
to the electron’s path with which the Cerenkov radiation is emitted. (Use the
result that the velocity of a relativistic particlev=c(1−γ−^2 )^1 /^2 .[Massof
pion=140 MeV,Mp=938 MeV; refractive index of CO 2 at STP= 1 .0004]
9.59 An electron incident on a glass block of refractive index 1.5 emits Cerenkov
radiation at an angle 45◦to its direction of motion. At what speed is the elec-
tron travelling?
[University of Cambridge, Tripos 2004]
9.60 Consider Cerenkov radiation emitted at angleθrelative to the direction of a
charged particle in a medium of refractive indexn. Show that its rest mass
energymc^2 is related to its momentum bymc^2 =pc(n^2 cos^2 θ−1)^1 /^2