1000 Solved Problems in Modern Physics

376 7 Nuclear Physics – I

Motion of a charged particle in a magnetic field

Centripetal force=Magnetic force

mv^2 /ρ=qvB (7.30)

MomentumP(GeV/c)= 0. 3 Bρ (7.31)

ρis in meters andBis in Tesla

1T= 10 kG

Cerenkov radiation

Electromagnetic radiation is emitted when a charged particle on passing through
a medium with a velocityv=βcwhich exceeds the phase velocity of lightc/n,
wherenis the index of refraction, the radiation is instantaneous and possesses a
sharply pronounced spatial symmetry.
The radiation is soft and is mostly emitted in the blue part of the spectrum. The
radiation is emitted on a conical surface BDA, as in Fig. 7.7

cosθ= 1 /βn (7.32)

Fig. 7.7Cerenkov radiation

The threshold velocity

β(thresh)= 1 /n (7.33)

The number of photons radiated in the interval dE=hdνby a particle of charge
ze in track length dxis given by

d^2 Nγ/dxdE=(αz^2 /c)[1−(1/β^2 n^2 )] (7.34)

Threshold Cerenkov counters can be used to discriminate between two relativis-
tic particles of the same momentumpand different massesm 1 andm 2 , if the heavier
particle (m 2 ) is just below the threshold. In that case

sin^2 θ 1 ≈(m 22 −m 12 )/p^2 (7.35)