376
7 Nuclear Physics – I
Motion of a charged particle in a magnetic field
Centripetal force = Magnetic force
mv
2
/ρ = qv B
(7.30)
Momentum P(GeV/c) = 0.3 Bρ
(7.31)
ρ is in meters and B is in Tesla
1 T = 10 k G
Cerenkov radiation
Electromagnetic radiation is emitted when a charged particle on passing through
a medium with a velocity v = βc which exceeds the phase velocity of light c/n,
where n is 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
cos θ = 1/ β n
(7.32)
Fig. 7.7 Cerenkov radiation
The threshold velocity
β (thresh) = 1/n
(7.33)
The number of photons radiated in the interval dE = h dν by a particle of charge
ze in track length dx is given by
d
2 N γ /dx dE = (α z
2
/c) [1 − (1/β
2 n
2 )]
(7.34)
Threshold Cerenkov counters can be used to discriminate between two relativistic particles of the same momentum p and different masses m 1 and m 2 , if the heavier
particle (m 2 ) is just below the threshold. In that case
sin
2
θ 1 ≈ (m 2
2
− m 1
2 )/ p
2
(7.35)