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9 Particle Physics – I
G.M counter
E =
V
r ln(b/a)
(9.19)
where E is the electric field, V is the applied voltage, r is the distance from the
anode, b and a are the diameters of the cathode and anode.
Dead time of a counter(τ )
n =
n 0
1 − n 0 τ
(9.20)
where n = true counts, n 0 = observed counts.
Double source method
τ =
N 1 + N 2 − N 12 + B
2(N 1 − B)(N 2 − B)
(9.21)
where N 1 and N 2 are the counting rates from individual sources, N 12 is the counting
rate from the combined sources and B is the background counting rate.
Cerenkov counter
cos θ =
1
βn
(9.22)
where θ is the opening angle, n = index of refraction
Threshold velocity β =
1
n
(9.23)
9.2 Problems
9.2.1 System of Units
9.1 Show that 1 kg = 5.6 × 10
26 GeV/c
2
9.2 In the natural system of units ( = c = 1) show that
(a) 1 m = 5.068 × 10
15 GeV
−1
(b) 1 GeV
−2
= 0.389 mb
(c) 1 s = 1.5 × 10
24 GeV
−1
9.3 In the natural system of units show that
(a) The Compton wavelength for an electron is λ c = 1/m e
(b) The Bohr radius of a hydrogen atom is 1/α m e
(c) The velocity of an electron in the ground state of hydrogen atom is αc