488 9 Particle Physics – I
G.M counter
E=V
rln(b/a)(9.19)
whereEis the electric field,Vis the applied voltage,ris the distance from the
anode,bandaare the diameters of the cathode and anode.
Dead time of a counter(τ)
n=n 0
1 −n 0 τ(9.20)
wheren=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)
whereN 1 andN 2 are the counting rates from individual sources,N 12 is the counting
rate from the combined sources andBis the background counting rate.
Cerenkov counter
cosθ=1
βn(9.22)
whereθis the opening angle,n=index of refraction
Threshold velocityβ=1
n(9.23)
9.2 Problems..................................................
9.2.1 SystemofUnits ...................................
9.1 Show that 1 kg= 5. 6 × 1026 GeV/c^2
9.2 In the natural system of units (=c=1) show that
(a) 1 m= 5. 068 × 1015 GeV−^1
(b) 1 GeV−^2 = 0 .389 mb
(c) 1 s= 1. 5 × 1024 GeV−^1
9.3 In the natural system of units show that
(a) The Compton wavelength for an electron isλc= 1 /me
(b) The Bohr radius of a hydrogen atom is 1/αme
(c) The velocity of an electron in the ground state of hydrogen atom isαc