490 9 Particle Physics – I9.11 Estimate the thickness of iron through which a beam of neutrinos with energy
200 GeV must travel if 1 in 10^9 of them is to interact. Assume that at high
energies the neutrino-nucleon total cross-section is 10−^42 Eνm^2 , whereEνis
the neutrino energy is in GeV. The density of iron is 7,900 kg m−^3 .[Massof
nucleon= 1. 67 × 10 −^27 kg.]9.12 (a) The cross-section for scattering of muons with air at atmospheric pressure
is 0.1 barns, and the natural lifetime of muons 2. 2 × 10 −^6 s. Explain what
is meant by the terms elastic scattering and lifetime. Which of these fac-
tors limits the distance over which a beam of muons can travel in air in a
laboratory, if the muon velocity is 10^6 ms−^1?
(Assume number density of air at STP= 2. 69 × 1025 m−^3 )
(b) Given your answer to (a), why is it possible to detect showers of muons at
ground level caused by the impact of primary cosmic ray particles with air
at around 12 km altitude? Given that the mean energy of muons detected
at ground level is≈4 GeV, calculate the distance (in air) over which the
number of such muons in a beam would reduce by a factor ofe. What kind
of interactions contribute to the scattering cross-section for these particles?
[1 barn= 10 −^28 m^2 ; mass of muon=105 MeV/c^2 ; number density of air
at STP= 2. 69 × 1025 m−^3 ]
9.13 Obtain an approximate value for the interaction length (in cm) of a fast proton
in lead from the following data:r 0 = 1. 3 × 10 −^13 cm, Atomic weight of lead=
207, Density of lead= 11 .3gcm−^3 , Avogadro’s number= 6 × 1023 molecules
mole−^1
[University of Durham 1962]9.14 A liquid hydrogen target of volume 125 cm^3 and density 0.071 g cm−^3 is
bombarded with a mono-energetic beam of negative pions with a flux 2×
107 m−^2 s−^1 and the reactionπ−+p→π^0 +nobserved by detecting the
photons from the decay of theπ^0. Calculate the number of photons emitted
from the target per second if the cross-section is 40 mb.9.15 A beam ofπ+mesons contaminated withμ+mesons is passed through an
iron absorber. Given that the interaction cross-section ofπ+mesons with
iron is 600 mb/nucleus, calculate the thickness of iron necessary to attenuate
theπ+beam by a factor of 500. Explain why muons will be reduced to a
much less extent. (The density of iron is 7,900 kg m−^2 , the atomic mass being
55.85 amu)9.16 A neutrino of high energy (E 0 >>m) undergoes an elastic scattering with
stationary electron of massm. The electron recoils at an angleφwith energy
T. Show that for small angle,φ=(2m/T)^1 /^2
9.17 Why the following reactions can not proceed as strong interactions
(a)π−+p→K−+Σ+
(b)d+d→^4 He+π^0?