6.2 Problems 331
6.114 A positron–electron pair production can occur in the interaction of a gamma
ray with electron, viaγ+e−→e−+e++e−. Determine the threshold.
6.115 Find the threshold energy for the pion production in the reactionN+N→
N+N+π,given
MNc^2 =940 MeV andmπc^2 =140 MeV
6.116 Show that a Fermi energy of 25 MeV lowers the threshold incident kinetic
energy for antiproton production by proton incident on nucleus to 4.3 GeV.
6.117 Find the threshold energy of the reaction
γ+p→K+
∗
+Λ
The laboratory proton is at rest. The following rest energies may be assumed,
for proton 940 MeV forK∗890 MeV, forΛ1,110 MeV
6.118 Find the threshold energy for the production of two pions by a pion incident
on a hydrogen target. Assume the rest masses of the pion and proton are 273
meand 1,837me, where the rest energy of the electronmec^2 = 0 .51 MeV
[University of Manchester 1959]
6.119 Calculate the threshold energy of the following reactionπ−+p→K^0 +Λ
The masses forπ−andp,K^0 andΛare, 140, 938, 498, 1,115 MeV respec-
tively
6.120 Show that the threshold kinetic energy in the Laboratory for the production
ofnpions in the collision of protons with a hydrogen target is given by
T= 2 nmπ(1+nmπ/ 4 mp)
wheremπandmpare respectively the pion and proton masses.
6.121 A gamma ray interacts with a stationary proton and produces a neutral pion
according to the scheme
γ+p→p+π^0
Calculate the threshold energy given Mp=940 MeV andMπ=135 MeV
6.122 Calculate the threshold energy of the reaction
π−+p→Ξ−+K++K^0
The masses forπ−,p,Ξ−,K+,K^0 are respectively 140, 938, 1,321, 494,
498, MeV
[University of Durham 1970]
6.123 Attempts have been made to produce a hypothetical new particle, theW+,
using the reactionν+p→p+μ−+W+where stationary protons are
bombarded with neutrinos. If a neutrino energy of 5 GeV is not high enough
for this reaction to proceed, estimate a lower limit for the mass of theW+
(mass of proton 938 MeV/c^2 , mass of muon 106 MeV/c^2 , neutrino has zero
rest mass)
[University of Manchester 1972]