6.2 Problems
331
6.114 A positron–electron pair production can occur in the interaction of a gamma
ray with electron, via γ + e
−
→ e
−
+ e
+
+ e
− . Determine the threshold.
6.115 Find the threshold energy for the pion production in the reaction N + N →
N + N + π, given
M N c
2
= 940 MeV and m π c
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 for K
∗ 890 MeV, for Λ 1,110 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
m e and 1,837 m e , where the rest energy of the electron m e c
2
= 0.51 MeV
[University of Manchester 1959]
6.119 Calculate the threshold energy of the following reaction π
−
+ p → K
0
+ Λ
The masses for π
− and p, K
0 and Λ are, 140, 938, 498, 1,115 MeV respectively
6.120 Show that the threshold kinetic energy in the Laboratory for the production
of n pions in the collision of protons with a hydrogen target is given by
T = 2nm π (1 + nm π /4m p )
where m π and m p are 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 M p = 940 MeV and M π = 135 MeV
6.122 Calculate the threshold energy of the reaction
π
−
+ p → Ξ
−
+ K
+
+ K
0
The masses for π
−
, 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, the W
+ ,
using the reaction ν + 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 the W
+
(mass of proton 938 MeV/c
2 , mass of muon 106 MeV/c
2 , neutrino has zero
rest mass)
[University of Manchester 1972]
331
6.114 A positron–electron pair production can occur in the interaction of a gamma
ray with electron, via γ + e
−
→ e
−
+ e
+
+ e
− . Determine the threshold.
6.115 Find the threshold energy for the pion production in the reaction N + N →
N + N + π, given
M N c
2
= 940 MeV and m π c
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 for K
∗ 890 MeV, for Λ 1,110 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
m e and 1,837 m e , where the rest energy of the electron m e c
2
= 0.51 MeV
[University of Manchester 1959]
6.119 Calculate the threshold energy of the following reaction π
−
+ p → K
0
+ Λ
The masses for π
− and p, K
0 and Λ are, 140, 938, 498, 1,115 MeV respectively
6.120 Show that the threshold kinetic energy in the Laboratory for the production
of n pions in the collision of protons with a hydrogen target is given by
T = 2nm π (1 + nm π /4m p )
where m π and m p are 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 M p = 940 MeV and M π = 135 MeV
6.122 Calculate the threshold energy of the reaction
π
−
+ p → Ξ
−
+ K
+
+ K
0
The masses for π
−
, 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, the W
+ ,
using the reaction ν + 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 the W
+
(mass of proton 938 MeV/c
2 , mass of muon 106 MeV/c
2 , neutrino has zero
rest mass)
[University of Manchester 1972]