9.2 Problems
491
9.18 From the data given calculate the mass of the hyper-fragment Λ He
5
Mass of Λ hyperon is 1115.58 MeV/c
2 , Mass of He
4 is 3727.32 MeV/c
2
Binding energy B Λ for He
5 is 3.08 MeV
[University of Dublin 1968]
9.19 Show that for a high energy electron scattering at an angle θ , the value of Q
2
is given approximately by
Q
2
= 2E i E f (1 − cos θ)
where E i and E f are the initial and final values of the electron energy and
Q
2 is the four-momentum transfer squared. State when this approximation is
justified.
9.2.4 Decay
9.20 Consider the decay process K
+
→ π
+
π
0 with the K
+ at rest. Find
(a) the total energy of the π
0 meson
(b) its relativistic kinetic energy
The rest mass energy is 494 MeV for K
+ , 140 MeV for π
+ , 135 MeV for π
0 .
9.21 A collimated beam of π-mesons of 100 MeV energy passes through a liquid
hydrogen bubble chamber. The intensity of the beam is found to decrease with
distance s along its path as exp(-as) with a = 9.1 × 10
−2 m
−1 . Hence calculate
the life time of the π-meson (Rest energy of the π-meson 139 MeV)
[University of Durham 1960]
9.22 One of the decay modes of K
+ mesons is K
+
→ π
+
+ π
+
+ π
− . What is the
maximum kinetic energy that any of the pions can have, if the K
+ decays at
rest? Given m K = 966.7 m e and m π = 273.2 m e
9.23 Show that the energy of the neutrino in the pion rest frame, E
ν , can be written
in natural units as
E
ν =
m
2
π − m
2
μ
/2m π
where m π and m μ are the masses of the charged pion and the muon, respectively. (You may assume here that the neutrino mass is negligible)
[University of Cambridge, Tripos 2004]
9.24 Find the maximum energy of neutron in the decay of Σ
+ hyperon at rest via the
scheme, Σ
+
→ n + μ
+
+ ν μ . The masses of Σ
+
, n, μ
+ and ν μ are 1, 189 MeV,
939 MeV, 106 MeV and zero, respectively.
9.25 A charged kaon, with an energy of 500 MeV decays into a muon and a neutrino. Sketch the decay configuration which leads to the neutrino having the
maximum possible momentum, and calculate the magnitude of this value
(mass of charged kaon is 494 MeV/c
2 , mass of muon is 106 MeV/c
2 )
491
9.18 From the data given calculate the mass of the hyper-fragment Λ He
5
Mass of Λ hyperon is 1115.58 MeV/c
2 , Mass of He
4 is 3727.32 MeV/c
2
Binding energy B Λ for He
5 is 3.08 MeV
[University of Dublin 1968]
9.19 Show that for a high energy electron scattering at an angle θ , the value of Q
2
is given approximately by
Q
2
= 2E i E f (1 − cos θ)
where E i and E f are the initial and final values of the electron energy and
Q
2 is the four-momentum transfer squared. State when this approximation is
justified.
9.2.4 Decay
9.20 Consider the decay process K
+
→ π
+
π
0 with the K
+ at rest. Find
(a) the total energy of the π
0 meson
(b) its relativistic kinetic energy
The rest mass energy is 494 MeV for K
+ , 140 MeV for π
+ , 135 MeV for π
0 .
9.21 A collimated beam of π-mesons of 100 MeV energy passes through a liquid
hydrogen bubble chamber. The intensity of the beam is found to decrease with
distance s along its path as exp(-as) with a = 9.1 × 10
−2 m
−1 . Hence calculate
the life time of the π-meson (Rest energy of the π-meson 139 MeV)
[University of Durham 1960]
9.22 One of the decay modes of K
+ mesons is K
+
→ π
+
+ π
+
+ π
− . What is the
maximum kinetic energy that any of the pions can have, if the K
+ decays at
rest? Given m K = 966.7 m e and m π = 273.2 m e
9.23 Show that the energy of the neutrino in the pion rest frame, E
ν , can be written
in natural units as
E
ν =
m
2
π − m
2
μ
/2m π
where m π and m μ are the masses of the charged pion and the muon, respectively. (You may assume here that the neutrino mass is negligible)
[University of Cambridge, Tripos 2004]
9.24 Find the maximum energy of neutron in the decay of Σ
+ hyperon at rest via the
scheme, Σ
+
→ n + μ
+
+ ν μ . The masses of Σ
+
, n, μ
+ and ν μ are 1, 189 MeV,
939 MeV, 106 MeV and zero, respectively.
9.25 A charged kaon, with an energy of 500 MeV decays into a muon and a neutrino. Sketch the decay configuration which leads to the neutrino having the
maximum possible momentum, and calculate the magnitude of this value
(mass of charged kaon is 494 MeV/c
2 , mass of muon is 106 MeV/c
2 )