9.2 Problems 491
9.18 From the data given calculate the mass of the hyper-fragmentΛHe^5
Mass ofΛhyperon is 1115.58 MeV/c^2 ,MassofHe^4 is 3727.32 MeV/c^2
Binding energyBΛfor He^5 is 3.08 MeV
[University of Dublin 1968]
9.19 Show that for a high energy electron scattering at an angleθ,thevalueofQ^2
is given approximately by
Q^2 = 2 EiEf(1−cosθ)
whereEiandEfare 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 processK+→π+π^0 with theK+at rest. Find
(a) the total energy of theπ^0 meson
(b) its relativistic kinetic energy
The rest mass energy is 494 MeV forK+, 140 MeV forπ+, 135 MeV forπ^0.9.21 A collimated beam ofπ-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) witha= 9. 1 × 10 −^2 m−^1. Hence calculate
the life time of theπ-meson (Rest energy of theπ-meson 139 MeV)
[University of Durham 1960]
9.22 One of the decay modes ofK+mesons isK+→π++π++π−. What is the
maximum kinetic energy that any of the pions can have, if theK+decays at
rest? GivenmK= 966. 7 meandmπ= 273 .2me
9.23 Show that the energy of the neutrino in the pion rest frame,Eν′, can be written
in natural units as
E′ν=(
m^2 π−m^2 μ)
/ 2 mπwheremπandmμare the masses of the charged pion and the muon, respec-
tively. (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 ofΣ+hyperon at rest via the
scheme,Σ+→n+μ++νμ. The masses ofΣ+,n,μ+andνμare 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 neu-
trino. 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 )