(a) Write down a relationship between a particle's energy, mass and momentum using relativistic kinematics.
Estimate the minimum centre of mass energy required for the following reaction to take place:
e^+ + e^- -> e^+ + ̄̄̄ + ̄̄̄ + e^-.
The electron mass is 0.5 MeV/c^2 and the tau mass is 1776 MeV/c^2.
Find the minimum energy the positron must have for the above reaction to take place if it collides with a stationary electron.
(b) Explain the s and r processes, which produce heavy elements in stars. Include in your answer the role of ̂-decay and the equations of the nuclear reactions.
Explain why the s process occurs in normal stellar nucleosynthesis whereas the r process is most common in supernovae?
(c) A particle has spin 3/2 and is made up of 3 s quarks, which lie in the ground state energy level.
What is the charge and strangeness of the particle?
Explain why the existence of this particle supports evidence that quarks possess the colour quantum number.
The most probable decay of the particle is to a Ι, which has quark structure uds, and a K^-, which has quark structure ̄us. Draw the Feynman diagram for this decay.
(d) List 3 assumptions used to derive the Rutherford scattering formula
A beam of ̂ particles with kinetic energy T=4 MeV and current 10^6 particles per second is incident on a gold (197/79 Au) foil of thickness 2 m. Calculate the number of hits per second on a detector of area 1 cm^2 situated 100 cm from the foil at 25.
[The Rutherford scattering formula is given by d̂/d̂ = (Zze^2 / 16̂̂_0 T sin^2(̂/2))^2, where the symbols have their usual meanings. Gold has a density of 19.310^3 kg m^-3.]