1. Using Monte Carlo, evaluate the integral
0∫2Π (sinθ/θ)dθ
Explain the method as well as the interpretation of the result. Quote your answer with uncertainty to within the 95% confidence interval (2σ).
2. An exotic particle, the omicron, interacts with water through complete absorption. A 10MeV omicron traversing 1cm of water has a 12% chance of being absorbed. If a beam of 10MeV omicrons is fired through a 20cm block of water:
a) What percentage of the omicron beam passes completely through the block?
b) What percentage of the omicron beam is absorbed in the final 4cm of the block?
c) What thickness of water is required to absorb approximately 83% of the beam?
(Compare results with theoretical calculations)
3. A 3cm diameter circular beam of 1MeV photons is incident on the centre of a face of a cube of water with side lengths of 30cm. At the centre of the water cube is a cubic Germanium detector, with side lengths of 1cm and the same orientation as the water cube.
In water, photons of this energy range have a 0.1% chance of being fully absorbed every mm (photoelectric effect) and a 2% chance they are scattered every mm. Scattering events result in the photons travelling in a random direction and losing between 5 to 20% of their energy (linearly distributed).
Any photon hitting the Germanium detector is completely absorbed. Any photon leaving the water cube is discarded. Using Monte Carlo, simulate the scenario with a lower energy limit for photon transport of 1keV.
What is the average energy deposited in the Germanium detector per primary photon simulated? Give an estimate of the error to the 95% confidence interval. You may use the sample solution to the week 4 question 3 problem as a template.