Problem 1

The Super-Kamiokande neutrino detector is a deep underground 40m thick tank of water surrounded by photomultiplier tubes. Approximately 10 photoelectrons are observed in the photomultipliers for each 1 MeV energy deposited in the water. Background events are produced by cosmic ray muons and gamma rays from natural radioactivity.
(a) Estimate the maximum energy of cosmic ray muons which stop in the tank. (b) Estimate the detector's standard deviation resolution, s/E, for measuring the energy of 2.6 MeV gamma rays from Tl²⁰⁸ decays.

The density of water (H₂O)is 1 g/cm³; the atomic weight and nuclear charge of hydrogen and oxygen are A=1, Z=1 and A=16, Z=8 respectively.

Problem 2

The total cross section for muon neutrino interactions with protons is

where K= 0.4¥10^-38 cm²/GeV² and s=E_cm² is the square of the c.o.m. energy of the neutrino proton interaction. What is the rate of interactions for a beam of 125 GeV neutrinos with an intensity of 1¥10¹¹ per second passing through a 1.7 metre long liquid hydrogen bubble chamber.

The density of liquid hydrogen is 0.063 g/cm³; the mass of a hydrogen atom is 1.7¥10^-24 g. Assume the diameter of the neutrino beam is less than the diameter of the bubble chamber.

Problem 3

Consider muons of momentum 20 MeV/c scattering from a uranium oxide (U₃O₈) target at with a scattering angle of 120°. (The scattering angle is the angle between the initial and final muon direction.)
(a) Why is scattering from oxygen nuclei negligible compared to the scattering from uranium nuclei?
(b) How large is the cross-section for scattering at 90° compared to the cross section for scattering at 120°?

The atomic weight and nuclear charge of oxygen and uranium are A=16, Z=8 and A=238, Z=92 respectively.

Problem 4

Neutrons decay into a proton, an electon, and an electron antineutrino. Why do neutrons decay but protons don't?