PHY357S: Monday, 6 January 1997

Problem Set 1

due Wednesday, 22 January 1997

These questions are based on Chapters 1-5 and the Appendices of Frauenfelder and Henley.
If you have any questions about these problems, ask me - preferably before the evening of 19 January. You can contact me at dbailey@physics.utoronto.ca, Room 919, or at 978-4993.

Each problem is of equal weight, but not all problems may be marked.

Problem 1

The Fermilab Tevatron superconducting synchrotron is currently the world's highest energy particle accelerator. Assume the synchrotron has radius of 1 km, a maximum dipole magnetic field of 3.3T, and enough rf cavities to accelerate protons by 1 MeV per orbit. (a) What is the maximum momentum to which a proton could be accelerated in the Tevatron? (b) What is the maximum momentum to which an electron could be accelerated?

Problem 2

(a) Like germanium or silicon, carbon in the form of diamond is also a semiconductor, so it is possible to build diamond particle detectors. The energy needed to produce an ion pair in diamond is W=5eV. Estimate the energy resolution of a diamond semiconductor detector for 100 KeV x-rays. (b) Diamonds are a bit expensive for large detectors; cheaper and denser materials are usually used. Estimate how many metres thick a detector made from iron would need to be to completely absorb a 24 GeV electron? (i.e. How thick must it be so the electron shower dies within the detector.) (c) How thick an iron detector is needed to stop a 24 GeV muon?

Problem 3

Consider the following interaction observed by University of Toronto physicists working on the ZEUS experiment at the DESY laboratory in Hamburg, Germany.

In this interaction a 29 GeV/c electron collides head-on with an 800 GeV/c proton, producing an electron, a positive muon, a negative muon, and a bunch of other stuff (denoted X). The vector momentum (in GeV/c) of the intial electron and proton are (0,0,-29) and (0,0,800) GeV/c; the vector momenta of the final state e-, µ+ and µ- are (0,-5,26), (20,3,55), and (10,1,55) respectively.

(a) What is the centre-of-mass energy, Ecm, of the collision?

(b) Is the µ+ µ- pair consistant with being produced by the decay of a meson? (Asume the uncertainty on the µ+ µ-mass is 10%.) Is the pair consistent with being produced by the decay of any other known subatomic particle listed in Tables A3, A4, or A5 of Frauenfelder and Henley?

(c) What is the total invariant mass of the bunch of other stuff, X?