PHY357S: Wednesday, 11 March 1998

Problem Set 4

due Monday, 23 March 1998

(Late penalty is 10% per day, and no problem set is accepted after March 25.)

These problems are based on Chapters 1-14 of Frauenfelder and Henley (F&H) and the lectures.
If you have any questions about these problems, ask me.

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

 

1) Estimate the expected branching ratio for the decay X- -> X0X-, where X- is any known particle or combination of known particles.

 

2) F&H Problem 12.1

 

3) Scientists in an advanced civilization have discovered a mysterious astrophysical object which seems to be a ball of electrons 10 km across weighing 6x1055 kg. (Proponents of this idea claim that the electric charge of the electrons is neutralized by new massless "mirror" charged particles which do not interact with normal neutrinos.)

Most scientists are skeptical of such an outrageous claim, however, so it is proposed to x-ray the Mystery Ball with a 10 GeV neutrino beam fired right through the centre of the ball and measured on the other side. The neutrinos are produced by pion decays from an accelerator on a planetoid orbiting the Mystery Ball at a distance of 9.92x105km. (Because of strong electromagnetic fields, the accelerator could not be placed on the surface of the Mystery Ball.) The neutrino detector is on the surface of the Mystery Ball on the opposite side from the accelerator.

In addition to the physical constants we already know, the advanced civilization knows that the mixing angle between the electron and muon neutrinos is qn=p/4, tau neutrinos do not mix, and the mass of the electron and muon neutrinos are mne=0 and mnm=0.0025 eV/c2.

What is the ratio of electron neutrinos to muon neutrinos expected to be observed in the detector if the Mystery Ball really is a uniform ball of electrons.

 

4) (a) Estimate the size of a nucleon from F&H Figure 14.1.
   (b) F&H Problem 14.14