Issued Wed Jan 29 Due Wed, Feb 12

Required reading: F+H Ch. 5+6

There are a couple more HINTS for this homework assignment.

1-i) F+H 5.8b

(Hint: The order of magnitude of my answer is around microeV)

1-ii) To create a level splitting of the size of part i), but with an electron rather than a nucleus, what magnetic field would you need?

Are the magnetic fields in parts i) and ii) achievable in the lab?

2-i) Consider Eq. 5.24, but assume the two pions do not form a rho resonance, i.e. they are produced by random "phase space" alone. Find the upper and lower limits on m_12 in Fig. 5-12. (Assume the initial state is known, i.e. the initial lab energy and momenta are given and fixed. )

Hint: It's probably easiest to work in the center of mass frame of the initial particles. Call the total energy in that frame E_i, your answers may depend on this (fixed) quantity. Recall that, for any given particle or system of particles, the quantity E^2-p^2 is always frame invariant.

2-ii) Given the "phase space" curve in Fig. 5-12, what must the initial pion beam energy have been, if the target was stationary protons?

3-i) 5.21

Hint: If you think about it in the right way, this is a very simple problem!

ii) If , find

4-i) 5.34 (See the hints for problem 2. In the center of mass frame, what do you suppose "threshold" production looks like?)

4-ii) 5.38 (This is meant to be a "quicky" - just a simple sketch with a few words of explanation is fine)

5) F+H 2.21

(Hint: My answer for the fixed target is about 5 orders of magnitude larger than the answer for colliding beams, which has an order of magnitude of around 10^30/s)

6-i) F+H 6.3 (Note: the density of Cu is 8.9 g/cc)

6-ii) F+H 6.13a only. Also, make a plot of your form factor F(q).

(Hint: Please show your work - the answer is given in table 6.1)