- Due in class on Jan. 15.
- Will be handed back for corrections or revisions until we're happy.
- Suggestions and hints will become available through the 880.05 web page.
- Answers to articulation problems are limited to four reasonable length sentences. You should imagine answering a question from a graduate student at a colloquium on the current topic. This is hard!
- Checkpoint questions should be fairly quick; if you are having a hard time, talk to classmates or the instructors.
- For any of the problems you can use any math tool such as maple or mathematica. Provide a printout of the session.

- Why is QCD asymptotically free but QED is not?
- A ferromagnet minimizes its energy by having its spins aligned. So why do the spins become randomly aligned above the Curie temperature?
- Why is the light-cone momentum fraction $x_+$ a useful variable?
- Why is pseudorapidity often used instead of rapidity by experimentalists?
- Why does the $e^+e^-$ curve in Figure 3.1 in Wong lie above the $pp$ curve?

- What is force in natural units? (Include the correct powers of $\hbar$ and c.)
- What is the energy of a "leading" proton with transverse momentum 400 MeV/c and $x_+ = 0.7$, if it is the product of a collision of a 10 GeV proton beam and a fixed target?
- Is the top graph in Figure 3.2 roughly consistent with Figure 3.1?
- Estimate the average $p_T$ from Figure 3.3 in Wong. Is it what you expect?
- Use Mathematica or Maple or some other computer math/graphics tool
to compare
*graphically*the rapidity $y$ and pseudorapidity $\eta$ for a pion with fixed $p_T = 300$ MeV/c as a function of the pion energy.

At the CERN-SPS fixed target facility, beam energies can reach 200 GeV/nucleon in the laboratory frame. RHIC, the colliding beam facility that is being constructed at Brookhaven, is to have energies of 200 GeV/nucleon in the center of mass frame.

Assume that in a collision one-half of the center-of-mass energy goes into creating pions, whose density determines the temperature.

- What is the maximum beam momentum at the CERN-SPS?
- Compare the $\sqrt{s}$ center-of-mass energies of the two facilities.
- What is the ratio of the longitudinal to transverse radii of the projectiles in the lab frame before collision for each facility?
- Make a classical estimate of the corresponding density as a function of time. (Estimate the density profile at several relevant times.)
- What temperature can be attained? Specify your assumptions.
- Make a rough sketch of the rapidity distributions you expect for spectator nucleons (ones that don't interact) and produced hadrons. Indicate the beam rapidities quantitatively.
- What measurements would be needed to determine the rapidity and pseudorapidity?

Copyright © 1997,1998 Richard Furnstahl and James Steele.