Issued Fri, Jan 17 Due Mon, Jan 27

1) I took the "real" formula and set all the hbars and c's to one. So, you must puzzle out where hbar's and c's must go to get units of wavelength back. There are many ways to do this - easiest is probably to remember that , and =197 MeV fm. Just stare at the eqn and decide how to arrange 's... (You must look up the muon mass, and convert fm to cm...)

2a) Answer for p and E are in the neighborhood of 500 MeV (in natural units, c=1), but they are not identical to each other.

I use cgs units for this, and other problems this week, where

(1 dyne = 1 esu * 1 gauss),

and also 1 esu^2 = 1 dyne cm^2.

are handy unit conversion equations.

2b) The trick here is to remember that the lifetime of pions in the lab is *longer* than the free lifetime, because of relativity. Lifetime is increased by the "gamma" factor (which you can find easily, given energy and mass...)

4) Use F+H figure 3.5 (for lead). The curve is not flat in the range of 50 to 100 MeV, but for a rough estimate, you could just take some average value (pulled from the graph, say around 75 MeV) and use that.

The dE/dx curve for C is not shown, but eq'n 3.2 says that dE/dx goes like n (electron density), which in turn goes like density * Z/A (Z is the charge number, A the atomic weight) So, given the estimate for Pb, C will be similar, but slightly larger by the ratio (Z/A)(carbon)/ (Z/A)(lead)

5) E=800 MeV is probably high enough that Eq'n 3.3 is good enough.

I get a suprisingly large rate of temperature rise - if you put 1 cm^3 of Cu in the beam at Los Alamos, you darn well better do some pretty intense cooling!!

6a) Read F+H section 4.2 (Eq'n 4.3 is what you need)

6b) Another possible "unit crisis" problem. But it's really pretty simple, I looked up the formula in my introductory E+M textbook: In cgs units,

, with E in ergs, B in gauss, and volume in cm^3.

Or, if you prefer mks units,

with E in joules, B in Tesla, volume in m^3, and mu_0 you have to look up... (For cgs units, see my hints for 2a above...)