Homework #1

Each problem is worth 10 points

1. Martin & Shaw, Problem 1.2.
    

2. Martin & Shaw, Problem 1.3.
    

3. Martin & Shaw, Problem 1.4.
    

4. Martin & Shaw, Problem 1.5.
    

5. Derive the relationship between the units of length and time in the natural and SI systems of units, i.e. show that 1 GeV^-1 = 0.2 fm or 1 GeV^-1 = 6.6x10^-25 s. In natural units, are you higher or older?
    

6. In the natural system of units, what are the units of:
       a. Electric charge
       b. Voltage;
       c. Electric current;
       d. Magnetic field;
       e. Force?
   In each case express the corresponding SI units in natural units.
   
   The following two problems are intended for you to practice relativistic kinematics. Read Appendices A.1 and A.2 to refresh your knowledge of Lorentz transformations and solve the following two problems:
    

7. HERA was an electron-proton collider with the electron and proton beam energies of 30 and 820 GeV, respectively.
       a. What was the c.o.m. energy at HERA?
       b. Find the energy of an electron beam, which would create the same
           c.o.m. energy in collisions with stationary protons.
    

8. The GZK effect. Ultrarelativistic cosmic protons could be effectively stopped over short distances (on a cosmological scale!) if their energy is sufficient for the following scattering process on the photons of Cosmic Microwave Background (CMB):
                                       p + g -> D,
   to be allowed kinematically. Consequently, one does not expect to observe any protons above this threshold (called the GZK-threshold) to reach the Earth. Find the GZK threshold, given the mass of the proton and D of 0.938 GeV and 1.232 GeV, respectively, and the typical energy of a CMB photon of 2.35x10^-13 GeV.

Hint: consider a head-on collision of a proton with a photon, which corresponds to the highest possible energy released in collision.

This page was last modified January 24, 2007
 by Greg Landsberg