1. Find the differential elastic cross section for particles incident along the z axis (from negative side) on the surface z = (x2 + y2)/a; 0 ≤ z ≤ a. Calculate the total cross section.
2. Find the collision cross section of positively charged spherical nuclei of charge Z, radius R, and mass m. E is the energy of the incident nuclei in the laboratory frame.
3. Estimate the change in the direction of 100 GeV proton colliding with an impact parameter b = RAu with a gold nucleus.
4. Find the differential elastic cross section of ee (electron-electron) scattering in the laboratory frame (electron with energy E0 incident on the electron at rest) (a) as function of the scattering angle, and (b) as function of the energy of the scattered electron.