Sample Test Problems

1. Calculate the differential cross section, ${d\sigma\over d\Omega}$, for high energy scattering of particles of momentum p, from a spherical shell delta function
   
   $$V({\bf r}) = \lambda \delta (r-r_0)$$
   
   
   Assume that the potential is weak so that perturbation theory can be used. Be sure to write your answer in terms of the scattering angles.
2. Assume that a heavy nucleus attracts $K_0$ mesons with a weak Yakawa potential $V(r)={V_0 \over r}e^{-\alpha r}$. Calculate the differential cross section, ${d\sigma\over d\Omega}$, for scattering high energy $K_0$ mesons (mass $m_K$) from that nucleus. Give your answer in terms of the scattering angle $\theta$.