In reality, the cross section becomes large but not infinite. These infinities come about because we have not properly accounted for the finite lifetime of the intermediate state when we derived the second order perturbation theory formula. If the energy width of the intermediate states is included in the calculation, as we will attempt below, the cross section is large but not infinite. The

These resonances in the cross section **can dominate scattering**.
Again both resonant terms in the cross section,
**occur if an intermediate state has the right energy** so that
energy is conserved.

Jim Branson 2013-04-22