The Nucleus Resolved, Ch Reaction mechanisms: resonances, the compound nucleus, direct reactions and the optical model
Problem
Someone argues: "The optical model potential for 5MeV protons scattering from a mid-mass nucleus has an imaginary part Wopt=−3.0MeV. The continuity equation gives a probability-removal rate 2∣Wopt∣/ℏ for the wavefunction, and probability that disappears from the wavefunction must correspond to protons that are destroyed, so the imaginary potential describes real annihilation of protons inside the nucleus."
((a)) Compute the removal rate 2∣Wopt∣/ℏ and the corresponding mean life, in seconds.
((b)) Explain what is wrong with the claim that the protons are destroyed, and say where the removed flux reappears.
((c)) At this bombarding energy, a few MeV above the Fermi surface, give a one-line reason from the nucleon mean free path for why Wopt is concentrated at the nuclear surface rather than spread through the volume.