Question

8. Nucleon resonances with spin 3/2 include the Δ(1232) (with charge states ++, +, 0, and , plus similar higher energy resonances, Δ(1600), Δ(1700) and Δ(1920). In each case, the number in parentheses indicates the (approximate) resonance mass (or rest energy) in MeV. When pions of energy Er scatter from nucleons (protons and neutrons) in a target at rest in the lab frame, these resonances can be produced, e.g., π + N → Δ(1232). Each resonance appears as a peak in the total scattering cross-section plotted as a function of the (lab frame) pion energy E. At what energies E do these resonances appear? (We are interested here in approximate results, ignoring isospin breaking. So you can take the nucleon mass to be 940 MeV and the pion mass to be 140 MeV. Your final answers should be given only with two significant figures.)