A researcher seeks a general analytic relationship between the electron recoil angle…
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
A researcher seeks a general analytic relationship between the electron recoil angle ϕ and the photon scattering angle θ for any Compton collision where the target electron is initially at rest. The researcher ignores electron binding effects and treats the photon energy as arbitrary.
(a) Taking the incident photon to define the +x axis and using symbol-only algebra (no numbers), derive an expression for tanϕ solely in terms of θ, fundamental constants, and the incident photon wavelength λ0. Express your result in its simplest form.
(b) Show that in the limit of long incident wavelength (photon energy \ll mec2) the derived expression reduces to ϕ≈90∘−21θ. Provide each step in the limiting process.
(c) Discuss qualitatively how the recoil angle behaves for photon energies that are much larger than mec2. Your discussion should reference the analytic form obtained in part (a).