General Relativity: An Introduction for Physicists · Problem 5.14

Special relativity revisited — Hobson, Efstathiou & Lasenby

Physics · inverse-compton-scattering

Problem

Inverse Compton scattering occurs whenever a photon scatters off a particle moving with a speed very nearly equal to that of light. Suppose that a particle of rest mass

m_0

and total energy

E

collides head on with a photon of energy

E_\gamma

. Show that the scattered photon has energy

E\left(1 + \frac{m_0^2 c^4}{4EE_\gamma}\right)^{-1}.

Ultra-high-energy cosmic rays have energies up to

10^{20}\,\mathrm{eV}

. How much energy can a cosmic ray proton transfer to a microwave background photon?

Related theory

Delbruck Scattering Light Scattering Light

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