An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 5.1

Elementary Processes of Quantum Electrodynamics — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · qed-coulomb-scattering

Problem

Repeat the computation of Problem 4.4, part (c), this time using the full relativistic expression for the matrix element. You should find, for the spin-averaged cross section,

\frac{d\sigma}{d\Omega} = \frac{\alpha^2}{4|\mathbf{p}|^2 \beta^2 \sin^4(\theta/2)} \left(1 - \beta^2 \sin^2 \frac{\theta}{2}\right),

where

\mathbf{p}

is the electron's 3-momentum and

\beta

is its velocity. This is the *Mott formula* for Coulomb scattering of relativistic electrons. Now derive it in a second way, by working out the cross section for electron-muon scattering, in the muon rest frame, retaining the electron mass but sending

m_\mu \to \infty

Related theory

Qed Scattering Amplitudes

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