Griffiths Introduction to Elementary Particles · Problem 5.16

The Feynman Calculus — David J. Griffiths

Physics — QFT · positronium-lifetime

Problem

The cross section for

e^+ + e^- \to 3\gamma

, in the triplet spin configuration, is

\sigma = \frac{16}{9}(\pi^2 - 9)\alpha^3\left(\frac{\hbar^2}{m^2 c v}\right)

Find the lifetime of positronium in the

1^3S_1

state. [The experimental answer is

1.45 \times 10^{-7}

sec.]