Principles of Quantum Mechanics · Problem 19.11

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · scattering-identical-particles

Problem

Two identical spin-

\frac{1}{2}

fermions scatter off each other. Working in the center-of-mass frame, show that: (a) In the spin-singlet state,

\frac{d\sigma}{d\Omega} = |f(\theta) + f(\pi - \theta)|^2

. (b) In the spin-triplet state,

\frac{d\sigma}{d\Omega} = |f(\theta) - f(\pi - \theta)|^2

. (c) For an unpolarized beam,

\frac{d\sigma}{d\Omega} = |f(\theta)|^2 + |f(\pi-\theta)|^2 - \text{Re}[f(\theta)f^*(\pi-\theta)]