= Golden-rule derivation of the Born cross-section
For box-normalized <plane waves> in volume $\mathcal V$, a potential has <matrix element> $\widetilde W(\mathbf k_f-\mathbf k_i)/\mathcal V$. The final-state density per energy and <solid angle> is $\mathcal V m k_f/[(2\pi)^3\hbar^2]$. Dividing the golden-rule rate by incident flux $\hbar k_i/(m\mathcal V)$ gives $(m^2/4\pi^2\hbar^4)(k_f/k_i)|\widetilde W|^2$. Elastic scattering has $k_f=k_i$; the arbitrary box volume cancels.
Back to article page
