One-photon exchange between the two electrons. The virtual photon carries momentum transfer $t = (p_1 - p_1')^2$.
The computational chain
From diagram to number—every step of the amplitude calculation.
The diagram
Two electrons exchange a single virtual photon. The photon carries momentum $k = p_1 - p_1'$ with $k^2 = t$.
Feynman rules expression
$$i\mathcal{M}_t = \frac{ie^2}{t}\left[\bar{u}(p_1')\gamma^\mu u(p_1)\right]\left[\bar{u}(p_2')\gamma_\mu u(p_2)\right]$$
Each electron line contributes a current $\bar{u}\gamma^\mu u$. The photon propagator $-ig_{\mu\nu}/t$ connects them, contracting the Lorentz indices.
Spin-averaged squared amplitude
$$\overline{|\mathcal{M}_t|^2} = \frac{2e^4(s^2+u^2)}{t^2}$$
Average over initial spins (factor 1/4), sum over final spins. The completeness relations convert spinor products into traces. In the massless limit the result depends only on Mandelstam variables. The $1/t^2$ pole gives the forward scattering peak.