Past exam of the short options paper shared by Parts A and B of the physics course of the University of Oxford / 2019 / S10 / 1 / d

After thermalization, approximate the electron and Positron as initially at rest in their centre-of-momentum frame. Their total energy is $2m_e{c}^2$ and total momentum is zero. Two photons must therefore have equal energies and opposite momenta, since $|{\mathbf{p}}_{\gamma }|=E_{\gamma }/c$. Conservation of energy givesResidual pair momentum and electron binding cause small departures from exact collinearity and exact photon energy; the standard PET calculation neglects them.