= Solution
Nuclear-field <Pair production>[pair creation] is $\gamma Z\to e^-e^+Z$. A <virtual photon> exchanged with the <nucleus> supplies recoil <momentum>, while the real <photon> and <virtual photon> attach to the <electron> line joining the outgoing pair. The figure shows a representative graph. The second attachment ordering must be included in the full <Probability amplitude>[amplitude]. A real <photon> cannot create a free massive pair in vacuum: its <invariant mass> is zero, whereas $(p_{e^-}+p_{e^+})^2\ge4m_e^2$. <Recoil>[Nuclear recoil] resolves that kinematic obstruction and permits <Four-momentum conservation>[energy-momentum conservation].
\Image[/past-exam-of-the-particle-physics-course-of-the-university-of-oxford/2017-electromagnetic-shower-vertices.png]
{title=Representative nuclear-field pair-production and bremsstrahlung diagrams}
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