Relativistic production of a massive particle and a photon ($E_B=({\mathcal{E}}^2+m^2{c}^4)/(2\mathcal{E}),E_{\gamma }=({\mathcal{E}}^2-m^2{c}^4)/(2\mathcal{E})$)

In the centre-of-momentum frame with total energy $\mathcal{E}$, four-momentum conservation for a final massive particle of rest mass $m>0$ and one photon gives equal and opposite three-momenta. The energy–momentum relation and $|{\mathbf{p}}_{\gamma }|=E_{\gamma }/c$ give the displayed energies, andThe photon has positive energy when $\mathcal{E}>m{c}^2$. Kinematics fixes the speed and the opposition of the two final directions, while an angular distribution requires information about the interaction.