Ab initio QED treatment of the two-photon annihilation of positrons with bound electrons

The process of a positron $\text{unicode}x2013$ bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on $\mathit{\text{ab}}\mathit{\text{initio}}$ QED description of the process is worked out. The developed approach is applied to evaluate the annihilation of a positron with $K$-shell electrons of a silver atom, for which a strong contradiction between theory and experiment was previously stated. The results obtained here resolve this long-standing disagreement and, moreover, demonstrate a sizeable difference with approaches so far used for calculations of the positron $\text{unicode}x2013$ bound-electron annihilation process, namely, the $\mathit{\text{Lee’s}}$ and $\mathit{\text{impulse}}$ approximations.