Ab initio QED Treatment of the Two-Photon Annihilation of Positrons with Bound Electrons

Abstract

The process of a positron -bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on ab 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 -bound-electron annihilation process, namely, the Lee's and impulse approximations.

Two-photon Annihilation of Positrons with K-shell Electrons of H-like ions

“…To the best of our knowledge, the only rigorous QED calculation of this process was performed recently by some of us in Ref. [25]. In that work, the finite-basis-set approach was used for the construction of the virtual electron-positron state propagator.…”

“…In the present investigation we aim to overcome the limitations of the approach of Ref. [25]. This is achieved by representing the electron-positron propagator in the presence of the binding nuclear field with the exact Dirac-Coulomb Green function.…”

A search for a cosmologically-relevant boson in muon decay

“…A GL0055 LEGe, just 8 mm in diameter and 5 mm in axial length [50] (one fourth the volume of the unit used for environmental background studies, rendering those conservative) is seen as the best commercial germanium diode choice for a X 0 search reaching the lowest possible values of β X . For this specific beam configuration, detector geometry, and energy range of interest, the expected dominant background arises from partial energy depositions by the small fraction of Michel positrons undergoing annihilation with electrons while still in flight [53][54][55], and those backward-emitted that escape the detector. Their contributions surpass those from low-energy Michel positrons having trajectories fully-contained in Ge (Fig.…”