Z.A. Mandrykina1, V.A. Zaytsev1, V.A. Yerokhin2, and V.M. Shabaev1
1Department of Physics, St. Petersburg State University, 199034 St. Petersburg, Russia
2Center for Advanced Studies, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251, Russia

Investigations of the interactions of positron - the simplest antimatter particle - with atoms, molecules, and solids are of fundamental and practical interest. One of the most important acts of interaction is the process of annihilation with electrons in the matter. The investigation of this process has led to the development of positron-emission tomography, methods to study the defects in metals and semiconductors, and many other applications. The annihilation with inner-shell electrons of heavy systems is of particular interest. Such processes provide a unique opportunity to perform antimatter research in the presence of a strong electrical field of the nucleus which is several orders of magnitude larger than one at modern laser facilities. Moreover, new experimental studies on the interactions of positrons with various ionic and atomic targets are expected in the near future due to the appearance of positron facilities of a new generation at the Lawrence Livermore National Laboratory (California, USA) and the ELI-NP Research Center (Bucharest, Romania). All these and many other applications, as well as experimental studies, require a quantitative understanding of the positron-electron annihilation processes in the presence of a strong nucleus field.
The annihilation of positrons with bound electrons can proceed via the emission of one, two, or more photons. While two-quantum annihilation is most likely to occur in light systems, it is expected that one-photon annihilation may dominate in heavy systems [1]. The exact description of the process of the one-photon annihilation of positrons with bound electrons of heavy systems can be performed quite easily was first performed already in 1964 by Johnson with co-authors [2]. However, the probabilities of the annihilation processes with the emission of one and two photons were not compared due to the lack of a satisfactory theoretical description of the two-photon process.
Such description was performed for the very first time in Ref. [3]. Here we improve the approach developed in this work by describing the virtual electron-positron state propagator by the exact Dirac-Coulomb Green function instead of the B-splines finite basic set method [4]. The improved approach allows to extract and subtract the infrared divergences occurring when one of the emitted photons possesses low energy. We apply the developed approach for the calculation of the cross section of the two-quantum annihilation of positrons with K-shell electrons of H-like ions and compare it with one for the single-quantum channel.

References

1. Drukarev E. G., Mikhailov A. I. High-Energy Atomic Physics / E. G. Drukarev, A. I. Mikhailov, Cham: Springer International Publishing, 2016.
2. Johnson W. R., Buss D. J., Carroll C. O. Single-Quantum Annihilation of Positrons // Physical Review. 1964. № 5A (135). C. A1232–A1235.
3. Zaytsev V. A. [и др.]. Ab initio QED treatment of the two-photon annihilation of positrons with bound electrons // Physical Review Letters. 2019. № 9 (123). C. 093401.
4. Johnson W. R., Blundell S. A., Sapirstein J. Finite basis sets for the Dirac equation constructed from B splines // Physical Review A. 1988. № 2 (37). C. 307–315.