European Physical Journal Plus, sa.5, ss.1-7, 2021 (SCI İndekslerine Giren Dergi)
We developed a model for a para-Positronium system by taking into account the annihilation
condition which requires l = 0. A para-Positronium system composed by an electron-antielectron pair is an
unstable system that decays predominantly into two gamma photons via self annihilation process. This is
because of the conservation of (overall) charge conjugation parity. Our 2+1 dimensional model was based
on an exact solution of a two-body Dirac-Coulomb type equation (one-time). The result non-perturbative
spectra was found to have a form of quasi normal modes that naturally give proper and damping oscillations
of the system. As a result, with a single equation, not only the binding energies and total annihilation
energy transmitted by the annihilation photons but also the life times, .., for each state
of l = 0 levels of the para-Positronium was obtained. With this unique presentation of above mentioned
characteristic of the system, we also calculated transition frequencies and transition times between differing
n level of l = 0. This also gave us an opportunity to discuss the screening effect from electronic environment
of the system. For this, the effective dielectric constant of the medium that surrounds the annihilation
point was adapted into the calculated non-perturbative spectra. This may provide an important tool for
the positron annihilation lifetime spectroscopy studies and for development of related techniques.