EUROPEAN PHYSICAL JOURNAL C, vol.84, no.801, pp.1-7, 2024 (SCI-Expanded)
In this study, we explore how a fermion–
antifermion ( f f ) pair interacts via an exponentially decaying
potential. Using a covariant one-time two-body Dirac equation, we examine their relative motion in a three-dimensional
flat background. Our approach leads to coupled equations
governing their behavior, resulting in a general second-order
wave equation. Through this, we derive analytical solutions
by establishing quantization conditions for pair formation,
providing insights into their dynamics. Notably, we find that
such interacting f f systems are unstable and decay over
time, with the decay time depending on the Compton wavelength of the fermions.