  In this study, we explore how a fermion-antifermion ($f\overline{f}$) 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 $f\overline{f}$ systems are unstable and decay
over time, with the decay time depending on the Compton wavelength of the
fermions.
