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To understand the oscillatory behavior exhibited in the timelike
electromagnetic form factors of nucleons, we propose a toy model based on the
Jost function of the $N\bar N$ pair into the timelike form factors with the
help of the distorted-wave Born approximation. By constructing a simple
square-well potential reflecting the final-state interaction of $N\bar N$, we
naturally represent the damped oscillatory phenomenon in the timelike
electromagnetic form factors of nucleons. Especially, our study reveals that
the ``period" of the oscillation is approximately determined by the Yukawa
interaction range $1/m_\pi$. Other possible potentials are also discussed. The
threshold enhancements of the cross sections for $e^+e^-\to n\bar n$,
$\Lambda\bar\Lambda$, and $\Lambda_c\bar\Lambda_c$ can also be understand
within this scenario.
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