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 $N\overline{N}$ 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 $N\overline{N}$, 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 $e^{+}{e}^{-}\to n\overline{n}$, $\mathrm{\Lambda }\overline{\mathrm{\Lambda }}$, and ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ can also be understand within this scenario.

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• Form factors
• Hadron-hadron interactions
• Nucleons