In this paper we study the promotion phenomenon in potential scattering. In Sec. 3 we give the general formulas for the scattering amplitude at threshold, and show that the asymptotic form of the scattering amplitude as the momentum transfer squared approaches infinity is determined not only by the right-hand-plane Regge poles [$\alpha \mathrm{}\left(0\right)>-\frac{1}{2}$], but also by the left-hand-plane zeros of $Y\left(\lambda \right)$. In Sec. 3 we study the leading Regge pole $\alpha \left({k_t}^2\right)$ over the whole region $-\infty <{k_t}^2<0\mathrm{}$ for a weak and attractive Yukawa potential, and find that it is indeed promoted from -1 to -½ within a small neighborhood of the threshold. We also obtain the leading zero of $Y\left(\lambda \right)$ if the potential is repulsive. Together with the results in Sec. 2, we have, therefore, the explicit asymptotic form of the scattering amplitude. In Sec. 4 we study a general $n\mathrm{th}$ Born term and find that its leading term is promoted from $s^{-1\mathrm{}}{\left(\ln s\right)}^{n-1\mathrm{}}$ to $s^{-\frac{1}{2}}{\left(\ln s\right)}^{n-2\mathrm{}}$ at threshold. Summing over these leading terms, we obtain results in complete agreement with those in Secs. 2 and 3, both for attractive and for repulsive potentials, off or at threshold.

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