库仑核相移余切的本质奇异性和零能有效射程函数核部分的有限极限
An essential singularity of the cotangent of the Coulomb-nuclear phase shift, and a finite limit of the nuclear part of the effective-range function derived at zero energy
摘要：
对任意轨道动量$l$，当能量为$E\rightarrow0$时，导出了库仑核相移$δ^{(cs)}_l$，$\cotδ^{(cs)}_l$和有效射程函数（ERF）核部分$Δ_l(k)$的有限极限.证明了$\cotδ^{(cs)}_l$在零能量处有本质奇异性，而$Δ_l(k)$没有.找到了$Δ_l(0)$的显式有限极限，利用$Δ_l(k)$作为亚纯函数的性质，可以将重新归一化的散射振幅从物理能量区域解析延拓到束缚态极点。然后，利用实验相移数据推导出渐近归一化系数（ANC），并将其应用于核天体物理中重要的辐射俘获过程，以产生新的元素。我们的结果与已发表的$S$波散射的结果一致。
英文摘要：
The Coulomb-nuclear phase shift $δ^{(cs)}_l$, $\cotδ^{(cs)}_l$ and a finite limit of the nuclear part $Δ_l(k)$ of the effective-range function (ERF) are derived for an arbitrary orbital momentum $l$ when energy $E\rightarrow0$. It is proved that $\cotδ^{(cs)}_l$ has an essential singularity at zero energy, but $Δ_l(k)$ does not. The explicit finite limit of $Δ_l(0)$ is found. The property of $Δ_l(k)$ as a meromorphic function makes possible the analytical continuation of a re-normalized scattering amplitude from the physical energy region to a bound state pole. Then the asymptotic normalization coefficients (ANC) can be deduced from experimental phase-shift data and applied to radiative capture processes which are important in nuclear astrophysics for new elements creation. Our results are in agreement with the results published for $S$ wave scattering.
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