库仑力对散射振幅极点位置及其残差的影响
Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue
摘要：
对于有效射程函数$K_l(k^2)$的标准展开式以及当函数$K_0(k^2)$有极点时，导出了任意轨道动量$l$的原子核衰变为两个带电粒子的顶点常数的显式表达式.作为物理例子，我们考虑了s波中原子核${}^3\rm{He}$的束缚态和原子核${^2}$ He和${^3}$ He的共振态，以及p波中原子核${}^5\rm{He}$和${}^5\rm{Li}$的共振态.对于系统$Np$和$Nd$的极轨线被构造在动量和重整化顶点常数的复平面中。它们对应于当库仑力逐渐减小到零时从共振态到虚态的转变。
英文摘要：
Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\rm{He}$ and the resonant states of the nuclei ${^2}$He and ${^3}$He in the s-wave, and those of ${}^5\rm{He}$ and ${}^5\rm{Li}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.
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