We discuss the extent to which the often assumed independence of the phase of the elastic scattering amplitude from momentum transfer in the domain of only small $$t$$ constrains the dependence of the phase on $$t$$ in general. Based on analyticity, we prove that if the scattering amplitude phase is independent of the transferred momentum in the domain of its small values in strong couplings, then this remains the case in the whole physical domain. Moreover, if such independence holds in any domain of physical energies including values infinitely close to the first inelastic threshold from below, then the whole scattering amplitude vanishes. We also discuss the relation between the dependence of the phase on $$t$$ and the size of the interaction domain.

中文翻译：

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弹性散射振幅相位对动量传递的依赖性

我们讨论了通常假设的弹性散射振幅相位与动量传递的独立性在只有很小的 $$t$$ 域中限制了相位对 $$t$$ 的依赖性的程度。基于解析性，我们证明如果散射幅度相位在强耦合中其小值域中的传递动量独立，那么在整个物理域中仍然如此。此外，如果这种独立性在任何物理能量域中都成立，包括从下方无限接近第一个非弹性阈值的值，那么整个散射幅度就会消失。我们还讨论了相位对 $$t$$ 的依赖性与交互域大小之间的关系。