Abstract

The Levinson theorem relates the difference of the phase shifts at the threshold and at infinity to the number of bound states. The theorem is modified in view of the fact that Castillejo–Dalitz–Dyson (CDD) poles and Jaffe–Low primitives corresponding to zeros of the \(D\) function on the unitary cut are present in the scattering amplitude. It is shown that, in general, the difference of the phase shifts at the threshold and at infinity is determined by the number of bound states, the number of CDD poles, and the number of primitives. Some consequences of this theorem that concern the properties of the nucleon–nucleon interaction are discussed.

中文翻译：

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Levinson定理在散射振幅相移的渐近值上的推广

摘要

莱文森定理将阈值和无穷大处的相移差与结合态的数量相关联。考虑到以下事实，修改了该定理：在散射幅度中存在与单一切口上\（D \）函数的零相对应的Castillejo-Dalitz-Dyson（CDD）极点和Jaffe-Low图元。结果表明，通常，阈值和无穷大处的相移差由结合态数，CDD极数和基元数确定。讨论了该定理涉及核子-核子相互作用特性的一些结果。