关于散射相移渐近值的Levinson定理的推广
A generalization of the Levinson theorem about the asymptotic value of the scattering phase shift
摘要：
在量子散射理论中，存在阈值和无穷远处的散射相移的差与束缚态的数目之间的关系，该关系由Levinson定理建立。散射振幅中的Castillejo、Dalitz和Dyson极点以及对应于酉割上$D$函数零点的Jaffe和Low基元的存在，修正了Levinson定理.散射相移的渐进值由束缚态的数量、Castillejo、Dalitz和Dyson极点的数量以及基元的数量决定。讨论了广义定理在核子-核子相互作用性质方面的一些结果。
英文摘要：
In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of Castillejo, Dalitz and Dyson poles in the scattering amplitude, as well as Jaffe and Low primitives, corresponding to zeros of $D$ function on the unitary cut, modify the Levinson theorem. The asymptotic value of the scattering phase shift is shown to be determined by the number of bound states, the number of Castillejo, Dalitz and Dyson poles, and the number of primitives. Some consequences of the generalized theorem with respect to properties of nucleon-nucleon interactions are discussed.
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