A generalization of the Levinson theorem about the asymptotic value of the scattering phase shift

Abstract

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.

arXiv comment5 pages, 2 figures, accepted for publication in Physics of Atomic Nuclei

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Cited by in corpus (1)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules