Does the Multiple-scattering Series in the Pion-deuteron Scattering Actually Converge?

Abstract

It is demonstrated that the well-known answer for the multiple-scattering series (MSS) for a light particle interacting to a pair of static nucleons, calculated in the Fixed Centers Approximation (FCA), works well for a wide region of the two-body complex scattering length $a$. However, this approach is not applicable in a narrow region surrounding the real positive $a$ half-axis, where the MSS does not converge. Simultaneously, for real positive $a$'s the 3-body system forms an infinite set of bound states.

9 pages

References in corpus (2)

• A new perspective on the Faddeev equations and the $\bar{K}NN$ system from chiral dynamics and unitarity in coupled channels
• The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory

Cited by in corpus (4)

• Roy-Steiner-equation analysis of pion-nucleon scattering
• Investigations of the $D$-multi-$\rho$ interactions
• Three-body scattering problem in the fixed center approximation: the case of attraction
• Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems