Inelastic Resonances and Castillejo-Dalitz-Dyson Singularities

James B. Hartle and C. Edward Jones
Phys. Rev. 140, B90 – Published 11 October 1965
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Abstract

By considering many coupled two-body-channel scattering amplitudes that possess a unique continuation in the angular-momentum variable l, we show: (1) that several methods of obtaining the single-channel ND solution for the elastic amplitude with an inelasticity factor agree with the corresponding many-channel matrix ND solution at high l; (2) that in order to preserve agreement when continuing to low angular momentum one must generally introduce Castillejo-Dalitz-Dyson (CDD) cuts or poles into the single-channel D function; (3) that the integral equations for ND may be continued in l, automatically yielding the CDD cuts mentioned above. Finally, we introduce a distinction between elastic and inelastic resonance poles based on continuation in l and show that the latter will not appear in calculations that fail to include the requisite CDD singularities.

  • Received 19 May 1965

DOI:https://doi.org/10.1103/PhysRev.140.B90

©1965 American Physical Society

Authors & Affiliations

James B. Hartle and C. Edward Jones

  • Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

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Issue

Vol. 140, Iss. 1B — October 1965

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